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

Chapter: Appendix B - Design Examples

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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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Suggested Citation:"Appendix B - Design Examples." National Academies of Sciences, Engineering, and Medicine. 2023. Wind Drag Coefficients for Highway Signs and Support Structures. Washington, DC: The National Academies Press. doi: 10.17226/26914.
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B-1   A P P E N D I X B Design Examples B1 DESIGN EXAMPLE 1 Application This design example addresses estimating normal wind loads for strength design and fatigue design for an overhead bridge-type monotube structure supporting two traffic signs. Information • Length of monotube: Lt = 80 ft • Diameter of monotube: dtube = 3.5 ft (circular cross-section) • Sign 1: dynamic message sign with height h1 = 8 ft, width b1 = 30 ft, thickness d1 = 3 ft, and ground clearance distance hg1 = 20 ft • Sign 2: thin static sign with height h2 = 6 ft, width b2 = 12 ft, thickness d2 = 0.17 ft, and ground clearance distance hg2 = 21 ft • Gap between the two signs: s = 2.1 ft • Signs positioned so that the distances between their exterior lateral edge and the corresponding end of the monotube are equal: L1-2 = L7-8 (Figure B1) Figure B1: Monotube supporting two highway signs, showing Zone 1 to Zone 8 for which drag coefficients need to be determined

B-2 Wind Drag Coefficients for Highway Signs and Support Structures • Signs: Kds = 0.85 • Monotube: Kdm = 0.85 Loads on the signs Using the proposed methodology Sign 1: b1/h1 = 3.75, h1/(h1 + hg1) = 0.29, As1 = b1h1 = 240 ft2 Use Figure 3.1 to get Cd0s1 = 1.22 Sign 2: b2/h2 = 2, h2/(h2 + hg2) = 0.22, As2 = b2h2 = 72 ft2 Use Figure 3.1 to get Cd0s2 = 1.17 Modification factors: Effect of sign thickness: Kt1 = Kt2 = 1 Effect of add-on signs: Ka1 = Ka2 = 1 Effect of proximity of another sign: 2s/(b1 + b2) = 0.1 < 0.5 and 2s/(b1 + b2) > 0.02 |As1 − As2|/(As1 + As2) = 0.54 > 0.5 As1 > As2 Kp1 = 1.1, Kp2 = 1.3 Effect of sign support structure: dtube/h1 = 0.44 > 0.25, Ks1 = 1.07 dtube/h2 = 0.58 > 0.25, Ks2 = 1.07 Drag coefficients for the signs: Cds1 = Kt1Ka1Kp1Ks1Cd0s1 = 1.44 Cds2 = Kt2Ka2Kp2Ks2Cd0s2 = 1.63 Estimation of wind load acting on each sign (using units of mph for V): Fs1 = 0.00256V2KzKdsGCds1As1 = 11,338 lbf Fs2 = 0.00256V2KzKdsGCds2As2 = 3,850 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Dynamic message sign: Cds1AASHTO = 1.70 Fs1AASHTO = 0.00256V2KzKdsGCds1AASHTOAs1 = 13,384 lbf B1.1 Estimation of Wind Loads for Strength Design Main assumptions based on LRFDLTS-1 specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1) Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): Static sign: b2/h2 = 2 Cds2AASHTO = 1.19 Fs2AASHTO = 0.00256V2KzKdsGCds2AASHTOAs2 = 2,810 lbf

Design Examples B-3 Drag coefficient for the isolated monotube: Re = 9200Vdtube = 3.7 × 106 (using units of mph for V) AR = Lt/dtube = 22.9 Use Figure 3.7 to get Cd0t = 0.37 Lengths and drag coefficients for Zones 1 to 8 (Figure B1): • Zone 3: Behind-the-sign region L3 = b1 = 30 ft, Km,3 = 0, Cdt,3 = 0 • Zone 6: Behind-the-sign region L6 = b2 = 12 ft, Km,6 = 0, Cdt,6 = 0 • Zone 2: Flow-acceleration region h1/dtube = 2.3 < 15, L2 = 0.8(b1h1)0.5 so L2 = 12.4 ft, Km,2 = 2, Cdt,2 = Km,2Cd0t = 0.74 Calculate: L1-2 = L7-8 = (Lt − b1 − b2 − s)/2 = 17.95 ft (Figure B1) • Zone 1: Uniform-flow region L1 = 1-2 − L2 = 5.55 ft, Km,1 = 1, Cdt,1 = 0.37 • Zone 4: Gap region associated with Sign 1 L4 = s/2 = 1.05 ft, h1/dtube = 2.3 < 15, L4/(b1h1)0.5 = 0.07 < 0.15, Km,4 = 1, Cdt,4 = 0.37 • Zone 5: Gap region associated with Sign 2 L5 = s/2 = 1.05 ft, h2/dtube = 1.7 < 15, L5/(b2h2)0.5 = 0.12 < 0.15, Km,5 = 1, Cdt,5 = 0.37 • Zone 7: Flow-acceleration region h2/dtube = 1.7 < 15, L7 = 0.8(b2h2)0.5 so L7 = 6.8 ft, Km,7 = 2, Cdt,7 = 0.74 • Zone 8: Uniform-flow region L8 = L7-8 − L7 = 11.15 ft, Km,8 = 1, Cdt,8 = 0.37 Wind load acting on the monotube: Fm = 0.00256V2KzKdmG = 0.00256V 2KzKdmG = 2,430 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdtube = 322 > 78 (using units of mph for V) CdtAASHTO = 0.45 FmAASHTO = 0.00256V2Kz KdmGCdtAASHTOAm = 0.00256V2Kz KdmGCdtAASHTO (L1 + L2 + L4 + L5 + L7 + L8)dtube = 1,963 lbf Difference between the proposed and the current specification (Fm − FmAASHTO)/FmAASHTO = 24% ∑8i=1 (Cdt,i Ai) Difference between the proposed and the current specifications (Fs1 − Fs1AASHTO)/Fs1AASHTO = −15% (Fs2 − Fs2AASHTO)/Fs2AASHTO = 37% Loads on the sign support structure Using the proposed methodology Total wind load acting on the monotube and the two signs Using the proposed methodology Total wind load acting on the monotube and two signs: F = Fs1 + Fs2 + Fm = 11,338 + 3,850 + 2,430 = 17,618 lbf ∑8i=1 (Cdt,i Li dtube) L

B-4 Wind Drag Coefficients for Highway Signs and Support Structures B1.2 Estimation of Wind Loads for Fatigue Design B1.2.1 Natural wind gust The equivalent static natural wind gust pressure is calculated by assuming IF = 1 (Importance Category I, overhead non-cantilevered sign support). Wind velocity was VNW = 11.2 mph (AASHTO specifications). Loads on the signs Using the proposed methodology Drag coefficients for traffic signs are independent of the Reynolds number Drag coefficients for traffic signs have the same values as those estimated in Section B1.1: CdNWs1 = Cds1 = 1.44 CdNWs2 = Cds2 = 1.63 Equivalent static natural wind gust pressure on each sign, determined from PNWs = 5.2CdNWsIF: PNWs1 = 5.2CdNWs1IF = 7.49 psf PNWs2 = 5.2CdNWs2IF = 8.48 psf Using the current AASHTO specifications Estimation of drag coefficients for each sign, based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): CdNWs1AASHTO = Cds1AASHTO = 1.70 CdNWs2AASHTO = Cds2AASHTO = 1.19 PNWs1AASHTO = 5.2CdNWs1AASHTOIF = 8.84 psf PNWs2AASHTO = 5.2CdNWs2AASHTOIF = 6.19 psf Loads on the sign support structure Using the proposed methodology ReNW = 9200VNWdtube = 3.6 × 105 AR = Lt/dtube = 22.9 Use Figure 3.7 to get Cd0NWt = 0.50 Using the current AASHTO specifications Total wind load acting on monotube and the two signs based on current AASHTO specifications: FAASHTO = Fs1AASHTO + Fs2AASHTO + FmAASHTO = 13,384 + 2,810 + 1,963 = 18,157 lbf Difference between the proposed and the current specifications (F − FAASHTO)/FAASHTO = −3% Using the same analysis as the one performed in Section B1.1, determine the length of each zone and the drag coefficients for Zones 1 to 8, CdNWt (Figure B1). Then, determine the equivalent static natural wind gust pressure from PNW = 5.2CdNWtIF: • Zone 1: Uniform-flow region L1 = 5.55 ft, Km,1 = 1, CdNWt,1 = Km,1Cd0NWt = 0.50, PNWt,1 = 5.2CdNWt,1IF = 2.6 psf • Zone 2: Flow-acceleration region L2 = 12.4 ft, Km,2 = 2, CdNWt,2 = Km,2Cd0NWt = 1.0, PNWt,2 = 5.2CdNWt,2IF = 5.2 psf

Design Examples B-5 • Zone 7: Flow-acceleration region L7 = 6.8 ft, Km,7 = 2, CdNWt,7 = Km,7Cd0NWt = 1.0, PNWt,7 = 5.2CdNWt,7IF = 5.2 psf • Zone 8: Uniform-flow region L8 = 11.15 ft, Km,8 = 1, CdNWt,8 = Km,8Cd0NWt = 0.50, PNWt,8 = 5.2CdNWt,8IF = 2.6 psf Using the current AASHTO specifications Estimation of static natural wind gust pressure acting on monotube, based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVNWdtube = 31.36 < 39 (using units of mph for VNW) CdNWtAASHTO = 1.10 PNWtAASHTO = 5.2CdNWtAASHTOIF = 5.72 psf Static natural wind gust pressures acting on Zones 1 to 8 of monotube: PNWt,1AASHTO = 5.72 psf PNWt,2AASHTO = 5.72 psf PNWt,3AASHTO = 0 PNWt,4AASHTO = 5.72 psf PNWt,5AASHTO = 5.72 psf PNWt,6AASHTO = 0 PNWt,7AASHTO = 5.72psf PNWt,8AASHTO = 5.72psf B1.2.2 Truck-induced gust The equivalent static truck gust pressure is calculated assuming that IF = 1 (Importance Category I, overhead non-cantilevered sign support). Wind velocity was VTG = 65 mph (AASHTO specifications). Loads on the signs Using the proposed methodology Drag coefficients for traffic signs are independent of the Reynolds number Drag coefficients for traffic signs have the same values as those estimated in Section B1.1: CdTGs1 = Cds1 = 1.44 CdTGs2 = Cds2 = 1.63 Equivalent static truck-induced gust pressure on each sign, determined from PTGs = 18.8CdTGsIF: PTGs1 = 18.8CdTGs1IF = 27.07 psf PTGs2 = 18.8CdTGs2IF = 30.64 psf Using the current AASHTO specifications Estimation of drag coefficients for each sign, based on current AASHTO specifications • Zone 3: Behind-the-sign region L3 = 30 ft, Km,3 = 0, CdNWt,3 = Km,3Cd0NWt = 0, PNWt,3 = 0 • Zone 4: Gap region associated with Sign 1 L4 = 1.05 ft, Km,4 = 1, CdNWt,4 = Km,4Cd0NWt = 0.50, PNWt,4 = 5.2CdNWt,4IF = 2.6 psf • Zone 5: Gap region associated with Sign 2 L5 = 1.05 ft, Km,5 = 1, CdNWt,5 = Km,5Cd0NWt = 0.50, PNWt,5 = 5.2CdNWt,5IF = 2.6 psf • Zone 6: Behind-the-sign region L6 = 12 ft, Km,6 = 0, CdNWt,6 = Km,6Cd0NWt = 0, PNWt,6 = 0

B-6 Wind Drag Coefficients for Highway Signs and Support Structures Using the proposed methodology ReTG = 9200VTGdtube = 2.1 × 106 AR = Lt/dtube = 22.9 Use Figure 3.7 to get Cd0TGt = 0.37 Using the same analysis as the one performed in Section B1.1, determine the length of each zone and the drag coefficients for Zones 1 to 8, CdTGt (Figure B1). Then, determine the equivalent static natural wind gust pressure from PTG = 18.8CdTGtIF: • Zone 1: Uniform-flow region L1 = 5.55 ft, Km,1 = 1, CdTGt,1 = Km,1Cd0TGt = 0.37, PTGt,1 = 18.8CdTGt,1IF = 6.96 psf • Zone 2: Flow-acceleration region L2 = 12.4 ft, Km,2 = 2, CdTGt,2 = Km,2Cd0TGt = 0.74, PTGt,2 = 18.8CdTGt,2IF = 13.91 psf • Zone 3: Behind-the-sign region L3 = 30 ft, Km,3 = 0, CdTGt,3 = Km,3Cd0TGt = 0, PTGt,3 = 0 • Zone 4: Gap region associated with Sign 1 L4 = 1.05 ft, Km,4 = 1, CdTGt,4 = Km,4Cd0TGt = 0.37, PTGt,4 = 18.8CdTGt,4IF = 6.96 psf • Zone 5: Gap region associated with Sign 2 L5 = 1.05 ft, Km,5 = 1, CdTGt,5 = Km,5Cd0TGt = 0.37, PTGt,5 = 18.8CdTGt,5IF = 6.96 psf • Zone 6: Behind-the-sign region L6 = 12 ft, Km,6 = 0, CdTGt,6 = Km,6Cd0TGt = 0, PTGt,6 = 0 • Zone 7: Flow-acceleration region L7 = 6.8 ft, Km,7 = 2, CdTGt,7 = Km,7Cd0TGt = 0.74, PTGt,7 = 18.8CdTGt,7IF = 13.91 psf • Zone 8: Uniform-flow region L8 = 11.15 ft, Km,8 = 1, CdTGt,8 = Km,8Cd0TGt = 0.37, PTGt,8 = 18.8CdTGt,8IF = 6.96 psf Using the current AASHTO specifications Estimation of truck-induced gust pressure acting on monotube, based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVTGdtube = 182 > 78 (using units of mph for VTG) CdTGtAASHTO = 0.45 PTGtAASHTO = 18.8CdTGtAASHTOIF = 8.46 psf Truck-induced gust pressures acting on Zones 1 to 8 of the monotube: PTGt,1AASHTO = 8.46 psf PTGt,2AASHTO = 8.46 psf PTGt,3AASHTO = 0 PTGt,4AASHTO = 8.46 psf PTGt,5AASHTO = 8.46 psf PTGt,6AASHTO = 0 PTGt,7AASHTO = 8.46 psf PTGt,8AASHTO = 8.46 psf Loads on the sign support structure (Table 3.8.7-1 in LRFDLTS-1): CdTGs1AASHTO = Cds1AASHTO = 1.70 CdTGs2AASHTO = Cds2AASHTO = 1.19 PTGs1AASHTO = 18.8CdTGs1AASHTOIF = 31.96 psf PTGs2AASHTO = 18.8CdTGs2AASHTOIF = 22.37 psf

