Wind Drag Coefficients for Highway Signs and Support Structures (2023)

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13   Findings 2.1 Drag Coefficients for Highway Signs This chapter presents the results of the simulations used to validate the numerical model and to produce the data needed to propose general methodologies for determining wind loads on highway signs, including signs of complex shapes, and their support structures. 2.1.1 Preliminary Simulations In this research, several simulations are performed for a constant-thickness dynamic message sign (Figure 2.1) with the following dimensions: • The sign has a width b = 29.25 ft and a height h = 8.2 ft. • The constant sign thickness d = 3.5 ft. • The sign is placed at a height above ground hg = 16.4 ft. • The domain width is about 240 ft, and height equals about 108 ft. • The distance between inflow and the sign is 88 ft, and the distance between the sign and the outlet is close to 300 ft. A nested grid system is used to generate high-quality meshes, with a minimum wall normal distance of about two wall units around the faces of the sign. Simulations are performed with sufficiently large Reynolds numbers (Re > 5 × 105) to ensure that the value of the drag coefficient (Cd) is independent of the Reynolds number (e.g., large incoming wind velocity regime). After several iterations, a determination was made that using four regions with different levels of grid density, together with the boundary layer meshing function available in the STAR CMM+ grid generator, is sufficient to produce a grid-independent solution. Figure 2.2 shows the following views of one of the meshes used in the simulations: • Figure 2.2a visualizes the mesh on the surface of the sign. • Figure 2.2b depicts the mesh in a 3-D image. • Figure 2.2c visualizes the mesh in a vertical-streamwise plane cutting through the middle of the sign, showing the four regions with different grid density levels as well as the mesh refine- ment near the bottom boundary. Solutions obtained using grids with more than 3 million cells are found to be grid independent. Figures 2.3 to 2.5 depict the mean flow solution around an isolated dynamic message sign placed at a distance above the ground (hg). As expected for a flow around a bluff body, as the flow passes the sign, it accelerates around the four edges of the sign, and a region of flow separation (negative mean streamwise velocities in Figure 2.3) forms behind the sign. The recirculation flow region contains two symmetrical recirculation flow bubbles bordered by separated shear layers (shown in Figure 2.4) forming between the slow-moving flow inside the recirculation region C H A P T E R 2

14 Wind Drag Coefcients for Highway Signs and Support Structures Figure 2.1. Main geometrical variables for a thin or thick (dynamic message) sign above the ground. 2.2a: Mesh on the surface of the sign 2.2b: 3-D view of mesh on sign surface and in vertical-streamwise plane cutting through the middle of the sign 2.2c: 2-D view of mesh in a vertical-streamwise plane cutting through the middle of the sign Figure 2.2. View of grid used to mesh the computational domain around a dynamic message sign placed above the ground. 2.3a: Vertical plane cutting through the middle of the sign 2.3b: Horizontal plane cutting the sign at mid-height level Figure 2.3. Streamwise velocity distribution in the mean ow around a dynamic message sign placed above the ground.

Findings 15 and the faster-moving ow around the sign. Although the separated shear layers are (anti) symmetrical in Figure 2.4b, the bottom separated shear layer is more energetic when compared to the one forming at the top edge of the sign. is disparity happens because of the suction eect as the ow accelerates between the sign’s bottom face and the ground. e main feature observed in the mean pressure elds in Figure 2.5 is the strong pressure increase near the front face of the eld (where the incoming ow decelerates because of the formation of strong adverse pressure gradients away from the front face of the sign). Moreover, a low-pressure region forms at the back of the sign that contains the recirculation ows. is pressure dierential is the main reason why the dynamic message sign is subject to a net posi- tive wind load. The mean pressure distributions on the front and back faces of the sign are shown in Figure 2.6, and these distributions are not uniform. is is true especially for the back face of the sign, but even on the front face, the pressure decays signicantly near the edges of the sign. e wind load is estimated as the dierence between the total pressure forces acting on the front and back faces of the sign. ese forces are obtained by integrating the pressure distributions over the corresponding face of the sign. en, the wind load is nondimensionalized with the frontal area of the sign and the incoming wind velocity to obtain a mean drag coecient. e predicted value of the mean drag coecient Cd is 1.22 for the simulation described in Figures 2.3 to 2.6. Additional simulations are then performed for the same highway sign but with varying dis- tances (1) between the top face of the sign and the top face of the computational domain and (2) between the side faces of the sign and the corresponding side face of the computational 2.4a: Vertical plane cutting through the middle of the sign 2.4b: Horizontal plane cutting the sign at mid-height level Figure 2.4. Out-of-plane vorticity (1/s) distribution in the mean ow around a dynamic message sign placed above the ground. Note: The pressure field is defined with respect to the pressure at a point situated in the inlet plane where a zero value is assigned for the pressure. 2.5a: Vertical plane cutting through the middle of the sign 2.5b: Horizontal plane cutting the sign at mid-height level Figure 2.5. Pressure distribution (psi) in the mean ow around a dynamic message sign placed above the ground.

16 Wind Drag Coefcients for Highway Signs and Support Structures domain. An increase in either of these distances reduces the sign blockage ratio. e determi- nation was made that the drag coecient is independent of the domain size once these lengths exceed three times the width (3 × b) and nine times the height (9 × h), respectively. ese results are important for setting up the simulations to determine drag coecients for highway signs deployed in the eld where, in contrast to wind-tunnel studies, the airow is not constrained by any boundaries other than the ground surface. Another issue investigated here is the possible inuence of the inclination of the front face of the DMS on the drag coecient. Information collected from three of the leading DMS cabinet manufacturers (Daktronics, Skyline, Ledstar) indicate that some of these cabinets are manufac- tured with a slight inclination of the front face, typically around 3 degrees with respect to the vertical. For example, the VF-2020 walk-in access signs, one of the most popular models manu- factured by Daktronics, have a permanent forward tilt angle of 3 degrees. eir front access signs tend to have a at face (constant thickness). To investigate this eect, an additional simulation is performed for a dynamic message sign with the same area (b = 29.25  and h = 8.2 ) as the one used in the domain-size dependency and grid dependency studies but with an inclined face, as follows: • e mean thickness of the sign is the same (d = 3.5 ) as in the previous simulations, but the front face is inclined by 3 degrees for the vertical. • e maximum thickness is d = 3.72 , and the minimum thickness is d = 3.28 . • The predicted value of Cd is 1.222, only 0.002 higher than the value predicted for the constant-thickness dynamic message sign. Two more simulations are performed as follows, with inclined faces corresponding to two of the signs in the wind-tunnel experiments of Chowdhury et al. (2015): • For a sign with h = 2 , b/h = 1, and d/h = 0.7, the simulations predict Cd = 1.064 for the vari- able thickness DMS cabinet and Cd = 1.06 for the constant-thickness DMS cabinet. • For a sign with h = 2 , b/h = 5, and d/h = 0.7, the simulations predict Cd = 1.183 for the variable thickness DMS cabinet and Cd = 1.19 for the constant-thickness DMS cabinet. ese results mean that it is reasonable to assume that variable thickness DMS cabinets have the same drag coecient as the corresponding constant-thickness dynamic message sign. Note: The pressure field is defined with respect to the pressure at a point situated in the inlet plane where a zero value is assigned for the pressure. Figure 2.6. Mean pressure distribution (psi) on front face (top) and back face (bottom) of dynamic message sign.

Findings 17 A simulation is also conducted for the canonical case of a 2-D thin plate (a wide rectangular plate spanning the whole width of the computational domain) situated far from any solid boundaries (i.e., no ground surface). Periodic boundary conditions are applied in the spanwise direction. The level of mesh refinement follows the same rules as those for the simulations of flow past a DMS cabinet. For large plate Reynolds numbers (Re > 200,000), the drag coefficient is within 3% of the values indicated in the literature based on laboratory experiments (Cd ≈ 1.9). 2.1.2 Validation for Isolated Rectangular Signs Using Wind-Tunnel Data As part of this research, several validation simulations are conducted for rectangular signs of constant thickness, using the setup and wind-tunnel data of Chowdhury et al. (2015). These state-of-the-art experiments, conducted in a large wind-tunnel facility, are one of the few that determined drag coefficients for both static signs and DMSs. The experiments are conducted with a 1:3 scaling ratio. In the wind-tunnel experiments and validation simulations, the following conditions apply: • The sign height is h = 2 ft, and the ground clearance is hg = 6.56 ft. • The wind-tunnel cross-section is 14.1 ft high and 20 ft wide. • The center of the sign is 7.55 ft from the bottom surface of the wind tunnel. • The inflow velocity profile and the average turbulence level in the simulations are close to those measured in the wind-tunnel experiment (power-law profile with an exponent of 0.25). • The mean wind velocity is 49.2 ft/s at the 7.55 ft elevation. Four representative wind-tunnel experiments are simulated that correspond to Chowdhury et al. (2015) cases 1, 2, 7, and 9: • The sign widths are b = 1.97 ft and b = 9.84 ft. • The sign aspect ratios are b/h = 1 and b/h = 5. • Two sign thicknesses d are considered (d = 0.2 ft and d = 1.41 ft)—corresponding to signs with d/h = 0.1 and d/h = 0.7, respectively—which cover the typical range of sign thickness ratios used for walk-in access signs and front access signs. This first series of four simulations is conducted in a computational domain with a cross- section identical to that of the wind tunnel. No-slip boundary conditions are applied at the walls of the wind tunnel. The calculation of the drag coefficient follows the procedure described by Chowdhury et al. (2015), which uses the measured velocity at 2.95 ft above the top of the sign (11.48 ft above the bottom surface of the wind tunnel) to determine a drag coefficient free of blockage effects. The predicted values of the drag coefficient (Cdʹ) are listed in Table 2.1. Also shown are the estimated values of the drag coefficient from the wind-tunnel experiments (Cdʹʹ). The agree- ment between the two is very good; the difference is less than 3% for all cases. Moreover, the h (ft) d (ft) b/h d/h Cd' Cd" Cd 2.0 0.2 5 0.1 1.25 1.24 1.21 2.0 1.41 5 0.7 1.17 1.19 1.19 2.0 0.2 1 0.1 1.17 1.16 1.13 2.0 1.41 1 0.7 1.00 0.97 1.065 2.0 0.033 5 0.016 1.24 1.27 1.23 Table 2.1. Drag coefficients predicted for dynamic message signs and thin signs corresponding to wind-tunnel experiments of Chowdhury et al. (2015).

18 Wind Drag Coefficients for Highway Signs and Support Structures simulations capture the qualitative trend of decreasing Cdʹ with increasing sign depth ratio d/h, as observed in the wind-tunnel experiment. This effect is present at all aspect ratios. Consistent with the results also observed for thin signs, Cdʹ increases with rising sign aspect ratio b/h if the sign thickness is constant. Given that the main goal of the project is determining drag coefficients under field condi- tions where blockage effects are nonexistent, a second series of four simulations is conducted, corresponding to the same four wind-tunnel experiments. These simulations are performed in a much larger domain with symmetry boundary conditions at the lateral boundaries. The cross- section of the computational domain is increased, from h = 14.1 ft to h = 39.4 ft and from b = 20 ft to b = 80 ft. For simulations conducted in very large computational domains (negligible flow blockage effects), the drag coefficient Cd can be estimated by using the mean incoming flow velocity over the height of the sign (Table 2.1). For three of the four cases, the approximate procedure pro- posed by Chowdhury et al. (2015) to correct for several effects present in wind-tunnel experi- ments yields results very close to the Cd estimated from simulations performed in very large computational domains where these effects are not present. The difference is slightly larger only for the thick sign (b/h = 1 and d/h = 0.7). The simulations in large domains reconfirm the trends observed in the experiments and simulations conducted in a domain of the same cross-section as that of the wind tunnel. The drag coefficient Cd increases with rising aspect ratio and decreases with increasing thickness ratio. The simulations of the experimental test cases of Chowdhury et al. (2015) are performed with a power-law profile for the incoming wind with an exponent of 0.25, corresponding to the conditions in the wind-tunnel experiments. As is customary, the reported drag coefficient is calculated with the mean incoming velocity over the sign height. To investigate the effect of the incoming wind conditions, additional simulations are conducted with a constant wind velocity equal to the mean incoming velocity over the sign height in those simulations with a power-law inflow wind profile. This report notes the following values obtained for large-domain simulations for which Cd is directly comparable to the corrected values reported by Chowdhury et al. (2015): • For a sign with b/h = 1 and d/h = 0.7, Cd = 1.065 for the simulation conducted with a power- law inflow velocity profile, and Cd = 1.072 for the simulation performed with a constant inflow velocity profile. • For a sign with b/h = 5 and d/h = 0.7, Cd = 1.19 for the simulation conducted with a power-law velocity profile, and Cd = 1.21 for the simulation performed with a constant inflow velocity profile. A clear conclusion from these simulations is that the effect of the incoming wind velocity pro- file on the drag coefficient for highway signs is very small—provided that the drag coefficient is always calculated with the mean approaching wind velocity over the height of the sign. 2.1.3 Validation for Isolated Rectangular Signs Using Field Data Although flow conditions are better controlled in wind-tunnel experiments, the drag coeffi- cients estimated from such experiments are subject to several effects, most importantly the flow blockage effect (as discussed in Chowdhury et al. 2015). Most experimental studies report only the measured uncorrected values of the drag coefficient. These values, especially those obtained in experiments conducted in small wind tunnels, are larger than the values expected in the field. Empirical corrections may be applied to correct for these effects.

Findings 19 Chowdhury et al. (2015) appear to propose the most comprehensive method for such correc- tions. For comprehensive validation of the numerical model proposed in this study, it is highly suitable to perform further validation of the model using data from field experiments. Such validation is the most relevant for this project even though the conditions in the field experi- ments could not be fully controlled and the accuracy of some of the measured variables could be lower when compared to measurements in wind-tunnel experiments (e.g., average incoming flow velocity over the height of the sign, some temporal variation in velocity during the field experiment because of changing wind conditions). The literature review reveals only two field experiments for rectangular signs that report high- quality data: Quinn, Baker, and Wright (2001) and Smith, Zuo, and Mehta (2014). Quinn, Baker, and Wright (2001) report their results after performing the following field experiment for a thin square sign: • Aspect ratio b/h = 1, with b = h = 2.46 ft and d = 0.164 ft. • The sign is placed perpendicular to the incoming wind. The distance to the ground hg = 5.35 ft, and the incoming wind velocity is around 49.2 ft/s. Validation simulations are performed at field conditions in a domain whose size is deter- mined using the rules described in Section 2.1.1. The reported value of Cd from the field experiment is 1.08 with a measurement error estimated at ± 0.1 (i.e., 0.98–1.18). The simulation predicts that Cd = 1.13. Smith, Zuo, and Mehta (2014) report their results after conducting the following field experi- ment for a rectangular DMS cabinet: • Width b = 24.6 ft; height h = 12.3 ft; and d = 5.75 ft (with b/h = 2 and h/d ≈ to 2.1). • The sign is placed perpendicular to the incoming wind. The distance to the ground hg = 12.3 ft, and the incoming wind velocity is 33–56 ft/s. The reported mean value of Cd from field experiments is 1.13, with field tests producing Cd values between 1.06 and 1.2. The simulation predicts that Cd = 1.19. 2.1.4 Validation for Rectangular Signs that Include an Add-on Sign, Using Wind-Tunnel Data Dr. James Buchholz and his group at IIHR—Hydroscience & Engineering carried out experi- ments with thin rectangular signs that include an add-on sign (Figure 2.7), utilizing a recircu- lating wind-tunnel facility at the University of Iowa. Appendix A describes the experimental facility and instrumentation used to measure the wind loads on the signs and the velocity at relevant positions. Given the cross-section of the wind tunnel (35.5 in. by 29.5 in.), the experiments use the following values for the main variables: • The sign height h0 = 0.79 in. • The ground clearance distance hg = 1.97 in. • The mean incoming wind velocity is close to 164 ft/s. Numerical simulations are conducted in a domain with wall bottom, top, and lateral surfaces that correspond to the wind-tunnel and base plane surfaces present in the experiments. The inlet section in the numerical simulations corresponds to the streamwise location away from the leading edge of the base plane where the velocity profile is measured in the experiments.

20 Wind Drag Coefcients for Highway Signs and Support Structures As shown in Figure 2.7, the height and width of the main sign are h and b, respectively. e dimensions of the add-on sign are ha and ba. e following three series of experiments and vali- dation simulations are conducted for these signs: • Series 1: add-on sign positioned on the le side of the main sign: h = h0; b = 5h0; ba = 0.5h0; ba/ha = 1, 3, 8. • Series 2: add-on sign positioned on the le side of the main sign: h = h0; b = 5h0; ba = 1.25h0; ba/ha = 1, 3, 8. • Series 3: add-on sign horizontally centered relative to the main sign: same as Series 2. Wind forces are determined for the full thin sign (i.e., the main rectangular sign with the add-on sign) and for the main rectangular sign only (i.e., with no add-on sign). For the thin signs (Series 1 to 3), the numerical simulation predicts Cd0 = 1.10 for an isolated sign with an aspect ratio AR = 5 and h0 = 0.087 in.—very close to the value inferred from the experiment, Cd0 = 1.101. As the results summarized in Tables 2.2, 2.3, and 2.4 indicate, the agree- ment between the validation simulations and the experiments is very good for the three series that consider an add-on sign placed on top of a rectangular thin sign. For all cases, the experi- mentally determined values of Cd/Cd0 are less than 1.05. 2.1.5 Validation for Side-by-Side Rectangular Signs, Using Wind-Tunnel Data Dr. Buchholz’s group also performed experiments with side-by-side rectangular signs (Figure 2.8). e experimental facility, instrumentation, measurement procedures, and values h0 (m) AR ba/ha ARa Cd/Cd0 (simulation) Cd/Cd0 (experiment) 0.02 5 0.5 1 1.032 1.048 0.02 5 0.5 3 1.030 1.042 0.02 5 0.5 8 0.990 1.033 Table 2.2. Drag coefcients for a static sign (h0 5 0.02 m, AR 5 5) with a small add-on sign with ARa 5 ba /ha positioned on the left side of the main sign (Series 1). Figure 2.7. Main geometrical variables for the case when an add-on sign is attached to a main rectangular sign.

Findings 21 of the main variables (h0, hg, mean wind velocity) are the same as those described in Section 2.1.4 and Appendix A. Validation simulations are conducted using the same procedure detailed in Section 2.1.4. As shown in Figure 2.8, the heights and widths of the two signs are h1, b1, and h2, b2, respec- tively. Four series of experiments and validation simulations are conducted with varying gap distance s: • Series 1: thin signs of comparable sizes with relatively high AR; h1 = h2 = h0; b1 = 5h0, b2 = 4h0; gap distance s = 5, 10, 15, 20, 60, 140 mm (0.20, 0.39, 0.59, 0.79, 2.36, and 5.51 in.). • Series 2: same as Series 1 but with thick signs of constant thickness d = 0.5h0. • Series 3: thin signs of signicantly dierent sizes with h1 = h2 = h0; b1 = 5h0, b2 = h0; s = 5, 10, 15, 20, 60, 140 mm (0.20, 0.39, 0.59, 0.79, 2.36, and 5.51 in.). • Series 4: thick signs (d = 0.5h0) of comparable sizes with relatively low AR; h1 = h2 = h0; b1 = 2h0, b2 = 2.5h0; s = 2.5, 5, 10, 15, 60, 140 mm (0.10, 0.20, 0.39, 0.59, 2.36, and 5.51 in.). Wind forces are also determined on the individual (isolated) signs used in the experiments performed with side-by-side signs: • For isolated thin signs (Series 1), the predicted Cd0 values (i.e., the drag coecients for the isolated signs) are 1.07 (AR = 4) and 1.10 (AR = 5). e corresponding values estimated based on experiments are 1.08 (AR = 4) and 1.10 (AR = 5). h0 (m) AR ba/ha ARa Cd/Cd0 (simulation) Cd/Cd0 (experiment) 0.02 5 1.25 1 1.018 1.026 0.02 5 1.25 3 1.020 1.032 0.02 5 1.25 8 1.026 1.044 Table 2.4. Drag coefcients for a static sign (h0 = 0.02 m, AR = 5) with a large add-on sign with ARa = ba /ha positioned centered with respect to the main sign (Series 3). h0 (m) AR ba/ha ARa Cd/Cd0 (simulation) Cd/Cd0 (experiment) 0.02 5 1.25 1 1.03 1.032 0.02 5 1.25 3 1.03 1.037 0.02 5 1.25 8 1.03 1.038 Table 2.3. Drag coefcients for a static sign (h0 5 0.02 m, AR 5 5) with a large add-on sign with ARa 5 ba /ha positioned on the left side of the main sign (Series 2). Figure 2.8. Main geometrical variables for two side-by-side signs placed above the ground.

22 Wind Drag Coefcients for Highway Signs and Support Structures • For the thick signs (d/h = 0.5) used in Series 2, the predicted Cd0 values are 1.11 (AR = 4) and 1.13 (AR = 5). • e corresponding values estimated based on wind-tunnel experiments are 1.13 (AR = 4) and 1.17 (AR = 5). • For isolated thin signs (Series 3), the predicted Cd0 values are 1.05 (AR = 1) and 1.105 (AR = 5). • e corresponding values estimated based on experiments are 1.056 (AR = 1) and 1.10 (AR = 5). • For the thick signs (d/h = 0.5) used in Series 4, the predicted Cd0 values are 1.06 (AR = 2) and 1.08 (AR = 2.5). e corresponding values estimated based on wind-tunnel experiments are 1.046 (AR = 2) and 1.082 (AR = 2.5). As evident in Figures 2.9 to 2.12, the agreement between the Cd/Cd0 values estimated for side- by-side signs (Figure 2.8) based on wind-tunnel measurements and validation simulations is over- all very good. e simulations qualitatively and quantitatively capture the main trends observed experimentally in the variation of the normalized drag coecient Cd/Cd0 for each sign as follows: • e amplication of the wind loads because of the proximity of another sign is larger for a smaller sign (e.g., the AR = 4 signs for Series 1 and 2, the AR = 1 thin sign for Series 3, and the AR = 2 thick sign for Series 4). Figure 2.9. Normalized drag coefcient Cd/Cd0 for side-by-side thin signs with AR 5 4 and AR 5 5 (Series 1). Figure 2.10. Normalized drag coefcient Cd/Cd0 for side-by-side thick (d/h 5 0.5) signs with AR = 4 and AR = 5 (Series 2).

