Design of Roadside Barrier Systems Placed on MSE Retaining Walls (2010)

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22 Pavements are often built on top of MSE walls. The most common scenario is the case of an MSE wall supporting the access embankment for an overpass. Because cars and trucks travel on top of the MSE wall, traffic barriers are required. In the case of a concrete pavement, these barriers are rigidly tied to the pavement to provide the resistance needed when an impact load is generated by an errant car or truck. In the case of an asphalt pavement, that resistance is not available and the barrier must resist the impact load on its own. In this case, a barrier–moment slab system is used (Figures 3.1 and 3.2) and the resistance is generated by the inertia force required to lift the moment slab. This chapter discusses only the barrier and moment slab design, not the MSE wall design. A barrier built on top of an MSE wall needs to be designed to satisfy three criteria during impact: (1) the barrier must have sufficient strength to con- tain the impacting vehicle, (2) the barrier must not overturn, and (3) the barrier must not slide away. This chapter addresses criteria 2 and 3 by defining the magnitude of the static and dynamic loads that can be resisted by a barrier attached to a moment slab. Both analytical and experimental approaches are used to better understand the behavior of the barrier– moment slab system. 3.1 Description of Barrier The barrier used in the stability study was a TxDOT T201 barrier with a height of 0.69 m (27 in.) above grade and designed for TL-3 use. Figure 3.2 shows the dimensions of the vertical barrier and coping system as designed by RECO. The strength capacity of this vertical barrier is 325.34 kN (73.14 kips) calculated by ultimate strength analysis. The pri- mary components of the barrier–moment slab system include a precast vertical barrier and coping section and a cast-in- place moment slab. The precast vertical barrier is 241 mm (9.5 in.) thick at the top. The cast-in-place concrete moment slab is 1.37 m (4.5 ft) wide measured from the back of the panel to the end of the moment slab. In the field, the moment slab is typically 6.1 m (20 ft) to 9.15 m (30 ft) long between joints. In this study, a smaller 3.05 m (10 ft) long moment slab and barrier section was used so that the desired movement could be imparted to the barrier without structural failure. The precast barrier unit was connected to the cast-in-place moment slab by 12 No. 6 bars. The reinforcing bars in the moment slab consist of 12 transverse No. 6 bars and 5 longi- tudinal No. 4 bars. The center of gravity (CG) of the barrier system including the precast barrier, cast-in-place moment slab, and the soil above the moment slab is located as shown on Figure 3.2. The rotation point used for the overturning analysis is at the toe of the coping as shown in Figure 3.2. A concrete pad was placed under the inside leg of the coping so that the point of rotation would be well defined. The outside leg of the coping was unsupported. The moment arm l is from the CG of the barrier to the rotation point. The point of load appli- cation is located near the top of the barrier. The moment arm h is from the point of application of the load to the point of rotation A. The moment slab was cast in place on a well-graded road base material with a significant amount of fines and particles as large as 50 mm (2 in.). This material was heavily compacted by a hydraulic plate tamper attached to the back of a backhoe. The dry density and water content of the soil in place were 18.6 kN/m3 (118.3 pcf) and 7.17%, respectively. 3.2 Static Analyses and Static Test The purpose of the static analyses and static test is to explain the behavior of the barrier under static loading and to determine the maximum static force that can be resisted by a barrier in a sliding failure mode and in an overturning failure mode. C H A P T E R 3 Barrier Stability Study

The static force (Fo) required to generate overturning of the barrier–moment slab assembly is: where l = moment arm of the weight of the system (0.369 m or 1.2 ft) h = moment arm of the force applied to the system [1.21 m (3.97 ft); see Figure 3.2]. It is assumed that the vertical barrier, moment slab, and overburden soil act as one system for the overturning analysis. The required static forces Fs and Fo are shown on Figure 3.3 as a function of the length of the barrier–moment slab system. For the 3.05 m (10 ft) length barrier system, the required static force is 46.96 kN (10.6 kips) for sliding and 20.9 kN (4.7 kips) for overturning. Therefore, overturning controls the stability of the barrier in this case. There could be some situations where the friction between the bottom of the barriers and the soil is low enough that sliding occurs. As such both criteria should be checked. 3.2.2 Quasi-static Finite Element Analysis To further study of the static response of the barrier– moment slab system, a finite element model of the 3.05 m (10 ft) long barrier–moment slab system was developed (Fig- ure 3.4) for use in LS-DYNA. LS-DYNA (20) is a general- purpose, nonlinear, explicit finite element code used to analyze the nonlinear dynamic response of three-dimensional struc- tures. The code was originally developed by John Hallquist at Lawrence Livermore National Laboratory and has since been enhanced by Livermore Software Technology Corporation. F W l ho = ( )3 2- 23 Rotation Point, A C.G. Load Figure 3.2. Details of the vertical barrier system. Figure 3.1. MSE retaining wall with a barrier. 3.2.1 Static Analytical Solution The static analysis for sliding and overturning is conducted using equilibrium equations. The static force (Fs) required to generate sliding is: where W = weight of the barrier, moment slab, and soil sys- tem (69.6 kN or 15.7 kips) tan φ = moment slab–soil friction coefficient φ = frictional angle of the soil For this analysis, it is assumed that the moment slab–soil interface is rough enough that the failure plane is in the soil. The equation for overturning equates the resisting moment and the moment causing overturning due to the applied force. F Ws = tan ( )φ 3 1-