Design Examples B-7 B2 DESIGN EXAMPLE 2 Application This design example addresses estimating normal and transverse wind loads for an overhead bridge-type 3-chord truss structure supporting one dynamic message sign. The vertical columns (posts) supporting the truss are included in the calculation. Information • Diameter of each vertical column (post): dp = 2 ft • Length of each column (post), including the cap: Lp = 32.7 ft • Area of each column truss connection of triangular shape: Actc = 3.0 ft2 (Figure B2) Distance between the axes of the front-face chords: hb − ha = 6 ft (Figure B2) • Distance between axes of two vertical secondary members of front face: ∆L = 10 ft (Figure B2) Total length of each chord member: Lc = 100 ft • Diameter of each chord member: dc = 0.5 ft (circular cross-section) • Diameter of secondary truss members: dt = 0.42 ft (circular cross-section) (Figure B2) • Dynamic message sign with h = 6 ft, b = 36 ft, d = 1.8 ft, hg = 20 ft • Dynamic message sign: centered with respect to columns • Neglect presence of gusset plates Note: Some of the main geometrical variables are also indicated. Figure B2: Design plans for the Michigan 3-chord truss

B-8 Wind Drag Coefficients for Highway Signs and Support Structures Note: The sketches show elevation views looking toward the front of the truss. The back chord of the truss is not shown. Figure B3: Sketches used to determine the projected lengths of secondary truss members for the Michigan DOT truss Note: The figure also shows the lengths of the different zones defined for the front-face chords (Zone 1 to Zone 5) and for the back-face chords (Zone 1’ to Zone 5’). H1 H2 H3 Figure B4: Sketch of the Michigan DOT truss structure supporting a dynamic message sign, showing the five zones for which drag coefficients will be determined for front-face chords and and for back-face chord Main Assumptions Based on LRFDLTS-1 Specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1)

Design Examples B-9 Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): • Sign: Kds = 0.85 • Chord members: Kdc = 0.85 • Secondary truss members: Kdt = 0.85 • Column (post): Kdp = 0.95 • Column-to-truss connection: Kdctc = 0.85 B2.1 Estimation of Wind Loads if Wind Is Normal to the Sign and the Plane of Sign Support Structure (Normal Wind Loads) Loads on the (dynamic message) sign Using the proposed methodology b/h = 6, h/(h + hg) = 0.23, As = bh = 216 ft2 Use Figure 3.1 to get Cd0s = 1.24 Modification factors: Effect of sign thickness: Kt = 1 Effect of add-on signs: Ka = 1 Effect of proximity of another sign: Kp = 1 Effect of sign support structure: 2dc/h = 0.16 > 0.1, Ks = 1.04 Drag coefficients for the sign: Cds = KtKaKpKsCd0s = 1.29 Estimation of wind load acting on the sign (using units of mph for V): Fs = 0.00256V2KzKdsGCdsAs = 9,141 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Dynamic message sign: CdsAASHTO = 1.70 FsAASHTO = 0.00256V2KzKdsGCdsAASHTOAs = 12,045 lbf Difference between the proposed and the current specifications (Fs − FsAASHTO)/FsAASHTO = −24% Loads on the front-face chords of the truss structure Using the proposed methodology Drag coefficient for the isolated chord Re = 9200Vdc = 5.3 × 105 (using units of mph for V) AR = Lc/dc = 200 Use Figure 3.7 to get Cd0c = 0.60 Drag coefficient for the front-face chords: Top front-face chord (H1): KuH1 = 1, CduH1 = KuH1Cd0c = 0.60 Bottom front-face chord (H2): KuH2 = 0.9, CduH2 = KuH2Cd0c = 0.54

B-10 Wind Drag Coefficients for Highway Signs and Support Structures L3 = b = 36 ft Km3H1 = 0, Cd3H1 = 0 Km3H2 = 0, Cd3H2 = 0 Calculate: L1-2 = L4-5 = (Lc − b)/2 = 32 ft (Figure B4) • Zone 2: Flow-acceleration region L2 = 0.5(bh)0.5, so L2 = 7.35 ft Km2H1 = 1.4, Cd2H1 = Km2H1CduH1 = 0.84 Km2H2 = 1.4, Cd2H2 = Km2H2CduH2 = 0.756 • Zone 1: Uniform-flow region L1 = L1-2 − L2 = 24.65 ft Km1H1 = 1, Cd1H1 = Km1H1CduH1 = 0.60 Km1H2 = 1, Cd1H2 = Km1H2CduH2 = 0.54 • Zone 4: Flow-acceleration region L4 = 0.5(bh)0.5, so L4 = 7.35 ft Km4H1 = 1.4, Cd4H1 = Km4H1CduH1 = 0.84 Km4H2 = 1.4, Cd4H2 = Km4H2CduH2 = 0.756 • Zone 5: Uniform-flow region L5 = L4-5 − L4 = 24.65 ft Km5H1 = 1, Cd5H1 = Km5H1CduH1 = 0.60 Km5H2 = 1, Cd5H2 = Km5H2CduH2 = 0.54 Wind loads acting on chords H1 and H2: FH1 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 688 lbf FH2 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 618 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdc = 46 (using units of mph for V) CdH1AASHTO = 129/(CvVdc)1.3 = 0.89 CdH2AASHTO = 129/(CvVdc)1.3 = 0.89 FH1AASHTO = 0.00256V2Kz KdcGCdH1AASHTOAH1 = 0.00256V2KzKdcGCdH1AASHTO(L1 + L2 + L4 + L5)dc = 934 lbf FH2AASHTO = 0.00256V2KzKdcGCdH2AASHTOAH2 = 0.00256V2KzKdcGCdH2AASHTO(L1 + L2 + L4 + L5)dc = 934 lbf Difference between the proposed and the current specifications (FH1 − FH1AASHTO)/FH1AASHTO = −26% (FH2 − FH2AASHTO)/FH2AASHTO =−34% Loads on the back-face chord of the truss structure Using the proposed methodology Drag coefficient for the back-face chord: Back-face chord (H3): KuH3 = 0.9, CduH3 = KuH3Cd0c = 0.54 • Zone 3: Behind-the-sign region Lengths and drag coefficients for the front-face chords H1 and H2 (Figure B4): ∑5i=1(CdiH2Ai,H2) ∑5i=1(CdiH1Ai,H1) ∑ 5 i=1(CdiH1Lidc) ∑5i=1(CdiH2Lidc)

Design Examples B-11 Km2H3 = 1.4, Cd2H3 = Km2H3CduH3 = 0.756 • Zone 1': Uniform-flow region L1' = L1-2 − L2' = 32 − 11 = 21 ft Km1H3 = 1, Cd1H3 = Km1H3CduH3 = 0.54 • Zone 4': Flow-acceleration region L4' = 0.75(bh)0.5, so L4' = 11 ft Km4H3 = 1.4, Cd4H3 = Km4H3CduH3 = 0.756 • Zone 5': Uniform-flow region L5' = L4-5 − L4' = 32 − 11 = 21 ft Km5H3 = 1, Cd5H3 = Km5H3CduH3 = 0.54 Wind load acting on chord H3: FH3 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 645 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdc = 46 (using units of mph for V) CdH3AASHTO = 129/(CvVdc)1.3 = 0.89 FH3AASHTO = 0.00256V2KzKdcGCdH3AASHTOAH3 = 0.00256V2KzKdcGCdH3AASHTO(L1' + L2' + L4' + L5')dc = 934 lbf Difference between the proposed and the current specifications (FH3 − FH3AASHTO)/FH3AASHTO = −31% Notes: The members are distributed in three groups (A to C). The three 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 B5: Convention used in labeling Michigan DOT truss members for Design Example 2 (with truss span of 100 ft) Lengths and drag coefficients for the unshielded back-face chord H3 (Figure B4): • Zone 3': Behind-the-sign region L3' = b = 36 ft Km3H3 = 0, Cd3H3 = 0 • Zone 2': Flow-acceleration region L2' = 0.75(bh)0.5, so L2' = 11 ft ∑5i=1(CdiH3Ai,H3) ∑5i=1(CdiH3Lidc)

B-12 Wind Drag Coefficients for Highway Signs and Support Structures Note: The figure also displays the approximate position of the five zones (Zone m1 to Zone m5) to which secondary members are assigned. Figure B6: Sketch of the Michigan DOT truss structure showing secondary truss members that are part of the front face of the truss (top) and the two inclined faces (bottom) Loads on the secondary members of the truss structure The secondary truss members and their relative positions are visualized in Figures A5 and A6. Projected lengths of secondary members (Figure B3) are estimated as mt1 = hb − ha − dc = 5.5 ft Lmt2 = = 11.0 ft Lmt3 = Lmt2/2 = 5.5 ft where Lmt3 is the projected length of an inclined-face member in a plane perpendicular to wind direction. Using the proposed methodology Drag coefficient for the isolated secondary truss members of projected lengths Lmt1, Lmt2, Lmt3: Re = 9200Vdt = 4.4 × 105 (using units of mph for V) AR1 = Lmt1/dt = 5.5/0.42 = 13.1 AR2 = Lmt2/dt = 11.0/0.42 = 26.2 AR3 = Lmt3/dt = 5.5/0.42 = 13.1 Use Figure 3.7 to estimate drag coefficients for the secondary truss members of the same diameter but different projected lengths and (projected) aspect ratios: Cd0t = Cd0t1 = Cd0t2 = Cd0t3 ≈ 0.52 Lengths and drag coefficients for all secondary members (Figures A5 and A6): Assign each secondary member to a zone (Zone m1 to Zone m5 in Figure B6) according to the rules. Note that if a member is part of more than one zone, then that member needs to be assigned to one of the two zones. In the following zone map, the members assigned to each zone are listed in parentheses: • Zone m3: Behind-the-sign region Lm3 = b = 36 ft Km3a = 0, Cd3a = 0 (A6, A7, A8, A9, A10, A11, A12) Less than 35% of A6 is in the flow-acceleration region Less than 35% of A12 is in the flow-acceleration region Km3b = 0, Cd3b = 0 (B6, B7, B8, B9, B10, B11, B12, B13) Less than 35% of B6 is in the flow-acceleration region Less than 35% of B13 is in the flow-acceleration region Km3c = 0, Cd3c = 0 (C6, C7, C8, C9, C10, C11, C12, C13) Less than 35% of C6 is in the flow-acceleration region Less than 35% of C13 is in the flow-acceleration region √Lmt1 2+(ΔL–dt) 2

Design Examples B-13 • Zone m2: Flow-acceleration region Lm2 = 0.65(bh)0.5, so Lm2 = 9.5 ft Km2a = 1.25, Cd2a = Km2aCd0t = 0.65 (A4, A5) More than 35% of A4 is in the flow-acceleration region Km2b = 0.7, Cd2b = Km2bCd0t = 0.364 (B4, B5) More than 35% of B4 is in the flow-acceleration region Km2c = 0.7, Cd2c = Km2cCd0t = 0.364 (C4, C5) More than 35% of C4 is in the flow-acceleration region • Zone m4: Flow-acceleration region Lm4 = 0.65(bh)0.5, so Lm4 = 9.5 ft Km4a = 1.25, Cd4a = Km4aCd0t = 0.65 (A13, A14) More than 35% of A14 is in the flow-acceleration region Km4b = 0.7, Cd4b = Km4bCd0t = 0.364 (B14, B15) More than 35% of B15 is in the flow-acceleration region Km4c = 0.7, Cd4c = Km4cCd0t = 0.364 (C14, C15) More than 35% of C15 is in the flow-acceleration region • Zone m1: Uniform-flow region Lm1 = (Lc − Lm2 − Lm3 − Lm4)/2 = 22.5 ft Km1a = 1, Cd1a = Km1aCd0t = 0.52 (A0, A1, A2, A3) Km1b = 0.6, Cd1b = Km1bCd0t = 0.312 (B0, B1, B2, B3) Km1c = 0.6, Cd1c = Km1cCd0t = 0.312 (C0, C1, C2, C3) • Zone m5: Uniform-flow region Lm5 = (Lc − Lm2 − Lm3 − Lm4)/2 = 22.5 ft Km5a = 1, Cd5a = Km5aCd0t = 0.52 (A15, A16, A17, A18) Km5b = 0.6, Cd5b = Km5bCd0t = 0.312 (B16, B17, B18, B19) Km5c = 0.6, Cd5c = Km5cCd0t = 0.312 (C16, C17, C18, C19) Table B1: Drag coefficients, projected length of secondary members, projected area of secondary members, and wind loads acting on secondary members along the wind direction (estimated based on proposed methodology) Note: Results are given for secondary members of the three groups (A to C) of the 3-chord bridge-type truss structure considered in Design Example 2. Index i Member Region Cdm,ai Lmt,Ai (ft) Amt,Ai (ft2) Fm,Ai (lbf) 1 A0 11 4.62 78.8 2 A1 Uniform-flow region 0.52 5.5 2.31 39.4 3 A2 11 4.62 78.8 4 A3 5.5 2.31 39.4 5 A4 Flow-acceleration region 0.65 11 4.62 98.5 6 A5 5.5 2.31 49.2 7 A6 11 4.62 0 8 A7 5.5 2.31 0 9 A8 11 4.62 0 10 A9 Behind-the-sign region 0 5.5 2.31 0 11 A10 11 4.62 0 12 A11 5.5 2.31 0 13 A12 11 4.62 0

B-14 Wind Drag Coefficients for Highway Signs and Support Structures 14 A13 Flow-acceleration region 0.65 5.5 2.31 49.2 15 A14 11 4.62 98.5 16 A15 5.5 2.31 39.4 17 A16 Uniform-flow region 0.52 11 4.62 78.8 18 A17 5.5 2.31 39.4 19 A18 11 4.62 78.8 Index i Member Region Cdm,Bi Lmt,Bi (ft) Amt,Bi (ft2) Fm,Bi (lbf) 1 B0 23.6 2 B1 Uniform-flow region 0.312 5.5 2.31 23.6 3 B2 23.6 4 B3 23.6 5 B4 Flow-acceleration region 0.364 5.5 2.31 27.6 6 B5 27.6 7 B6 0 8 B7 0 9 B8 0 10 B9 Behind-the-sign region 0 5.5 2.31 0 11 B10 0 12 B11 0 13 B12 0 14 B13 0 15 B14 Flow-acceleration region 0.364 5.5 2.31 27.6 16 B15 27.6 17 B16 23.6 18 B17 Uniform-flow region 0.312 5.5 2.31 23.6 19 B18 23.6 20 B19 23.6 Index i Member Region Cdm,Ci Lmt,Ci (ft) Amt,Ci (ft2) Fm,Ci (lbf) 1 C0 23.6 2 C1 Uniform-flow region 0.312 5.5 2.31 23.6 3 C2 23.6 4 C3 23.6 5 C4 Flow-acceleration region 0.364 5.5 2.31 27.6 6 C5 27.6 7 C6 0 8 C7 0 9 C8 0 10 C9 Behind-the-sign region 0 5.5 2.31 0 11 C10 0 12 C11 0 13 C12 0 14 C13 0 15 C14 Flow-acceleration region 0.364 5.5 2.31 27.6