Findings 23 • For Series 3, the peak value of Cd/Cd0 for the sign with AR = 1 is close to 1.27 in the experiments and to 1.25 in the simulations. • For Series 4, the peak value of Cd/Cd0 for the sign with AR = 2 is close to 1.25 in the experiment and to 1.23 in the simulations. • Even in Series 1 and 2 where the sizes of the two signs are similar, the predicted peak value of Cd/Cd0 for the smaller sign (AR = 4) is close to the experimentally measured value (1.2). ese results show that signs situated in the vicinity of other signs can experience signicantly larger wind loads (e.g., by as much as 30%) compared to the same sign if it is not situated in the proximity of another sign (isolated sign). 2.1.6 Isolated Rectangular Highway Signs e validated numerical model is used to perform a series of simulations with isolated static (thin) and dynamic message (thick) signs. e rst part of this section summarizes drag coecients for thin rectangular highway signs placed above the ground. e main geometrical variables are Figure 2.12. Normalized drag coefcient Cd/Cd0 for side-by-side thick (d/h 5 0.5) signs with AR 5 2 and AR 5 2.5 (Series 4). Figure 2.11. Normalized drag coefcient Cd/Cd0 for side-by-side thin signs with AR 5 1 and AR 5 5 (Series 3).

24 Wind Drag Coefficients for Highway Signs and Support Structures shown in Figure 2.1. The thickness of the thin rectangular sign is held constant (d of 0.167 ft). The following four series of simulations investigate the effect of the sign aspect ratio b/h, sign height h, ground clearance distance hg, and ground clearance ratio h/(h + hg): • Series 1: h = 8 ft; hg = 20 ft; b/h = 1, 2, 3, 5, 10, 15, 20; h/(h + hg) = 0.29. • Series 2: h = 8 ft; hg = 16.5 ft and 23 ft; b/h = 1, 10, 20. • Series 3: h = 4 ft; hg = 20 ft; b/h = 1, 5, 10, 20; h/(h + hg) = 0.17. • Series 4: h = 20 ft; hg = 20 ft; b/h = 1, 2, 5, 20; h/(h + hg) = 0.5. Some of the simulation results are shown in Table 2.5 (Series 1) and Figure 2.13 (Series 1, 3, and 4). These results demonstrate the following: • Cd increases monotonically with increasing aspect ratio b/h for constant h and hg. The drag coefficient also increases with rising h, or nondimensionally with h/(h + hg), for constant hg and b/h. The first result is already documented in the LRFDLTS-1 specifications, but the specifications do not account for the second result. • For b/h close to 1, the effect of varying h/(h + hg) on Cd is small (e.g., Cd = 1.14 for h = 4 ft and h = 8 ft while Cd = 1.22 for h = 20 ft). • However, for b/h significantly larger than 1, Cd increases with increasing h and h/(h + hg). For example, the increase in Cd as h doubles is on the order of 10% for b/h = 10. • The larger values of Cd with increasing h and h/(h + hg) for constant hg and b/h are due to the stronger suction effect associated with amplification of the mean flow velocity between the ground and the lower edge of the sign. It is also relevant to compare the values reported in Table 2.5 with those of various experi- mental studies and with those in other specifications used by state DOTs, such as ASCE/SEI 7-16 (2017), as shown by the following: h (ft) b/h Cd h (ft) b/h Cd h (ft) b/h Cd 8.0 1 1.14 4.0 1 1.14 20 1 1.22 8.0 2 1.17 4.0 2 — 20 2 1.30 8.0 3 1.2 4.0 3 — 20 3 — 8.0 5 1.25 4.0 5 1.20 20 5 1.63 8.0 10 1.36 4.0 10 1.26 20 10 — 8.0 15 1.45 4.0 15 — 20 15 — 8.0 20 1.57 4.0 20 — 20 20 — Table 2.5. Variation of Cd with b/h and h for rectangular thin static signs with hg = 20 ft and d = 0.167 ft. Note: The figure presents results for different ground clearance ratios h/(h + hg). Figure 2.13. Variation of drag coefficient with b/h for thin rectangular signs.

Findings 25 • For b/h = 1, the current simulations predict Cd = 1.14 for height h < 8 ft and Cd = 1.22 for h = 20 ft. These values are close to the value (Cd = 1.16) predicted by the wind-tunnel experiments of Chowdhury et al. (2015) for thin plates with b/h = 1. Even more important, these values are close to the value (Cd = 1.08 ±0.1) predicted by the field experiment of Quinn, Baker, and Wright (2001) for thin plates with b/h = 1. Both Newberry and Eaton (1974) and ASCE 7, in ASCE 7-95 (1995) and ASCE/SEI 7-16 (2017), indicate slightly larger values (1.24 and 1.2, respectively), but this result is expected as these values are obtained from wind-tunnel experiments with plates of height h < 8 ft. The blockage ratio effect is not taken into account when reporting these values. • For b/h = 2 and h = 8 ft, the current simulations predict Cd = 1.17. This value is close to the one reported by Newberry and Eaton (1974). • For b/h = 5, the current simulations predict Cd = 1.2 and Cd = 1.25 for h = 4 ft and h = 8 ft, respectively. These values are very close to the one (Cd = 1.21) reported by Newberry and Eaton (1974). • For b/h = 10 and h < 8 ft, the current simulations predict that Cd = 1.26 and 1.36. These values are comparable to the Cd value (1.39) reported by Newberry and Eaton (1974) and the one (1.29) given by ASCE/SEI 7, in ASCE 7-95 (1995) and ASCE/SEI 7-16 (2017). • For b/h = 20 and h = 8 ft, the current simulations predict Cd = 1.57. This value falls between the Cd (1.5) specified by ASCE 7-95 (1995) and ASCE/SEI 7-16 (2017) and the one (1.62) noted by Newberry and Eaton (1974). A second series of simulations considers dynamic message signs above the ground. Catalogs from several main manufacturers (e.g., Daktronics, Ledstar) confirm that such front access and walk-in access signs are manufactured in a wide array of dimensions. Chowdhury et al. (2015) also report data on typical dynamic message signs from three main manufacturers (Daktronics, Ledstar, and Skyline). Data in their study—and data obtained directly from the manufacturers and a survey of state DOTs—show the following: • Most dynamic message signs have aspect ratios b/h between 1 and 6, although the maximum aspect ratio can be as high as 10. • The sign thickness ratio d/h varies between 0.1 and 0.7 for most signs, although a high per- centage of the designs fall in a narrower range (0.12 < d/h < 0.55). • Most of these signs are installed so that the ground clearance distance is 16.5 ft < hg < 23 ft. • Walk-in access signs are typically thicker and have a higher aspect ratio while most front-access signs are thinner with a lower aspect ratio. Some of the walk-in access signs are manufactured with a small forward tilt angle of their front face. (Section 2.1.1 notes that the presence of an inclined face has a negligible effect on the drag coefficient.) Therefore, the results reported in this and subsequent sections are primarily for constant- thickness dynamic message signs, using the following two base designs: • For walk-in access signs, a base design is used with b = 30 ft, h = 8 ft, and d = 4 ft (b/h = 3.75 and d/h = 0.5). This design is very close to that of the VF-2020 sign by Daktronics. • For front access signs, a base design is employed with b = 15 ft, h = 8 ft, and d = 1.3 ft (b/h = 1.9 and d/h = 0.16). • Note that the d/h values for these two base designs are close to the maximum and minimum values of the range representative of most common designs (i.e., 0.12 < d/h < 0.55). The following four series of simulations investigate the effect of varying b/h, hg, h/(h + hg), d, and d/h (for completeness, several simulations, Series 3, use dynamic message signs with vary- ing sign thickness): • Series 1: h = 8 ft; hg = 20 ft; d = 4 ft; b/h = 1, 2, 3, 5, 6. • Series 2: h = 8 ft; hg = 20 ft; d = 1.3 ft; b/h = 1, 3, 6.

26 Wind Drag Coefficients for Highway Signs and Support Structures • Series 3: h = 8 ft; hg = 20 ft; d = 4 ft with 3 degrees inclined upstream face; b/h = 1, 6. • Series 4: h = 8 ft; hg = 16.5 and 23 ft; d = 4 ft; b/h = 1, 6. The drag coefficients predicted for Series 1 and 2 are given in Table 2.6 and Figure 2.14. The following observations can be made: • For constant b/h, a monotonic decrease of Cd with increasing sign thickness is observed. This result is consistent with the trend observed experimentally by Chowdhury et al. (2015). • For the thin signs, Cd increases monotonically with increasing b/h for a constant d. If b/h < 5, Cd increases with decreasing thickness d or d/h (Figure 2.14). • However, even when b/h = 1, the difference in Cd between d = 0.167 ft and d = 4 ft is less than 4% (Table 2.6). • The drag coefficient is basically insensitive to d/h when b/h > 5. • The field experiments of Smith, Zuo, and Mehta (2014) predict Cd = 1.13 ±0.07 for a dynamic message sign with b/h = 2 and h/d = 2.1. This Cd value is close to the one (1.135) predicted for h/d = 2 (Table 2.6). The effect of a variable sign thickness (nonparallel front and back faces) is investigated for dynamic message signs with a mean thickness d = 4 ft and height h = 8 ft, with the following findings: • For signs with b/h = 1, Cd decreases from 1.1 for a constant-thickness sign to 1.085 for a vari- able thickness sign. • For signs with b/h = 6, Cd decreases from 1.265 for a constant-thickness sign to 1.255 for a variable thickness sign. The effect of varying the ground clearance distance hg while holding h and b/h constant is small. This result is observed for both thin static signs and dynamic message signs with d = 4 ft. Figure 2.15 and Table 2.7 summarize the predicted drag coefficients for signs with b/h = 1 and h (ft) hg (ft) d (ft) b/h Cd d (ft) Cd d (ft) Cd 8.0 20.0 4 1 1.100 1.3 1.128 0.167 1.14 8.0 20.0 4 2 1.135 1.3 — 0.167 1.17 8.0 20.0 4 3 1.177 1.3 1.190 0.167 1.20 8.0 20.0 4 5 1.241 1.3 — 0.167 1.25 8.0 20.0 4 6 1.265 1.3 1.276 0.167 1.28 Table 2.6. Variation of Cd with b/h and sign thickness d for rectangular signs with constant h and hg. Figure 2.14. Variation of Cd with b/h for rectangular signs of varying thickness ratio d/h.

Findings 27 b/h = 6 when 16.5 ft < hg < 23 ft. For both b/h = 1 and b/h = 6, Cd decreases monotonically with increasing hg. Simulations also show that Cd increases with increasing h/(h + hg) when h is constant. This result is consistent with the trends in Table 2.5 and Figure 2.13 where h/(h + hg) is varied by changing h. The rate of decrease of Cd with increasing hg is larger for signs with greater b/h. This result is expected given that the suction effect between the ground and the bottom edge of the sign is stronger for signs of larger width. In the case of thick highway signs at a certain finite distance above the ground, the suction effect between the bottom face of the sign and the ground can induce a reduction in the pressure, which can produce a negative lift force acting on the sign. Although this effect is present, data from the current numerical simulations show that the mean vertical force acting on the sign is very small, even for thick signs with d ≥ 1.3 ft. Results show the following: • The ratio between the vertical force and the streamwise force is less than 0.2% for the simula- tions conducted for signs with d ≥ 1.3 ft. • For all simulations performed with isolated dynamic message signs, the lift coefficient defined with the incoming velocity and the area of the bottom face of the sign is less than 0.02. • Based on these data, the effect of the vertical force acting on the sign can be neglected in most cases. The main conclusion of the series of simulations conducted for isolated rectangular signs of different thicknesses is that the drag coefficient slightly decreases with increasing sign thickness. This result is fully consistent with that of the wind-tunnel experimental study performed by Chowdhury et al. (2015). Given that the maximum difference is less than 4%, there is no need for special provisions to select Cd for dynamic message signs. Rather, the drag coefficient for static signs and dynamic message signs should be specified as a function of the sign aspect ratio and the ground clearance ratio. hg (ft) h (ft) d (ft) b/h Cd d (ft) b/h Cd 16.5 8 4 1 1.102 0.167 1 1.143 19.7 8 4 1 1.100 0.167 1 1.140 23.0 8 4 1 1.091 0.167 1 1.136 16.5 8 4 6 1.272 0.167 6 1.273 19.7 8 4 6 1.265 0.167 6 1.266 23.0 8 4 6 1.244 0.167 6 1.247 Table 2.7. Effect of varying b/h for dynamic message signs (d 5 4 ft) and thin static signs (d 5 0.167 ft) with constant h and hg. b Note: Blue symbols are practically on top of the black symbols (see also Table 2.7). Figure 2.15. Variation of Cd with hg, h/(h 1 hg), and b/h for dynamic message signs (d 5 4 ft, d/h 5 0.5) and thin static signs (d 5 0.167 ft, d/h 5 0.02) with h 5 8 ft.

28 Wind Drag Coefficients for Highway Signs and Support Structures 2.1.7 Rectangular Highway Signs that Include an Add-On Sign Many highway signs include a smaller add-on sign (Figure 2.7). The add-on sign of height ha, width ba, and thickness da is generally attached near one of the lateral edges of the main (larger) sign or is horizontally centered with respect to the middle of the main sign. No procedure is available to determine the drag coefficient for a highway sign with an add-on sign. Three series of simulations investigate the effects of ba/ha, ba/b, and ha/h and the effect of the relative position of the add-on sign (e.g., lateral side versus centered): • Series 1: add-on sign at the lateral edge of main sign: ba = 3 ft; ba/b = 0.1; and ba/ha = 1, 3, 8. • Series 2: add-on sign at the lateral edge of main sign: ba = 7.5 ft; ba/b = 0.25; and ba/ha = 1, 3, 8. • Series 3: add-on sign horizontally centered relative to main sign: ba = 3 ft; ba/b = 0.1; and ba/ha = 1, 3, 8. All simulations are conducted under the following conditions: • hg = 20 ft. • d = da = 0.167 ft. • h = 8 ft. • b = 30 ft. The following drag coefficients are calculated: • Individual drag coefficients for the main sign (Cd) and the add-on sign (Cda). • Drag coefficient for the whole sign (Cdwa), using the total drag force and the sum of the areas of the main sign and add-on sign. Results of these calculations show the following main trends: • In the case when the add-on sign is placed at the lateral edge of the main sign and when ba is much smaller than b (e.g., ba/b = 0.1), the drag coefficient of the main sign is slightly larger than that of the same sign without the add-on sign and decreases monotonically with an increasing aspect ratio of the add-on sign (Figure 2.16a and Table 2.8). • For ba/b = 0.1, the drag coefficient of the add-on sign decreases monotonically with increasing ba/ha (from Cda = 1.1 for b/h = 1 to Cda = 0.7 for b/h = 8), and its values are significantly smaller than those expected for an isolated thin sign of the same dimensions as the add-on sign. 2.16a: ba = 3 ft 2.16b: ba = 7.5 ft Note: The figure also shows the drag coefficient for the full sign. Figure 2.16. Variations of drag coefficients for the main sign and for the add-on sign attached to it (with ba/ha when a small add-on sign is placed at the lateral edge of a main sign).

Findings 29 The results are qualitatively similar for the case of a wider add-on sign (ba = 7.5 ft, ba/b = 0.25) attached to the main sign (Figure 2.16b and Table 2.8), including the following: • For the main sign, the decrease of Cd with increasing ba/ha is more important compared to the one observed for a smaller add-on sign. Meanwhile, the decay of Cda with increasing ba/ha is much less important. • For ba/b = 0.25, the add-on sign drag coefficient values are between 1 and 1.2. In the simulations where the add-on sign (ba/b = 0.1) is horizontally centered with respect to the main sign, Cd and Cda also decrease with increasing ba/ha (Table 2.9 and Figure 2.17). For the same ba/ha, the effect of a centrally positioned add-on sign on Cd is marginally larger compared to the case of an add-on sign at the lateral edge of the main sign (Tables 2.8 and 2.9). For all simulations with ba/b = 0.1 or ba/b = 0.25, the drag coefficient for the full sign (Cdwa) is less than 4% larger than the value for the isolated main sign (Cd = 1.221) (Tables 2.8 and 2.9), with the following implications: • This result means that an approximate way to account for the presence of the add-on sign is to estimate Cd for an equivalent isolated rectangular sign of width b and height (bh + baha)/b (as described in Section 2.1.4). ba (ft) ba/ha Cd Cda Cdwa 3 1 1.232 1.096 1.227 3 3 1.226 0.904 1.222 3 8 1.224 0.728 1.221 — — 1.221 — — 7.5 1 1.361 1.181 1.274 7.5 3 1.267 1.118 1.231 7.5 8 1.250 1.008 1.225 — — 1.221 — — Note: The table also gives the drag coefficient for the full sign (Cdwa) and the drag coefficient for the main sign with no add-on sign attached to it (Cd = 1.221). Table 2.8. Variations of drag coefficients for main sign (b 5 30 ft, h 5 8 ft, hg 5 20 ft) and for add-on sign (ba 5 3 ft and ba 5 7.5 ft) placed at lateral edge of main sign with ba/ha. ba (ft) ba/ha Cd Cda Cdwa 3 1 1.323 1.185 1.256 3 3 1.259 1.115 1.225 3 8 1.248 0.997 1.222 — — 1.221 — — Note: The table also gives the drag coefficient for the full sign (Cdwa) and the drag coefficient for the main sign with no add-on sign attached to it (Cd = 1.221). Table 2.9. Variations of drag coefficients for the main sign (b 5 30 ft, h 5 8 ft, hg 5 20 ft) and for add-on sign (ba 5 3 ft) attached to it with ba/ha and horizontally centered with respect to the main sign.

30 Wind Drag Coefficients for Highway Signs and Support Structures • An amplification factor close to 1.05 can then be applied to estimate the drag coefficient for the full sign. These results are consistent with those obtained from the wind-tunnel experiments discussed in Section 2.1.4, which also show that the maximum amplification of drag coefficients for static rectangular signs with an add-on sign is on the order of 5% (compared to drag coefficients mea- sured for the isolated static sign). 2.1.8 Side-by-Side Highway Signs In many cases, more than one sign is attached to the same sign support structure. If the dis- tance between the lateral edges of the two signs is relatively small, the incoming airflow interacts with both signs, and this can affect the drag coefficients for each of the two side-by-side signs (Cd1, Cd2) compared to the values expected for isolated signs of the same dimensions. For a cer- tain range of the gap distance between the two signs, the acceleration of airflow between the two signs results in reduced pressure at the back of the signs, which induces an increase in wind loads on the two signs when compared to the case when each sign is isolated. This effect is similar to that observed for airflow past other side-by-side obstacles with incom- ing normal airflow relative to the plane defined by the obstacles. For example, in the experiments of Mahbub Alam, Moriya, and Sakamoto (2003) and Mahbub Alam, Zhou, and Wang (2011), an amplification of up to 30% is observed for the drag coefficients of side-by-side cylinders of rectangular and circular cross-sections when compared to the corresponding values measured for isolated cylinders at the same Reynolds number. The wind-tunnel experiments reported in Section 2.1.5 capture this effect for side-by-side rectangular signs. These studies show that for a relatively small value of the gap distance between the two signs, the wind load on the smaller sign can be as much as 27% higher than the wind load value measured for the same sign with no other sign at its side. No procedure is available to determine the drag coefficients for the two signs as a function of the gap spacing s between the two signs with dimensions of h1, b1, d1 and h2, b2, d2 when the signs are positioned at a distance hg above the ground (Figure 2.8). Numerical simulations performed under field conditions can provide the data needed to propose such a procedure. In the current research, several series of simulations are conducted with hg of 20 ft. In some of these simulations, the thickness of the two signs is the same (d1 = d2 = 0.167 ft or d1 = d2 = 4 ft) while in others a dynamic message sign (d1 = 4 ft) is placed next to a thin static sign (d2 = 0.167 ft). Some of these simulations are conducted with signs of equal front-face size (b1 = b2, h1 = h2) while Figure 2.17. Variations of drag coefficients for sign panels with ba/ha when a small add-on sign (ba = 3 ft) is horizontally centered with respect to the main sign.