responded to the block used in the static load test. The model was initialized to account for gravitational loading on the soil mass before the application of the static load. The barrier system failed by overturning, not by sliding. The result of the simulation is presented in Figure 3.5 as a load-displacement curve. The maximum load in the simula- tion is 35 kN (7.9 kips) while the static hand calculations gives 21.8 kN (4.9 kips). The difference is the soil resistance at the edges of the moment slab, which is accounted for in the simu- lation but not in the hand calculations. 3.2.3 Full-Scale Static Test on Barrier The purpose of the static load test was to verify the magni- tude of force on the barrier required to initiate movement of the barrier–moment slab system. The setup for the static load test of the barrier system is illustrated in Figures 3.6 and 3.7. A reaction post was anchored to an existing concrete apron. The load was applied to the top edge of the vertical concrete barrier by means of a hydraulic cylinder. The load was distrib- uted over a longitudinal barrier length of 1 m (3 ft) through the use of a steel spreader beam with a wood block applied to its face. An in-line load cell was used to measure the applied load. The load was applied in steps of 2.5 kN (500 lb), with each step lasting about 5 min. Displacement of the barrier, coping, and moment slab was recorded at the end of each load step using two dial gauges and a linear variable differential transformer (LVDT) displacement sensor (D1). The LVDT was positioned behind and along the centerline of the barrier near its top edge. A dial gauge was placed along the same centerline near the bot- tom edge of the coping (D2). These two displacement mea- surement devices were secured to a steel frame. When the lateral load applied to the top of the barrier reached 36 kN (8 kips), the 24 (a) (b) Figure 3.4. Quasi-static finite element model at (a) rest and (b) end of the time. Figure 3.3. Required static force to induce sliding or overturning. Over the past 10 years, LS-DYNA has been extensively used in the performance evaluation of roadside safety hardware. The vertical barrier, the moment slab, and the support pad at the bottom of the coping were represented by solid elements and defined as elastic materials (designated as MAT type 1 in LS-DYNA) with concrete material properties shown in Table 3.1. The soil was also represented by solid elements and defined as an elastic-plastic material (designated as MAT type 25 in LS-DYNA) with the properties shown in Table 3.1. Details of soil material model are presented in Chapter 5. The barrier stability model had a total of 34,274 solid elements. The interface between the soil and barrier was modeled using contacts to capture the interface force generated between the concrete structure and the soil. A wood block was used as a means of providing distribution of the applied controlled quasi-static loading definition. The size of the wood block cor-

soil began to crack along the edges of the moment slab. The load test was stopped at a load of 40 kN (9 kips). The force-displacement curves generated from the test data are shown in Figure 3.8. The load-deflection response of the barrier–moment slab system was linear up to a load of 22.3 kN (5 kips). This load corresponds quite well with the load capacity of this 3 m (10 ft) barrier system based on the static equilibrium analysis shown previously (Figure 3.3). Figure 3.8 indicates that the barrier had moved 1 mm (0.04 in.) at a load of 22.3 kN (5 kips). Upon further loading beyond 22.3 kN (5 kips), the displacement of the barrier increased in a more rapid, nonlinear manner. As shown in Figure 3.8, the final horizontal displacement at the top of the barrier (D1) was 18 mm (0.69 in.), while the displacement at the bottom of the coping (D2) was only 3 mm (0.114 in.). This indicates that the barrier–moment slab system experienced 25 Figure 3.5. Comparison of static test and finite element static model. Material Model E (psi) (lb/in3) Concrete Vertical barrier, moment slab, and concrete pad 3.62E+6 0.17 0.084 Soil Overburden soil and support soil 0.00288 0.35 0.076 E is Young’s modulus, is Poisson’s ratio, and is the mass density. Table 3.1. Material properties of vertical barrier, moment slab, and soil. (a) (b) Figure 3.6. Static test at (a) beginning of test and (b) end of test (note crack).