Design Examples B-15 16 C15 27.6 17 C16 23.6 18 C17 Uniform-flow region 0.312 5.5 2.31 23.6 19 C18 23.6 20 C19 23.6 Wind loads acting on the secondary members of Groups A to C (Table B1): Fm = = 0.00256V2KzKdtG + 0.00256V2KzKdtG + + 0.00256V2KzKdtG = 0.00256V2KzKdtG +0.00256V2KzKdtG = 1,370 lbf Table B2: Drag coefficients, projected length of secondary members, projected area of secondary members, and wind loads acting on secondary members along wind direction (estimated based on AASHTO specifications) Note: Results are given for secondary members of the three groups (A to C) of the 3-chord bridge-type truss structure considered in Design Example 2. Index i Member Region Cdm,ai AASHTO Lmt,Ai (ft) Amt,Ai (ft2) Fm,Ai AASHTO (lbf) 1 A0 11 4.62 166.8 2 A1 5.5 2.31 83.4 3 A2 Unshielded region 1.10 11 4.62 166.8 4 A3 5.5 2.31 83.4 5 A4 11 4.62 166.8 6 A5 5.5 2.31 83.4 7 A6 11 4.62 0 8 A7 5.5 2.31 0 9 A8 11 4.62 0 10 A9 Shielded region 0 5.5 2.31 0 11 A10 11 4.62 0 12 A11 5.5 2.31 0 13 A12 11 4.62 0 14 A13 5.5 2.31 83.4 15 A14 11 4.62 166.8 16 A15 Unshielded region 1.10 5.5 2.31 83.4 17 A16 11 4.62 166.8 18 A17 5.5 2.31 83.4 19 A18 11 4.62 166.8 Index i Member Region Cdm,BiAASHTO Lmt,Bi (ft) Amt,Bi (ft2) Fm,Bi AASHTO (lbf) 1 B0 83.4 2 B1 83.4 ∑l9 i = 1 Fm,Cii = 1 Fm,Ai + ∑20i = 1 Fm,Bi + ∑20 ∑l9i = 1 (Cdm,Ai Amt,Ai) ∑l9i = 1 (Cdm,Ai Lmt,Ai dt) 0.00256V2KzKdtG ∑20i = 1 (Cdm,Ci Lmt,Ci dt) ∑20i = 1 (Cdm,Bi Lmt,Bi dt) ∑20i = 1 (Cdm,Ci Amt,Ci) ∑20i = 1 (Cdm,Bi Amt,Bi)

B-16 Wind Drag Coefficients for Highway Signs and Support Structures 3 B2 Unshielded region 1.10 5.5 2.31 83.4 4 B3 83.4 5 B4 83.4 6 B5 83.4 7 B6 0 8 B7 0 9 B8 0 10 B9 Shielded region 0 5.5 2.31 0 11 B10 0 12 B11 0 13 B12 0 14 B13 0 15 B14 83.4 16 B15 83.4 17 B16 Unshielded region 1.10 5.5 2.31 83.4 18 B17 83.4 19 B18 83.4 20 B19 83.4 Index i Member Region Cdm,CiAASHTO Lmt,Ci (ft) Amt,Ci (ft2) Fm,Ci AASHTO (lbf) 1 C0 83.4 2 C1 83.4 3 C2 Unshielded region 1.10 5.5 2.31 83.4 4 C3 83.4 5 C4 83.4 6 C5 83.4 7 C6 0 8 C7 0 9 C8 0 10 C9 Shielded region 0 5.5 2.31 0 11 C10 0 12 C11 0 13 C12 0 14 C13 0 15 C14 83.4 16 C15 83.4 17 C16 Unshielded region 1.10 5.5 2.31 83.4 18 C17 83.4 19 C18 83.4 20 C19 83.4 Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Assume a zero wind load for shielded members Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdt = 38.6 < 39 (using units of mph for V) Cd0tAASHTO = 1.10 (unshielded region) Cd0tAASHTO = 0 (shielded region)

Design Examples B-17 Wind loads acting on the secondary members of Groups A to C (Table B2): FmAASHTO = = 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 3,501 lbf Difference between the proposed and the current specifications (Fm − FmAASHTO)/FmAASHTO = −61% Loads acting on each column (post) of the truss structure Using the proposed methodology For circular members that are not members of a truss or a monotube: Calculate the drag coefficient for the isolated vertical column (post) of circular cross-section based on Table 3.8.7-1 in LRFDLTS-1 Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdp = 184 > 78 (using units of mph for V) Cdp = 0.45 Wind loads acting on the two columns (posts): Fp = 2 × 0.00256V2KzKdpGCdpAp= 2 × 0.00256V2KzKdpGCdpLpdp = 2,158 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdp = 184 > 78 (using units of mph for V) CdpAASHTO = 0.45 FpAASHTO = 2 × 0.00256V2KzKdpGCdpAASHTOAp = 2 × 0.00256V2KzKdpGCdpAASHTOLpdp = 2,158 lbf Difference between the proposed and the current specifications (Fp − FpAASHTO)/FpAASHTO = 0% Total normal wind load acting on the truss structure and the sign Using the proposed methodology Total wind load acting on the truss structure and the sign: F = Fs + FH1 + FH2 + FH3 + Fm + Fp = 9,141 + 688 + 618 + 645 + 1,370 + 2,158 = 14,620 lbf Using the current AASHTO specifications Total wind load acting on the truss structure and the sign: FAASHTO = FsAASHTO + FH1AASHTO + FH2AASHTO + FH3AASHTO + FmAASHTO + FpAASHTO = 12,045 + 934 + 934 + 934 + 3,501 + 2,158 = 20,506 lbf Difference between the proposed and the current specifications (F − FAASHTO)/FAASHTO = −29% ∑19i=1 F AASHTO + ∑20m,Ai i=1 F AASHTOm,Cii=1 F AASHTO + ∑20m,Bi ∑19i=1 (CAASHTOA )dm,Ai mt,Ai ∑20i=1 (CAASHTOA )dm,Bi mt,Bi ∑20i=1 (CAASHTOA )dm,Ci mt,Ci ∑19i=1 (CAASHTOL dt)dm,Ai mt,Ai ∑ 20 i=1 (CAASHTOL dt)dm,Bi mt,Bi ∑20i=1 (CAASHTOL dt)dm,Ci mt,Ci

B-18 Wind Drag Coefficients for Highway Signs and Support Structures B2.2 Estimation of Wind Loads if Wind Is Parallel to the Sign and the Plane of the Support Structure (Transverse Wind Loads) The incoming wind is assumed to be oriented from left to right in Figures B2, B5, and B6. This means that the secondary members directly exposed to the incoming (transverse) wind are A0, B0, and C0. All of the other secondary truss members are shielded. Loads on the lateral (left) face of the (dynamic message) sign Using the proposed methodology Lateral face of height h, width d, and area As d/h = 0.3, h/(h + hg) = 0.23, As = dh = 10.8 ft2 Use Figure 3.1 to get Cd0s = 1.15 Assume Cds = Cd0s = 1.15 Estimation of wind load acting on the sign: Fs = 0.00256V2KzKdsGCdsAs = 407 lbf Loads on the truss chords These loads are neglected because the chords are parallel to the wind direction. Loads on the secondary members of the truss structure Note: The sketch shows a side view looking toward the lateral side of the truss. Figure B7: Sketch used to determine projected lengths of secondary truss members for Michigan DOT bridge-type truss for transverse wind loading The secondary truss members and their relative positions are shown in Figure B5. Initially, one has to estimate the projected lengths of the secondary members: • The centerlines of chord members and secondary truss members projected in the side view (Figure B7) form an equilateral triangle (dashed line). • The length of each side of the triangle is hb − ha, so the projected length of each secondary truss member is: Lmt = hb − ha − dc = 5.5 ft (projected) Using the proposed methodology Drag coefficient for the isolated secondary truss members of projected lengths Lmt: Re = 9200Vdt = 4.4 × 105 (using units of mph for V) AR = Lmt/dt = 5.5/0.42 = 13.1 Use Figure 3.7 to get drag coefficients for the secondary truss members Cd0t ≈ 0.52

Design Examples B-19 Lengths and drag coefficients for all secondary members (Figure B5): Assign the secondary members exposed to the wind (A0, B0, C0) to the unshielded region, and assign all of the other secondary members to the shielded region. The members assigned to each zone are listed in parentheses. • Zone m1: Unshielded region Km1a =1, Cd1a = 0.52 (A0) Km1b =1, Cd1b = 0.52 (B0) Km1c =1, Cd1c = 0.52 (C0) • Zone m2: Shielded region Km2a = 0.6, Cd2a = 0.31 (A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18) Km2b = 0.6, Cd2b = 0.31 (B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14, B15, B16, B17, B18, B19) Km2c = 0.6, Cd2c = 0.31 (C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18, C19) Table B3: Drag coefficients, projected length of secondary members, projected area of secondary members, and wind loads acting on secondary members along wind direction Note: Results are given for secondary members of the three groups (A to C) of the 3-chord bridge-type truss structure considered in Design Example 2. Index i Member Region Cdm,Ai Lmt,Ai (ft) Amt,Ai (ft2) Fm,Ai (lbf) 1 A0 Unshielded region 0.52 39.4 2 A1 23.5 3 A2 23.5 4 A3 23.5 5 A4 23.5 6 A5 23.5 7 A6 23.5 8 A7 Shielded region 0.31 5.5 2.31 23.5 9 A8 23.5 10 A9 23.5 11 A10 23.5 12 A11 23.5 13 A12 23.5 14 A13 23.5 15 A14 23.5 16 A15 23.5 17 A16 23.5 18 A17 23.5 19 A18 23.5 Index i Member Region Cdm,Bi Lmt,Bi (ft) Amt,Bi (ft2) Fm,Bi (lbf) 1 B0 Unshielded region 0.52 39.4 2 B1 23.5 3 B2 23.5

B-20 Wind Drag Coefficients for Highway Signs and Support Structures 4 B3 23.5 5 B4 23.5 6 B5 23.5 7 B6 23.5 8 B7 23.5 9 B8 Shielded region 0.31 5.5 2.31 23.5 10 B9 23.5 11 B10 23.5 12 B11 23.5 13 B12 23.5 14 B13 23.5 15 B14 23.5 16 B15 23.5 17 B16 23.5 18 B17 23.5 19 B18 23.5 20 B19 23.5 Index i Member Region Cdm,Ci Lmt,Ci (ft) Amt,Ci (ft2) Fm,Ci (lbf) 1 C0 Unshielded region 0.52 39.4 2 C1 23.5 3 C2 23.5 4 C3 23.5 5 C4 23.5 6 C5 23.5 7 C6 23.5 8 C7 Shielded region 0.31 5.5 2.31 23.5 9 C8 23.5 10 C9 23.5 11 C10 23.5 12 C11 23.5 13 C12 23.5 14 C13 23.5 15 C14 23.5 16 C15 23.5 17 C16 23.5 18 C17 23.5 19 C18 23.5 20 C19 23.5

Design Examples B-21 Wind loads acting on secondary members of Groups A to C (Table B3): Fm = = 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 1,434 lbf Loads on the column-to-truss connections Drag coefficient for the column-to-truss connection: Cdctc = 1.7 (for flat members, use Table 3.8.7-1 in LRFDLTS-1) Wind loads acting on four column-to-truss connections: Fctc = 4 × 0.00256V2KzKdctcGCdctcActc = 668 lbf Loads on the column (post) supporting the truss structure Using the proposed methodology For circular members that are not members of a truss or a monotube: Use Table 3.8.7-1 in LRFDLTS-1 to calculate drag coefficient for isolated vertical column (post): Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdp = 184 > 78 (using units of mph for V) Cdp = 0.45 Wind loads acting on the two columns (posts): Fp = 2 × 0.00256V2KzKdpGCdpAp = 2 × 0.00256V2KzKdpGCdpLpdp = 2,158 lbf Total transverse wind load acting on the support structure and the sign F = Fs + Fm + Fctc + Fp = 407 + 1,434 + 668 + 2,158 = 4,667 lbf ∑19i = 1 i = 1 F + ∑20m,Ai F + ∑20m,Bi i = 1 F m,Ci ∑19i = 1 (C A )dm,Ai mt,Ai ∑20i = 1 (C A )dm,Bi mt,Bi ∑20i = 1 (C A )dm,Ci mt,Ci ∑19i = 1 (C L dt)dm,Ai mt,Ai ∑20i = 1 (C L dt)dm,Bi mt,Bi ∑20i = 1 (C L dt)dm,Ci mt,Ci

B-22 Wind Drag Coefficients for Highway Signs and Support Structures B3 DESIGN EXAMPLE 3 Application This design example shows how to estimate normal wind loads for a cantilever-type 4-chord truss structure supporting two traffic signs. The example considers the wind loads on the gusset plates. Information • Diameter of the column (post): 2.5 ft • Distance between the axes of the front-face chords: hb − ha = 7 ft Length of each chord member: Lc = 40.5 ft • Diameter of each chord member: dc = 0.56 ft (circular cross-section) Diameter of secondary truss member: dt = 0.24 ft (circular cross-section) • Two identical static traffic signs: h1 = h2 = 10 ft, b1 = b2 = 10 ft, hg1 = hg2 = 20 ft, d1 = d2 = 0.18 ft (di is the thickness of sign i) • Distance between the (interior) edges of the two signs: s = 8 ft • Length of each chord from the exterior edge of Sign 1 to the free end of truss: L1 = L1' = 0.5 ft (Figure B10) • Height of the exposed part of the gusset plates with respect to the chord: hgp = 0.5 ft • Width of the gusset plates (see Figure B8): bgp1 = 1.1 ft (for the front- and back-face plates), bgp2 = 1.5 ft (for the top- and bottom-face plates) bgp3 = 0.7 ft (for the front- and back-face plates P0, Q20, R0, and S20, all situated at the extremity of the truss), as shown in Figure B9 • Only forces on the front- and back-face gusset plates are estimated because they provide the main contribution to the wind loads Main Assumptions Based on LRFDLTS-1 Specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1) Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): • Signs: Kds = 0.85 • Chord members: Kdc = 0.85 • Secondary truss members: Kdt = 0.85 • Gusset plates: Kdg = 0.85