Findings 31 in others a smaller sign is placed next to a sign with a larger area. The main effect investigated is how the drag coefficients for the two signs change with the nondimensional gap spacing 2s/(b1 + b2) and how fast they approach the values corresponding to the case of an isolated sign of the same dimensions. The following four series of simulations investigate the case when two rectangular thin static signs are placed next to each other: • Series 1: h1 = h2 = 8 ft; b1 = b2 = 30 ft; d1 = d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.0. • Series 2: h1 = h2 = 8 ft; b1 = 30 ft, b2 = 10 ft; d1 = d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.5. • Series 3: h1 = 8 ft, h2 = 2.5 ft; b1 = b2 = 30 ft; d1 = d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.0. • Series 4: h1 = h2 = 2.5 ft; b1 = b2 = 10 ft; d1 = d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 2.0. Two series of simulations analyze the case when one rectangular thin static sign is located next to a dynamic message sign: • Series 5: h1 = h2 = 8 ft; b1 = b2 = 30 ft; d1 = 4 ft, d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.0. • Series 6: h1 = 8 ft, h2 = 8 ft; b1 = 30 ft, b2 = 10 ft; d1 = 4 ft, d2 = 0.167 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.5. One last series of simulations investigates the case when two rectangular dynamic message signs are placed next to each other: • Series 7: h1 = h2 = 8 ft; b1 = b2 = 15 ft; d1 = d2 = 4 ft; 2s/(b1 + b2) = 0.05, 0.2, 0.4, and 1.0. Table 2.10 summarizes the drag coefficient predictions for cases with two side-by-side thin static signs. h1 (ft) b1 (ft) h2 (ft) b2 (ft) 2s/(b1 + b2) Cd1 Cd2 8 30 8 30 0.05 1.382 1.382 8 30 8 30 0.20 1.386 1.386 8 30 8 30 0.40 1.319 1.319 8 30 8 30 1.00 1.267 1.267 8 30 — — — 1.221 — 8 60 — — — 1.300 — 8 30 8 10 0.05 1.244 1.425 8 30 8 10 0.20 1.238 1.422 8 30 8 10 0.40 1.236 1.351 8 30 8 10 1.50 1.234 1.209 8 30 — — — 1.221 — — — 8 10 — — 1.150 8 30 2.5 30 0.05 1.241 1.510 8 30 2.5 30 0.20 1.235 1.420 8 30 2.5 30 0.40 1.234 1.375 8 30 2.5 30 1.00 1.228 1.292 8 30 — — — 1.221 — — — 2.5 30 — — 1.254 2.5 10 2.5 10 0.05 1.269 1.269 2.5 10 2.5 10 0.20 1.263 1.263 2.5 — 2.5 10 0.40 1.231 1.231 2.5 10 2.5 10 2.00 1.186 1.186 2.5 10 — — — 1.177 — Table 2.10. Variations of drag coefficients for two thin static signs with nondimensional gap distance of 2s/(b1 1 b2) and relevant drag coefficients for isolated signs.

32 Wind Drag Coefficients for Highway Signs and Support Structures For identical side-by-side signs, the main findings related to the drag coefficient values are as follows: • Drag coefficient first increases with the decrease in distance between the two signs, s or 2s/(b1 + b2). For signs with h1 = h2 = 8 ft and b1 = b2 = 30 ft, the drag coefficient increases with reducing gap distance and reaches a maximum for 2s/(b1 + b2) ≈ 0.2 before starting to decay toward the value corresponding to one isolated sign of the same height but twice the width (e.g., Cd = 1.3 for a plate with h = 8 ft and with b = 2b1 = 60 ft). The drag coefficient is Cd = 1.221 for the case when each sign is isolated. The expectation is that this value would be approached for very large values of the (nondimensional) gap dis- tance. The drag coefficient for side-by-side signs is still slightly larger than the value expected for isolated signs, even when the gap distance is equal to the width of the two signs, such as Cd = 1.267 for 2s/(b1 + b2) = 1. The peak amplification of the drag coefficient for the two side-by-side signs (Cd = 1.386), with respect to the value predicted for the same isolated plates (Cd = 1.221), is close to 20%. • For smaller thin static signs with h1 = h2 = 2.5 ft and b1 = b2 = 10 ft, the peak value of Cd occurs when 2s/(b1 + b2) < 0.05. The peak amplification of the drag coefficient for the two side-by-side signs (Cd = 1.269), with respect to the value predicted for the same isolated plates (Cd = 1.177), is close to 10%. In the case of two thin static signs of unequal size, the largest relative increase of Cd resulting from the interaction of the side-by-side signs is observed for the smallest sign (Table 2.10). The main trends in the variation of the drag coefficients are as follows: • The peak increase of the drag coefficient for the larger sign (h1 = 8 ft, b1 = 30 ft), compared to the value observed for the same isolated sign, is less than 2% in the series of simulations where the smaller sign has the same height but a smaller width. The peak drag coefficient for the smaller sign (h2 = 8 ft, b2 = 10 ft) is about 25% larger than the corresponding value for the same isolated sign. • The results are qualitatively similar in the series of simulations conducted with the same larger sign positioned next to a sign of smaller height (h2 = 2.5 ft, b2 = 30 ft). The peak value of Cd1 is less than 2% larger than the comparable value for the isolated larger sign. For the smaller sign, the Cd2 peak value is close to 20% larger than the corresponding value for the isolated smaller sign. Table 2.11 summarizes the predicted mean drag coefficients when a dynamic message sign (d1 = 4 ft) is placed next to a thin static sign (d2 = 0.167 ft). In this case, the following findings are observed: • The peak amplification of the drag coefficient with respect to the value predicted for the isolated sign is slightly larger for the thicker sign. • When both signs have the same area (h1 = h2 = 8 ft, b1 = b2 = 30 ft), the peak increase of the drag coefficient is nearly 20% for the dynamic message sign but only close to 10% for the thin sign. • For a large dynamic message sign (h1 = 8 ft, b1 = 30 ft) placed next to a smaller thin sign (h2 = 8 ft, b2 = 10 ft), the peak increase of the drag coefficient is less than 2% for the dynamic message sign but almost 30% for the smaller thin sign. This result is consistent with the trends noted for the case when one large thin sign is placed next to one small thin sign. The trends identified for two identical side-by-side thin signs also hold for two dynamic message signs. When two dynamic message signs—h1 = h2 = 8 ft, b1 = b2 = 15 ft, and d1 = d2 = 4 ft—are placed next to each other (Table 2.12), the following trends are observed: • As the distance between the two dynamic message signs decreases, the drag coefficient increases monotonically, reaching a maximum value of 1.401 when 2s/(b1 + b2) = 0.2. This result

Findings 33 corresponds to an increase of about 23% compared to the value expected for isolated signs of the same size and thickness (Cd = 1.133). • When 2s/(b1 + b2) < 0.2, the drag coefficients start decreasing toward the value expected for a sign of the same height but double the width (Cd = 1.203). In the case of isolated dynamic message signs, the lift coefficient (CL) acting on a dynamic message sign next to another thin sign or dynamic message sign is less than 0.02. Based on these data, the effect of the vertical force acting on the sign can be neglected in most cases if the wind is assumed to be steady and perpendicular to the signs. Alternatively, a lift coefficient CL = 0.02 can be used to estimate the magnitude of the vertical lift force. This vertical wind load is oriented toward the ground and is due to acceleration of the airflow between the bottom face of the sign and the ground. For design purposes, the main conclusions from these results are as follows: • The interaction between any two signs can be neglected if 2s/(b1 + b2) > 1.5. • For smaller values of the nondimensional gap distance, the drag coefficients for both signs are larger compared to the values for corresponding isolated signs. The peak increase of the drag coefficients can attain 20% to 25% for signs of similar size. When the size of the two signs is significantly different, the smaller sign’s peak drag coefficient Note: The table also includes the relevant drag coefficients for the signs when each sign is isolated. h1 (ft) b1 (ft) h2 (ft) b2 (ft) 2s/(b1 + b2) Cd1 Cd2 8 30 8 30 0.05 1.434 1.293 8 30 8 30 0.2 1.391 1.287 8 30 8 30 0.4 1.315 1.280 8 30 8 30 1.0 1.258 1.270 8 30 — — — 1.2 — — — 8 30 — — 1.221 8 30 8 10 0.05 1.216 1.478 8 30 8 10 0.2 1.216 1.493 8 30 8 10 0.4 1.211 1.437 8 30 8 10 1.5 1.209 1.303 8 30 — — — 1.2 — — — 8 10 — — 1.177 Table 2.11. Variations of drag coefficients for dynamic message sign (Cd1) and for thin static sign (Cd2) with nondimensional gap distance 2s/(b1 + b2). Note: The table also includes the relevant drag coefficients for the signs when each sign is isolated. h1 (ft) b1 (ft) h2 (ft) b2 (ft) 2s/(b1 + b2) Cd1 Cd2 8 15 8 15 0.05 1.240 1.240 8 15 8 15 0.1 1.346 1.346 8 15 8 15 0.2 1.401 1.401 8 15 8 15 0.4 1.271 1.271 8 15 8 15 1.1 1.194 1.194 8 15 — — — 1.133 — 8 30 — — — 1.203 — Table 2.12. Variations of drag coefficients for two dynamic message signs with nondimensional gap distance 2s/(b1 1 b2).

34 Wind Drag Coefficients for Highway Signs and Support Structures may be up to 30% larger than the comparable value predicted for the same isolated small sign. Meanwhile, the peak increase of Cd for the larger sign is much smaller. These peak increase results are fully consistent with the values determined based on the wind-tunnel experiments reported in Section 2.1.5. 2.1.9 Isolated Highway Signs Placed on a Monotube Support Structure Wind loads on highway signs and the associated drag coefficients can differ once the sign is mounted on a support structure because of the additional blockage and the modification of incoming airflow induced by the sign support structure. This section considers overhead, bridge-type, and cantilever-type monotube (single-chord) structures of circular cross-sections supporting rectangular signs of varying sign aspect ratios. The diameter of the monotube of a circular cross-section is denoted as dtube. Figure 2.18 pro- vides the following specific information on the general setup of the simulations used to investi- gate the effect of the sign support structure on the drag coefficients for highway signs mounted on a bridge-type monotube structure: • The distance between the centerline of the monotube and the ground is 24.1 ft such that hg = 20 ft for a sign of height h = 8.2 ft. • The span of the monotube is 98.5 ft. • The distance between the back of the sign and the extremity of the monotube is ds = 0.85 ft. The simulations consider the following signs: • Thin static rectangular sign with a large b/h (h = 8.2 ft, b/h = 3.75, and d = 0.17 ft). • Static rectangular sign with a small b/h (h = 8.2 ft, b/h = 1, and d = 0.17 ft). • Constant-thickness dynamic message sign (h = 8.2 ft, b/h = 3.75, and d = 4 ft). In the first series of simulations, the diameter of the monotube dtube is held constant at 2.6 ft, and the sign dimensions are varied. In the second series of simulations, the diameter of the monotube supporting a sign (h = 8.2 ft, b/h = 3.75, and d = 0.17 ft) varies with dtube = 1.3 ft, 2.6 ft, and 3.9 ft. Table 2.13 summarizes the drag coefficients predicted for the highway sign in the two series of simulations. For the series of simulations conducted with dtube = 2.6 ft, the drag coefficient for a thin sign placed on the monotube structure is 3% higher than that for the case of an isolated sign when no monotube is behind the sign. For a dynamic message sign with d = 4 ft, the increase in drag coefficient is close to 5%. The drag coefficient increases as the diameter of the monotube enlarges, but the effect is small (e.g., Cd increased from 1.25 for dtube = 1.3 ft to 1.29 for dtube = 3.9 ft). Figure 2.18. Rectangular highway sign attached to an overhead bridge-type monotube structure.

Findings 35 Several simulations are performed for rectangular signs attached to an overhead cantilever- type monotube structure. The specific design under consideration is used by the New York State DOT (Figure 2.19), with the following dimensions and configuration: • The diameter of the circular monotube is 2.6 ft. • The distance between the centerline of the monotube and the ground is 24.1 ft. • The sign ground clearance hg = 20 ft. • The span of the cantilever monotube structure is 50 ft. • The sign is placed such that one of its edges is aligned with the end of the monotube. A comparison of the results in Tables 2.13 and 2.14 shows that for the same monotube diam- eter and same sign dimensions, the drag coefficient for the highway signs remains essentially the same when the sign is attached to an overhead bridge-type monotube structure or an overhead cantilever-type monotube structure. The effect of the monotube is to increase the drag coef- ficient by as much as 6% to 7% compared to the estimated drag coefficient for the isolated sign (i.e., no monotube behind the sign). This effect should be accounted for once dtube/h becomes larger than 0.25. 2.1.10 Isolated Highway Signs Placed on a Truss Support Structure This section considers overhead, bridge-type, and cantilever-type truss structures support- ing rectangular signs of varying sign aspect ratios. The focus is on 4-chord truss structures, but results are also included for 3-chord truss structures. Figure 2.20 illustrates main geometrical variables for the case when the sign is attached to a truss structure containing multiple chords. An overhead bridge-type 4-chord truss formerly used by the Iowa DOT (Figure 2.21) is used to illustrate the effect of the truss support structure on the drag coefficient for the highway sign. The main dimensions of the truss support structure and the range of the main variables in the simulations are as follows: • The truss span is 100.0 ft. • The diameter of the vertical columns or posts is 0.82 ft; the diameter of the chords is dc = 0.4 ft; and the diameter of the other members is 0.27 ft. • The distance between the top and bottom chords defines the truss structure height hb − ha = 6 ft. • The distance between the bottom chords and the ground (ha) is varied so that the ground clearance distance for the signs is held constant at hg = 20 ft. Table 2.13. Drag coefficient for a thin static sign attached to an overhead bridge-type monotube structure. Note: The table also includes the drag coefficient for the same sign with no monotube structure behind it. h (ft) b/h d (ft) dtube (ft) dtube/h Cd 8.2 3.75 0.17 2.6 0.32 1.26 8.2 3.75 0.17 — — 1.22 8.2 1.0 0.17 2.6 0.32 1.18 8.2 1.0 0.17 — — 1.143 8.2 3.75 4.0 2.6 0.32 1.26 8.2 3.75 4.0 — — 1.20 8.2 3.75 0.17 1.3 0.16 1.25 8.2 3.75 0.17 2.6 0.32 1.26 8.2 3.75 0.17 3.9 0.48 1.29

36 Wind Drag Coefficients for Highway Signs and Support Structures Figure 2.19. Overhead cantilever-type monotube structure used by New York State DOT (used with permission from the New York State Department of Transportation). Note: The table also includes the drag coefficient for the same sign with no monotube structure behind it. h (ft) b/h d (ft) dtube (ft) dtube/h Cd 8.2 3.75 0.17 2.6 0.32 1.26 8.2 3.75 0.17 — — 1.22 8.2 1.0 0.17 2.6 0.32 1.175 8.2 1.0 0.17 — — 1.143 8.2 3.75 4.0 2.6 0.32 1.255 8.2 3.75 4.0 — — 1.20 Table 2.14. Drag coefficient for thin highway sign attached to an overhead cantilever-type monotube structure.

Findings 37 Figure 2.20. Main geometrical variables for highway sign mounted on overhead cantilever-type truss structure. Notes: The top panel of the figure shows an overall frontal view of the truss with the sign and the position of the ground. The other two panels show a view of the bottom and front faces of the truss. Figure 2.21. Former Iowa DOT truss design used in simulations with highway signs supported by an overhead bridge-type 4-chord truss structure.

38 Wind Drag Coefficients for Highway Signs and Support Structures • In all simulations, the elevation of the bottom chords falls within the range (18 ft to 26.2 ft) documented by the survey of state DOTs. • Based on the state DOT survey results, h/(hb − ha) < 4 for all simulations. • The distance between the back of the highway sign and the front face of the 4-chord truss is 0.8 ft. Figure 2.22 illustrates the computational model developed for the 4-chord truss structure. The following two series of simulations are conducted for the case when only one highway sign is supported by the truss: • Series 1: This series of simulations investigates the effect of the sign aspect ratio for a thin sign of thickness d = 0.17 ft; height h = 8.2 ft; and varying aspect ratio b/h = 1, 2, 3.75, and 8. An additional simulation is performed with a thin sign of larger height (h = 20 ft) and aspect ratio b/h = 1.5. In addition, one simulation is conducted for a thin rectangular sign with h = 8.2 ft and b/h = 3.75 for the case when the incoming wind is oriented toward the back face of the sign. • Series 2: This series of simulations considers the effect of the sign aspect ratio for a dynamic message sign of constant thickness (d = 4 ft); height h = 8.2 ft; and varying aspect ratio b/h = 1, 3.75, and 5. In addition, a thin static sign simulation is performed with an angle of attack of the incoming wind of 85 degrees instead of the standard value of 90 degrees. Series 1: For the first series of simulations, the predicted drag coefficients for the static sign attached to the truss (h = 8.2 ft) are as follows: • Cd = 1.12 for b/h = 1. • Cd = 1.15 for b/h = 2. • Cd = 1.21 for b/h = 3.75. • Cd = 1.32 for b/h = 8. The corresponding drag coefficients for the case when no truss is present behind the sign are very close (less than 2.5% difference). This result is not unexpected given the high porosity of the truss structure. In contrast, for the static sign with h = 20 ft and b/h = 1.5, the predicted value of the drag coefficient is Cd = 1.258. This value is basically the same as the one predicted for the case with no truss behind the sign. Figure 2.22. Computational model of a former Iowa DOT truss design used in simulations with highway signs supported by an overhead 4-chord bridge-type truss structure.

Findings 39 When the thin sign (h = 8.2 ft, b/h = 3.75) is positioned on the back face of the truss relative to the incoming wind direction, the drag coefficient is smaller because of the partial shielding provided by the truss members in front of the sign. The predicted drag coefficient is Cd = 1.13, about 7% smaller than the case when the same sign is positioned on the front face of the truss for the incoming wind direction (Cd = 1.21). This means that when estimating the maximum wind load on the sign, designers should always consider the case when the sign is in front of the sign support structure for the incoming wind direction. Series 2: For the second series of simulations, the predicted drag coefficients for the dynamic message sign (h = 8.2 ft, d = 4 ft) attached to the truss are as follows: • Cd = 1.090 for b/h = 1. • Cd = 1.2 for b/h = 3.75. • Cd = 1.238 for b/h = 5 (Table 2.15). These values are within 2% of those predicted for the case when the truss structure is not behind the sign. The drag coefficients predicted for a thin sign (h = 8 ft and b/h = 3.75) under different incoming wind conditions are as follows: • With the incoming wind perpendicular to the panel, Cd = 1.21 (Table 2.15). • The drag coefficient for an angle of attack of 85 degrees is calculated with the resultant force in the direction perpendicular to the panel and the incoming wind velocity along this direction, U0cos(50); this value is Cd = 1.22. Thus, a small angle of inclination of the panel has a negligible effect on the drag coefficient. Therefore, the current project focuses on reporting drag coefficient values for the standard case where the wind direction is perpendicular to the traffic sign. An overhead bridge-type 3-chord truss used by the Michigan DOT (Figure 2.23) is employed to illustrate the effect of the following truss support structure on the drag coefficient for the highway sign attached to that truss: • The truss span is 100.0 ft. • The diameter of the vertical columns is 2 ft; the diameter of the chords is dc = 0.5 ft; and the diameter of the other members is 0.42 ft. • The truss structure height is hb − ha = 6 ft. • The ground clearance distance for the signs is held constant at hg = 20 ft. • The distance between the back of the signs and the front face of the truss is 0.5 ft. Figure 2.24 shows the computational model corresponding to the 3-chord truss structure. A first set of three simulations investigates the effect of the sign aspect ratio for a thin sign h (ft) b/h d (ft) dc (ft) 2dc/h Cd 8.2 1.0 0.17 0.4 0.097 1.12 8.2 2.0 0.17 0.4 0.097 1.15 8.2 3.75 0.17 0.4 0.097 1.21 8.2 8.0 0.17 0.4 0.097 1.32 20.0 1.5 0.17 0.4 0.040 1.26 8.2 1.0 4.0 0.4 0.097 1.09 8.2 3.75 4.0 0.4 0.097 1.20 8.2 5.0 4.0 0.4 0.097 1.24 Table 2.15. Drag coefficient for thin highway sign attached to overhead bridge-type 4-chord truss structure.

40 Wind Drag Coefficients for Highway Signs and Support Structures Figure 2.23. Michigan DOT 3-chord truss used in simulations with highway signs supported by an overhead bridge-type 3-chord truss structure (used with permission from the Michigan Department of Transportation). Figure 2.24. Computational model of Michigan DOT truss design utilized in simulations with highway signs supported by an overhead 3-chord bridge-type truss structure.

Findings 41 (thickness d = 0.17 ft) with height h = 8.2 ft and varying aspect ratio b/h = 1, 3.75, and 8. A fourth simulation is performed with a dynamic message sign (d = 4 ft) with height h = 8.2 ft and aspect ratio b/h = 3.75. In the case of a sign mounted on a 4-chord truss, the drag coefficient predicted for a thin sign placed on the 3-chord truss increases with the sign aspect ratio (Table 2.16), and the values are very close—within 4% of those predicted for the corresponding highway sign with no truss behind it. For the dynamic message sign with b/h = 3.75, the predicted value is Cd = 1.24, the same as that for a thin sign of much smaller thickness. Simulations are also conducted for the following overhead cantilever-type 4-chord truss (used by the Iowa DOT) supporting one highway sign (Figure 2.25): • The truss span is 40 ft. • The diameter of the vertical column is 2.5 ft; the diameter of the chords is dc = 0.56 ft; and the diameter of the other members is 0.24 ft. • The truss structure height is hb − ha = 7 ft. • The distance between the bottom chords of the truss and the ground (ha) is varied so that the ground clearance distance for the signs is maintained as a constant, hg = 20 ft. The corresponding computational model is depicted in Figure 2.26. A series of simulations considers a thin sign. The main geometrical variables are as follows: • Sign thickness d = 0.17 ft with height h = 8.2 ft and varying aspect ratio b/h = 1, 3.75, and 4.6. • The distance between the vertical column and the edge of the sign in these simulations is s = 31.8 ft, 9.25 ft, and 2.25 ft for the respective b/h values. An additional simulation is performed with a thin sign of larger height (h = 20 ft) and aspect ratio b/h = 1.5. The drag coefficients for these thin signs are reported in Table 2.17. The results are consistent with those obtained for bridge-type trusses. Similar to previous results for signs positioned on trusses supporting one highway sign, the predicted drag coefficients are within 3% of those for the same sign with no truss behind the sign. Given that the front face of the 3-chord and 4-chord trusses considered in the current analysis contains two chords, an amplification factor of 1.04 can be used to account for the possible increase in the drag coefficient of the sign mounted on the truss (compared to the value pre- dicted for the isolated sign). This correction should be applied if 2dc/h > 0.1. The amplification factor for signs mounted on a monotube would be larger (1.07), but this result is because typi- cally dtube/h > 0.25. This analysis leads to the following general rules that can be applied for signs mounted on either monotubes or truss support structures: • An amplification factor of 1.07 should be used if dtube/h > 0.25 or 2dc/h > 0.25. • An amplification factor of 1.04 should be used if 0.1 < dtube/h < 0.25 or 0.1 < 2dc/h < 0.25. • No amplification factor is needed if dtube/h < 0.1 or 2dc/h < 0.1. h (ft) b/h d (ft) dc (ft) 2dc /h Cd 8.2 1.0 0.17 0.5 0.122 1.145 8.2 3.75 0.17 0.5 0.122 1.24 8.2 8.0 0.17 0.5 0.122 1.31 8.2 3.75 4.0 0.5 0.122 1.24 Table 2.16. Drag coefficient for thin highway sign attached to an overhead bridge-type 3-chord truss structure.