26 (a) (b) Figure 3.8. Results of static test of (a) D1 and (b) D2. HYDRAULIC RAM W24x42 SPREADER BAR LOAD CELL 27 1/2" 6'-6 3/4" 47 1/4" 3" 5" LVDT (D1) Dial Gauge (D2) Finished Grade Accelerometer Unreinforced concrete apron Figure 3.7. Static test installation. mostly a rotation failure with some sliding. At the time the load test was stopped, the shear strength of the soil had been exceeded and the load-deflection curve was nearly asymptotic. Figure 3.5 shows the load test results compared to the numer- ical simulation. This comparison indicates that the static resis- tance is made of two components: the component due to the weight of the moment slab and overburden soil, and the component due to the friction between the moment slab– overburden soil and the surrounding soil. Back-calculations indicate that the average shear strength of the concrete–soil interface at that shallow depth was 6.3 kPa or 126 psf. The results confirm that overturning is the likely mode of failure since slid- ing develops more resistance. This comparison also gives cred- ibility to the numerical simulation. 3.3 Dynamic Analyses and Dynamic Test The purpose of these dynamic analyses is to explain, theo- retically, the behavior of the barrier during impact and the results of the full-scale impact test. The purpose of the full-scale impact test is to verify the theoretical results and collect data at full scale. 3.3.1 Full-Scale Dynamic Test (Bogie Test) on Barrier Upon completion of the static load test, the soil on and around the moment slab was recompacted for a dynamic bogie impact. Two accelerometers were mounted to the bar-

27 (a) before test (b) after 13 mph test (c) after 18 mph test Figure 3.9. Bogie test photo. rier system to help analyze its dynamic behavior: one behind and along the centerline of the barrier at the height of impact oriented to measure longitudinal acceleration, and one on the end of the moment slab oriented to measure vertical acceler- ation. Additionally, the bogie vehicle was instrumented with an accelerometer. In the first test, the 2,268 kg (5,000 lb) bogie vehicle [Fig- ure 3.9(a)] impacted the center of the vertical barrier head-on at a speed of approximately 20.9 km/h (13 mph). The barrier system after impact is shown in Figure 3.9(b). The targets affixed to the end of the vertical barrier section were used as ref- erence points to determine angular and translational displace- ment of the barrier from high-speed video. From the film analysis, the maximum dynamic displacement of the barrier was 200 mm (4.9 in.) at the top and 69 mm (2.7 in.) at the ground level [Figure 3.10(a)]. The maximum dynamic rota- tion angle of the barrier–coping section was 4.8 degrees. In addition to the rotation, the barrier also experienced approx- imately 25 mm (1 in.) of sliding. After the bogie impact, the barrier rebounded slightly and came to rest with a permanent displacement of 61 mm (2.4 in.) at the top and 36 mm (1.4 in.) at the ground level, with a rotation angle of 3.5 degrees. Data obtained from the bogie-mounted accelerometer were analyzed and the results are presented in Figure 3.11. The accel- eration history was treated using a 50-millisecond (ms) mov- ing average (which is typically the duration selected for design) and then an SAE 60 Hz filter (which is used to reduce the noise in the data). As shown in Figure 3.11(b), the maximum decel- eration was 8.5 g.Based on this acceleration and the mass of the bogie, the maximum impact force was calculated to be 189 kN

28 (a) (b) (c) (d) Figure 3.11. (a) Force, (b) acceleration, (c) velocity, and (d) displacement of bogie of the 13 mph dynamic test. (a) (b) A C B A C B Figure 3.10. Horizontal displacement of barrier measured from the film of the (a) 13 mph and (b) 18 mph impact test.