Design Examples B-23 Note: Some of the main geometrical variables are indicated in the figure. Figure B8: Design plans for the cantilever-type 4-chord truss

B-24 Wind Drag Coefficients for Highway Signs and Support Structures Notes: The members are distributed in five groups (A to E). The four chords are labeled H1 to H4. Members from different groups labeled with the same number are situated at about the same spanwise location. Also shown are the gusset plates of the front face (Groups P and Q) and the back face (Groups R and S). Figure B9: Convention used in labeling the cantilever-type 4-chord truss members for Design Example 3 (with truss span of 40.5 ft)

Design Examples B-25 Note: The figure also shows the lengths of the different zones defined for the front-face chords (Zone 1 to Zone 7) and for the back-face chords (Zone 1’ to Zone 7’). Figure B10: Sketch of the 4-chord truss structure supporting two highway signs, showing the seven zones for which drag coefficients will be determined for the front-face chords (H1 and H2) and for the back-face chords (H3 and H4) Loads on the Signs Using the proposed methodology Sign 1: b1/h1 = 1, h1/(h1 + hg1) = 0.33, As1 = b1h1 = 100 ft2 Use Figure 3.1 to get Cd0s1 = 1.16 Sign 2: b2/h2 = 1, h2/(h2 + hg2) = 0.33, As2 = b2h2 = 100 ft2 Use Figure 3.1 to get Cd0s2 = 1.16 Modification factors: Effect of sign thickness: Kt1 = Kt2 = 1 Effect of add-on signs: Ka1 = Ka2 = 1 Effect of proximity of another sign: 2s/(b1 + b2) = 0.8 < 1.5 and 2s/(b1 + b2) > 0.5 |As1 − As2|/(As1 + As2) = 0 < 0.5 Kp1 = Kp2 = 1.1

B-26 Wind Drag Coefficients for Highway Signs and Support Structures Effect of sign support structure: 2dc/h1 = 0.112 > 0.1, Ks1 = 1.04 2dc/h2 = 0.112 > 0.1, Ks2 = 1.04 Drag coefficients for the signs: Cds1 = Kt1Ka1Kp1Ks1Cd0s1 = 1.33 Cds2 = Kt2Ka2Kp2Ks2Cd0s2 = 1.33 Estimation of wind loads acting on the two signs (using units of mph for V): Fs1 = 0.00256V2KzKdsGCds1As1 = 4,363 lbf Fs2 = 0.00256V2KzKdsGCds2As2 = 4,363 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Static Sign 1: b1/h1 = 1 Cds1AASHTO = 1.12 Fs1AASHTO = 0.00256V2KzKdsGCds1AASHTOAs1 = 3,674 lbf Static Sign 2: b2/h2 = 1 Cds2AASHTO = 1.12 Fs2AASHTO = 0.00256V2KzKdsGCds2AASHTOAs2 = 3,674 lbf Difference between the proposed and the current specifications (Fs1 − Fs1AASHTO)/Fs1AASHTO = 19% (Fs2 − Fs2AASHTO)/Fs2AASHTO = 19% Loads on the front-face chords of the truss structure Using the proposed methodology Re = 9200Vdc = 5.9 × 105 (using units of mph for V) AR = Lc/dc = 72 Use Figure 3.7 to get Cd0c = 0.55 Drag coefficient for the isolated front-face chords: Top front-face chord (H1): KuH1 = 1, CduH1 = KuH1Cd0c = 0.55 Bottom front-face chord (H2): KuH2 = 0.9, CduH2 = KuH2Cd0c = 0.50 Lengths and drag coefficients for Zone 1 to Zone 7 for front-face chords (Figure B10): • Zone 2: Behind-the-sign region L2 = b1 = 10 ft Km2H1 = 0, Cd2H1 = 0 Km2H2 = 0, Cd2H2 = 0 • Zone 5: Behind-the-sign region L5 = b2 = 10 ft Km5H1 = 0, Cd5H1 = 0 Km5H2 = 0, Cd5H2 = 0 • Zone 1: Flow-acceleration region L1 = 0.5 ft and L1/(b1h1)0.5 = 0.05 < 0.5 so that there is no uniform-flow region near the left free end Km1H1 = 1.4, Cd1H1 = Km1H1CduH1 = 0.77 Km1H2 = 1.4, Cd1H2 = Km1H2CduH2 = 0.7 • Zone 3: Gap region associated with Sign 1 L3 = s/2 = 4 ft, L3/(b1h1)0.5 = 0.4 > 0.35 and L3/(b1h1)0.5 = 0.4 < 0.5 Km3H1 = 1.4, Cd3H1 = Km3H1CduH1 = 0.77 Km3H2 = 1.4, Cd3H2 = Km3H2CduH2 = 0.7

Design Examples B-27 • Zone 4: Gap region associated with Sign 2 L4 = s/2 = 4 ft, L4/(b2h2)0.5 = 0.4 > 0.35 and L4/(b2h2)0.5 = 0.4 < 0.5 Km4H1 = 1.4, Cd4H1 = Km4H1CduH1 = 0.77 Km4H2 = 1.4, Cd4H2 = Km4H2CduH2 = 0.7 Calculate: L6-7 = Lc − b1 − s − b2 − L1 = 12 ft (Figure B10) • Zone 6: Flow-acceleration region L6 = 0.5(b2h2)0.5, so L6 = 5 ft Km6H1 = 1.4, Cd6H1 = Km6H1CduH1 = 0.77 Km6H2 = 1.4, Cd6H2 = Km6H2CduH2 = 0.7 • Zone 7: Uniform-flow region L7 = L6-7 − L6 = 7 ft Km7H1 = 1, Cd7H1 = Km7H1CduH1 = 0.55 Km7H2 = 1, Cd7H2 = Km7H2CduH2 = 0.5 Estimation of wind loads acting on chords H1 and H2: FH1 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 261 lbf FH2 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 237 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdc = 51.52 (using units of mph for V) CdH1AASHTO = 129/(CvVdc)1.3 = 0.77 CdH2AASHTO = 129/(CvVdc)1.3 = 0.77 FH1AASHTO = 0.00256V2KzKdcGCdH1AASHTOAH1 = 0.00256V2KzKdcGCdH1AASHTO(L1 + L3 + L4 + L6 + L7)dc = 290 lbf FH2AASHTO = 0.00256V2KzKdcGCdH2AASHTOAH2 = 0.00256V2KzKdcGCdH2AASHTO(L1 + L3 + L4 + L6 + L7)dc = 290 lbf Difference between the proposed and the current specifications (FH1 − FH1AASHTO)/FH1AASHTO = −10% (FH2 − FH2AASHTO)/FH2AASHTO = −18% Loads on the back-face chords of the truss structure Using the proposed methodology Drag coefficient for the isolated chords: Back-face chords (H3 and H4): KuH3 = 0.6, CduH3 = KuH3Cd0c = 0.33 KuH4 = 0.54, CduH4 = KuH4Cd0c = 0.30 Lengths and drag coefficients for Zone 1' to Zone 7' for back-face chords (Figure B10): • Zone 2': Behind-the-sign region L2' = b1 = 10 ft Km2H3 = 0, Cd2H3 = 0 Km2H4 = 0, Cd2H4 = 0 • Zone 5': Behind-the-sign region L5' = b2 = 10 ft Km5H3 = 0, Cd5H3 = 0 Km5H4 = 0, Cd5H4 = 0 ∑7i=1(CdiH1Lidc) ∑7i=1(CdiH2Ai,H2) ∑7i=1(CdiH1Ai,H1) ∑7i=1(CdiH2Lidc)

B-28 Wind Drag Coefficients for Highway Signs and Support Structures • Zone 1': Flow-acceleration region L1' = 0.5 ft and L1'/(b1h1)0.5 = 0.05 < 0.75 so there is no uniform-flow region near the left free end Km1H3 = 1.6, Cd1H3 = Km1H3CduH3 = 0.53 Km1H4 = 1.6, Cd1H4 = Km1H4CduH4 = 0.48 • Zone 3': Gap region associated with Sign 1 L3' = s/2 = 4 ft, L3'/(b1h1)0.5 = 0.4 > 0.15 and L3'/(b1h1)0.5 = 0.4 < 0.75 Km3H3 = 1.6, Cd3H3 = Km3H3CduH3 = 0.53 Km3H4 = 1.6, Cd3H4 = Km3H4CduH4 = 0.48 • Zone 4': Gap region associated with Sign 2 L4' = s/2 = 4 ft, L4'/(b2h2)0.5 = 0.4 > 0.15 and L4'/(b2h2)0.5 = 0.4 < 0.75 Km4H3 = 1.6, Cd4H3 = Km4H3CduH3 = 0.53 Km4H4 = 1.6, Cd4H4 = Km4H4CduH4 = 0.48 • Zone 6': Flow-acceleration region L6' = 0.75(bh)0.5, so L6' = 7.5 ft Km6H3 = 1.6, Cd6H3 = Km6H3CduH3 = 0.53 Km6H4 = 1.6, Cd6H4 = Km6H4CduH4 = 0.48 • Zone 7': Uniform-flow region L7' = L6-7 − L6' = 4.5 ft Km7H3 = 1, Cd7H3 = Km7H3CduH3 = 0.33 Km7H4 = 1, Cd7H4 = Km7H4CduH4 = 0.3 Estimation of wind loads acting on chords H3 and H4: FH3 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 183 lbf FH4 = 0.00256V2KzKdcG = 0.00256V2KzKdcG = 166 lbf Using the current AASHTO specifications Assume that wind load is zero on any back member shielded by a front member: FH3AASHTO = 0 FH4AASHTO = 0 Notes: The top sketch is an elevation view. The bottom sketch is a plan view showing how secondary truss members connect to gusset plates. ∑7i=1(CdiH3Ai,H3) ∑7i=1(CdiH4Ai,H4) ∑7i=1(CdiH3Lidc) ∑7i=1(CdiH4Lidc) Figure B11: Sketches used to determine the projected lengths of secondary truss members for cantilever-type 4-chord truss

Design Examples B-29 Note: The figure shows the approximate positions of the six zones (Zone m1 to Zone m6) to which secondary members are assigned. Figure B12: Sketch of the cantilever-type 4-chord truss structure showing secondary truss members that are part of the front face of the truss (top), secondary members that are part of the back face of the truss (middle), and interior-diagonal members connecting the front and back faces (bottom) Loads on the secondary members of the truss structure The secondary truss members and their relative positions are visualized in Figures B9 and B12. Initially, one should estimate the projected lengths of secondary members (Figure B11): Lmt1 = hb − ha − dc − 2hgp = 5.4 ft Lmt2 = = 8.7 ft (projected) Lmt3 = ∆L/2 − Lgp2 = 2.5 ft (projected) Using the proposed methodology Drag coefficient for the isolated secondary members: √Lmt1 2+(ΔL–Lgp1) 2 Re = 9200Vdt = 2.5 × 105 (using units of mph for V) AR1 = Lmt1/dt = 22.5 AR2 = Lmt2/dt = 36.3 AR3 = Lmt3/dt = 10.4

B-30 Wind Drag Coefficients for Highway Signs and Support Structures Use Figure 3.7 to get Cd0t = Cd0t1 = Cd0t2 = Cd0t3 ≈ 0.55 Lengths and drag coefficients for Zone m1 to Zone m6 for all secondary members (Figure B12): Each secondary member is assigned to a zone (Zone m1 to Zone m6 in Figure B12) according to the rules. If a member is part of more than one zone, that member needs to be assigned to one of the two zones. In the following zone map, the members assigned to each zone are listed in parentheses: • Zone m2: Behind-the-sign region Lm2 = b1 = 10 ft Km2a = 0, Cd2a = Km2aCd0t = 0 (A0, A2, A4) Km2b = 0, Cd2b = Km2bCd0t = 0 (B0, B2, B4) Km2c = 0, Cd2c = Km2cCd0t = 0 (C0, C1, C2, C3, C4) Km2d = 0, Cd2d = Km2dCd0t = 0 (D0, D1, D2, D3, D4) Km2e = 0, Cd2e = Km2eCd0t = 0 (E0, E4) • Zone m4: Behind-the-sign region Lm4 = b2 = 10 ft Km4a = 0, Cd4a = 0 (A10, A12) Less than 50% of A10 is in the gap region Km4b = 0, Cd4b = 0 (B10, B12) Less than 50% of B10 is in the gap region Km4c = 0, Cd4c = 0 (C9, C10, C11, C12, C13) Less than 50% of C9 is in the gap region Km4d = 0, Cd4d = 0 (D9, D10, D11, D12, D13) Less than 50% of D9 is in the gap region Km4e = 0, Cd4e = 0 (E12) • Zone m1: Flow-acceleration region Lm1 = 0.5 ft and Lm1/(b2h2)0.5 = 0.05 < 0.65, so there is no uniform-flow region near the left free end; no secondary members are part of Zone m1 • Zone m3: Gap region Lm3 = s = 8 ft and s/2(b1h1)0.5 = 0.4 < 0.8 and s/2(b2h2)0.5 = 0.4 < 0.8, so there is no need to further assign each secondary member to a half-gap region because the Km coefficients are the same Km3a = 1.35, Cd3a = Km3aCd0t = 0.74 (A6, A8) More than 50% of A6 is in the gap region Km3b = 1.3, Cd3b = Km3bCd0t = 0.72 (B6, B8) More than 50% of B6 is in the gap region Km3c = 0.3, Cd3c = Km3cCd0t = 0.17 (C5, C7) More than 50% of C5 is in the gap region Km3c = 0, Cd3c = Km3cCd0t = 0 (C6, C8) C6 and C8 are parallel to the wind direction Km3d = 0.3, Cd3d = Km3dCd0t = 0.17 (D5, D7) More than 50% of D5 is in the gap region Km3d = 0, Cd3d = Km3dCd0t = 0 (D6, D8) D6 and D8 are parallel to the wind direction Km3e = 0.9, Cd3e = Km3eCd0t = 0.5 (E8) • Zone m5: Flow-acceleration region Lm5 = 0.65(b2h2)0.5, so Lm5 = 6.5 ft Km5a = 1.25, Cd5a = Km5aCd0t = 0.69 (A14, A16) More than 35% of A14 is in the flow-acceleration region