42 Wind Drag Coefficients for Highway Signs and Support Structures Figure 2.25. Iowa DOT truss design used in simulations with highway signs supported by an overhead cantilever-type 4-chord truss structure (used with permission from the Iowa Department of Transportation).

Findings 43 h (ft) b/h d (ft) dc (ft) 2dc/h Cd 8.2 1.0 0.17 0.56 0.137 1.13 8.2 3.75 0.17 0.56 0.137 1.23 8.2 4.6 0.17 0.56 0.137 1.26 20.0 1.5 0.17 0.56 0.056 1.32 Table 2.17. Drag coefficient for thin highway sign attached to an overhead cantilever-type 4-chord truss structure. Figure 2.26. Computational model of Iowa DOT truss design used in simulations with highway signs supported by an overhead 4-chord cantilever-type truss structure. 2.1.11 Isolated Highway Signs Placed on a Grade Separation Structure Traffic signs not only are specifically placed on dedicated sign support structures but also are sometimes attached to bridges spanning a roadway. The general layout is shown in Figure 2.27. Two representative configurations are considered. In Configuration 1 (Figure 2.28), a solid barrier rail is present at each edge of the bridge deck. In Configuration 2 (Figure 2.29), a solid sepa- ration rail is in place at the edges of the traffic lanes. The main geometrical dimensions are summarized in Figures 2.27, 2.28, and 2.29. Simulations are conducted with the following values of the main geometrical variables: • The ground clearance is hg = 19 ft beneath the beams and girders supporting the bridge deck. • The thin static sign is always positioned so that its lower edge is situated at h0 = 1 ft above the bottom edge of the girder.

44 Wind Drag Coefficients for Highway Signs and Support Structures Figure 2.29. Main geometrical variables for Configuration 2 where a separation rail is present at the edges of traffic lanes. Figure 2.28. Main geometrical variables for Configuration 1 where a solid barrier rail is present at the edges of the bridge deck. Figure 2.27. Main geometrical variables for the case of a highway sign mounted on a grade separation structure.

Findings 45 • The thickness of the bridge deck is assumed to be hd = 0.67 ft. • The height of the solid barrier rail hbr is assumed to be 3.3 ft for Configuration 1 and 2.83 ft for Configuration 2. The height of the beam is hb = 5 ft. • ds2 − ds1 = 3.5 ft, leaving ds1 as the only variable accounting for the distance between the sign and the support structure. For each of the two configurations, three series of simulations are conducted with varying heights (h = 8 ft and h = 16 ft) and widths (b = 30 ft and b = 8 ft) of the thin static sign, as follows: • h = 8 ft and b = 30 ft. • h = 16 ft and b = 30 ft. • h = 16 ft and b = 8 ft. Simulations are conducted with the wind directed toward both the front face and the back face of the sign to obtain information on the variation of wind load over the sign’s height. Given the highly nonuniform distribution of pressure on the sign, drag coefficients are calculated not only for the whole sign surface (Cd) but also for the main subzones (Cdlz, Cdmz, and Cduz) defined in Figures 2.30 and 2.31 for Configuration 1 and Configuration 2, respectively. The main subzones are defined as follows: • Lower subzone: This subzone extends from the bottom of the sign to the bottom of the bridge deck. • Middle subzone: If the top of the sign is below the top of the barrier rail (or the top of the separation rail), the middle subzone extends from the bottom of the bridge deck to the top of the sign. If the top of the sign projects above the top of the barrier rail (or the top of the separa- tion rail), the middle subzone extends from the bottom of the bridge deck to the top of the rail. • Upper subzone: This subzone extends from the top of the rail to the top of the sign. The drag coefficients for the subzones can be used to calculate the associated wind load that acts at the centroid of each subzone. The heights of these subzones are denoted as hlz, hmz, and huz (as depicted in Figures 2.30 and 2.31). For a rectangular sign of width b, the corresponding 2.30a: Wind directed toward the front face of the sign 2.30b: Wind directed toward the back face of the sign Note: In the left frames, the sign projects above the barrier rail; in the right frames, the sign does not extend above the barrier rail. Figure 2.30. Subzones for which drag coefficients and wind loads applied at their centroids are calculated when wind is directed toward the front face of the sign (2.30a) and toward the back face of the sign (2.30b) supported by a grade separation structure (Configuration 1).

46 Wind Drag Coefficients for Highway Signs and Support Structures subzone areas are Al, Am, and Au. The wind loads acting on each subzone are computed by using the incoming wind velocity and the corresponding area. The point of application of each wind load is situated at the centroid (mid-height and mid-width) of each subzone. Most simulations are performed with ds1 = 1.0 ft and ds1 = 3.3 ft, which is within the range of distances where most signs are positioned on the support structure. Additional simulations with ds1 as high as 66.0 ft are performed for cases when the incoming wind is directed toward the front face of the sign, which helps in understanding how the pressure distribution over the sign varies with increasing ds1 and how it compares with the limiting case of an isolated sign when there is no bridge behind the sign. 2.1.11.1 Drag Coefficients for the Case When the Wind Is Directed Toward the Front Face of the Sign The following three series of simulations are conducted for Configurations 1 and 2: • Series 1: The first series of simulations, with the wind directed toward the front face of the sign, considers the case of a highway sign with its top edge at a level comparable to that of the top of the barrier rail or separation rail. As a result, the incoming flow is deflected by both the sign and the bridge, so the effect of the bridge is felt over the whole height of the sign. • Series 2: The second series of simulations is conducted to understand how the drag coefficient varies when a large part of the highway sign (roughly the top half) does not have a nonporous obstacle behind it. • Series 3: The third series of simulations considers a sign with its top part above the top edge of the barrier rail or separation rail. However, the sign width and the sign aspect ratio b/h are smaller compared to the values in the second series of simulations. Configuration 1, Series 1: For the first series of simulations conducted for Configuration 1, the drag coefficient for the isolated thin static sign (no bridge behind it) is Cd = 1.22. When the bridge is present, the drag coefficient Cd for the whole sign increases significantly because of a suction effect (Table 2.18). This effect is generated as some of the airflow going over the top 2.31a: Wind directed toward the front face of the sign 2.31b: Wind directed toward the back face of the sign Note: In the left frames, the sign projects above the separation rail; in the right frames, the sign does not extend above the separation rail. Figure 2.31. Subzones for which drag coefficients and wind loads applied at their centroids are calculated when wind is directed toward the front face of the sign (2.31a) and toward the back face of the sign (2.31b) supported by a grade separation structure (Configuration 2).

Findings 47 edge of the sign moves downward in the space between the sign and the region defined by the bridge, the girders, and the rail. This accelerated flow decreases the pressure on the back face of the sign (e.g., based on the Bernoulli equation), which induces an increase in the pressure force acting on the sign. For very small values of ds1, the pressure distribution on the sign is qualitatively very different from the one observed for an isolated sign, with a dip in the pressure force detected at elevations close to the bottom edge of the bridge deck (Figure 2.32a). The largest suction effect is observed for ds1 ≈1 ft, with Cd = 1.7. This value of the drag coefficient is more than 30% higher than the value for an isolated sign. As ds1 further increases, Cd decreases toward the value for an isolated sign. Table 2.18 also lists the predicted drag coefficient for a very large value of ds1 (66 ft), with a Cd that approaches the value expected for an isolated sign. That test case is included just to get an idea of the distance where no effect of the bridge structure on the pressure field is induced on the sign in front of the bridge. For the range of typical values used for ds1, the amplification of Cd is on the order of 30%. Table 2.18 also includes the drag coefficients corresponding to the predicted wind loads over the two subzones defined in Figure 2.30 for the case when the top of the sign is beneath the top of the barrier rail (i.e., h − hlz < hd + hbr). Consistent with the net pressure distributions in Fig- ure 2.32a, the drag coefficient is slightly larger for the subzone above the bridge deck compared to the subzone below the bridge deck (i.e., Cdmz > Cdlz). Configuration 1, Series 2: For the second series of simulations for Configuration 1, the drag coefficient for the isolated thin static sign (no bridge behind the sign) is Cd = 1.32. The results in Table 2.19 indicate that when ds1 < 6.6 ft, the values of Cd are close to 1.7, which means that the drag force is about 25% to 30% higher than that predicted for the isolated sign. Only for ds1 > 15 ft, the drag coefficient starts decaying toward the value expected for an isolated sign. Except for very small values of ds1, the pressure distribution on the panel in the vertical direction is qualitatively like that observed for an isolated sign (Figure 2.32b). As expected, the drag coefficient is the smallest for the subzone situated below the bridge deck because of the deceleration of incoming airflow induced by the lower parts of the beams. Table 2.18. Drag coefficients for thin static sign mounted on grade separation structure (with wind directed toward front face of sign) as a function of distance between the sign and the bridge deck (ds1). h (ft) b (ft) b/h ds1 (ft) Cd hlz (ft) hmz (ft) huz (ft) Cdlz Cdmz Cduz 8 30 3.75 1.0 1.70 4 4 — 1.60 1.79 — 8 30 3.75 3.3 1.63 4 4 — 1.53 1.73 — 8 30 3.75 6.6 1.60 4 4 — 1.57 1.63 — 8 30 3.75 16.5 1.51 4 4 — 1.45 1.57 — 8 30 3.75 66.0 1.22 4 4 — 1.15 1.29 — 16 30 1.87 1.0 1.72 4 4 8 1.48 1.89 1.75 16 30 1.87 3.3 1.70 4 4 8 1.41 1.88 1.76 16 30 1.87 6.6 1.70 4 4 8 1.36 1.88 1.78 16 30 1.87 33.0 1.55 4 4 8 1.32 1.67 1.61 16 8 0.5 1.0 1.44 4 4 8 0.86 1.49 1.71 16 8 0.5 3.3 1.55 4 4 8 1.08 1.60 1.76 16 8 0.5 6.6 1.44 4 4 8 1.00 1.43 1.67 16 8 0.5 33.0 1.26 4 4 8 1.09 1.32 1.31 Notes: The geometric layout for Configuration 1 is shown in Figure 2.28. This table also gives the height and drag coefficient for each sign subzone.

48 Wind Drag Coefficients for Highway Signs and Support Structures 2.32a: h = 8 ft and b = 30 ft 2.32b: h = 16 ft and b = 30 ft 2.32c: h = 16 ft and b = 8 ft Note: The horizontal lines show the vertical extent of the different subzones depicted in Figure 2.30. Figure 2.32. Mean differential pressure distribution over the height of a thin sign mounted on a grade separation structure (Configuration 1) with wind directed toward the front face of the sign.

Findings 49 Compared to the lower subzone, the drag coefficients are about 30% larger for the two subzones between the bridge deck and the top of the sign (Table 2.18). The vertical nonuniformity in the net pressure distribution over the height of the sign is mostly related to the asymmetry of the wake flow due to the presence of the barrier rail and the other solid elements of the bridge that modify the mean airflow pattern and pressure distribution at the back of the sign (compared to the case of an isolated sign). Configuration 1, Series 3: For the third series of simulations conducted for Configuration 1, the drag coefficient for the isolated thin static sign (no bridge behind the sign) is Cd = 1.18. The drag coefficient variation with increasing ds1 is qualitatively like that observed in the other two simulation series. The maximum value of the drag coefficient (Cd = 1.55) is observed for ds1 = 3.3 ft. This value is about 25% to 30% larger than the predicted value for the same sign with no bridge present. For larger values of ds1, the drag coefficient starts to decay monotonically with increasing ds1, reaching Cd = 1.26 for ds1 = 33 ft. For ds1 < 33 ft, the net pressure distributions over the height of the sign are qualitatively dif- ferent from those observed for an isolated sign (Figure 2.32c). For relatively low values of ds1, the top part of the sign is subject to significantly larger pressure forces than the bottom part where the exposed part of the beams contributes to decelerating the incoming airflow. The presence of the barrier rail, deck, and beams also influences the airflow patterns developing in the wake of the sign, modifying the pressure distribution on the back of the sign compared to the case of an isolated sign. For ds1 ≤ 3.3 ft, the drag coefficient over the upper subzone situated above the top of the rail is more than 60% higher than Cd for the isolated sign—while the drag coefficients for the subzones below the top of the rail are 10% to 15% lower than Cd for the isolated sign (Table 2.18). Consistent with the net pressure distributions shown in Figure 2.32c, the drag coefficient for the middle subzone (Cdmz ≈ 1.5) is still larger than the drag coefficient for the isolated sign but is lower than that for the upper subzone (Cduz ≈ 1.75). Configuration 2, Series 1: Similar to Configuration 1, the first series of simulations conducted for Configuration 2 shows an increase in the drag coefficient for the traffic sign compared to the value for the case when the bridge is not present. This increase is due to a suction effect between the sign and the bridge elements. Similar to the results for Configuration 1, the Cd for the first h (ft) b (ft) b/h ds1 (ft) Cd hlz (ft) hmz (ft) huz (ft) Cdlz Cdmz Cduz 8 30 3.75 1.0 1.60 4 3.5 0.5 1.58 1.70 1.07 8 30 3.75 3.3 1.59 4 3.5 0.5 1.56 1.70 1.08 8 30 3.75 6.6 1.56 4 3.5 0.5 1.51 1.69 1.04 8 30 3.75 33.0 1.33 4 3.5 0.5 1.27 1.46 0.91 16 30 1.87 1.0 1.53 4 3.5 8.5 1.35 1.57 1.60 16 30 1.87 3.3 1.61 4 3.5 8.5 1.32 1.71 1.71 16 30 1.87 6.6 1.68 4 3.5 8.5 1.37 1.79 1.78 16 30 1.87 33.0 1.49 4 3.5 8.5 1.21 1.60 1.58 16 8 0.5 1.0 1.49 4 3.5 8.5 1.00 1.72 1.63 16 8 0.5 3.3 1.46 4 3.5 8.5 1.05 1.42 1.67 16 8 0.5 6.6 1.40 4 3.5 8.5 1.03 1.35 1.60 16 8 0.5 33.0 1.25 4 3.5 8.5 1.07 1.30 1.32 Notes: The geometric layout for Configuration 2 is illustrated in Figure 2.29. The table also gives the height and drag coefficient for each sign subzone. Table 2.19. Drag coefficients for a thin static sign mounted on a grade separation structure (with wind directed toward the front face of the sign) as a function of distance between the sign and the bridge deck (ds1).

50 Wind Drag Coefcients for Highway Signs and Support Structures simulation series for Conguration 2 monotonically decreases with increasing ds1 starting with ds1 = 1.0 , which has the largest predicted drag coecient (Cd = 1.6) (Table 2.19). is Cd value is close to the maximum value obtained for Conguration 1 (Cd = 1.7) and about 30% larger than the value predicted for an isolated sign. For ds1 = 33 , Cd = 1.33, which is about 10% larger than the value predicted for an isolated sign. e mean pressure distributions in Figure 2.33a demonstrate that for all values of ds1, the vertical variation of the net width-averaged pressure is qualitatively like that observed for an isolated sign. e drag coecients for the sign subzones beneath and above the bridge deck are comparable (Table 2.19). e height of the subzone above the separation rail is negligible, so the Cd value reported for the upper subzone is not relevant. 2.33c: h = 16 ft and b = 8 ft Note: The horizontal lines show the vertical extent of the different subzones in Figure 2.31. 2.33a: h = 8 ft and b = 30 ft 2.33b: h = 16 ft and b = 30 ft Figure 2.33. Mean differential pressure distribution over the height of a thin sign mounted on a grade separation structure (Conguration 2), with wind directed toward the front face of the sign.

Findings 51 Configuration 2, Series 2: For the second series of Configuration 2 simulations, the drag coefficient for the isolated thin static sign (no bridge behind it) is Cd = 1.32. The maximum value of the drag coefficient (Cd = 1.68) is obtained when ds1 = 6.6 ft (Table 2.19). The maximum drag coefficient is about 25% to 30% higher than the one predicted for the isolated sign. For ds1 > 15 ft, the drag coefficient starts decaying with increasing ds1 toward the value expected for an isolated sign. It should be noted that for Configuration 1, the largest drag coefficient (Cd = 1.72) is obtained for ds1 = 1 ft, with Cd remaining close to constant until ds1 = 6.6 ft. Despite these qualitative differences, the maximum drag coefficient values are close for the two configurations. The mean pressure distributions in Figure 2.33b show a number of patterns. For ds1 > 1.5 ft, the vertical variation of the net pressure is qualitatively like that observed for an isolated sign. Only for very small values of ds1 is the pressure distribution qualitatively different, with larger net pressure values observed near the bottom part of the sign, up to a vertical distance of about 3 ft, which corresponds roughly to the lower edge of the bridge deck. Consistent with the trends shown by the vertical variation of net pressure force in Figure 2.33b for ds1 ≤ 3.3 ft, the drag coefficient over the lower subzone of the sign (Cdlz ≈ 1.33) is about 20% to 25% lower than the drag coefficients over the middle and upper subzones (Cdmz ≈ Cduz ≈ 1.7). This effect is due to the exposed parts of the beams that contribute to decelerating the incoming airflow. Configuration 2, Series 3: For the third series of simulations for Configuration 2, the drag coefficient for the isolated thin static sign (no bridge behind the sign) is Cd = 1.18. The drag coefficient decreases monotonically with increasing ds1 (Table 2.19). The maximum value of the drag coefficient (Cd = 1.49) is obtained for ds1 = 1 ft. This value is about 25% larger than the predicted value for an isolated sign. By comparison, the maximum drag coefficient value predicted for Configuration 1 is Cd = 1.55. For ds1 < 33 ft, the vertical pressure distributions are qualitatively different from those observed for an isolated sign. As for Configuration 1, the vertical distributions of the net pressure in Figure 2.33c differ significantly from that predicted for an isolated sign, except for very large ds1 values (ds1 > 33 ft). For ds1 ≤ 3.3 ft, the net pressure values over the top part of the sign are much larger when the sign is mounted on a grade separation structure (compared to the case of an isolated sign). The drag coefficient for the lower subzone beneath the bridge deck (Cdlz ≈ 1) is about 60% lower when compared to the drag coefficients for the middle and upper subzones. The main conclusions from the three series of simulations conducted for both configurations indicate the following: • For highway signs mounted on a grade separation structure, the expected increase in the drag coefficient is as much as 30% compared to the case with no bridge behind the sign. • If the top of the sign is situated around or below the top of the rail, the drag coefficients for the subzones above and below the bridge deck level are comparable, with 10% to 15% higher values for the subzone above the bridge deck. However, if the top of the sign extends signifi- cantly above the top of the rail, the vertical distribution of the width-averaged wind load on the sign is much more nonuniform. • The drag coefficient for the region below the bridge deck is significantly lower than the drag coefficients of the two subzones above the bridge deck level. 2.1.11.2 Drag Coefficients for the Case When the Wind Is Directed Toward the Back Face of the Sign In the case when the wind is directed toward the back face of the sign, the total wind load acting on the sign is less than the one acting on the same sign with no bridge (isolated sign). However, if the top of the sign extends above the barrier rail or separation rail, the vertical distribution of the wind load on the sign is more nonuniform compared to the ones observed

52 Wind Drag Coefficients for Highway Signs and Support Structures for instances when the wind is directed toward the front face of the sign. This outcome occurs because the (upper) region of the sign situated above the rail is the only unshielded region. The results in Table 2.20 indicate that for a sign with h = 8 ft, if the top of the sign is placed below the top of the rail, the drag coefficients for the two subzones are much smaller than the one for an isolated sign (Cd = 1.22). This finding is a direct consequence of the shielding induced by the bridge beams and the rail. For Configuration 1, even if the top of the sign extends above the top of the rail (e.g., signs with h = 16 ft, in Table 2.20), the wind loads over the subzone situated between the bottom of the bridge deck and the top of the rail remain relatively low because of the proximity between the barrier rail and the back of the sign. This observation applies to signs with b/h ≤ 1 and b/h > 1. In contrast, in the Configuration 2 simulations, the drag coefficients for the middle subzone between the bottom of the bridge deck and the top of the separation rail are non- negligible regardless of the value of b/h. Still, these drag coefficients are smaller than both the ones predicted for the top (unshielded) subzone and the one predicted for the isolated sign (Cdmz ≈ 0.65Cd0). The drag coefficients reported in Tables 2.20 and 2.21 for signs with h = 16 ft demonstrate that the wind loads acting over the unshielded upper subzone (situated above the top of the rail) are significant. The value of the drag coefficient for this subzone varies little with the b/h ratio. h (ft) b (ft) b/h ds1 (ft) Cd hlz (ft) hmz (ft) huz (ft) Cdlz Cdmz Cduz 8 30 3.75 1.0 −0.11 4 4 — −0.07 −0.14 — 8 30 3.75 3.3 −0.09 4 4 — −0.08 −0.10 — 16 30 1.87 1.0 0.26 4 4 8 0.06 0.01 0.51 16 30 1.87 3.3 0.52 4 4 8 0.11 0.14 0.69 16 8 0.5 1.0 0.20 4 4 8 0.01 −0.12 0.49 16 8 0.5 3.3 0.14 4 4 8 −0.03 −0.08 0.39 Notes: The geometric layout for Configuration 1 is shown in Figure 2.28. The table also gives the height and drag coefficient for each sign subzone. Table 2.20. Drag coefficients for a thin static sign mounted on a grade separation structure in Configuration 1 (wind directed toward the back face of the sign) as a function of the distance between the sign and the bridge deck (ds1). Notes: The geometric layout for Configuration 2 is depicted in Figure 2.29. The table also gives the height and drag coefficient for each sign subzone. h (ft) b (ft) b/h ds1 (ft) Cd hlz (ft) hmz (ft) huz (ft) Cdlz Cdm Cduz 8 30 3.75 1.0 −0.02 4 3.5 0.5 −0.05 −0.02 0.16 8 30 3.75 3.3 0.01 4 3.5 0.5 −0.08 0.06 0.19 16 30 1.87 1.0 1.15 4 3.5 8.5 0.20 1.03 1.56 16 30 1.87 3.3 1.19 4 3.5 8.5 0.32 0.97 1.59 16 8 0.5 1.0 0.95 4 3.5 8.5 0.26 0.71 1.39 16 8 0.5 3.3 0.94 4 3.5 8.5 0.28 0.66 1.42 Table 2.21. Drag coefficients for a thin static sign mounted on grade separation structure in Configuration 2 (wind directed toward the back face of the sign) as a function of the distance between the sign and the bridge deck (ds1).