(42.5 kips) [Figure 3.11(a)]. The velocity–time and horizontal displacement–time histories of the bogie are shown in Fig- ure 3.11(c) and (d), respectively. The maximum acceleration of the barrier, as measured by the accelerometer at the top of the barrier, was 2.8 g in the impact direction [Figure 3.12(a)]. The velocity–time history of the barrier, as calculated by inte- gration of the acceleration data, is shown in Figure 3.12(b). Fig- ure 3.12(c) presents the horizontal displacement–time history of the barrier as determined by double integration of the accel- eration data and through analysis of high-speed film. The maximum acceleration of the moment slab, as mea- sured by the accelerometer on the end of the moment slab (Figure 3.13),was 2.2 g in the vertical direction [Figure 3.13(a)]. The velocity–time history and vertical displacement–time history of the end of the moment slab, as calculated by inte- gration of the acceleration data, is shown in Figure 3.13(b) and (c), respectively. The maximum vertical displacement of the moment slab at its free edge was computed to be 91.4 mm (3.6 in.). After recompacting the soil on and around the moment slab, a second full-scale impact test was performed at a higher velocity of 28.97 km/h (18 mph). The barrier system after impact is shown in Figure 3.9(c). From the film analysis, the maximum dynamic displacement of the barrier was 198.4 mm (7.81 in.) at the top of the barrier and 104 mm (4.09 in.) at the groundline. The maximum dynamic rotation angle of the barrier–coping section was 7.84 degrees. The displacement at the bottom of the coping was computed to be less than 7.6 mm (0.3 in.) [Figure 3.10(b)]. This displacement indicates that sliding did not occur. The acceleration history was treated using the same manner as with the 13 mph test. The maxi- mum deceleration was 10.9 g as shown in Figure 3.14(b). Using the acceleration and mass of the bogie impact vehicle, the maximum impact force was calculated to be 240.65 kN (54.1 kips) (Figure 3.14). The maximum 50 msec average acceleration of the barrier, as measured by the accelerometer at the top of the barrier, was 2.5 g in the direction of impact [see Figure 3.15(a)]. The 29 (a) (b) (c) Figure 3.12. (a) Acceleration, (b) velocity, and (c) displacement of barrier of 13 mph dynamic test.

displacement–time history obtained from double integration of the acceleration history looked suspect and was thought to be in error. Therefore, high-speed film was used to determine the displacement–time history of the barrier shown in Fig- ure 3.15(b). The maximum acceleration of the moment slab, as mea- sured by the accelerometer on the end of the moment slab (Fig- ure 3.16), was 3.9 g in the vertical direction. The acceleration data was lost at some time during test; therefore, the maximum displacement of the moment slab could not be determined. Figure 3.17 shows the comparison of the load-displacement curves for the static test and the dynamic tests. As can be seen, the ratio between peak dynamic force and the peak static force is 4.5 for the 20.9 km/h (13 mph) impact test and 5.4 for the 28.97 km/h (18 mph) impact test. After the second dynamic bogie impact test, the overburden soil was removed to permit inspection of the moment slab and the connection between the coping and moment slab. Prior to impact [see Figure 3.18(a)], no cracking was evi- dent in the barrier, coping, or moment slab. After impact, thin cracks were observed in the coping and moment slab on each side of the test specimen as shown in Figure 3.18. A red marker was used to highlight the cracks to assist with documentation. Cracking observed on the top surface of the moment slab is shown in Figure 3.19. These cracks coincide with the location of reinforcing bars connecting the coping to the moment slab. The cracks in the center of the moment slab (directly beneath the point of impact on the barrier) are longer and more pronounced than those toward the ends of the moment slab. The close-up view shown in Figure 3.19(d) illustrates the transverse cracks over the reinforcing bars as well as a longitudinal crack along the cold joint between the coping and moment slab. Again, a red marker was used to highlight the cracks to assist with visualization and documentation. 30 (a) (b) (c) Figure 3.13. (a) Acceleration, (b) velocity, and (c) displacement of moment slab of the 13 mph dynamic test.

31 (a) (b) (c) (d) Figure 3.14. (a) Force, (b) acceleration, (c) velocity, and (d) displacement of bogie of the 18 mph dynamic test. (a) (b) Figure 3.15. (a) Acceleration and (b) displacement of barrier of 18 mph dynamic test.

The trace of this force as a function of time was simplified to a triangular shape as shown in Figure 3.20(a). The friction force is equal to the coefficient of friction tan φ, where φ is the fric- tion angle of the soil–moment slab interface, multiplied by the total weight (W) of the barrier. The weight of the barrier sys- tem as shown in Figure 3.2 is 69.6 kN (15.65 kips). The friction angle of the soil was taken as 35 degrees. The mass of the bar- rier system is 7,096 kg (486 slug or 15,640 lb mass). Knowing the impact force, the friction force, and the mass of the barrier system, the acceleration of the barrier can be found using Equation 3-4. The result is shown in Figure 3.20(b). The veloc- ity history as a function of time was obtained by integration of the acceleration–time history curve [Figure 3.20(c)]. Similarly, the displacement history as a function of time was obtained by double integration of the acceleration–time history curve [Fig- ure 3.20(d)]. Overturning The fundamental equation for the rotation of the barrier (21) is: where ΣMA is the sum of the external moments around point A applied to the barrier, which has a mass moment of inertia (IA) around the point of rotation and an angular acceleration (α). The external moments are the moment due to the impact force and the moment due to the weight of the barrier (Fig- ure 3.2) which gives: As mentioned before, the impact force [Figure 3.20(a)] and the weight of the barrier are known. The moment arms h F h W l IAimpact -×( )− ×( ) = α ( )3 6 M IA A=∑ α ( )3 5- 32 (a) (b) Figure 3.16. (a) Acceleration and (b) displacement of moment slab of the 18 mph dynamic test. Figure 3.17. Comparison of static and dynamic overturning tests. 3.3.2 Dynamic Analytical Simple Solution Sliding The fundamental equation of motion is: where ΣFx = sum of the external forces applied to the mass (m) a = acceleration of the mass. In the horizontal direction, the external forces consist of the impact force at the top of the barrier (Fimpact) and the friction force (Ffriction) at the bottom of the barrier. The impact force is obtained from the product of the mass of the bogie times the acceleration of the bogie [Figure 3.11(a)]. F F maimpact friction -− =  ( )3 4 F max =∑  ( )3 3-