Design Examples B-31 Km5b = 1.2, Cd5b = Km5bCd0t = 0.66 (B14, B16) More than 35% of B14 is in the flow-acceleration region Km5c = 0.3, Cd5c = Km5cCd0t = 0.17 (C15, C17) More than 35% of C17 is in the flow-acceleration region Km5c = 0, Cd5c = Km5cCd0t = 0 (C14, C16) C14 and C16 are parallel to the wind direction Km5d = 0.3, Cd5d = Km5dCd0t = 0.17 (D15, D17) More than 35% of D17 is in the flow-acceleration region Km5d = 0, Cd5d = Km5dCd0t = 0 (D14, D16) D14 and D16 are parallel to the wind direction Km5e = 0.7, Cd5e = Km5eCd0t = 0.39 (E16) • Zone m6: Uniform-flow region Lm6 = Lc − Lm1 − Lm2 − Lm3 − Lm4 − Lm5 = 5.5 ft Km6a = 1, Cd6a = Km6aCd0t = 0.55 (A18, A20) Less than 35% of A18 is in the flow-acceleration region Km6b = 0.7, Cd6b = Km6bCd0t = 0.39 (B18, B20) Less than 35% of B18 is in the flow-acceleration region Km6c = 0.3, Cd6c = Km6cCd0t = 0.17 (C19) Km6c = 0, Cd6c = Km6cCd0t = 0 (C18, C20) C18 and C20 are parallel to the wind direction Km6d = 0.3, Cd6d = Km6dCd0t = 0.17 (D19) Km6d = 0, Cd6d = Km6dCd0t = 0 (D18, D20) D18 and D20 are parallel to the wind direction Km6e = 0.3, Cd6e = Km6eCd0t = 0.17 (E20) Table B4: Drag coefficients, projected length of secondary members, projected area of secondary members, and wind loads acting on secondary members along the wind direction (estimated based on the current methodology) Note: Results are given for secondary members that are part of each of the five groups (A to E) of the 4-chord cantilever-type truss structure considered in Design Example 3. Index i Member Region Cdm,Ai Lmt,Ai (ft) Amt,Ai (ft2) Fm,Ai (lbf) 1 A0 5.4 1.30 0 2 A2 Behind-the-sign region 0 8.7 2.08 0 3 A4 5.4 1.30 0 4 A6 Gap region 0.74 8.7 2.08 50.1 5 A8 5.4 1.30 31.5 6 A10 Behind-the-sign region 0 8.7 2.08 0 7 A12 5.4 1.30 0 8 A14 Flow-acceleration region 0.69 8.7 2.08 47.2 9 A16 5.4 1.30 29.3 10 A18 Uniform-flow region 0.55 8.7 2.08 37.7 11 A20 5.4 1.30 23.4 Index i Member Region Cdm,Bi Lmt,Bi (ft) Amt,Bi (ft2) Fm,Bi (lbf) 1 B0 5.4 1.30 0

B-32 Wind Drag Coefficients for Highway Signs and Support Structures 2 B2 Behind-the-sign region 0 8.7 2.08 0 3 B4 5.4 1.30 0 4 B6 Gap region 0.72 8.7 2.08 49.3 5 B8 5.4 1.30 30.6 6 B10 Behind-the-sign region 0 8.7 2.08 0 7 B12 5.4 1.30 0 8 B14 Flow-acceleration region 0.66 8.7 2.08 45.2 9 B16 5.4 1.30 28.0 10 B18 Uniform-flow region 0.39 8.7 2.08 26.7 11 B20 5.4 1.30 16.6 Index i Member Region Cdm,Ci Lmt,Ci (ft) Amt,Ci (ft2) Fm,Ci (lbf) 1 C0 — — 0 2 C1 2.5 0.60 0 3 C2 Behind-the-sign region 0 — — 0 4 C3 2.5 0.60 0 5 C4 — — 0 6 C5 0.17 2.5 0.60 3.3 7 C6 Gap region 0 — — 0 8 C7 0.17 2.5 0.60 3.3 9 C8 0 — — 0 10 C9 2.5 0.60 0 11 C10 — — 0 12 C11 Behind-the-sign region 0 2.5 0.60 0 13 C12 — — 0 14 C13 2.5 0.60 0 15 C14 0 — — 0 16 C15 Flow-acceleration region 0.17 2.5 0.60 3.3 17 C16 0 — — 0 18 C17 0.17 2.5 0.60 3.3 19 C18 0 — — 0 20 C19 Uniform-flow region 0.17 2.5 0.60 3.3 21 C20 0 — — 0 Index i Member Region Cdm,Di Lmt,Di (ft) Amt,Di (ft2) Fm,Di (lbf) 1 D0 — — 0 2 D1 2.5 0.60 0 3 D2 Behind-the-sign region 0 — — 0 4 D3 2.5 0.60 0 5 D4 — — 0 6 D5 0.17 2.5 0.60 3.3 7 D6 Gap region 0 — — 0 8 D7 0.17 2.5 0.60 3.3 9 D8 0 — — 0 10 D9 2.5 0.60 0

Design Examples B-33 11 D10 — — 0 12 D11 Behind-the-sign region 0 2.5 0.60 0 13 D12 — — 0 14 D13 2.5 0.60 0 15 D14 0 — — 0 16 D15 Flow-acceleration region 0.17 2.5 0.60 3.3 17 D16 0 — — 0 18 D17 0.17 2.5 0.60 3.3 19 D18 0 — — 0 20 D19 Uniform-flow region 0.17 2.5 0.60 3.3 21 D20 0 — — 0 Index i Member Region Cdm,Ei Lmt,Ei (ft) Am,Ei (ft2) Fm,Ei (lbf) 1 E0 Behind-the-sign region 0 5.4 1.30 0 2 E4 5.4 1.30 0 3 E8 Gap region 0.50 5.4 1.30 21.3 4 E12 Behind-the-sign region 0 5.4 1.30 0 5 E16 Flow-acceleration region 0.39 5.4 1.30 16.6 6 E20 Uniform-flow region 0.17 5.4 1.30 7.3 Wind loads acting on the secondary members of Groups A to E (Table B4): Fm = = 0.00256V2KzKdtG +0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 0.00256V2KzKdtG +0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG + 0.00256V2KzKdtG = 493 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Assume a zero wind load for the shielded members Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdt = 22.08 < 39 (using units of mph for V) Cd0tAASHTO = 1.10 (unshielded region) Cd0tAASHTO = 0 (shielded region) Table B5: Drag coefficients, projected length of secondary members, projected area of secondary members, and wind loads acting on secondary members along the wind direction (estimated based on AASHTO specifications) Note: Results are given for secondary members that are part of each of the five groups (A to E) of the 4-chord cantilever-type truss structure considered in Design Example 3. Index i Member Region Cdm,Ai AASHTO Lmt,Ai (ft) Amt,Ai (ft2) Fm,Ai AASHTO (lbf) 1 A0 5.4 1.30 0 2 A2 Shielded region 0 8.7 2.08 0 3 A4 5.4 1.30 0 4 A6 Unshielded region 1.10 8.7 2.08 75.1 ∑11i = 1 i = 1 F + ∑11m,Ai F + ∑21m,Bi i = 1 F i = 1 F m,Ci + ∑21 m,Di + ∑6i = 1 F m,Ei ∑11i = 1 (Cdm,Bi Amt,Bi) ∑21i = 1 (Cdm,Di Amt,Di) ∑11i = 1 (Cdm,Bi Lmt,Bidt) ∑21i = 1 (Cdm,Di Lmt,Didt) ∑11i = 1 (Cdm,Ai Lmt,Aidt) ∑21i = 1 (Cdm,Ci Lmt,Cidt) ∑6i = 1 (Cdm,Ei Lmt,Eidt) ∑21i = 1 (Cdm,C Amt,Ci) ∑6i = 1 (Cdm,Ei Amt,Ei) ∑11i = 1 (Cdm,Ai Amt,Ai)

B-34 Wind Drag Coefficients for Highway Signs and Support Structures 5 A8 5.4 1.30 46.9 6 A10 Shielded region 0 8.7 2.08 0 7 A12 5.4 1.30 0 8 A14 8.7 2.08 75.1 9 A16 Unshielded region 1.10 5.4 1.30 46.9 10 A18 8.7 2.08 75.1 11 A20 5.4 1.30 46.9 Index i Member Region Cdm,Bi AASHTO Lmt,Bi (ft) Amt,Bi (ft2) Fm,Bi AASHTO (lbf) 1 B0 5.4 1.30 0 2 B2 Shielded region 0 8.7 2.08 0 3 B4 5.4 1.30 0 4 B6 Unshielded region 1.10 8.7 2.08 75.1 5 B8 5.4 1.30 46.9 6 B10 Shielded region 0 8.7 2.08 0 7 B12 5.4 1.30 0 8 B14 8.7 2.08 75.1 9 B16 Unshielded region 1.10 5.4 1.30 46.9 10 B18 8.7 2.08 75.1 11 B20 5.4 1.30 46.9 Index i Member Region Cdm,Ci AASHTO Lmt,Ci (ft) Amt,Ci (ft2) Fm,Ci AASHTO (lbf) 1 C0 — — 0 2 C1 2.5 0.60 0 3 C2 Shielded region 0 — — 0 4 C3 2.5 0.60 0 5 C4 — — 0 6 C5 1.10 2.5 0.60 21.6 7 C6 Unshielded region 0 — — 0 8 C7 1.10 2.5 0.60 21.6 9 C8 0 — — 0 10 C9 2.5 0.60 0 11 C10 — — 0 12 C11 Shielded region 0 2.5 0.60 0 13 C12 — — 0 14 C13 2.5 0.60 0 15 C14 0 — — 0 16 C15 1.10 2.5 0.60 21.6 17 C16 0 — — 0 18 C17 Unshielded region 1.10 2.5 0.60 21.6 19 C18 0 — — 0 20 C19 1.10 2.5 0.60 21.6 21 C20 0 — — 0

Design Examples B-35 Index I Member Region Cdm,Di AASHTO Lmt,Di (ft) Amt,Di (ft2) Fm,Di AASHTO (lbf) 1 D0 — — 0 2 D1 2.5 0.60 0 3 D2 Shielded region 0 — — 0 4 D3 2.5 0.60 0 5 D4 — — 0 6 D5 1.10 2.5 0.60 21.6 7 D6 Unshielded region 0 — — 0 8 D7 1.10 2.5 0.60 21.6 9 D8 0 — — 0 10 D9 2.5 0.60 0 11 D10 — — 0 12 D11 Shielded region 0 2.5 0.60 0 13 D12 — — 0 14 D13 2.5 0.60 0 15 D14 0 — — 0 16 D15 1.10 2.5 0.60 21.6 17 D16 0 — — 0 18 D17 Unshielded region 1.10 2.5 0.60 21.6 19 D18 0 — — 0 20 D19 1.10 2.5 0.60 21.6 21 D20 0 — — 0 Index i Member Region Cdm,Ei AASHTO Lmt,Ei (ft) Am,Ei (ft2) Fm,Ei AASHTO (lbf) 1 E0 Shielded region 0 5.4 1.30 0 2 E4 5.4 1.30 0 3 E8 Unshielded region 1.10 5.4 1.30 46.9 4 E12 Shielded region 0 5.4 1.30 0 5 E16 Unshielded region 1.10 5.4 1.30 46.9 6 E20 5.4 1.30 46.9 Wind loads acting on the secondary members of Groups A to E (Table B5): FmAASHTO = = 0.00256V2KzKdtG +0.00256V2KzKdtG +0.00256V2KzKdtG 0.00256V2KzKdtG +0.00256V2Kz KdtG 0.00256 = +0.00256V2KzKdtG +0.00256V2KzKdtG +0.00256V2KzKdtG +0.00256V2 KzKdtG = 1,089 lbf Difference between the proposed and the current specifications (Fm − FmAASHTO)/FmAASHTO = −55 % ∑11i=1 F AASHTO + ∑11m,Ai i=1 F AASHTO + ∑21m,Ci i=1 F AASHTO + ∑6m,Di i=1 F AASHTOm,Eii=1 F AASHTO + ∑21m,Bi ∑11i=1 (C AASHTOA )dm,Ai mt,Ai ∑ 11 i=1 (C AASHTOA )dm,Bi mt,Bi ∑21i=1 (C AASHTOA ) +dm,Ci mt,Ci ∑11i=1 (C AASHTOL dt )dm,Bi mt,Bi ∑21i=1 (C AASHTOA )dm,Bi mt,Di ∑21i=1 (C AASHTOL dt )dm,Di mt,Di ∑6i=1 (C AASHTOL dt )dm,Ei mt,Ei ∑6i=1 (C AASHTOA )dm,Ei mt,Ei ∑21i=1 (C AASHTOL dt )dm,Ci mt,Ci ∑11i=1 (C AASHTOL dt )dm,Ai mt,Ai V2KzKdtG

B-36 Wind Drag Coefficients for Highway Signs and Support Structures Note: The figure also shows the approximate positions of the five zones (Zone g1 to Zone g5) to which gusset plates are assigned. Figure B13: Sketch of the cantilever-type 4-chord truss structure, showing the exposed part of the gusset plates that are part of the front face of the truss (top) and of the back face of the truss (bottom) Loads on the gusset plates of the truss structure Using the proposed methodology Drag coefficient for the isolated gusset plate: Cd0gp = 1.25 Lengths and drag coefficients for all of the gusset plates (Figures B9 and B13): • Zone g2: Behind-the-sign region Lg2 = b1 = 10 ft Front-face gusset plates: Kmgp = 0, Cdgp = KmgpCd0gp = 0 (P0, P4, Q0, Q4) Back-face gusset plates: Kmgp = 0, Cdgp = KmgpCd0gp = 0 (R0, R4, S0, S4) • Zone g1: Unshielded region Lg1 = 0.5 ft No gusset plates in Zone g1 • Zone g3: Unshielded region Lg3 = s = 8 ft Front-face gusset plates: Kmgp = 1.1, Cdgp = KmgpCd0gp = 1.38 (P8, Q8) Back-face gusset plates: Kmgp = 0.3, Cdgp = KmgpCd0gp = 0.38 (R8, S8) • Zone g4: Behind-the-sign region Lg4 = b2 = 10 ft Front-face gusset plates: Kmgp = 0, Cdgp = KmgpCd0gp = 0 (P12, Q12) Back-face gusset plates: Kmgp = 0, Cdgp = KmgpCd0gp = 0 (R12, S12) • Zone g5: Unshielded region Lg5 = Lc − Lg1 − Lg2 − Lg3 − Lg4 = 12 ft Front-face gusset plates: Kmgp = 1.1, Cdgp = KmgpCd0gp = 1.38 (P16, P20, Q16, Q20) Back-face gusset plates: Kmgp = 0.3, Cdgp = KmgpCd0gp = 0.38 (R16, R20, S16, S20)