Findings 53 However, for Configuration 1, the drag coefficient for this subzone is smaller than the one for an isolated sign (Cduz ≈ 0.45Cd0) while the opposite is true for Configuration 2 (Cduz ≈ 1.2Cd0). This difference arises because the barrier rail for Configuration 1 is closer to the back of the sign, so the shielding is stronger when compared to Configuration 2 where the separation rail is situated at a larger distance from the back of the sign and where the airflow moving over the barrier rail reattaches on the bridge deck before hitting the back of the sign. In Configuration 1, the main reason for Cduz << Cd0 is that most of the top part of the sign is situated inside the region of separated flow bounded by the separated shear layer originating at the top edge of the barrier rail on the bridge side opposite to the one where the sign is attached. The height of this region increases with the distance from the origin of the shear layer. Although such an effect is also evident for Configuration 2, the height of this region at the location of the sign is much lower—both because the height of the separation rail is less than that of the barrier rail and especially because the distance is smaller between the sign and the separation rail on the bridge side opposite to the one with the sign. 2.1.12 Side-by-Side Highway Signs Placed on a Monotube Support Structure This section considers overhead, bridge-type, and butterfly-type monotube (single-chord) structures of circular cross-sections supporting two rectangular highway signs of varying sizes. Figure 2.34 provides specific information on the setup of the simulations used to investigate the effect of the sign support structure on drag coefficients for two highway signs mounted on a bridge-type monotube structure of circular cross-section. Simulation sign dimensions and positions are as follows: • The distance between the centerline of the monotube and the ground is 21.8 ft so that hg = 20 ft for a sign of height h = 8.2 ft. • The span of the monotube is 100.0 ft. • The distance between the back of the sign and the extremity of the monotube is ds = 0.85 ft. • The signs are placed symmetrically with respect to the middle of the monotube. • The diameter of the monotube is 2.6 ft. Series 1: The first series of simulations considers the case of two identical rectangular thin signs: • The dimensions of the two signs are h = 8.2 ft, b1/h = b2/h = 3.75, and d1 = d2 = 0.17 ft. • The two identical thin signs are attached to the monotube structure. • The effect of varying the gap distance between the two signs, s, is investigated. Simulations are performed for three values of the nondimensional gap distance 2s/(b1 + b2): 0.05, 0.2, and 0.4. Figure 2.34. Two rectangular signs attached to an overhead bridge-type monotube structure.

54 Wind Drag Coefficients for Highway Signs and Support Structures Series 2: The second series of simulations considers the case of a thin rectangular sign placed next to a dynamic message sign on the monotube structure: • The dimensions of the thin rectangular sign are h = 8.2 ft, b1/h = 3.75, d1 = 0.17 ft. • The dimensions of the dynamic message sign are h = 8.2 ft, b2/h = 3.75, d2 = 4 ft. • Simulations are performed with 2s/(b1 + b2) = 0.05, 0.2, and 0.4. Table  2.22 summarizes the drag coefficient predictions for two side-by-side traffic signs mounted on a bridge-type monotube structure. For identical side-by-side thin signs (h = 8.2 ft and b1/h = b2/h = 3.75), the drag coefficient first increases monotonically with decreasing distance between the two plates. The drag coeffi- cient reaches a maximum of Cd = 1.45 when 2s/(b1 + b2) = 0.2 before starting to decay monotoni- cally with decreasing distance between the two plates toward the value corresponding to one single sign of the same height but twice the width. It should be noted that if the monotube struc- ture is not present, Cd = 1.3 for a thin rectangular sign with h = 8.2 ft and b = 2b1 = 60 ft. For very large distances between the same but now isolated thin signs, the predicted drag coefficient is Cd = 1.221. The qualitative behavior of Cd with decreasing gap distance is the same as that observed for side-by-side signs with no monotube structure behind them (as discussed in Section 2.1.8). Table 2.22 also contains the drag coefficients from the corresponding simulations conducted with no monotube structure behind the two signs. The presence of the monotube behind the signs results in an increase of up to 5% in the drag coefficient for each sign (compared to the case when the monotube is not included in the simulation). For an isolated sign of the same dimensions with no monotube behind it, the maximum increase of the drag coefficient for the two side-by-side signs in front of the monotube is close to 20%. For an isolated sign of twice the width of each side-by-side sign, the increase in Cd nears 12%. For a thin static sign next to a thick dynamic message sign, the drag coefficient for each sign increases monotonically with decreasing gap distance, but the relative maximum increase is larger for the thicker sign. For both signs, a monotube produces a slight increase in the drag coefficient for the signs (compared to the case when no monotube is present), but the increase is less than 5% for all values of the nondimensional gap distance reported in Table 2.22. h (ft) b1/h d1 (ft) b2/h d2 (ft) dtube (ft) 2s/(b1 + b2 ) Cd1 Cd2 8.2 3.75 0.17 3.75 0.17 2.6 0.05 1.41 1.41 8.2 3.75 0.17 3.75 0.17 — 0.05 1.382 1.382 8.2 3.75 0.17 3.75 0.17 2.6 0.2 1.45 1.45 8.2 3.75 0.17 3.75 0.17 — 0.2 1.386 1.386 8.2 3.75 0.17 3.75 0.17 2.6 0.4 1.37 1.37 8.2 3.75 0.17 3.75 0.17 — 0.4 1.319 1.319 8.2 3.75 0.17 3.75 4.0 2.6 0.05 1.352 1.49 8.2 3.75 0.17 3.75 4.0 — 0.05 1.293 1.434 8.2 3.75 0.17 3.75 4.0 2.6 0.2 1.35 1.46 8.2 3.75 0.17 3.75 4.0 — 0.2 1.287 1.391 8.2 3.75 0.17 3.75 4.0 2.6 0.4 1.345 1.38 8.2 3.75 0.17 3.75 4.0 — 0.4 1.280 1.315 Note: The table also gives the drag coefficients for the two side-by-side signs with no monotube structure behind them. Table 2.22. Drag coefficients for two side-by-side signs (height h) attached to an overhead bridge-type monotube structure (diameter dtube) and drag coefficients for two side-by-side signs with no monotube structure behind them.

Findings 55 The maximum increase of Cd for the thick dynamic message sign in front of the mono- tube—Cd = 1.49 when 2s/(b1 + b2) = 0.05—is almost 25% compared to the limiting case of an isolated thick sign with no monotube present (Cd = 1.2). The presence of the monotube results in an increase of about 5% in the maximum drag coefficient for the thick dynamic message sign (Cd = 1.49) compared to the drag coefficient for the same thick sign with no monotube present (Cd = 1.434). As for the cases of side-by-side signs with no monotube, the proximity of the highway signs induces an increase of Cd in the simulations where side-by-side signs are placed in front of the monotube. This effect is evident even for relatively large nondimensional gap distances between the two signs. The presence of the monotube results in an increase of about 5% of the maximum drag coefficients for the side-by-side signs. Thus, the same amplification factors proposed for monotubes supporting only one sign can be used for monotubes supporting multiple signs. 2.1.13 Side-by-Side Highway Signs Placed on a Truss Support Structure This section considers overhead, bridge-type, and butterfly-type truss structures supporting side-by-side rectangular signs with varying sign aspect ratios. This section focuses on 4-chord truss structures. Figure 2.35 illustrates the main geometrical variables when two highway signs are attached to a truss structure. Simulations are conducted for the case when two side-by-side static signs are attached to a 4-chord bridge-type truss previously employed by the Iowa DOT (Figures 2.21 and 2.22). This truss is one of the ones used in Section 2.1.10 to determine drag coefficients for single signs attached to bridge-type trusses. This truss and its components have the following dimensions: • The truss span is 100.0 ft. • The diameter of the vertical columns (posts) is 0.82 ft. • The diameter of the chords is dc = 0.4 ft. • The diameter of the other (secondary) members is 0.27 ft. Simulations are conducted for two identical thin static signs with the following: • h = h1 = h2 = 8.2 ft. • b1 = b2 = b = 30 ft. • b/h = 3.75. • hg = 20 ft. • Gap distance s = 1.5 ft, 12 ft, and 30 ft. Figure 2.35. Main geometrical variables for highway signs mounted on an overhead bridge-type truss structure.

56 Wind Drag Coefficients for Highway Signs and Support Structures Table 2.23 contains the predicted drag coefficients for the three simulations. Similar to the case of single signs mounted on a truss support structure, the presence of the truss behind the two signs has a very small influence on the drag coefficient for the two signs (less than 3% varia- tion in Cd). This result is expected given the high porosity of the truss structure. Simulations are also conducted for an overhead butterfly-type 4-chord truss supporting one highway sign at each of its two ends (Figure 2.36). The chord sizes and secondary-member sizes are the same as those for the cantilever-type truss (as shown in Figures 2.25 and 2.26). The dimensions of the butterfly-type truss are as follows: • The total truss length is 37 ft, 8 in. • The post is placed at the horizontal midpoint of the truss. • The diameter of the post is 2.5 ft; the diameter of the chords is dc = 0.56 ft; and the diameter of the other members is 0.24 ft. • The truss structure height is hb − ha = 7 ft. The following main geometrical variables defining the butterfly-type truss with two highway signs attached to it are depicted in Figure 2.37: • The distance between the back of the signs and the front face of the truss is 0.8 ft. • The distance between the bottom chords of the truss and the ground (ha) varies so that the ground clearance distance for the two signs remains constant at hg = 20 ft. • One of the lateral edges of each sign is situated close to the end of the corresponding side of the truss (Figure 2.36). h (ft) b/h d (ft) dc (ft) s (ft) 2s/(b1 + b2) Cd 8.2 3.75 0.17 0.4 1.5 0.05 1.34 8.2 3.75 0.17 0.4 12 0.4 1.30 8.2 3.75 0.17 0.4 30.75 1.0 1.26 Table 2.23. Drag coefficient for two side-by-side thin highway signs attached to a bridge-type 4-chord truss structure. Figure 2.36. Computational model used in simulations when two highway signs are supported by a butterfly-type truss structure.

Findings 57 Two simulations are conducted for identical thin signs with the following dimensions: • d = d1 = d2 = 0.17 ft. • h = h1 = h2 = 8 ft. • b = b1 = b2. • Aspect ratio b/h = 1 and 2.2. A third simulation is conducted for identical thin signs of larger height, with the following dimensions: • h = h1 = h2 = 20.0 ft. • b = b1 = b2. • Aspect ratio b/h = 0.9. A fourth simulation is conducted for two identical dynamic message signs with the follow- ing dimensions: • d = d1 = d2 = 4.0 ft. • h = h1 = h2 = 8 ft. • b = b1 = b2. • Aspect ratio b/h = 2.2. The simulations with b/h = 2.2 correspond to small gap distances between the two signs. Table 2.24 includes the predicted drag coefficients for the four simulations. The presence of the truss behind the two signs has a very small influence on the drag coefficient for the two Figure 2.37. Main geometrical variables for highway signs mounted on an overhead butterfly-type truss structure. h (ft) b/h d (ft) dc (ft) s (ft) 2s/(b1 + b2) Cd 8.2 1.0 0.17 0.56 24.0 2.93 1.17 8.2 2.2 0.17 0.56 6.8 0.37 1.40 20.0 0.9 0.17 0.56 4.0 0.22 1.58 8.2 2.2 4.0 0.56 6.8 0.37 1.39 Table 2.24. Drag coefficient for two identical side-by-side highway signs attached to an overhead butterfly-type 4-chord truss structure.

58 Wind Drag Coefficients for Highway Signs and Support Structures signs (less than 3% variation in Cd). Thus, the same amplification factors proposed for trusses supporting only one sign can be used for trusses supporting multiple signs. In addition, for the three cases with 2s/(b1 + b2) less than 0.4, the predicted drag coefficients for the two side-by-side signs of identical dimensions are about 10% larger than the drag coefficient for an isolated sign of the same dimensions. 2.2 Wind Loads on Sign Support Structures Besides inducing forces on signs, the incoming wind also generates drag forces on the mem- bers of the support structures themselves. Depending on the specific design of the support struc- ture, some members may be shielded by other members that are part of the front face. Therefore, this section starts by looking at drag coefficient predictions for both back-to-back members of infinite length and isolated members of finite length. After that, the discussion turns to results of simulations performed with monotube and truss support structures supporting one or two highway signs. Estimations are provided for the lateral variation of drag coefficients along the monotube and truss chords as a function of the distance from the lateral edges of the signs mounted on them. Drag coefficients are also estimated for members shielded by other members of the support structure. These drag coefficients are nor- malized by the values expected for the corresponding isolated members. 2.2.1 Drag Coefficients for Isolated and Back-to-Back Members of Infinite Length The flow conditions and drag coefficient for isolated members depend on the Reynolds number (Re), defined as Vd/vair where V is the incoming wind speed, d is the diameter or projected width of the member, and vair is the molecular viscosity of the air. The attached boundary layers on an isolated cylinder are laminar for Re < 200,000, and the flow is subcritical. The flow is supercritical (i.e., attached boundary layers are turbulent at separation) for Re > 400,000. This section provides information on how the drag coefficients for infinitely long circular and L-shaped members vary with the nondimensional distance between the two members. This section also compares current predictions of drag coefficients for isolated infinitely long circu- lar cylinders with the standard values cited in the literature and with the equations included in Table 3.8.7-1 of the AASHTO LRFDLTS-1 specifications. For the simulations conducted for subcritical flow conditions (10,000 < Re < 50,000), the predicted drag coefficient for an isolated cylinder is 1.15–1.23 (Figure 2.38). This value is in very Figure 2.38. Variation of the drag coefficient with the Reynolds number for infinitely long cylinders of circular cross-section.

Findings 59 good agreement with published experimental data (e.g., Wieselsberger 1921, Fage and Warsap 1929, Achenbach 1968). In their experiments, the cylinders span the whole width of the wind tunnel (i.e., the ends of the cylinder are attached to the two sidewalls), which corresponds to what is generally known as an infinitely long cylinder. The curve labeled Experiments in Figure 2.38 represents the best fit for these experimental data sets and is the standard curve included in fluid mechanics textbooks. The LRFDLTS-1 specifications use a constant value of 1.1 before the start of the transition regime (Figure 2.38). For Re = 5 × 106, the Cd value predicted by the simulations (Cd = 0.47) is very close to the one recommended in the LRFDLTS-1 specifications (Cd = 0.45) for Re > 800,000. The simulations predict a wider range of Reynolds numbers over which transition occurs because the drag coefficient is strongly dependent on the predicted position of the separation point for members without sharp edges. Figure 2.39a illustrates the simulation setup for the circular back-to-back members of identi- cal diameter d. Three series of simulations investigate the effect of the nondimensional distance between the centerlines of the two cylinders, w/d, and the effect of a small (vertical) misalign- ment of the two cylinders relative to the incoming wind velocity, v/d. Simulations are conducted with both subcritical and supercritical flow conditions. The specific simulation conditions are as follows: • Series 1: w/d = 1.5, 3, 6, 15, 40; Re = 10,000; v/d = 0. • Series 2: w/d = 1.5, 3, 6, 15, 40; Re = 500,000; v/d = 0. • Series 3: w/d = 1.5, 3, 6, 15; Re = 10,000; v/d = 0.5. Table 2.25 lists the drag coefficients for the upstream (Cd1) and downstream (Cd2) cylinders. The main findings for the Series 1 simulations, conducted with Re = 10,000 and v/d = 0, are as follows: • The minimum value of the drag coefficient for the upstream cylinder is Cd1 = 0.96 for w/d = 1.5. • For w/d > 1.5, Cd1 increases monotonically with w/d to reach the value expected for an isolated cylinder for w/d ≈ 40. • For w/d > 40, the pressure distribution on the upstream cylinder is not affected by the pres- ence of the downstream cylinder. • For very small distances between the two cylinders, a suction effect acts on the downstream cylinder situated in the wake of the upstream cylinder. This effect explains the small negative value of the drag coefficient for the downstream cylinder (Cd2 = −0.22 for w/d = 1.5). • The drag coefficient then increases monotonically with increasing distance to reach Cd2 = 0.93 for w/d = 40. For very large values of the nondimensional distance between the cylinders (e.g., for w/d >> 100), Cd2 will also eventually approach the value predicted for an isolated cylinder. 2.39a: Members of circular cross-section 2.39b: L-shaped members Figure 2.39. Main geometrical variables for the case of airflow past back-to-back members.

60 Wind Drag Coefficients for Highway Signs and Support Structures For an isolated cylinder, the polar angle at which the flow separates increases from about 90 degrees for Re = 10,000 to around 108 degrees for Re ≈ 500,000. The change of the sepa- ration line on the cylinder is the main reason for the reduced value (Cd = 0.59) of the drag coefficient for an isolated cylinder at Re = 500,000 when compared to the value predicted for Re = 10,000. The main findings for the Series 2 simulations, conducted with Re = 500,000 (attached boundary layers are turbulent before flow separates) and v/d = 0, are as follows: • The minimum value of Cd1 occurs for w/d = 3 (Cd1 = 0.56). • For subcritical flow conditions, Cd1 reaches the value predicted for an isolated cylinder for w/d ≥ 40. Overall, Cd1 is subject to much less variation with increasing w/d for supercritical flow conditions. • Qualitatively, the evolution of the drag coefficient for the downstream cylinder is like that observed for subcritical flow conditions. For small w/d, Cd2 is also negative (e.g., Cd2 = −0.13 for w/d = 1.5) and then increases monotonically with rising w/d to reach Cd2 = 0.49 for w/d = 40. In some cases, the wind direction is not exactly perpendicular to the sign support structure and its members. Thus, some of the downstream members are less shielded by the upstream members (compared to the case when back-face members are perfectly aligned with front-face members). As a result, the back-face members may be subject to larger wind loads. To address such situations, Series 3 simulations are performed with Re = 10,000 and a slight vertical displacement of the downstream cylinder (v/d = 0.5). In these simulations, the down- stream cylinder is partially exposed to the incoming flow rather than entirely shielded by the upstream cylinder. The main findings are as follows: • For the same w/d, Cd2 is larger in the simulations conducted with v/d = 0.5 compared to those with v/d = 0 (Table 2.25). • For the upstream cylinder, Cd1 increases monotonically with rising w/d but needs a larger dis- tance between the two cylinders to approach the value of 1.2 expected for an isolated cylinder. Figure 2.39b illustrates the simulation setup for the case of back-to-back L-shaped members of side length d. A series of simulations investigates the effect of the nondimensional distance d (ft) w/d Re v/d Cd1 Cd2 0.33 1.5 10,000 0.0 0.96 −0.22 0.33 3 10,000 0.0 1.12 0.42 0.33 6 10,000 0.0 1.18 0.45 0.33 15 10,000 0.0 1.19 0.70 0.33 40 10,000 0.0 1.20 0.93 0.33 1.5 500,000 0.0 0.55 −0.13 0.33 3 500,000 0.0 0.56 0.30 0.33 6 500,000 0.0 0.57 0.36 0.33 15 500,000 0.0 0.58 0.43 0.33 40 500,000 0.0 0.59 0.49 0.33 1.5 10,000 0.5 0.90 0.64 0.33 3 10,000 0.5 1.12 0.70 0.33 6 10,000 0.5 1.16 0.73 0.33 15 10,000 0.5 1.17 0.76 Table 2.25. Drag coefficients for the upstream and downstream cylinders as a function of the distance w between the two cylinders of diameter d, vertical distance v, and cylinder Reynolds number.

Findings 61 between the two members. Simulations are conducted with the following values of the main variables: • w/d = 1.5, 3, 6, 15, 40. • Re = 10,000. The separation point on an L-shaped member is dictated by the geometry. Consequently, the value of the Reynolds number has only a small influence on the drag coefficient for the isolated L-shaped member. The predicted drag coefficient is Cd = 2.25 for an isolated L-shaped member for Re = 10,000. This value is close to the one predicted for members of rectangular shape (Cd ≈ 2). Results in Table  2.26 show that the maximum reduction in the drag coefficient for the upstream member occurs for w/d = 3 (Cd1 = 1.71). As w/d increases, so does Cd1. For w/d = 40, Cd1 reaches the value for an isolated member. Simulations predict Cd2 < 0 for small distances between the two members. For w/d > 4, Cd2 is positive and increases monotonically with w/d to reach Cd2 = 1.5 for w/d = 40. 2.2.2 Drag Coefficients for Finite-Length Members Monotubes, truss chords, and secondary truss members are finite-length members. The aspect ratio AR is defined as the ratio between the length of the member L and its diameter or maximum width d in a plane perpendicular to the incoming wind direction. Most of the litera- ture reports data for infinitely long members of circular or rectangular cross-sections. In experi- ments, the case of an infinitely long cylinder corresponds to a member spanning the whole width of the flume or wind tunnel, with the member perpendicular to the lateral walls of the flume or wind tunnel. In such cases, no airflow moves around the ends of the member because the member is connected to the lateral walls of the flume or wind tunnel. In the case of numerical studies, this condition is simulated by using periodic boundary conditions in the spanwise direction. Table 2.27 (circular shape) and Table 2.28 (L-shaped) show drag coefficient values as a func- tion of the Reynolds number and the aspect ratio. For AR of infinity (infinitely long members), d (ft) w/d Re Cd1 Cd2 0.33 1.5 10,000 1.92 −0.30 0.33 3 10,000 1.71 −0.47 0.33 6 10,000 2.18 0.79 0.33 15 10,000 2.24 1.02 0.33 40 10,000 2.25 1.50 Table 2.26. Drag coefficients for the upstream and downstream L-shaped members as a function of distance w between the two members of width d. Re Cd AR = ∞ Cd AR = 230 Cd AR = 20 1 × 104 1.20 0.78 0.67 5 × 104 1.23 0.75 0.62 5 × 105 0.60 0.57 0.49 1.5 × 106 0.55 0.53 0.37 Table 2.27. Drag coefficients for isolated circular cylinders as a function of the aspect ratio and the Reynolds number.