Design Examples B-37 ∑6i=1 C A dgp,Pi gp,Pi Table B6: Drag coefficients, projected area of gusset plates, and wind loads acting on gusset plates (estimated using the proposed methodology) Note: Results are given for gusset plates that are part of each of the four groups (P to S) of the 4-chord cantilever-type truss structure considered in Design Example 3. Index i Members Region Cdgp,Pi Agp,Pi (ft2) Fgp,Pi (lbf) 1 P0 Behind-the-sign region 0 0.35 0 2 P4 0 0.55 0 3 P8 Unshielded region 1.38 0.55 24.9 4 P12 Behind-the-sign region 0 0.55 0 5 P16 Unshielded region 1.38 0.55 24.9 6 P20 1.38 0.55 24.9 Index i Members Region Cdgp,Qi Agp,Qi (ft2) Fgp,Qi (lbf) 1 Q0 Behind-the-sign region 0 0.55 0 2 Q4 0 0.55 0 3 Q8 Unshielded region 1.38 0.55 24.9 4 Q12 Behind-the-sign region 0 0.55 0 5 Q16 Unshielded region 1.38 0.55 24.9 6 Q20 1.38 0.35 15.8 Index i Members Region Cdgp,Ri Agp,Ri (ft2) Fgp,Ri (lbf) 1 R0 Behind-the-sign region 0 0.35 0 2 R4 0 0.55 0 3 R8 Unshielded region 0.38 0.55 6.8 4 R12 Behind-the-sign region 0 0.55 0 5 R16 Unshielded region 0.38 0.55 6.8 6 R20 0.38 0.55 6.8 Index i Members Region Cdgp,Si Agp,Si (ft2) Fgp,Si (lbf) 1 S0 Behind-the-sign region 0 0.55 0 2 S4 0 0.55 0 3 S8 Unshielded region 0.38 0.55 6.8 4 S12 Behind-the-sign region 0 0.55 0 5 S16 Unshielded region 0.38 0.55 6.8 6 S20 0.38 0.35 4.4 Wind loads acting on the gusset plates of Groups P, Q, R, and S (Table B6): Fgp = 0.00256V2KzKdgG +0.00256V2KzKdgG ∑6i=1 F +∑6gp,Pi i=1 F +∑6gp,Qi i=1 F +∑6gp,Ri i=1 F =gp,Si ∑6i=1 C A dgp,Ri gp,Ri ∑6i=1 C A dgp,Si gp,Si+ 0.00256V2KzKdgG + 0.00256V2KzKdgG = 178 lbf ∑6i=1 C A dgp,Qi gp,Qi

B-38 Wind Drag Coefficients for Highway Signs and Support Structures Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Assume a zero wind load for the shielded plates bgp1/hgp = 2.2 Cdgp1AASHTO = 1.20 (unshielded region) Cdgp1AASHTO = 0 (shielded region) bgp3/hgp = 1.4 Cdgp3AASHTO = 1.19 (unshielded region) Cdgp3AASHTO = 0 (shielded region) Table B7: Drag coefficients, projected area of gusset plates, and wind loads acting on gusset plates (estimated using AASHTO specifications) Note: Results are given for gusset plates that are part of each of the four groups (P to S) of the 4-chord cantilever-type truss structure considered in Design Example 3. Index I Members Region Cdgp,PiAASHTO Agp,Pi (ft2) Fgp,Pi AASHTO (lbf) 1 P0 Shielded region 0 0.35 0 2 P4 0 0.55 0 3 P8 Unshielded region 1.2 0.55 21.6 4 P12 Shielded region 0 0.55 0 5 P16 Unshielded region 1.2 0.55 21.6 6 P20 1.2 0.55 21.6 Index I Members Region Cdgp,QiAASHTO Agp,Qi (ft2) Fgp,Qi AASHTO (lbf) 1 Q0 Shielded region 0 0.55 0 2 Q4 0 0.55 0 3 Q8 Unshielded region 1.2 0.55 21.6 4 Q12 Shielded region 0 0.55 0 5 Q16 Unshielded region 1.2 0.55 21.6 6 Q20 1.19 0.35 13.7 Index I Members Region Cdgp,RiAASHTO Agp,Ri (ft2) Fgp,Ri AASHTO (lbf) 1 R0 Shielded region 0 0.35 0 2 R4 0 0.55 0 3 R8 Unshielded region 1.20 0.55 21.6 4 R12 Shielded region 0 0.55 0 5 R16 Unshielded region 1.20 0.55 21.6 6 R20 1.20 0.55 21.6 Index I Members Region Cdgp,SiAASHTO Agp,Si (ft2) Fgp,Si AASHTO (lbf) 1 S0 Shielded region 0 0.55 0 2 S4 0 0.55 0 3 S8 Unshielded region 1.20 0.55 21.6

Design Examples B-39 4 S12 Shielded region 0 0.55 0 5 S16 Unshielded region 1.20 0.55 21.6 6 S20 1.19 0.35 13.7 Wind loads acting on the gusset plates of Groups P, Q, R, and S (Table B7): FgpAASHTO = = 0.00256V2KzKdgG +0.00256V2KzKdgG +0.00256V2KzKdgG +0.00256V2KzKdgG = 243 lbf Difference between the proposed and the current specifications (Fgp − FgpAASHTO)/FgpAASHTO = 27% Total wind load acting on the truss structure and the signs Using the proposed methodology F = Fs1 + Fs2 + FH1 + FH2 + FH3 + FH4 + Fm + Fgp = 4,363 + 4,363 + 261 + 237 + 183 + 166 + 493 + 178 = 10,244 lbf Using the current AASHTO specifications FAASHTO = Fs1AASHTO + Fs2AASHTO + FH1AASHTO + FH2AASHTO + FH3AASHTO + FH4AASHTO + FmAASHTO + FgpAASHTO = 3,674 + 3,674 + 290 + 290 + 0 + 0 + 1,089 + 243 = 9,260 lbf Difference between the proposed and the current specifications (F − FAASHTO)/FAASHTO = 11% ∑6i=1 F AASHTO + ∑6gp,Pi i=1 F AASHTO + ∑6gp,Qi i=1 F AASHTO + ∑6gp,Ri i=1 F AASHTOgp,Si ∑6i=1 (C AASHTOA )dgp,Pi gp,Pi ∑6i=1 (C AASHTOA )dgp,Ri gp,Ri ∑ 6 i=1 (C AASHTOA )dgp,Si gp,Si ∑6i=1 (C AASHTOA )dgp,Qi gp,Qi

B-40 Wind Drag Coefficients for Highway Signs and Support Structures B4 DESIGN EXAMPLE 4 Application This design example shows how to estimate normal wind loads for an overhead bridge-type monotube structure supporting two traffic signs. Information • Length of monotube: Lt = 90 ft • Diameter of monotube: dtube = 4.0 ft (circular cross-section) • Sign 1: static sign with a main sign panel with hm1 = 8 ft, bm1 = 32 ft, d1 = 0.16 ft, hg1 = 22 ft and with an add-on sign panel on the left side with ba1 = 10 ft, ha1 = 2 ft, da1 = 0.16 ft • Sign 2: static sign with h2 = 6 ft, b2 = 6 ft, d2 = 0.16 ft, hg2 = 22 ft Distance between the (interior) edges of the two signs: s = 19 ft • Signs are positioned so that the middle of the gap between their (interior) lateral edges is at the middle of the monotube (as shown in Figure B14) Main Assumptions Based on LRFDLTS-1 Specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1) Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): • Signs: Kds = 0.85 • Monotube: Kdm = 0.85 Figure B14: Sketch of the monotube supporting two highway signs, showing the eight zones for which drag coefficients need to be determined

Design Examples B-41 Loads on the Signs Using the proposed methodology Sign 1: Sign 1 is equivalent to a rectangular sign with b1 = bm1 and h1 = (bm1hm1 + ba1ha1)/b1 b1 = 32 ft, h1 = 8.625 ft, b1/h1 = 3.70, h1/(h1 + hg1) = 0.28, As1 = b1h1 = 276 ft2 Use Figure 3.1 to get Cd0s1 = 1.22 Sign 2: b2/h2 = 1, h2/(h2 + hg2) = 0.21, As2 = b2h2 = 36 ft2 Use Figure 3.1 to get Cd0s2 = 1.14 Modification factors: Effect of sign thickness: Kt1 = Kt2 = 1 Effect of add-on signs: Ka1 = 1.05 Ka2 = 1 Effect of proximity of another sign: 2s/(b1 + b2) = 1 < 1.5 and 2s/(b1 + b2) = 1 > 0.5 |As1 − As2|/(As1 + As2) = 0.77 > 0.5 As1 > As2 Kp1 = 1.05, Kp2 = 1.15 Effect of sign support structure: dtube/h1 = 0.46 > 0.25, Ks1 = 1.07 dtube/h2 = 0.66 > 0.25, Ks2 = 1.07 Drag coefficients for the signs: Cds1 = Kt1Ka1Kp1Ks1Cd0s1 = 1.44 Cds2 = Kt2Ka2Kp2Ks2Cd0s2 = 1.40 Wind loads acting on the signs (using units of mph for V): Fs1 = 0.00256V2KzKdsGCds1As1 = 13,039 lbf Fs2 = 0.00256V2KzKdsGCds2As2 = 1,653 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Sign 1: bm1/hm1 = 4 Cdm1AASHTO = 1.20 Fm1AASHTO = 0.00256V2KzKdsGCdm1AASHTOAm1 = 10,078 lbf ba1/ha1 = 5 Cda1AASHTO = 1.20 Fa1AASHTO = 0.00256V2Kz Kds GCda1AASHTOAa1 = 787 lbf Fs1AASHTO = Fm1AASHTO + Fa1AASHTO = 10,865 lbf Sign 2: b2/h2 = 1 Cds2AASHTO = 1.12 Fs2AASHTO = 0.00256V2KzKdsGCds2AASHTOAs2 = 1,323 lbf

B-42 Wind Drag Coefficients for Highway Signs and Support Structures Difference between the proposed and the current specifications (Fs1 − Fs1AASHTO)/Fs1AASHTO = 20% (Fs2 − Fs2AASHTO)/Fs2AASHTO = 25% Loads on the monotube Using the proposed methodology Drag coefficient for the isolated monotube: Re = 9200Vdt = 4.2 × 106 (using units of mph for V) AR = Lt/dtube = 22.5 Use Figure 3.7 to get Cd0t = 0.37 Lengths and drag coefficients for Zones 1 to 8 (Figure B14): • Zone 2: Behind-the-sign region L2 = b1 = 32 ft, Km,2 = 0, Cdt,2 = Km,2Cd0t = 0 • Zone 6: Behind-the-sign region L6 = b2 = 6 ft, Km,6 = 0, Cdt,6 = Km,6Cd0t = 0 • Zone 1: Flow-acceleration region Calculate L1 = Lt/2 − s/2 − b1 = 3.5 ft h1/dtube = 2.2 < 15, L1/(b1h1)0.5 = 0.2 < 0.8 so there is no uniform-flow region near left free end Km,1 = 2, Cdt,1 = Km,1Cd0t = 0.74 • Zone 3: Gap region associated with Sign 1 L3 = s/2 = 9.5 ft, h1/dtube = 2.2 < 15, L3/(b1h1)0.5 = 0.57 > 0.35, and L3/(b1h1)0.5 = 0.57 < 0.8 So, Km,3 = 2, Cdt,3 = Km,3Cd0t = 0.74 • Zone 5: Flow-acceleration region part of the gap region associated with Sign 2 Calculate L4-5 = s/2 = 9.5 ft, h2/dtube = 1.5 < 15, L4-5/(b2h2)0.5 = 1.6 > 0.35 L5 = 0.8(b2h2)0.5, so L5 = 4.8 ft Km,5 = 2, Cdt,5 = Km,5Cd0t = 0.74 L5 < L4-5 so there is a uniform-flow region (see Zone 4 below) • Zone 4: Uniform-flow region part of the gap associated with Sign 2 L4 = L4-5 − L5 = 4.7 ft, Km,4 = 1, Cdt,4 = Km,4Cd0t = 0.37 • Zone 7: Flow-acceleration region Calculate L7-8 = Lt/2 − s/2 − b2 = 29.5 ft (Figure B14) h2/dtube = 1.5 < 15, L7 = 0.8(b2h2)0.5 = 4.8 ft, Km,7 = 2, Cdt,7 = Km,7Cd0t = 0.74 • Zone 8: Uniform-flow region L8 = L7-8 − L7 = 24.7 ft, Km,8 = 1, Cdt,8 = Km,8Cd0t = 0.37 Estimated wind load acting on the monotube: Fm = 0.00256V2KzKdmG = 0.00256V2KzKdmG = 3,621 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdtube = 368 > 78 (using units of mph for V) CdmAASHTO = 0.45 FmAASHTO = 0.00256V2Kz KdmGCdmAASHTOAm = 0.00256V2KzKdmGCdmAASHTO(L1 + L3 + L4 + L5 + L7 + L8)dtube = 3,070 lbf Σ8i = 1 (Cdt,i Ai) Σ8i = 1 (Cdt,i Lidtube)

Design Examples B-43 (Fm − FmAASHTO)/FmAASHTO = 18% Total wind load acting on the monotube and the two signs Using the proposed methodology Total wind load acting on the monotube and the two signs: F = Fs1 + Fs2 + Fm = 13,039 + 1,653 + 3,621 = 18,313 lbf Using the current AASHTO specifications FAASHTO = Fs1AASHTO + Fs2AASHTO + FmAASHTO = 10,865 + 1,323 + 3,070 = 15,258 lbf Difference between the proposed and current specifications (F − FAASHTO)/FAASHTO = 20% Difference between the proposed and the current specifications

B-44 Wind Drag Coefficients for Highway Signs and Support Structures Figure B15: Sketch of the monotube supporting the three highway signs, showing the nine zones for which drag coefficients need to be determined B5 DESIGN EXAMPLE 5 Application This design example shows how to estimate normal wind loads for strength design and for fatigue design for an overhead bridge-type monotube structure supporting three traffic signs. Information • Length of monotube: Lt = 90 ft • Diameter of monotube: dtube = 3.0 ft (circular cross-section) • Sign 1: static sign with h1 = 20 ft, b1 = 20 ft, d1 = 0.16 ft, hg1 = 21 ft • Sign 2: static sign with h2 = 6 ft, b2 = 18 ft, d2 = 0.16 ft, hg2 = 28 ft • Sign 3: dynamic message sign with h3 = 8 ft, b3 = 35 ft, d3 = 3.5 ft, hg3 = 27 ft • Distance between Sign 1 and Sign 2: s1-2 = 2 ft • Sign 1 and Sign 2 are centered horizontally with respect to the left half of the monotube so that sl-1 = s2-m (as shown in Figure B15) • Sign 3 is centered horizontally with respect to the right half of the monotube so that sm-3 = s3-r (as shown in Figure B15) B5.1 Estimation of Wind Loads for Strength Design Main assumptions based on LRFDLTS-1 specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1) Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): • Signs: Kds = 0.85 • Monotube: Kdm = 0.85