62 Wind Drag Coefficients for Highway Signs and Support Structures the values noted for members of circular cross-section are the same as those cited in Section 2.2.1. As expected, only a small reduction of Cd with increasing Reynolds number is observed for L-shaped members (e.g., from Cd = 2.25 for Re = 50,000 to Cd = 2.15 for Re = 1,500,000). For both types of members (circular and L-shaped), the drag coefficients for finite AR values are smaller than those for AR of infinity. The largest differences are observed for circular members at subcritical Reynolds numbers. For example, for Re = 10,000, the predicted drag coefficients are as follows: • Cd = 0.67 for AR = 20. • Cd = 0.78 for AR = 230. • Cd = 1.2 for AR = ∞. The differences are much smaller at supercritical Reynolds numbers (e.g., Re > 500,000, as documented in Table 2.27). A significant reduction in the drag coefficient of finite-length circular cylinders is evident as the flow regime changes from subcritical to supercritical. The drag coefficient values for circular cylinders of finite length are lower than the values expected for infinitely long circular cylinders because of the modification of separation line and vortex shedding in the wake of finite-length circular cylinders. This change is triggered by strong 3-D flow effects around the two ends of the member. The predicted values of the drag coefficient for finite-length circular cylinders in the subcritical regime are comparable to those (0.62–0.88) obtained experimentally by Goldstein (1965), Farivar (1981), and Sakamoto and Oiwake (1984). For L-shaped members, Cd decreases slightly with increasing Reynolds number for AR = 230 and AR = 20. Compared to the values predicted for long L-shaped members, the following reduction in Cd is observed: • Around 30% to 35% for AR = 230. • Roughly 35% to 40% for AR = 20 (Table 2.28). These percentages are comparable to those predicted for circular members at Re = 10,000 (Table 2.27). In the subcritical flow regime, the following Cd values are observed: • Cd = 1.2–1.23 for long members. • Cd = 0.75–0.78 for members with AR = 230. • Cd = 0.62–0.67 for members with AR = 20 (Table 2.27). Past the drag crisis at Re = 1,500,000, the drag coefficients for long members and for members with AR = 230 are close (Cd = 0.55 and Cd = 0.53, respectively). However, much shorter members are characterized by smaller drag coefficients (Cd = 0.37 for AR = 20). Based on the data in Tables 2.27 and 2.28, linear interpolation can be used to determine drag coefficients for members with 20 < AR < 230 and 10,000 < Re < 1,500,000. Given that Re Cd AR = ∞ Cd AR = 230 Cd AR = 20 5 × 104 2.25 1.49 1.43 1 × 105 2.17 1.48 1.40 2 × 105 2.16 1.47 1.30 1.5 × 106 2.15 1.42 1.28 Table 2.28. Drag coefficients for isolated L-shaped member as a function of the aspect ratio and the Reynolds number.

Findings 63 for Re > 1,500,000, Cd changes rather slowly with increasing Reynolds numbers, the values in Tables 2.27 and 2.28 for Re = 1,500,000 can be used for 1,500,000 < Re < 2,500,000. This approach should allow estimating the drag coefficient for the largest members of sign support structures, assuming design wind velocities up to 130 mph and chord diameters of less than 20 in. 2.2.3 Wind Loads on Monotubes Supporting Highway Signs The series of simulations conducted with one or two highway signs (described in Section 2.1.7 and Section 2.1.10, respectively) are used to estimate the wind loads acting on the monotube structure (Figures 2.18 and 2.34). At each spanwise position y along the axis of the monotube, the pressure and shear stress distributions are integrated over the circumference of the mono- tube, which allows calculation of the distribution of the wind loads per unit length along the axis of the monotube. The wind load per unit length can be expressed in nondimensional form as a drag coefficient Cd(y), using the incoming wind velocity and the diameter of the monotube of a circular cross-section. For all simulations, the wind loads on the part of the monotube directly shielded by a sign are negligible. The same data showed that wind loads near the lateral edges of each sign are ampli- fied because part of the incoming airflow approaching the highway sign is deflected laterally as it passes the sign. This deflection accelerates the airflow around the lateral, top, and bottom edges of each sign, resulting in an increase in the wind loads on the monotube structure over a certain distance away from the lateral edges of the sign. Although this increase in wind loads is mainly due to the local acceleration of streamwise flow velocity near certain parts of the monotube, it is more practical to characterize this increase in terms of a drag coefficient Cd(y) that assumes the same incoming flow velocity for the whole monotube. For a long monotube, the drag coefficient for the parts of the monotube situated at large distances from the traffic sign should approach the value for a horizontal circular cylinder at the corresponding Reynolds number defined with the approaching velocity and the diameter of the cylinder Cd0. Preliminary simulations to determine Cd0 are performed with monotubes of different diameters (dtube = 0.4 ft, 0.7 ft, 1.3 ft, 2.6 ft, and 3.9 ft, corresponding to the mono- tube structures used in Sections 2.1.7 and 2.1.10) and length of 100 ft supporting no traffic signs. As the Reynolds number for the monotube cylinder increases and the aspect ratio AR decreases, Cd0 decreases (e.g., from Re ≈ 90,000 for dtube = 0.4  ft to Re ≈ 800,000 for dtube = 3.9  ft). For the aforementioned dtube diameters, the predicted Cd0 values are 0.75, 0.62, 0.54, 0.47, and 0.45, respectively. These values are consistent with those reported in Table 2.27 for AR < 230. Given that the increase in wind velocity near the lateral edges of the signs is basically independent of the Reynolds number, the local drag coefficient along the monotube is further normalized by Cd0. For monotube structures supporting only one sign, y equal to 0 corresponds to the position of each of the two lateral edges of the sign, and the values of Cd/Cd0 are reported between each lateral edge and the corresponding extremity of the monotube (Figure 2.40). For monotube structures supporting two side-by-side signs, the same procedure is used between the “external-side” edge of each sign and the corresponding extremity of the monotube. In the gap distance between the two signs, Cd/Cd0 is reported between the “interior-side” edge of each sign (y = 0) and the middle of the gap distance between the interior-side edges of the two side-by-side signs. How fast Cd approaches Cd0 with increasing y is a function of the size and the inverse aspect ratio h/b of the sign. If the sign is larger, then the amount of airflow that needs to be deflected by the sign is larger. Consequently, the width of the flow-acceleration region forming around all four edges of the sign will be larger, so the region where Cd/Cd0 > 1 will also be larger. For signs with the same area, the amount of flow deflected laterally will be larger for

64 Wind Drag Coefficients for Highway Signs and Support Structures signs with larger h as more of the incoming airflow will be deflected close to the lateral edges of the sign (rather than close to its top and bottom edges). As a first-order approximation, the width of the region of flow amplification around the edges of the sign should be proportional to (bh)0.5. This length scale is used to represent the variation of Cd/Cd0 away from the lateral edges of each sign supported by the monotube. In the simulations of airflow past a monotube supporting a single highway sign, as reported in Section 2.1.9, the distance between the sign panel and the monotube is 0.92 ft. The mounting offset has a negligible effect on the spanwise variation of the normalized drag coefficient along the monotube. The following rules are used to determine the variation of Cd/Cd0: • For bridge-type monotube structures supporting a single highway sign, the variation of Cd/Cd0 with y/(bh)0.5 is identical away from the two lateral edges of the sign; thus, only the variation of Cd/Cd0 away from only one of the lateral edges is recorded in Figures 2.41 to 2.43. • For cantilever-type monotube structures supporting one highway sign, the variation of Cd/Cd0 is shown between the interior-side edge of the sign and the post (Figure 2.43). y=0 y=0 y>0 y>0 Notes: The variable y is measured starting at each of the two lateral edges of the sign. The variable y is always positive and increases with the distance from the corresponding edge of the sign. Figure 2.40. Definition of horizontal distance y, used to present in nondimensional form the variation of the drag coefficients along the chord in regions not shielded by the sign. Figure 2.41. Local amplification of normalized drag coefficient as a function of nondimensional distance from the lateral edge of the sign for a bridge-type monotube structure (dtube 5 2.6 ft) supporting one rectangular static sign (width b and height h). 2.41a: Thin rectangular signs of various dimensions 2.41b: Static sign (SS) or dynamic message sign (DMS) with h = 8.2 ft and b/h = 3.75

Findings 65 Figure 2.41a plots the lateral variation of Cd/Cd0 with y/(bh)0.5 for a thin static sign (d = 0.17 ft) placed on a bridge-type monotube structure of fixed diameter (dtube = 2.6 ft). The simulations use signs of the following different sizes: • b/dtube = 11, h/dtube = 3, h = 8.2 ft, b/h = 3.75. • b/dtube = 3, h/dtube = 3, h = 8.2 ft, b/h = 1. • b/dtube = 11, h/dtube = 6, h = 16.4 ft, b/h = 1.88. Figure 2.42. Local amplification of normalized drag coefficient as a function of distance from the lateral edge of the sign for a bridge-type monotube structure supporting one thin rectangular sign. Notes: dtube = 0.4 ft, 0.7 ft, 1.3 ft, 2.6 ft, and 3.9 ft. The monotube supports one thin rectangular static sign with a height h = 8.2 ft and an aspect ratio b/h = 3.75. Figure 2.43. Local amplification of normalized drag coefficient as a function of distance from the lateral edge of the sign for a cantilever-type monotube structure (dtube = 2.6 ft) supporting one thin rectangular static sign (width b and height h).

66 Wind Drag Coefficients for Highway Signs and Support Structures The part of the monotube situated very close to the edge of the sign is still shielded, which explains the very small values of Cd/Cd0 for y/(bh)0.5 < 0.1. Then, the wind loads increase rapidly with increasing y. The peak values of Cd/Cd0 are close to 2.5. At larger lateral distances, the wind loads enter a region of more-or-less monotonical decrease. The smallest sign (b = 8.2 ft, h = 8.2 ft) is the one for which Cd/Cd0 > 1.2 until y/(bh)0.5 ≈ 1.2. In the case of the other two sign sizes, the decay of Cd/Cd0 toward 1 is faster. The nondimensional distances in Figure 2.41a can be converted into nondimensional lateral distances expressed as a function of the monotube diameter, using (bh)0.5/dtube = 5.9 for the case where h = 8.2 ft, b/h = 3.75; (bh)0.5/dtube = 3.1 for the case where h = 8.2 ft, b/h = 1; and (bh)0.5/dtube = 8.3 for the case where h = 16.4 ft, b/h = 1.88. Figure 2.41b shows the effect of sign thickness. The variation of Cd/Cd0 is compared for signs with h = 8.2 ft and b/h = 3.75 mounted on a bridge-type monotube with diameter dtube = 2.6 ft. The thin sign is 0.17 ft thick while the dynamic message sign is 4 ft thick. The lateral extent of the shielding induced by the flow separation at the lateral edge of the upstream face of the dynamic message sign is larger, which is why the region of the sharp increase of the wind load starts slightly away from the edge of the dynamic message sign. However, the peak values of Cd/Cd0 are about 15% smaller—and the region of relatively large values of Cd/Cd0 is slightly narrower—for the dynamic message sign. For example, y/(bh)0.5 = 0.5 for the dynamic mes- sage sign, and y/(bh)0.5 = 0.7 for the thin static sign. For the two simulations in Figure 2.41b, (bh)0.5/dtube = 5.9. Figure 2.42 compares the variation of Cd/Cd0 for the case when a thin rectangular sign (height h = 8.2 ft and aspect ratio b/h = 3.75) is mounted on bridge-type monotube structures of varying diameter as follows: • dtube = 0.4 ft with a corresponding value of (bh)0.5/dtube = 39.3. • dtube = 0.7 ft with a corresponding value of (bh)0.5/dtube = 23.6. • dtube = 1.3 ft with a corresponding value of (bh)0.5/dtube = 11.8. • dtube = 2.6 ft with a corresponding value of (bh)0.5/dtube = 5.9. • dtube = 3.9 ft with a corresponding value of (bh)0.5/dtube = 3.9. The variation of Cd/Cd0 with y/(bh)0.5 contains two regimes. For small monotube diameters, the peak value of Cd/Cd0 increases with increasing dtube. The maximum peak value—Cd/Cd0 ≈ 2.5—is reached for dtube ≈ 1.3 ft. For larger values of dtube, the peak value Cd/Cd0 mildly decreases with increasing dtube. The nondimensional distance from the edge of the sign (where the peak Cd/Cd0 is recorded) increases monotonically with increasing dtube from y/(bh)0.5 = 0.2 for dtube ≈ 0.4 ft to y/(bh)0.5 ≈ 0.7 for dtube = 3.9 ft. The transition to the uniform incoming flow regime where Cd/Cd0 ≈ 1 varies between y/(bh)0.5 ≈ 0.4 for dtube = 0.4 ft and y/(bh)0.5 ≈ 1.0 for dtube = 2.6 ft. These results can be used to make some general estimations of the length of the region of accelerated flow forming next to the lateral edges of the sign and the average value of Cd/Cd0 inside this region. Simulations also consider the case when a thin static sign is placed at the extremity of a cantilever- type monotube structure with circular diameter dtube equal to 2.6 ft. These results, shown in Figure 2.43, are very close to those obtained when the same signs are mounted on a bridge-type monotube structure (Figure 2.41a). If the monotube structure supports more than one sign, the part of the monotube situated between the lateral edges of the side-by-side signs is subject to larger wind loads (compared to those expected for a monotube of the same diameter with no signs attached to it). The rel- evant nondimensional distance over which the amplification of the wind load is expected to

Findings 67 be significant is (b1h1)0.5 for the first sign and (b2h2)0.5 for the second sign (where the width and height of the two signs are b1, h1 and b2, h2, respectively). Simulations are conducted with two identical rectangular signs mounted on a bridge-type monotube structure. For the simulations reported in Section 2.1.12, h1 = h2 = h = 8.2 ft and b1 = b2 = b such that b/h = 3.75 for both thin signs (d1 = d2 = 0.17 ft). For both signs, the relevant nondimensional distance is (bh)0.5, and the variation of Cd/Cd0 in Figure 2.44 is shown between the lateral edge of one of the signs (y = 0) and the middle of the gap distance (y = s/2). The non- dimensional gap distance 2s/(b1 + b2) = s/b is varied between 0.05 and 1.5. Because the diameter of the monotube is kept constant (dtube = 2.6 ft, h/dtube = 3.15), Cd0 is the same for the five cases included in Figure 2.44. The main findings from these simulations are as follows: • For very small values of the gap distance, such as s = 1.5 ft or 2s/(b1+b2) = 0.05, the peak value of Cd/Cd0 occurs close to the middle of the gap distance. Although the peak value of Cd/Cd0 is greater than 1, the average value of Cd/Cd0 in the gap region between the two signs is very close to 1. For such cases, one can simply assume that Cd = Cd0 for 0 < y < s/2. • For very large values of the gap distance—for example, for s = 30 ft or 2s/(b1 + b2) = 1 and for s = 46 ft or 2s/(b1 + b2) = 1.52—the distribution of Cd/Cd0 away from the lateral edge of each sign approaches the value estimate for the case when only one sign is present, and Cd/Cd0 ≈ 1 for y/(bh)0.5 > 0.8. • For cases when 0.15 < s/2(bh)0.5 < 0.4, Cd/Cd0 > 1 over a significant part of the region defined by 0 < y < s/2. Results for the two cases—with s = 6 ft for 2s/(b1 + b2) = 0.2 and with s = 12 ft for 2s/(b1 + b2) = 0.4— suggest that using Cd/Cd0 = 1.6 over the gap distance should provide a good approximation of the wind loads acting on the monotube structure in the gap region between the two signs (as shown in Figure 2.44). Note: The plots show the distribution of Cd/Cd0 between the lateral edge of the sign (y = 0) and the middle of the gap distance between the two signs (y = s/2). Figure 2.44. Local amplification of normalized drag coefficient in the region situated between side- by-side signs for a bridge-type monotube structure (dtube 5 2.6 ft) supporting two identical thin rectangular static signs (width b and height h).

68 Wind Drag Coefficients for Highway Signs and Support Structures 2.2.4 Wind Loads on Trusses Supporting Highway Signs The series of simulations conducted with one or two highway signs (discussed in Sec- tions 2.1.8 and 2.1.11, respectively) are used to estimate the wind loads acting on the chords and secondary members of truss structures (Figures 2.20, 2.34, and 2.37). Like the approach adopted for monotubes, the distribution of wind loads per unit length along the axis of each chord is calculated by using the pressure and shear stress distributions on the surface of the chord. This distribution is then presented in a nondimensional way as a drag coefficient along the axis of the chord, Cd(y). The drag coefficients for the chords are normalized by the drag coefficients estimated from a simulation conducted with no secondary truss members and with no highway signs attached to the chords, Cd0. For multiple-chord trusses, Cd0 is generally different for each chord. Values of Cd/Cd0 that are greater than 1 or less than 1 are mainly attributable to a mean local incoming flow velocity upstream of the chord that differs from the mean incoming velocity for the truss and the highway sign. For trusses supporting only one sign, y = 0 corresponds to the position of each of the two lateral edges of the sign, and the values of Cd/Cd0 for each chord are reported between each lateral edge and the corresponding extremity of the truss. For trusses supporting two side-by-side signs, the same procedure is employed between the external lateral edge of each sign and the cor- responding extremity of the truss. In the gap distance between the two signs, Cd/Cd0 is reported between the interior lateral edge of each sign (y = 0) and the middle of the gap distance between the interior lateral edges of the signs. Similar to what was observed for monotubes, the width of the region of flow amplification around the edges of the sign should be proportional to (bh)0.5. This length scale is used to represent the variation of Cd/Cd0 away from the lateral edges of each sign supported by the truss. For each secondary member, the total streamwise wind load is estimated and converted into a drag coefficient Cd, defined by the incoming wind velocity and the projected area of the member in a plane perpendicular to the wind direction. This value is nondimensionalized with the drag coefficient for an isolated member of the same diameter placed perpendicular to the incoming wind direction, Cd0. Section 2.2.2 allows the approximate estimation of Cd0 for such members as a function of their shape, aspect ratio, and Reynolds number. Similar to what was observed for monotubes, each truss member or part of the chord can be located behind a highway sign—for example, in the region of relatively uniform approaching airflow velocity situated far from the highway signs; in a flow-acceleration region near one of the lateral edges of the signs; or if more than one sign is attached to the truss, in the region between the two side-by-side signs. Some of the chords and secondary members can be partially shielded by members that are part of the front face of the truss. 2.2.4.1 Bridge-Type 4-Chord Truss Supporting One Highway Sign The overhead bridge-type 4-chord truss used in the past by the Iowa DOT (Figure 2.21) is the first truss employed in the current simulations to estimate the normalized drag coefficients for the chords and the secondary members. This truss has the following characteristics: • The truss span is 100 ft. • The diameter of the chords is dc = 0.4 ft, and the diameter of the secondary members is 0.27 ft. • The distance between the back of the highway sign and the front face of the 4-chord truss is 0.8 ft.

Findings 69 Drag coefficients for the truss members are estimated for the following simulations performed with static signs and DMS cabinets: • For static signs, the simulations consider signs with height h = 8.2 ft and b/h = 1, 2, 3.75, and 8 and also signs with height h = 20 ft and b/h = 1.5. • For DMS cabinets (d = 4 ft), the simulations use signs with height h = 8.2 ft and b/h = 1 and 3.75. Figure 2.45 depicts the overhead bridge-type 4-chord truss, with each of the truss members labeled as part of a group that corresponds to one of the truss faces (A to D), as briefly described Notes: The secondary members are distributed into five groups (A to E). The 4-chord members are labeled H1 to H4. Secondary members from different groups labeled with the same number are situated at about the same spanwise location. Figure 2.45. Convention used in the labeling of the truss members for the overhead bridge-type 4-chord truss used in the past by the Iowa DOT.