Design Examples B-45 Loads on the signs Using the proposed methodology Sign 1: b1/h1 = 1, h1/(h1 + hg1) = 0.49, As1 = b1h1 = 400 ft2 Use Figure 3.1 to get Cd0s1 = 1.22 Static Sign 2: b2/h2 = 3, h2/(h2 + hg2) = 0.18, As2 = b2h2 = 108 ft2 Use Figure 3.1 to get Cd0s2 = 1.15 Dynamic Message Sign 3: b3/h3 = 4.375, h3/(h3 + hg3) = 0.23, As3 = b3h3 = 280 ft2 Use Figure 3.1 to get Cd0s3 = 1.22 Modification factors: Effect of sign thickness: Kt1 = Kt2 = Kt3 = 1 Effect of add-on signs: Ka1 = Ka2 = Ka3 = 1 Effect of proximity of another sign: 2s1-2/(b1 + b2) = 0.11 < 0.5 and 2s1-2/(b1 + b2) > 0.02 |As1 − As2|/(As1 + As2) = 0.57 > 0.5 As1 > As2 Kp1 = 1.1, Kp2 = 1.3 2(s2-m + sm-3)/(b2 + b3) = 0.28 < 0.5 and 2(s2-m + sm-3)/(b2 + b3) > 0.02 |As2 − As3|/(As2 + As3) = 0.44 < 0.5 As2 < As3 Kp2 = Kp3 = 1.25 For the middle sign (Sign 2), take the larger value between 1.3 and 1.25: Kp2 = 1.3, so Kp1 = 1.1, Kp2 = 1.3, Kp3 = 1.25 Effect of sign support structure: dtube/h1 = 0.15 < 0.25, Ks1 = 1.04 dtube/h2 = 0.5 > 0.25, Ks2 = 1.07 dtube/h3 = 0.375 > 0.25, Ks3 = 1.07 Drag coefficients for the signs: Cds1 = Kt1Ka1Kp1Ks1Cd0s1 = 1.40 Cds2 = Kt2Ka2Kp2Ks2Cd0s2 = 1.60 Cds3 = Kt3Ka3Kp3Ks3Cd0s3 = 1.63 Wind loads acting on the signs (using units of mph for V): Fs1 = 0.00256V2KzKdsGCds1As1 = 18,371 lbf Fs2 = 0.00256V2KzKdsGCds2As2 = 5,669 lbf Fs3 = 0.00256V2KzKdsGCds3As3 = 14,973 lbf

B-46 Wind Drag Coefficients for Highway Signs and Support Structures Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Sign 1: b1/h1 = 1 Cds1AASHTO = 1.12 Fs1AASHTO = 0.00256V2KzKdsGCds1AASHTOAs1 = 14,697 lbf Static sign 2: b2/h2 = 3 Cds2AASHTO = 1.20 Fs2AASHTO = 0.00256V2KzKdsGCds2AASHTOAs2 = 4,251 lbf Dynamic Message Sign 3: Cds3AASHTO = 1.70 Fs3AASHTO = 0.00256V2KzKdsGCds3AASHTOAs3 = 15,614 lbf Difference between the proposed and the current specifications (Fs1 − Fs1AASHTO)/Fs1AASHTO = 25% (Fs2 − Fs2AASHTO)/Fs2AASHTO = 33% (Fs3 − Fs3AASHTO)/Fs3AASHTO = −4% Loads on the monotube Using the proposed methodology Drag coefficient for the isolated monotube: Re = 9200Vdtube = 3.1 × 106 (using units of mph for V) AR = Lt/dtube = 30 Use Figure 3.7 to get Cd0t = 0.37 Lengths and drag coefficients for Zones 1 to 9 (Figure B15): • Zone 2: Behind-the-sign region L2 = b1 = 20 ft, Km,2 = 0, Cdt,2 = Km,2Cd0t = 0 • Zone 5: Behind-the-sign region L5 = b2 = 18 ft, Km,5 = 0, Cdt,5 = Km,5Cd0t = 0 • Zone 8: Behind-the-sign region L8 = b3 = 35 ft, Km,8 = 0, Cdt,8 = Km,8Cd0t = 0 • Zone 1: Flow-acceleration region Calculate L1 = sl-1 = (Lt/2 − s1-2 − b1 − b2)/2 = 2.5 ft h1/dtube = 6.7 < 15, L1/(b1h1)0.5 = 0.125 < 0.8 so there is no uniform-flow region near the left free end Km,1 = 2, Cdt,1 = Km,1Cd0t = 0.74 • Zone 3: Gap region associated with Sign 1: L3 = s1-2/2 = 1 ft, L3/(b1h1)0.5 = 0.05 < 0.15, so Km,3 = 1, Cdt,3 = Km,3Cd0t = 0.37 • Zone 4: Gap region associated with Sign 2 Calculate L4 = s1-2/2 = 1 ft, L4/(b2h2)0.5 = 0.10 < 0.15 So, Km,4 = 1, Cdt,4 = Km,4Cd0t = 0.37 • Zone 6: Gap region associated with Sign 2 Calculate s2-m = sl-1 = 2.5 ft, sm-3 = (Lt/2 − b3)/2 = 5 ft L6 = (s2-m + sm-3)/2 = 3.75 ft, h2/dtube = 2 < 15, L6/(b2h2)0.5 = 0.36 > 0.35, and L6/(b2h2)0.5 = 0.36 < 0.8 So, Km,6 = 2, Cdt,6 = Km,6Cd0t = 0.74

Design Examples B-47 L7 = (s2-m + sm-3)/2= 3.75 ft, h3/dtube = 2.6 < 15, L7/(b3h3)0.5 = 0.22 > 0.15, and L7/(b3h3)0.5 = 0.22 < 0.35 So, Km,7 = 1.6, Cdt,7 = Km,7Cd0t = 0.59 • Zone 9: Flow-acceleration region L9 = (Lt/2 − b3)/2 = 5 ft, h3/dtube = 2.6 < 15, L9/(b3h3)0.5 = 0.3 < 0.8 so there is no uniform-flow region near the right free end So, Km,9 = 2, Cdt,9 = Km,9Cd0t = 0.74 Estimated wind load acting on the monotube: Fm = 0.00256V2KzKdmG = 0.00256V2KzKdmG = 1,110 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVdtube = 276 > 78 (using units of mph for V) CdmAASHTO = 0.45 FmAASHTO = 0.00256V2KzKdmGCdmAASHTOAm = 0.00256V2KzKdmGCdmAASHTO (L1 + L3 + L4 + L6 + L7 + L9)dtube = 753 lbf Difference between the proposed and current specifications (Fm − FmAASHTO)/FmAASHTO = 47% Total wind load acting on the monotube and the three signs Using the proposed methodology F = Fs1 + Fs2 + Fs3 +Fm = 18,371 + 5,669 + 14,973 + 1,110 = 40,123 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) FAASHTO = Fs1AASHTO + Fs2AASHTO + Fs3AASHTO + FmAASHTO = 14,697 + 4,251 + 15,614 + 753 = 35,315 lbf Difference between the proposed and the current specifications (F − FAASHTO)/FAASHTO = 14% B5.2 Estimation of Wind Loads for Fatigue Design B5.2.1 Natural wind gust The equivalent static natural wind gust pressure is calculated by assuming IF = 1 (with Importance Category I, overhead non-cantilevered sign support). Wind velocity is VNW = 11.2 mph (per AASHTO specifications). Loads on the signs Using the proposed methodology Drag coefficients on the traffic signs are independent of the Reynolds number Drag coefficients on the traffic signs have the same values as those estimated in Section B5.1: CdNWs1 = Cds1 = 1.40 CdNWs2 = Cds2 = 1.60 CdNWs3 = Cds3 = 1.63 Equivalent static natural wind gust pressure on each sign is determined using the formula PNWs = 5.2CdNWsIF: PNWs1 = 5.2CdNWs1IF = 7.28 psf • Zone 7: Gap region associated with Sign 3 ∑9i = 1 (Cdt,i Ai) ∑9i = 1 (Cdt,i Li dtube)

B-48 Wind Drag Coefficients for Highway Signs and Support Structures PNWs2 = 5.2CdNWs2IF = 8.32 psf PNWs3 = 5.2CdNWs3IF = 8.48 psf Using the current AASHTO specifications Estimation of drag coefficients for each sign based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): CdNWs1AASHTO = Cds1AASHTO = 1.12 CdNWs2AASHTO = Cds2AASHTO = 1.20 CdNWs3AASHTO = Cds3AASHTO = 1.70 PNWs1AASHTO = 5.2CdNWs1AASHTOIF = 5.82 psf PNWs2AASHTO = 5.2CdNWs2AASHTOIF = 6.24 psf PNWs3AASHTO = 5.2CdNWs3AASHTOIF = 8.84 psf Loads on the sign support structure Using the proposed methodology ReNW = 9200VNWdtube = 3.1 × 105 AR = Lt/dtube = 30 Use Figure 3.7 to get Cd0NWt = 0.51 Using the same analysis as that in Section B5.1, the length of each zone and drag coefficients for Zones 1 to 9, CdNWt (Figure B15), can be determined. Then, the equivalent static natural wind gust pressure is determined from PNW = 5.2CdNWtIF. • Zone 1: Flow-acceleration region L1 = 2.5 ft, Km,1 = 2, CdNWt,1 = Km,1Cd0NWt = 1.02, PNWt,1 = 5.2CdNWt,1IF = 5.30 psf • Zone 2: Behind-the-sign region L2 = 20 ft, Km,2 = 0, CdNWt,2 = Km,2Cd0NWt = 0, PNWt,2 = 5.2CdNWt,2IF = 0 • Zone 3: Gap region associated with Sign 1 L3 = 1 ft, Km,3 = 1, CdNWt,3 = Km,3CdNWm = 0.51, PNWt,3 = 5.2CdNWt,3IF = 2.65 psf • Zone 4: Gap region associated with Sign 2 L4 = 1 ft, Km,4 = 1, CdNWt,4 = Km,4Cd0NWt = 0.51, PNWt,4 = 5.2CdNWt,4IF = 2.65 psf • Zone 5: Behind-the-sign region L5 = 18 ft, Km,5 = 0, CdNWt,5 = Km,5Cd0NWt = 0, PNWt,5 = 5.2CdNWt,5IF = 0 • Zone 6: Gap region associated with Sign 2 L6 = 3.75 ft, Km,6 = 2, CdNWt,6 = Km,6Cd0NWt = 1.02, PNWt,6 = 5.2CdNWt,6IF = 5.30 psf • Zone 7: Gap region associated with Sign 3 L7 = 3.75 ft, Km,7 = 1.6, CdNWt,7 = Km,7Cd0NWt = 0.82, PNWt,7 = 5.2CdNWt,7IF = 4.26 psf • Zone 8: Behind-the-sign region L8 = 35 ft, Km,8 = 0, CdNWt,8 = Km,8Cd0NWt = 0, PNWt,8 = 5.2CdNWt,8IF = 0 • Zone 9: Flow-acceleration region L9 = 5 ft, Km,9 = 2, CdNWt,9 = Km,9Cd0NWt = 1.02, PNWt,9 = 5.2CdNWt,9IF = 5.30 psf Using the current AASHTO specifications Estimation of static natural wind gust pressure acting on the monotube based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVNWdtube = 26.88 < 39 (using units of mph for VNW) CdNWtAASHTO = 1.10 PNWtAASHTO = 5.2CdNWtAASHTOIF = 5.72 psf

Design Examples B-49 Static natural wind gust pressures acting on Zones 1 to 9 of the monotube: PNWt,1AASHTO = 5.72 psf PNWt,2AASHTO = 0 PNWt,3AASHTO = 5.72 psf PNWt,4AASHTO = 5.72 psf PNWt,5AASHTO =0 PNWt,6AASHTO = 5.72 psf PNWt,7AASHTO = 5.72 psf PNWt,8AASHTO =0 PNWt,9AASHTO = 5.72 psf B5.2.2 Truck-induced gust The equivalent static truck gust pressure is calculated by assuming IF = 1 (Importance Category I, overhead non-cantilevered sign support). Wind velocity is VTG = 65 mph (per AASHTO specifications). Loads on the signs Using the proposed methodology Drag coefficients on the traffic signs are independent of the Reynolds number Drag coefficients on the traffic signs have the same values as those estimated in Section B5.1: CdTGs1 = Cds1 = 1.40 CdTGs2 = Cds2 = 1.60 CdTGs3 = Cds3 = 1.63 The equivalent static truck-induced gust pressure on each sign is determined using the formula PTGs = 18.8CdTGsIF: PTGs1 = 18.8Cds1IF = 26.32 psf PTGs2 = 18.8Cds2IF = 30.08 psf PTGs3 = 18.8Cds3IF = 30.64 psf Using the current AASHTO specifications Estimation of drag coefficients for each sign based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): CdTGs1AASHTO = Cds1AASHTO = 1.12 CdTGs2AASHTO = Cds2AASHTO = 1.20 CdTGs3AASHTO = Cds3AASHTO = 1.70 PTGs1AASHTO = 18.8CdTGs1AASHTOIF = 21.06 psf PTGs2AASHTO = 18.8CdTGs2AASHTOIF = 22.56 psf PTGs3AASHTO = 18.8CdTGs3AASHTOIF = 31.96 psf Loads on the sign support structure Using the proposed methodology ReTG = 9200VTGdtube = 1.8 × 106 AR = Lt/dtube = 30 Use Figure 3.7 to get Cd0TGt = 0.37 Using the same analysis as that in Section B5.1, the length of each zone and drag coefficients for Zones 1 to 9, CdTGt (Figure B15), can be determined. Then, the equivalent static natural wind gust pressure is determined from PTG = 18.8CdTGtIF.