70 Wind Drag Coefficients for Highway Signs and Support Structures in Table 2.29, or as part of a group including the members connecting the front and back faces of the truss (Group E). The four chords of the truss are labeled H1 to H4. Members with the same numerical value that are part of different groups (i.e., A, B, C, D, E) correspond to members situated at about the same spanwise location, making it easier to understand the relative location of truss members. The following drag coefficients are predicted for the chords part of the overhead bridge-type 4-chord truss: • For a chord (dc = 0.4 ft) of the truss, preliminary simulations indicate that Cd0 ≈ 0.75 for a chord Reynolds number of about 50,000 (also addressed in Table 2.27). • When the front face of the truss contains two chords, there is a drag reduction effect on the bottom chord because of the way that the flow accelerates between the two chords and between the bottom chord and the ground. Preliminary simulations conducted with no signs and no secondary members show that Cd0 ≈ 0.75 for the top chord (H1) and Cd0 ≈ 0.66 for the bottom chord (H2) of the front face. • Consistent with results obtained for back-to-back (infinitely long) circular members, the drag coefficient is reduced for chords that are part of the back face compared to chords that are part of the front face. The drag coefficient ratio is close to 0.59 for both the top and bottom chords such that Cd0 ≈ 0.44 for the top chord (H3) and Cd0 ≈ 0.38 for the bottom chord (H4) of the back face (Figure 2.45). These values are used when the variation of Cd/Cd0 is plotted with respect to the nondimen- sional distance from the lateral edge of the sign for the four chords in Figures 2.46, 2.47, and 2.48. Similar to what was observed for monotubes, the drag coefficient can be assumed to equal zero over the part of the chord behind the highway sign. Although Cd0 is not the same for the two front-face chords (H1 and H2)—or for the two back-face chords (H3 and H4)—Cd/Cd0 is rela- tively close for the two front-face chords (and for the two back-face chords). This result applies to all of the simulations conducted with thin static signs (e.g., sample results in Figures 2.46a and 2.46b) and with dynamic message signs (e.g., sample results in Figures 2.46c and 2.42d). Consequently, the following discussion focuses primarily on the results obtained for the front chord H1 and the back chord H3 that are part of the top face of the truss. One interesting result is that the peak Cd/Cd0 is higher for the back-face chord, even though Cd values are higher for the front chord compared to the drag coefficient for the corresponding back chord at any given transverse location. For example, the maximum value of Cd/Cd0 for H1 and H2 is between 1.4 and 1.8 for the static sign simulations (Figures 2.46a, 2.46b, and 2.47a) while the maximum value of Cd/Cd0 for H3 and H4 falls between 1.8 and 2.1 for the same static sign simulations (Figures 2.46a, 2.46b, and 2.47b). The peak value of Cd/Cd0 occurs at a larger value of y/(bh)0.5 for back-face chords H3 and H4, y/(bh)0.5 = 0.2–0.4, compared to front-face chords H1 and H2, y/(bh)0.5 = 0.1–0.15. This difference Group Description A Front-face truss members B Back-face truss members C Top-face truss members D Bottom-face truss members E Interior-diagonal truss members situated between front and back faces H Truss chords Table 2.29. Description of truss members forming each group for the 4-chord truss in Figure 2.45.

Findings 71 arises because the transverse deflection of the region of accelerating airflow forming near the lateral edge of the sign increases with distance from the sign. The results in Figure 2.47 show that in a good approximation, Cd/Cd0 ≈ 1 for y/(bh)0.5 > 0.5 for chords H1 and H2 and for y/(bh)0.5 > 0.75 for chords H3 and H4. In the case of dynamic message signs, results are qualitatively similar, as demonstrated by the transverse variation of Cd/Cd0 for the four chords in Figures 2.46c and 2.46d and by the comparison of transverse variations of Cd/Cd0 for the H1 and H2 chords for cases with static signs and dynamic message signs of the same height and width (Figure 2.48). Although the peak values of Cd/Cd0 for H1 and H3 are about the same in the simulations with thin signs and dynamic message Figure 2.46. Local amplification of drag coefficient for the four chords (dc 5 0.4 ft) as a function of distance from the lateral edge of the sign for a bridge-type 4-chord truss structure supporting one highway sign. 2.46a: Thin rectangular highway sign h = 8.2 ft and b/h = 2 2.46b: Thin rectangular static sign h = 20 ft and b/h = 1.5 2.46c: Dynamic message sign h = 8.2 ft and b/h = 1.0 2.46d: Dynamic message sign h = 8.2 ft and b/h =3.75 Figure 2.47. Local amplification of drag coefficient for the two chords (dc 5 0.4 ft) that are part of the top face of the truss as a function of the distance from the lateral edge of the sign for a bridge-type 4-chord truss structure supporting a thin rectangular highway sign with either h 5 8.2 ft and b/h 5 1, 2, 3.75, and 8 or h 5 20 ft and b/h 5 1.5. 2.47a: Chord H1 part of the front face 2.47b: Chord H3 part of the back face

72 Wind Drag Coefficients for Highway Signs and Support Structures signs with identical b and h, the nondimensional transverse location where the peak occurs is further away from the sign for dynamic message signs. This effect is larger for signs with a low b/h ratio. For example, for signs with h = 8.2 ft and b/h = 1, the peak values of Cd/Cd0 for chord H1 occur at y/(bh)0.5 = 0.12 for a static sign and at y/(bh)0.5 = 0.4 for a dynamic message sign. The peak values of Cd/Cd0 for chord H3 occur at y/(bh)0.5 = 0.4 for a static sign and at y/(bh)0.5 = 0.75 for a dynamic message sign. Preliminary simulations conducted for isolated secondary members of diameter 0.27  ft of the 4-chord truss design formerly used by the Iowa DOT—and with the same incoming velocity as in the simulations conducted with the whole truss and the highway signs—predict Cd0 = 0.63–0.7, depending on the aspect ratio AR of the member. These values are consistent with those in Table 2.27 for Re < 50,000 and AR < 100. As expected, secondary members that are part of the front face and are situated away from the highway sign (e.g., outside of the flow-acceleration regions) are subject to wind loads com- parable to those observed for the case when the same member is isolated (Cd/Cd0 ≈ 1 or, more precisely, Cd/Cd0 < 1.07). For example, Cd/Cd0 ≈ 1 for members A1 to A10 and A30 to A40 for the case of a thin highway sign with h = 8.2 ft and b/h = 1. As b/h increases, the region contain- ing members with Cd/Cd0 ≈ 1 shrinks. For a thin highway sign with h = 8.2 ft and b/h = 3.75, this region includes members A1 to A5 and A37 to A42 (Figure 2.45). This region of Cd/Cd0 ≈ 1 is practically absent for a sign with h = 8.2 ft and b/h = 8 where the region of flow acceleration penetrates up to the vertical columns of the truss. For the same h and b/h (e.g., for a sign with h = 8.2 ft and b/h = 3.75), the presence of a dynamic message sign instead of a thin highway sign does not change the number of members that are part of the region with Cd/Cd0 ≈ 1. For thin signs with the same width b but with a different h (e.g., h = 8.2 ft and b/h = 3.75 versus h = 20 ft and b/h = 1.5), the number of members that are part of the region with Cd/Cd0 ≈ 1 is about the same. Drag forces are negligible—Cd/Cd0 ≈ 0 or, more precisely, |Cd/Cd| < 0.12—for the truss members situated completely behind the highway sign. The small drag forces on most of these members are negative because these members are in the recirculation airflow region at the back of the sign. This is the case for members (shown in Figure 2.45) on all four faces of the truss in the simulations performed with a thin static sign: • Members A19 to A22, B19 to B22, C18 to C24, and D18 to D24 for a sign with h = 8.2 ft and b/h = 1. • Members A17 to A24, B17 to B24, C16 to C25, and D16 t o D25 for a sign with h = 8.2 ft and b/h = 2. • Members A8 to A35, B6 to B35, C7 to C35, and D7 to D35 for a sign with h = 8.2 ft and b/h = 8. 2.48a: Chord H1 part of the front face 2.48b: Chord H3 part of the back face Figure 2.48. Local amplification of drag coefficient for the two chords (dc 5 0.4 ft) that are part of the top face of the truss as a function of the distance from the lateral edge of the sign for a bridge-type 4-chord truss structure supporting either a thin rectangular highway sign or a dynamic message sign with h 5 8.2 ft and b/h 5 1 and 3.75.

Findings 73 Secondary members that are part of the back face and are situated in the wakes of the front- face members—but sufficiently far from the highway sign (e.g., outside of the flow-acceleration region)—are subjected to smaller forces compared to the corresponding front-face members (Cd/Cd0 ≈ 0.6–0.8). For example, in the thin static sign simulations, Cd/Cd0 ≈ 0.6–0.8 for members B1–B9 and B33–B42 for a sign with h = 8.2 ft and b/h = 1—and for members B1–B9 and B31–B40 for a sign with h = 8.2 ft and b/h = 2. No back-face members with Cd/Cd0 ≈ 0.6–0.8 are present for the widest sign, with h = 8.2 ft and b/h = 8. For the same h and b/h (e.g., in the simulations with h = 8.2 ft and b/h = 3.75), the presence of a dynamic message sign instead of a thin highway sign does not change the number of members that are part of the region with Cd/Cd0 ≈ 0.6–0.8. For both static signs and dynamic message signs, all members that are part of the top and bottom faces of the truss are subject to small wind loads (Cd/Cd0 < 0.3). This conclusion also applies to the members situated inside the flow-acceleration regions forming near the lateral edges of the signs. Interior-diagonal members connecting the front and back faces not situated in the wake of the highway sign are subject to relatively small drag forces (Cd/Cd0 < 0.3). For example, in the thin static sign simulations, Cd/Cd0 < 0.3 for members E2–E10 and E30–E41 for the sign with h = 8.2 ft and b/h = 1 and for members E2–E10 and E30–E39 for the sign with h = 8.2 ft and b/h = 2. No interior-diagonal members with Cd/Cd0 < 0.3 are present for the widest sign, with h = 8.2 ft and b/h = 8. For the same h and b/h (e.g., in the simulations with h = 8.2 ft and b/h = 3.75), the presence of a dynamic message sign instead of a static sign does not change the number of interior-diagonal members that are part of the region with Cd/Cd0 < 0.3. The only truss members with Cd/Cd0 > 1 are the front-face members situated entirely (or almost entirely) in the flow-acceleration regions forming close to the lateral edges of the highway sign. For a static sign with h = 8.2 ft and b/h = 1, the largest values are recorded for members A17 and A24 with Cd/Cd0 ≈ 1.15. Members A17 and A24 are even closer to the edge of the sign, but part of each of them is already in the wake of the sign, so for these members, Cd/Cd0 < 1. For a static sign with h = 8.2 ft and b/h = 2, the largest values are observed for members A15 and A26, with Cd/Cd0 ≈ 1.17. For a static sign with h = 8.2 ft and b/h = 8, the largest values are recorded for members A6 and A37, with Cd/Cd0 ≈ 1.23. For static signs with b = 30 ft, the peak value of Cd/Cd0 is 1.26 for b/h = 2 and 1.19 for b/h = 3.75. Overall, the peak value of Cd/Cd0 for members inside the flow-acceleration regions increases with the increase in the total area of the sign (e.g., with the increase of b for constant h or with the increase of h for constant b). For the same b and h, the peak value of Cd/Cd0 is about 5% larger in the simulation with a dynamic message sign compared to the value in the corresponding simulation with a static sign of equal b and h. Inside each region of flow acceleration next to the lateral edges of the traffic sign, the peak values of Cd/Cd0 for the back-face members are very close to those observed for the front-face members. The values of Cd/Cd0 are comparable for corresponding members situated on the front and back faces until close to the extremity of each region of flow acceleration. For interior-diagonal members inside the flow-acceleration regions, the peak value of Cd/Cd0 is close to 0.7, which is considerably larger than the values predicted for members outside of the flow-acceleration regions (Cd/Cd0 < 0.3). In general, only one or two interior-diagonal members are subject to large wind loads (Cd/Cd0 ≈ 0.7) on each side of the sign. In addition, the lateral extent of the flow-acceleration regions for inter-diagonal members is similar to the one determined for the four chords (Figure 2.46). 2.2.4.2 Bridge-Type 4-Chord Truss Supporting Two Highway Signs Details on the bridge-type 4-chord truss design (formerly used by the Iowa DOT) are given in Section 2.2.4.1. When no signs are attached to the truss, the predicted values of Cd0 for the

74 Wind Drag Coefficients for Highway Signs and Support Structures four chords and the isolated secondary truss members are identical to those in Section 2.2.4.1. A series of simulations addresses the case when the truss supports two identical thin highway signs with the following dimensions: • h1 = h2 = h = 8 ft. • b1 = b2 = b = 30 ft. • b/h = 3.75. • s = 1.5 ft, 12 ft, and 30 ft. An additional simulation considers the case when only one sign is supported by the truss, which formally corresponds to a case with s equal to infinity. Similar to the results reported in Section 2.2.4.1 for cases when only one sign is attached to the truss, Cd/Cd0 is relatively close for the two front-face chords and for the two back-face chords (Figure 2.49) even though Cd0 is not identical for the two front-face chords (H1 and H2) or for the two back-face chords (H3 and H4). Hence, this section focuses on results obtained for the front chord H1 and the back chord H3 that are part of the top face of the truss. Simulation results show that the drag coefficient can be assumed to be zero over the part of each chord situated behind the highway signs. Moreover, the distributions of Cd/Cd0 between the (exterior) lateral edge of each sign and the corresponding end of the truss are very close to those predicted in the simulations with only one sign attached to the truss. Consequently, the focus is on the variation of Cd/Cd0 over the part of the chords between the (interior) lateral edge of the sign and the middle of the gap distance between the two signs. The results in Figure 2.50 show the following: • For s/b ≥ 0.4 (s ≥ 12 ft), the peak value of Cd/Cd0 occurs at a larger distance from the lateral edge of the signs for the back-face chords H3 and H4, y/(bh)0.5 = 0.2–0.4, compared to the front- face chords H1 and H2, y/(bh)0.5 = 0.1–0.15. This difference occurs because the transverse deflection of the region of accelerating flow forming near the lateral edge of the sign increases with the (streamwise) distance from the sign. • For sufficiently large gap distances between the two signs, Cd/Cd0 ≈ 1—for example, if y/(bh)0.5 > 0.5 for chords H1 and H2 and if y/(bh)0.5 > 0.75 for chords H3 and H4. Figure 2.50 also includes the variation of Cd/Cd0 for an isolated plate (s of infinity). This variation is very similar to the one obtained in the simulation conducted with s/b = 1 until the middle of the Figure 2.49. Local amplification of the drag coefficient for the four chords (dc 5 0.4 ft) as a function of the distance from the lateral edge of the sign for a bridge-type 4-chord truss structure supporting two identical thin highway signs (h 5 8 ft and b/h 5 3.75) separated by a gap s. 2.49a: s = 12 ft and s/(b1 + b2) = 0.4 2.49b: s = 30 ft and s/(b1 + b2) = 1 Note: The drag coefficient is reported between the lateral edge of one of the signs (y = 0) and the middle gap distance between the two signs (y = s/2).

Findings 75 distance between the two signs (0 < y < s/2), which means that the interaction between the two signs is negligible in the case when s/b = 1. Other important observations include the following: • Even when the distance between the signs is not large enough for Cd/Cd0 to approach unity (i.e., 1) for all four chords (e.g., simulation with s/b = 0.4), the variation of Cd/Cd0 from the edge of each sign (y = 0) to y = s/2 is still fairly close to the one observed for an isolated sign. • For cases with a very small gap distance, Cd/Cd0 increases linearly between y = 0 and y = s/2, but Cd/Cd0 < 1 over most of this distance. As expected, drag coefficients for the secondary members situated behind the two signs and between the (exterior) sides of the two signs and the corresponding end of the truss are close to those determined for isolated signs. The same rules proposed for the case when the truss sup- ports only one sign should be used to determine the approximate values of Cd/Cd0 for these truss members. Consequently, only predictions of the drag coefficient for the secondary members in the gap between the two signs are discussed next. In the simulation with s = 1.5 ft, the gap is smaller than the length of the secondary truss members, so all of the members located between the two signs are partially shielded by the signs, which explains why the (maximum) values of Cd/Cd0 predicted for members in the gap between the two signs are much smaller than the values predicted in simulations using s = 12 ft and s = 30 ft. Relevant findings include the following: • For the front-face members (Figure 2.45), the peak values of Cd/Cd0 are close to 0.3 in the simulation with s = 1.5 ft. For s = 12 ft, the peak values of Cd/Cd0 are close to 1.3–1.35 while for s = 30 ft, the peak values of Cd/Cd0 are close to 1.25. • For the back-face members, Cd/Cd0 ≈ 0.3 in the simulation with s = 1.5 ft; Cd/Cd0 ≈ 1.35 in the simulation with s = 12 ft; and Cd/Cd0 = 1.15–1.2 in the simulation with s = 30 ft. • For the top- and bottom-face members, Cd/Cd0 = 0.1 in the simulation with s = 1.5 ft; Cd/Cd0 = 0.3 in the simulation with s = 12 ft; and Cd/Cd0 = 0.3 in the simulation with s = 30 ft. • For the interior-diagonal face members, Cd/Cd0 = 0.05 in the simulation with s = 1.5 ft; Cd/Cd0 = 0.7 in the simulation with s = 12 ft; and Cd/Cd0 = 0.6 in the simulation with s = 30 ft. 2.2.4.3 Bridge-Type 3-Chord Truss Supporting One Highway Sign A bridge-type 3-chord truss used by the Michigan DOT is the second truss used in the simulations to estimate normalized drag coefficients for chords and secondary members Figure 2.50. Local amplification of the drag coefficient for chords (dc 5 0.4 ft) that are part of the top face of the truss as a function of the distance from the lateral edge of the sign for a bridge-type 4-chord truss structure supporting two thin highway signs (h 5 8 ft and b/h 5 3.75) separated by a distance s (1.5 ft < s < 30 ft). 2.50a: Chord H1 part of the front face 2.50b: Chord H3 part of the back face Notes: The drag coefficient is reported between the lateral edge of one of the signs (y = 0) and the middle distance between the two signs (y = s/2). Also included are results for the case when only one highway sign is attached to the truss (s = ∞).

76 Wind Drag Coefficients for Highway Signs and Support Structures (Figures 2.23 and 2.24). This bridge-type 3-chord truss supporting a sign has the following characteristics: • The span of the truss is 100 ft. • The diameter of the chords is dc = 0.5 ft, and the diameter of the secondary members is 0.42 ft. • The distance between the back of the sign and the front face of the truss is 0.5 ft. Figure 2.51 shows the truss with each of the truss members labeled as part of a group that corresponds to one of the truss faces (A to C, as noted in Table 2.30). The three chords of the truss are labeled H1 to H3. To make it easier to understand the relative location of the truss members, secondary members with the same numerical value that are part of different groups correspond to members situated at about the same spanwise location. Drag coefficients for the truss members are estimated for simulations performed with the following signs: • Static sign with h = 8.2 ft and b = 8.2 ft. • Static sign with h = 8.2 ft and b = 30 ft. • Static sign with h = 8.2 ft and b = 64 ft. • Dynamic message sign (d = 4 ft) with h = 8.2 ft and b = 30 ft. For an isolated circular member of diameter dc = 0.42 ft and AR ≈ 230, the results in Table 2.27 indicate that Cd0 ≈ 0.75 for a chord Reynolds number slightly below 100,000. For an additional simulation performed with only the three chords of the truss placed above the ground, the predicted drag coefficient Cd0 for chords H1, H2, and H3 is 0.75, 0.65, and 0.61, Notes: The secondary members are distributed into three groups (A to C). The 3-chord members are labeled H1 to H3. Members from different groups labeled with the same number are situated at about the same spanwise location. Figure 2.51. Convention used in labeling truss members for the overhead bridge-type 3-chord truss structure. Table 2.30. Description of truss members forming each group for the 3-chord truss in Figure 2.51. Group Description A Front-face truss members B Inclined top-face truss members C Inclined bottom-face truss members H Truss chords

Findings 77 respectively. The slight reduction in Cd of the lower chord H2 (compared to the higher chord H1) is consistent with results obtained for the 4-chord truss (0.75 versus 0.66). As opposed to the 4-chord truss (considered in Section 2.2.4.1) where H3 and H4 are shielded by H1 and H2 and have lower drag coefficients (Cd0 for the back chords is lower by about 41% compared to the front chords), the drag coefficient for chord H3 of the 3-chord truss is just slightly smaller than that for the lower front chord. This happens because H3 is directly exposed to the incoming wind. Simulation results confirm that the drag coefficient can be assumed to equal zero over the part of the chord located behind the highway sign. Although Cd0 is not the same for the two front- face chords (H1 and H2), Cd/Cd0 is relatively close for the two front-face chords. This finding is valid for all of the simulations conducted with thin static signs and dynamic message signs (Figures 2.52a and 2.52b). For chord H3 (Figure 2.52c), the peak of Cd/Cd0 is smaller by about 30% and occurs at larger nondimensional distances, y/(bh)0.5 = 0.25–0.5, when compared to H1 and H2 at y/(bh)0.5 = 0.1–0.3. This result is similar to the one obtained for the 4-chord truss, as detailed in Section 2.2.4.1. Chord H3 is situated about 4.5 ft behind the highway sign, and the width of the flow-acceleration region induced by the sign increases with the distance from the back of the sign. For the dynamic message sign simulation, variations in Cd/Cd0 are close for all three chords, and Cd/Cd0 ≈ 1 for y/(bh)0.5 > 0.75 (Figure 2.52). Moreover, for signs of identical dimensions, the variation of Cd/Cd0 with y/(bh)0.5 is comparable to the directly exposed front-face chords in the 3-chord and 4-chord truss simulations (e.g., see results in Figure 2.53 for the H1 chord). This finding is not unexpected given that the airflow around the directly exposed chords should be very similar regardless of the truss geometry. This finding also means that rules to calculate Cd/Cd0 for the chords of a 4-chord truss also apply to the 3-chord truss. Figure 2.52. Local amplification of drag coefficient for the three chords (dc 5 0.4 ft) as a function of the distance from the lateral edge of the sign for a bridge-type 3-chord truss structure supporting either a thin rectangular traffic sign (h 5 8.2 ft and b/h = 1, 3.75, and 8.2) or a dynamic message sign (h 5 8.2 ft and b/h 5 3.75). 2.52a: Chord H1 2.52b: Chord H2 2.52c: Chord H3

78 Wind Drag Coefficients for Highway Signs and Support Structures Secondary truss members that are part of the front face situated away from the traffic sign (e.g., outside of the flow-acceleration regions) are subject to wind loads comparable to those observed when the same member is isolated (Cd/Cd0 = 1, ±0.05). For example, Cd/Cd0 ≈ 1 for members A1 to A5 and for A13 to A17 (Figure 2.51) in the simulation conducted with a static sign of height h = 8.2 ft and b/h = 1. As b/h increases, the region containing members with Cd/Cd0 ≈ 1 shrinks. For a static sign with h = 8.2 ft and b/h = 3.75, the region containing members with Cd/Cd0 ≈ 1 includes only members A1 to A2 and A16 to A17. Such a region (with Cd/Cd0 ≈ 1) is absent for a static sign with h = 8.2 ft and b/h = 8 because the region of flow acceleration penetrates up to the vertical columns supporting the truss. For the same h and b/h (e.g., for a sign with h = 8.2 ft and b/h = 3.75), the presence of a dynamic message sign instead of a static sign does not change the number of members that are part of the region with Cd/Cd0 ≈ 1. Drag forces are negligible—Cd/Cd0 ≈ 0 or, more precisely, |Cd/Cd0| < 0.1—for the secondary members situated completely behind the highway sign. This is the case for members on part of all three faces of the 3-chord truss (e.g., members A11, B9, B10, C9, and C10 for a static sign with h = 8.2 ft and b/h = 1; members A3 to A15, B3 to B17, and C3 to C17 for a static sign with h = 8.2 ft and b/h = 8, as shown in Figure 2.51). Some members that are partially behind the sign and partially in the flow-acceleration regions can be subject to relatively large drag forces (e.g., Cd/Cd0 = 0.45 for member A10 in the simulation with a static sign of height h = 8.2 ft and b/h = 1). For the geometry of the 3-chord truss analyzed here (Figure 2.51), no members of the two diagonal faces are directly shielded by members of the front face. The only truss members for which Cd/Cd0 > 1 are the front-face members situated entirely (or close to entirely) in the flow- acceleration regions forming next to the lateral edges of the highway sign. For a static sign with h = 8.2 ft and b/h = 1, the largest values are recorded for members A7 and A11 (Cd/Cd0 ≈ 1.20). For a thin static sign with h = 8.2 ft and b/h = 3.75, the largest values are observed for members A5 and A13 (Cd/Cd0 ≈ 1.25). For a static sign with h = 8.2 ft and b/h = 8, the largest values are recorded for members A1 and A17 (Cd/Cd0 ≈ 1.25). For the same b and h, the peak value of Cd/Cd0 is about 5% to 10% larger in the simulation with a dynamic message sign than in the cor- responding simulation conducted with a static sign. Although the inclined top-face and bottom-face members located outside the flow-acceleration region are nearly fully exposed to the incoming flow, they are subject to lower normalized drag coefficients compared to the corresponding front-face members. This result is expected Figure 2.53. Local amplification of drag coefficient for top chord of the front face H1 as a function of the distance from the lateral edge of the sign for bridge-type 3-chord and 4-chord truss structures supporting a rectangular highway sign (h 5 8.2 ft and b/h = 3.75). 2.53a: Static sign 2.53b: Dynamic message sign

Findings 79 because in the limit of an angle of inclination between the member and the horizontal plane of zero degrees, only the viscous drag contributes to the total drag force, so one can expect that Cd/Cd0 ≈ 0. For the geometry of the 3-chord truss analyzed here, Cd/Cd0 ≈ 0.6 for the secondary members of the inclined faces (Figure 2.51) situated in the region of close-to-uniform approaching flow. Inside the flow-acceleration region, the amplification of Cd/Cd0 for members of the inclined faces is smaller than that observed for the front-face members as Cd/Cd0 ≈ 0.65–0.7. The lat- eral extent of the flow-acceleration regions is similar to that determined for the three chords (Figure 2.53). 2.2.4.4 Cantilever-Type 4-Chord Truss Supporting One Highway Sign Normalized drag coefficients for the chords and the secondary members are also estimated for an overhead cantilever-type 4-chord truss used by the Iowa DOT (Figure 2.26). This truss and the sign attached to it have the following characteristics: • The diameter of the vertical column is 2.5 ft. • The diameter of the chords is dc = 0.56 ft, and the diameter of the other members is 0.24 ft. • The aspect ratio of the chords is AR = 71. The aspect ratio of secondary members is AR = 30–40. • The distance between the front face of the truss and the back of the sign is 0.77 ft. Simulations are performed for the following signs: • Thin highway sign of height h = 8.2 ft and b/h = 1, 3.75, and 4.6. • Thin highway sign of height h = 20 ft and b/h = 1.5. An additional simulation for a thin highway sign with h = 8.2 ft and b/h = 1 is performed with gusset plates included on the front and back faces of the truss (Figure 2.25) to be able to estimate wind loads on the gusset plates subject to nonnegligible forces. Figure 2.54 depicts the overhead cantilever-type 4-chord truss, with each of the truss mem- bers labeled as part of a group that corresponds to one of the truss faces (A to D, as listed in Table 2.31) or to a group including the members connecting the front and back faces of the truss (Group E). The four chords of the truss are labeled H1 to H4. For the simulation including gusset plates, Groups P to S correspond to rectangular gusset plates on the front and back faces of the truss (Figure 2.54 and Table 2.31). For a chord with dc = 0.56 ft and AR ≈ 70, preliminary simulations indicate Cd0 ≈ 0.65 for a Reynolds number of about 120,000 (also see Table 2.27). Similar to the bridge-type 4-chord truss considered in Section 2.2.4.1, a drag reduction effect is observed for the bottom chord of the front face because of the way the flow accelerates between the two front-face chords and between the bottom chord and the ground. Preliminary simulations conducted with no signs and no secondary members predict Cd0 ≈ 0.65 for the top chord (H1) and Cd0 ≈ 0.57 for the bottom chord (H2) of the front face. Also similar to results obtained for the 4-chord truss (AR ≈ 230, Re ≈ 50,000) considered in Section 2.2.4.1, the drag coefficient is reduced for the chords that are part of the back face with respect to the chords that are part of the front face. The ratio of the drag coefficient for the bot- tom chord to the top chord of the front face is 0.87. The drag coefficient ratio is close to 0.61 for both the top and bottom chords of the back face such that Cd0 ≈ 0.4 for the top chord (H3) and Cd0 ≈ 0.35 for the bottom chord (H4) (Figure 2.54). The drag coefficient ratio between the cor- responding front-face and back-face chords is 0.59, and that between the top and bottom chords of the front face is 0.88 for the 4-chord truss in Section 2.2.4.1. The drag coefficient is around 0.65 for the isolated secondary members (AR = 30–40, Re ≈ 50,000) of the current overhead cantilever-type 4-chord truss.

80 Wind Drag Coefficients for Highway Signs and Support Structures Figure 2.54. Convention used in labeling truss members for the overhead cantilever-type 4-chord truss used by the Iowa DOT. Table 2.31. Description of truss members forming each group for the 4-chord truss in Figure 2.54. Group Description A Front-face truss members B Back-face truss members C Top-face truss members D Bottom-face truss members E Interior-diagonal truss members situated between the front and back faces H Truss chords P Front-face top gusset plates Q Front-face bottom gusset plates R Back-face top gusset plates S Back-face bottom gusset plates

Findings 81 Similar to the bridge-type 4-chord truss considered in Section 2.2.4.1, the drag coefficient can be assumed to equal zero over the part of the chord situated behind the highway sign. Although Cd0 is not the same for the two front-face chords (H1 and H2) and the two back-face chords (H3 and H4), the value of Cd/Cd0 is relatively close for the two front-face chords and for the two back-face chords. This is the reason why Figure 2.55 presents only the variation of Cd/Cd0 with y/(bh)0.5 for the H1 and H3 chords. This variation is presented between the lateral edge of the sign and the vertical post supporting the truss. Overall, these variations are similar to those predicted for the bridge-type 4-chord truss (Figure 2.47). The peak values of the normalized drag coefficient are slightly larger for the cantilever-type 4-chord truss with Cd/Cd0 ≈ 2 (Figure 2.55). The peak value of Cd/Cd0 occurs at a larger value of y/(bh)0.5 for the back-face chords H3 and H4, y/(bh)0.5 = 0.15–0.3, when compared to the front- face chords H1 and H2, y/(bh)0.5 = 0.1–0.2. Some main results from the simulations conducted with various signs are as follows: • In the simulation with a highway sign of height h = 8.2 ft and b = 30 ft, a slight increase of Cd/Cd0 is observed for H1, and a large decrease of Cd/Cd0 is noted for H3 as the vertical post is approached—y/(bh)0.5 ≈ 0.6. • A similar behavior of Cd/Cd0 is present in the simulation with a highway sign of height h = 8.2 ft and b = 8.2 ft around the vertical post—y/(bh)0.5 ≈ 2.2—but this behavior is not visible in Figure 2.55 where Cd/Cd0 is shown only for y/(bh)0.5 < 1.5. The increase of Cd/Cd0 for chords H1 and H2 is due to the amplification of the streamwise velocity as the incoming wind is diverted on the sides of the vertical post (Figure 2.26). The decrease of Cd/Cd0 for chords H3 and H4 is due to the parts of these chords that penetrate in the wake induced by the vertical post supporting the truss. • In the simulation conducted with a highway sign of height h = 8.2 ft and b = 36 ft, the distance between the lateral edge of the sign and the corresponding lateral edge of the post is only 4 ft. In this case, the variation of Cd/Cd0 is similar to the one observed between two side-by-side signs separated by a small gap distance. Among the four simulations conducted with a thin sign, the distance between the lateral edge of the highway sign and the vertical post is much larger than the typical size of a secondary truss member only in the simulation with a sign of height h of 8.2 ft and b/h of 1. In the simulation conducted with a highway sign of height h = 8.2 ft and b/h = 4.6, most of the members are situated in the wake of the sign, with the remaining members in the flow- acceleration region generated between the sign and the vertical post. Members located behind Figure 2.55. Local amplification of drag coefficient for the two chords (dc 5 0.56 ft) that are part of the top face of the truss as a function of the distance from the lateral edge of the sign for a cantilever-type 4-chord truss structure supporting a thin rectangular highway sign. 2.55a: Chord H1 part of the front face 2.55b: Chord H3 part of the back face

82 Wind Drag Coefficients for Highway Signs and Support Structures the highway signs have values of |Cd/Cd0| < 0.15, so one can simply assume that Cd/Cd0≈ 0 for these members. For the simulation conducted with a sign of height h = 8.2 ft and b/h = 1, the width of the flow-acceleration region is only around 3.5 ft for the front face and around 6 ft near the back face (Figure 2.55). Given that the length of the secondary members is roughly between 6 ft and 9 ft—and given that even the members situated next to the edge of the sign are partially shielded by the sign—the peak Cd/Cd0 is only 1–1.15 for members in the flow-acceleration region (e.g., members A6 and A8 in Figure 2.54). For the front-face members in the region of uniform incoming flow (e.g., members A10 to A18), Cd/Cd0 ≈ 1.0–1.1. Back-face secondary members located in the wakes of the front-face members and outside of the flow-acceleration region (e.g., B8 to B18) are characterized by smaller normalized drag coefficients compared to the ones for corresponding front-face members (Cd/Cd0 ≈ 0.8). For the few back-face members situated close to entirely inside the flow-acceleration region, Cd/Cd0 ≈ 1.0. All members that are part of the top and bottom faces of the truss (e.g., C7 to C18; D7 to D18) are subject to small wind loads (Cd/Cd0 < 0.3). Interior-diagonal members connecting the front and back faces not in the flow- acceleration region (e.g., E12 and E16) are subject to relatively small drag forces (Cd/Cd0 < 0.4). The interior-diagonal members inside the flow-acceleration region (E8) and next to the vertical post (E20) are subject to higher drag forces (Cd/Cd0 ≈ 0.8). Analysis of simulation results for signs with height h = 8.2 ft and b/h = 3.75 and for signs with height h = 20 ft and b/h = 1.5 shows that for these two cases, the aforementioned values of the normalized drag coefficients for secondary members that are part of the different faces of the truss also apply. Overall, the values of Cd/Cd0 predicted for the secondary members of the cantilever-type 4-chord truss—as a function of their position inside the truss, their position rela- tive to the traffic sign, and the width of the flow-acceleration region—are close to those predicted for the bridge-type 4-chord truss discussed in Section 2.2.4.1. Gusset plates also contribute to the total wind load acting on the truss. Gusset plates are subject to negligible wind loads when they are situated in planes parallel to the incoming wind direction or are completely shielded by the highway sign. The same statement applies for the completely shielded part of the gusset plate situated behind the chords of the truss. To estimate wind loads on the exposed parts of the gusset plates, an additional simulation is performed. This case includes the gusset plates as part of the front and back faces of the truss in the computational model for a truss supporting a sign with height h = 8.2 ft and b/h = 1. Gusset plate details include the following: • Away from the vertical post, the height and width of the exposed parts of the gusset plates are 8 in. and 20 in., respectively (Figure 2.54). • Next to the vertical post, gusset plates with a width of only 10 in. are used. • The thickness of the gusset plates is 0.5 in. • The length of the members connected to the gusset plates is shortened so that they extend to the edge of the gusset plate. A drag coefficient of Cd0 = 1.24 is predicted for an isolated gusset plate with a width of 20 in. For a 10-in. gusset plate, Cd0 = 1.22. These values are consistent with drag coefficients for thin rectangular signs of small height given in Figure 2.13. The following values of Cd/Cd0 apply to specifically situated gusset plates: • Front-face gusset plates in the region of close-to-uniform incoming flow are characterized by Cd/Cd0 ≈ 1.0 (e.g., P12, Q12, P16, Q16). • For gusset plates close to the edge of the sign or the vertical post (e.g., P20, Q20), Cd/Cd0 ≈ 1.2. • For the gusset plates that are part of the back face, the simulation predicts Cd/Cd0 ≈ 0.2–0.3. This value also applies to the gusset plates next to the vertical post.

Findings 83 2.2.4.5 Butterfly-Type 4-Chord Truss Supporting Two Highway Signs Normalized drag coefficients for chords and secondary members are also estimated for an overhead butterfly-type 4-chord truss (Figure 2.36). The chord sizes and secondary-member sizes for the butterfly-type truss are the same as those for the cantilever-type truss described in Section 2.2.4.4. The total truss length is 37 ft, 8 in. The following four simulations consider the butterfly-type 4-chord truss: • The first simulation is performed for identical static signs (d = 0.17 ft) of height h = h1 = h2 = 8.2 ft; b = b1 = b2; and b/h = 1. This case is characterized by a relatively large distance between the lateral edges of the signs, s = 23.6 ft (s/b = 2.9). • Three more simulations are conducted for a relatively small distance between the lateral edges of the signs (s/b < 0.3) where very few or no secondary members are fully exposed to the incoming flow. These simulations are conducted with (1) thin highway signs with h = 8.2 ft, b/h = 2.2, and s = 4.6 ft; (2) thin highway signs with h = 20 ft, b/h = 0.9, and s = 4.0 ft; and (3) dynamic message signs (d = 4 ft) with h = 8.2 ft, b/h = 2.2, and s = 4.6 ft. Figure 2.56 shows the butterfly-type 4-chord truss, with each of the truss members labeled as part of a group that corresponds to one of the truss faces (A to D, listed in Table 2.32) or to a Figure 2.56. Convention used in labeling truss members for the overhead butterfly-type 4-chord truss.

84 Wind Drag Coefficients for Highway Signs and Support Structures group including the members connecting the front and back faces of the truss (Group E). The four chords of the truss are labeled H1 to H4. Given that the design of the butterfly-type truss is similar to that of the cantilever-type truss discussed in Section 2.2.4.4, the Cd0 values for the four chords and the range of Cd0 values for the secondary members are the same as those indicated for the cantilever-type truss. Simulation results show that the normalized drag coefficient can be assumed to equal zero over the part of each chord situated behind the highway signs. Similar to results for bridge-type and cantilever-type trusses, the variations of Cd/Cd0 for the butterfly-type truss are relatively close for the two front-face chords and for the two back-face chords. For this reason, Figure 2.57 presents the variation of Cd/Cd0 with y/(bh)0.5 only for the H1 and H3 chords. Results are not included in Figure 2.57 for the simulation with two dynamic message signs— d = 4 ft, with h = 8.2 ft, b/h = 2.2, and s = 4.6 ft—because the predictions are very similar to the corresponding simulation conducted with thin static signs of the same height and width. For the simulation conducted with two thin static signs with h = 20 ft and b/h = 0.9, the gap distance between the two signs is only s = 4.0 ft. This corresponds to s/b = 0.22. In terms of the s/b value, this case is very similar to the simulation with two thin highway signs with h = 8.2 ft, b/h = 2.2 (Figure 2.57), and s = 4.6 ft (s/b = 0.25). The main trends observed in the variation of Cd/Cd0 in the cases with s/b = 0.22 and s/b = 0.25 are as follows: • Cd/Cd0 increases rapidly away from the lateral edge of each sign to reach a maximum at y ≈ s/2. • For the case with s/b = 0.22, the peak values of Cd/Cd0 are around 1.4 for H1 and H2 and around 0.8 for H3 and H4 (Figure 2.57). Group Description A Front-face truss members B Back-face truss members C Top-face truss members D Bottom-face truss members E Interior-diagonal truss members situated between front and back faces H Truss chords Table 2.32. Description of truss members forming each group for the 4-chord truss in Figure 2.56. 2.57a: Chord H1 part of the front face 2.57b: Chord H3 part of the back face Note: The figure also shows the results for a thin highway sign (h = 8.2 ft, b/h = 1) supported by a cantilever-type truss of similar design. Figure 2.57. Local amplification of drag coefficient for the two chords (dc 5 0.56 ft) that are part of the top face of the truss as a function of the distance from the lateral edge of the sign for a butterfly-type 4-chord truss structure supporting two identical thin highway signs (h 5 8.2 ft, b/h 5 1 and 2.2).

Findings 85 • For the case with s/b = 0.25, the peak values of Cd/Cd0 are around 1.6 for H1 and H2 and around 1.0 for H3 and H4. • For all four chords, a constant value of Cd/Cd0 can be assumed over the gap distance between the signs. In the simulation conducted with 2s/(b1 + b2) = 2.9, Cd/Cd0 is plotted (in Figure 2.57) between the edge of one of the signs (h = 8.2 ft, b/h = 1) and the middle of the gap distance between the two signs—y = s/2 or y/(bh)0.5 = 1.45. Also shown in Figure 2.57 are results from a simulation performed with a cantilever-type truss of a similar design supporting an identical sign at its extremity. Not surprisingly, the variations of Cd/Cd0 for both the front-face chords and the back-face chords are very close, starting at the edge of the sign and continuing until y = s/2 is approached in the simulation with a butterfly-type truss. Then, similar to what is observed in simulations with a cantilever-type truss once the vertical post is approached, a region of higher values of Cd/Cd0 is present close to y = s/2 for chords H1 and H2—and a region of higher Cd/Cd0 values also is observed close to y = s/2 for the parts of chords H3 and H4 situated in the wake of the post. These results indicate that any rules proposed to determine Cd/Cd0 versus y/(bh)0.5 for cantilever- type trusses also apply to butterfly-type trusses. For all simulations, the assumption can be made that Cd/Cd0 ≈ 0 for the secondary members located behind the two signs. For the two simulations conducted with identical static signs where the edge of each sign is close to the vertical column of the butterfly-type truss (s/b = 0.22 and s/b = 0.25), the distance between the edge of the sign and the column is less than 2.5 ft. Given that the length of the secondary truss members is at least 6 ft, parts of the secondary members penetrating the space between the two signs are shielded by the two signs. Results for these two simulations confirm that wind loads on these members are rather low; Cd/Cd0 < 0.1 for most of them. The presence of dynamic message signs instead of thin highway signs has a negligible effect on wind loads acting on the secondary truss members. For the simulation conducted with two identical signs (h = 8.2 ft, b/h = 1) and a nondimen- sional gap distance 2s/(b1 + b2) = 2.9, the normalized drag coefficients are consistent with values obtained in the corresponding simulation performed for a cantilever-type truss supporting one thin highway sign of identical dimensions. The width of the acceleration region is about the same (3.5 ft), but the width of the region of close-to-uniform incoming flow is smaller in the simulation conducted with a butterfly- type truss. Although the total length of the butterfly-type and cantilever-type trusses is about the same, the butterfly-type truss supports two signs. The main trends observed in the variation of Cd/Cd0 in the simulation conducted with a nondimensional gap distance 2s/(b1 + b2) = 2.9 are as follows: • The peak Cd/Cd0 is around 1.25 for the members in the flow-acceleration region (e.g., members A4 and A6, Figure 2.56). • For the front-face members in the region of uniform incoming flow (e.g., members A8 to A13), Cd/Cd0 ≈ 1–1.1. • Back-face secondary members located in the wakes of the front-face members and outside of the flow-acceleration region (e.g., B8 to B11) are characterized by smaller normalized drag coefficients when compared to those for corresponding front-face members (Cd/Cd0 ≈ 0.8). For the back-face members located close to entirely inside of the flow-acceleration region, Cd/Cd0 ≈ 1.0 (e.g., B6). • All members not shielded by the sign and part of the top and bottom faces of the truss (e.g., C5 to C12; D5 to D12) are subject to small wind loads (Cd/Cd0 < 0.3).

86 Wind Drag Coefficients for Highway Signs and Support Structures • Interior-diagonal members that connect the front and back faces but are not close to the vertical column (e.g., E4 and E13) are subject to relatively small drag forces (Cd/Cd0 < 0.4). Those members situated next to the vertical column (E8 and E9) are subject to much larger drag forces (Cd/Cd0 ≈ 0.8). Overall, the Cd/Cd0 values predicted for the secondary members of the butterfly-type 4-chord truss—as a function of their position inside the truss, their position relative to the traffic signs and the vertical column, and the width of the flow-acceleration regions—are close to those pre- dicted for the cantilever-type 4-chord truss discussed in Section 2.2.4.4. Data from the simulations performed as part of Sections 2.2.3 and 2.2.4 support the current hypothesis that an accelerated-flow region forms near the lateral edges of highway signs. These data also provide critical information to approximate the length of this region and the mean value of Cd/Cd0 for the parts of the chords, secondary truss members, and gusset plates situated inside the accelerated flow region. Similarly, data from simulations performed with side-by-side signs provide the critical information needed to approximate Cd/Cd0 for chords and secondary members located between the lateral edge of one sign and the middle of the gap distance between the two signs. This information is used in Section 3.3 to develop a general method to approximate wind loads on highway sign support structures.