B-50 Wind Drag Coefficients for Highway Signs and Support Structures • Zone 1: Flow-acceleration region L1 = 2.5 ft, Km,1 = 2, CdTGt,1 = Km,1Cd0TGt = 0.74, PTGt,1 = 18.8CdTGt,1IF = 13.91 psf • Zone 2: Behind-the-sign region L2 = 20 ft, Km,2 = 0, CdTGt,2 = Km,2Cd0TGt = 0, PTGt,2 = 18.8CdTGt,2IF = 0 • Zone 3: Gap region associated with Sign 1 L3 = 1 ft, Km,3 = 1, CdTGt,3 = Km,3Cd0TGt = 0.37, PTGt,3 = 18.8CdTGt,3IF = 6.96 psf • Zone 4: Gap region associated with Sign 2 L4 = 1 ft, Km,4 = 1, CdTGt,4 = Km,4Cd0TGt = 0.37, PTGt,4 = 18.8CdTGt,4IF = 6.96 psf • Zone 5: Behind-the-sign region L5 = 18 ft, Km,5 = 0, CdTGt,5 = Km,5Cd0TGt = 0, PTGt,5 = 18.8CdTGt,5IF = 0 • Zone 6: Gap region associated with Sign 2 L6 = 3.75 ft, Km,6 = 2, CdTGt,6 = Km,6Cd0TGt = 0.74, PTGt,6 = 18.8CdTGt,6IF = 13.91 psf • Zone 7: Gap region associated with Sign 3 L7 = 3.75 ft, Km,7 = 1.6, CdTGt,7 = Km,7Cd0TGt = 0.59, PTGt,7 = 18.8CdTGt,7IF = 11.13 psf • Zone 8: Behind-the-sign region L8 = 35 ft, Km,8 = 0, CdTGt,8 = Km,8Cd0TGt = 0, PTGt,8 = 18.8CdTGt,8IF = 0 • Zone 9: Flow-acceleration region L9 = 5 ft, Km,9 = 2, CdTGt,9 = Km,9Cd0TGt = 0.74, PTGt,9 = 5.2CdTGt,9IF = 13.91 psf Using the current AASHTO specifications Estimation of truck-induced gust pressure acting on the monotube based on current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1): Cv = 0.8 for the extreme limit state (load combination that includes wind) CvVTGdtube = 156 > 78 (using units of mph for VTG) CdTGtAASHTO = 0.45 PTGtAASHTO = 18.8CdTGtAASHTOIF = 8.46 psf Truck-induced gust pressures acting on Zones 1 to 9 of the monotube: PTGt,1AASHTO = 8.46 psf PTGt,2AASHTO = 0 PTGt,3AASHTO = 8.46 psf PTGt,4AASHTO = 8.46 psf PTGt,5AASHTO = 0 PTGt,6AASHTO = 8.46 psf PTGt,7AASHTO = 8.46 psf PTGt,8AASHTO = 0 PTGt,9AASHTO = 8.46 psf

Design Examples B-51 B6 DESIGN EXAMPLE 6 Application This design example shows how to estimate normal wind loads for a traffic sign attached to a grade separation structure that includes a barrier rail (Configuration 1, as shown in Figure B16) or a separation rail (Configuration 2, as shown in Figure B17). The normal wind loads are evaluated first for the case when the wind is directed toward the front face of the sign and then for the case when the wind is directed toward the back face of the sign. Information • Height of beams supporting the bridge deck: hb =6 ft Thickness of bridge deck: hd = 1 ft • Height of barrier or separation rail: hbr = 3 ft • Static sign with h = 15 ft, b = 30 ft, ds = 0.16 ft, hg = 19 ft • Bottom edge of sign situated h0 = 1 ft above the bottom edge of the beams • In the example, top edge of sign situated above the top edge of the barrier or separation rail Main Assumptions Based on LRFDLTS-1 Specifications Design wind velocity: V = 115 mph (Figure 3.8-1b in LRFDLTS-1) Gust effect factor: G = 1.14 (Section 3.8.6 in LRFDLTS-1) Height and exposure factor: Kz = 1 Wind directionality factor (Table 3.8.5-1 in LRFDLTS-1): • Sign: Kds = 0.85 B6.1 Normal wind loads for Configuration 1 B16a: Front view

B-52 Wind Drag Coefficients for Highway Signs and Support Structures B16b: Side view showing wind loads for case when wind is directed toward the front face of the sign B16c: Side view showing wind loads for case when wind is directed toward the back face of the sign Figure B16: Sketch of the traffic sign placed on a grade separation structure with a barrier rail (Configuration 1), showing the three subzones for which drag coefficients need to be determined Case 1: Wind is directed toward the front face of the sign Using the proposed methodology b/h = 2, h/(h + h0 + hg) = 0.43, As = bh = 450 ft2 Use Figure 3.1 to get Cd0s = 1.30 Heights and drag coefficients for different subzones (Figure B16): b/h ≥ 1 hlz = hb − h0 = 5 ft h − hlz = 10 ft, hd + hbr = 4 ft, h − hlz > hd + hbr, so wind loads need to be estimated for three subzones • Lower subzone hlz = hb − h0 = 5 ft Kl = 1.1, Cdlz = 1.1Cd0s = 1.43 • Middle subzone hmz = hd + hbr = 4 ft Cdmz = 1.45Cd0s = 1.89 • Upper subzone huz = h − hlz − hmz = 6 ft Cduz = 1.3Cd0s = 1.70 Drag coefficient for the sign: Cds = (AlCdlz + AmCdmz + AuCduz)/As = (bhlzCdlz + bhmzCdmz + bhuzCduz)/As = 1.66 Wind loads acting at the centroids of each subzone (using units of mph for V): Flz = 0.00256V2KzKdsGCdlzAl = 7,037 lbf

Design Examples B-53 Fmz = 0.00256V2KzKdsGCdmzAm = 7,441 lbf Fuz = 0.00256V2KzKdsGCduzAu = 10,039 lbf Total wind load acting on the sign: Fs = Flz + Fmz + Fuz = 24,517 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Static sign: b/h = 2 CdsAASHTO = 1.19 FsAASHTO = 0.00256V2KzKdsGCdsAASHTOAs = 17,567 lbf Difference between the proposed and the current specifications (Fs − FsAASHTO)/FsAASHTO = 40% Case 2: Wind is directed toward the back face of the sign Using the proposed methodology b/h = 2, h/(h + h0 + hg) = 0.43, As = bh = 450 ft2 Use Figure 3.1 to get Cd0s = 1.30 Heights and drag coefficients for different subzones (Figure B16): b/h > 1 hlz = hb − h0 = 5 ft h − hlz = 10 ft, hd + hbr = 4 ft, h − hlz > hd + hbr, so wind loads need to be estimated for three subzones: • Lower subzone hlz = hb − h0 = 5 ft Cdlz = 0 • Middle subzone hmz = hd + hbr = 4 ft Cdmz = 0 • Upper subzone huz = h − hlz − hmz = 6 ft Cduz = 0.45 Cd0s = 0.59 Drag coefficient for the sign: Cds = (AlCdlz + AmCdmz + AuCduz)/As = (bhlzCdlz + bhmzCdmz + bhuzCduz)/As = 0.24 Wind loads acting at the centroids of each subzone (using units of mph for V): Flz = 0.00256V2KzKdsGCdlzAl = 0 lbf Fmz = 0.00256V2KzKdsGCdmzAm = 0 lbf Fuz = 0.00256V2KzKdsGCduzAu = 3,484 lbf Total wind load acting on the sign: Fs = Flz + Fmz + Fuz = 3,484 lbf B6.2 Normal wind loads for Configuration 2

B-54 Wind Drag Coefficients for Highway Signs and Support Structures B17a: Front view B17b: Side view showing wind loads for case when wind is directed toward the front face of the sign B17c: Side view showing wind loads for case when wind is directed toward the back face of the sign Figure B17: Sketch showing the traffic sign placed on a grade separation structure with a separation rail (Configuration 2), showing the three subzones for which drag coefficients need to be determined Case 1: Wind is directed toward the front face of the sign Using the proposed methodology b/h = 2, h/(h + h0+hg) = 0.43, As = bh = 450 ft2 Use Figure 3.1 to get Cd0s = 1.30 Heights and drag coefficients for different subzones (Figure B17): b/h > 1 hlz = hb − h0 = 5 ft h − hlz = 10 ft, hd + hbr = 4 ft, h − hlz > hd + hbr, so wind loads need to be estimated for three

Design Examples B-55 subzones: • Lower subzone hlz = hb − h0 = 5 ft Cdlz = 1.0Cd0s = 1.3 • Middle subzone hmz = hd + hbr = 4 ft Cdmz = 1.2Cd0s = 1.56 • Upper subzone huz = h − hlz − hmz = 6 ft Cduz = 1.2Cd0s = 1.56 Drag coefficient for the sign: Cds = (AlCdlz + AmCdmz + AuCduz)/As = (bhlzCdlz + bhmzCdmz + bhuzCduz)/As = 1.47 Wind loads acting at the centroid of each subzone (using units of mph for V): Flz = 0.00256V2KzKdsGCdlzAl = 6,397 lbf Fmz = 0.00256V2KzKdsGCdmzAm = 6,141 lbf Fuz = 0.00256V2KzKdsGCduzAu = 9,212 lbf Total wind load acting on the sign: Fs = Flz + Fmz + Fuz = 21,750 lbf Using the current AASHTO specifications (Table 3.8.7-1 in LRFDLTS-1) Static sign: b/h = 2 CdsAASHTO = 1.19 FsAASHTO = 0.00256V2KzKdsGCdsAASHTOAs = 17,567 lbf Difference between the proposed and current specifications (Fs − FsAASHTO)/FsAASHTO = 24% Case 2: Wind is directed toward the back face of the sign Using the proposed methodology b/h = 2, h/(h + h0 + hg) = 0.43, As = bh = 450 ft2 Use Figure 3.1 to get Cd0s = 1.30 Heights and drag coefficients for different subzones (Figure B17): b/h > 1 hlz = hb − h0 = 5 ft h − hlz = 10 ft, hd + hbr = 4 ft, h − hlz > hd+hbr, so wind loads need to be estimated for three subzones: • Lower subzone hlz = hb − h0 = 5 ft Cdlz = 0.2Cd0s = 0.26 • Middle subzone hmz = hd + hbr = 4 ft Cdmz = 0.65Cd0s = 0.84 • Upper subzone huz = h − hlz − hmz = 6 ft Cduz = 1.2Cd0s = 1.56

B-56 Wind Drag Coefficients for Highway Signs and Support Structures Cds = (AlCdlz + AmCdmz + AuCduz)/As = (bhlzCdlz + bhmzCdmz + bhuzCduz)/As = 0.93 Wind loads acting at the centroid of each subzone (using units of mph for V): Flz = 0.00256V2KzKdsGCdlzAl = 1,279 lbf Fmz = 0.00256V2KzKdsGCdmzAm = 3,307 lbf Fuz = 0.00256V2KzKdsGCduzAu = 9,212 lbf Total wind load acting on the sign Fs = Flz + Fmz + Fuz = 13,798 lbf Drag coefficient for the sign:

Design Examples B-57 B7 COMPARISON BETWEEN WIND LOADS CALCULATED WITH PROPOSED METHODOLOGY AND THOSE BASED ON AASHTO LRFDLTS-1 SPECIFICATIONS Table B8 summarizes the wind loads acting on the static and dynamic message signs in the six design examples. The table contains the values calculated using the proposed methodology, Fs; the values based on the current AASHTO specifications, FsAASHTO; and the relative difference between these two predictions. For the design examples that pertain to structures supporting multiple signs, the total wind load acting on all of the signs is also compared. Notably, the large wind loads on DMS cabinets, estimated based on the current AASHTO specifications, are mostly attributable to the unrealistically high value used for Cd (1.7) in the AASHTO specifications. For thin signs, the proposed methodology generally predicts larger wind loads (e.g., by 19% to 40%) compared to those obtained using the drag coefficients for rectangular static signs given in the current AASHTO specifications. Table B8: Summary of wind loads acting on static and dynamic message signs calculated using proposed methodology, Fs (lbf), and those based on the AASHTO specifications, FsAASHTO (lbf) Note: Results are included for Design Example 1 through Design Example 6. Design Example Fs (lbf) FsAASHTO (lbf) (Fs − FsAASHTO)/FsAASHTO Example 1: dynamic message sign 11,338 13,384 −15% Example 1: static sign 3,850 2,810 37% Example 1: all signs 15,188 16,194 −6% Example 2: dynamic message sign 9,141 12,045 −24% Example 3: Static Sign 1 4,363 3,674 19% Example 3: Static Sign 2 4,363 3,674 19% Example 3: all signs 8,726 7,348 19% Example 4: Static Sign 1 13,039 10,865 20% Example 4: Static Sign 2 1,653 1,323 25% Example 4: all signs 14,692 12,188 21% Example 5: Static Sign 1 18,371 14,697 25% Example 5: Static Sign 2 5,669 4,251 33% Example 5: dynamic message sign 14,973 15,614 −4% Example 5: all signs 39,013 34,562 13% Example 6: static sign (Configuration 1) 24,517 17,567 40% Example 6: static sign (Configuration 2) 21,750 17,567 24% Table B9 presents a similar comparison of the wind forces predicted using the proposed methodology, Fs, and based on the current AASHTO specifications for the sign support structures considered in Design Example 1 to Design Example 5. Results are also compared for the monotube sign support structure in Design Example 1, Design Example 4, and Design Example 5. Results are compared separately for the chords and secondary members of the trusses considered in Design Example 2 and Design Example 3. Table B9 also compares the wind loads acting on the whole support structure considered in these two examples.

B-58 Wind Drag Coefficients for Highway Signs and Support Structures The values in Table B9 do not include those for wind load acting on the signs supported by the structure, which are given in Table B8. Relative differences of between −20% and −50% are observed between predictions of the total wind load acting on the whole support structure based on the proposed methodology and those based on the AASHTO specifications. Table B9: Summary of wind loads acting on the main elements of the sign support structure calculated using the proposed methodology, Fs (lbf), and those based on the AASHTO specifications, FsAASHTO (lbf) Note: Results are included for Design Example 1 through Design Example 5. Design Example Fs (lbf) FsAASHTO (lbf) (Fs − Fs AASHTO)/FsAASHTO Example 1: monotube 2,430 1,963 24% Example 2: chord H1 688 934 −26% Example 2: chord H2 618 934 −34% Example 2: chord H3 645 934 −31% Example 2: truss chords 1,951 2,802 −30% Example 2: secondary members of truss 1,370 3,501 −61% Example 2: support structure without sign 5,479 8,461 −35% Example 3: chord H1 261 290 −10% Example 3: chord H2 237 290 −18% Example 3: truss chords 847 580 46% Example 3: secondary members of truss 493 1,089 −55% Example 3: support structure without signs 1,518 1,912 −21% Example 4: monotube 3,621 3,070 18% Example 5: monotube 1,110 753 47%

Abbreviations and acronyms used without de nitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration GHSA Governors Highway Safety Association HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation

Transportation Research Board 500 Fifth Street, NW Washington, DC 20001 ADDRESS SERVICE REQUESTED ISBN 978-0-309-69825-2 9 7 8 0 3 0 9 6 9 8 2 5 2 9 0 0 0 0

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With increased traffic, multilane highways, and complex highway interchanges, highway signs play an ever more important role in the safe operation of the nation’s transportation network. A detailed understanding of stresses during the service life of sign support structures is crucial for their safe and economic design.

The TRB National Cooperative Highway Research Program's NCHRP Research Report 1012: Wind Drag Coefficients for Highway Signs and Support Structures develops comprehensive methods for estimating wind loads and the associated drag coefficients for highway signs and overhead support structures for inclusion in the AASHTO Load and Resistance Factor Design Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals.

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