and l are known (Figure 3.2) and assumed to be constant in a first analysis. The mass moment of inertia around the center of gravity can be expressed as where the mi values are the mass components of the barrier and the xi and yi values are the distances in the x and y directions from the individual centers of gravity of the mass components I m x yCG i i i= +( )∑1 12 2 2 mi and the CG of the entire barrier. To obtain the mass moment of inertia (IA) with respect to an axis going through A different from the CG, one can use IA = ICG + m(x–2 + y–2) where the term x–2 + y–2 represents the square of the distance from the rotation point A to the CG. The mass moment of inertia (IA) was found to be 4,691 kg-m2 (3,460 slug ft2). Know- ing the impact force, the weight, the moment arms, and the 33 (a) before test (b) after test Figure 3.18. Cracking of coping and moment slab after 18 mph impact.

mass moment of inertia, one can obtain the angular accelera- tion (α) by using Equation 3-6. The linear acceleration at the point of impact is obtained by [Figure 3.21(b)]: Then the velocity history as a function of time at the same point [Figure 3.21(c)] was obtained by integration of the acceleration–time history curve. Similarly, the displacement history as a function of time was obtained by double integration of the acceleration–time history curve [Figure 3.21(d)]. Dynamic Analytical Advanced Solution This solution addresses only the overturning case because it is the controlling case. Indeed the sliding requires a higher impact force to occur as shown in the previous static and dynamic analytical solutions. When the barrier rotates around A, the moment arms h and l are not constant as assumed in the first analysis. They can be expressed as:  a ht t( ) ( )= ×α ( )3 7- where t is the time elapsed after impact and θ(t) is the rotation angle. The moment arms vary as shown in Figure 3.22(a) and (b). Because the moment arms vary with time, it is necessary to calculate the acceleration, velocity, and displacement in time steps. The results are shown on Figure 3.21. Also shown on Fig- ure 3.21 are the results obtained when assuming that the moment arms do not vary in time. As can be seen there is not much difference in the results. 3.3.3 Dynamic Finite Element Analysis A finite element analysis using LS-DYNA was performed to simulate the dynamic impact behavior of the 3.05 m (10 ft) long vertical barrier–moment slab system. The results were used to further investigate the overturning behavior of the sys- tem when subjected to a dynamic impact load and to calibrate l lt t( ) ( )= ( )0 3 9cos ( )θ - h ht t( ) ( )= ( )0 3 8cos ( )θ - 34 (c) Left end of moment slab CL (a) Center of moment slab CL (b) Right end of moment slab CL (d) Closeup near center of moment slab C L Figure 3.19. Cracks observed on top of moment slab after 18 mph impact.

the model to improve the accuracy of subsequent predictive simulations used to design additional impact experiments. The system geometry and material properties used for the model were the same as those used in the quasi-static model. A 2,268 kg (5,000 lb) bogie was used to hit the barrier at a speed of 20.9 km/h (13 mph). Additionally, two accelerome- ters were incorporated into the finite element model to obtain accelerations of the barrier and moment slab for a compar- ison with the accelerations measured in the bogie tests (Section 3.3.1). The model was initialized to account for gravitational loading on the soil mass before the dynamic bogie impact. Fig- ure 3.23 shows images from the 20.9 km/h (13 mph) dynamic bogie impact simulation. The deceleration of the bogie during impact as calculated by the finite element analysis is compared to the measured decel- eration of the bogie in Figure 3.11(b). The comparison is rea- sonably good. The acceleration of the top of the barrier during the impact as calculated by the finite element analysis is com- pared to the measured acceleration at the top of the barrier in Figure 3.12(a). The comparison is also reasonably good. The horizontal displacement at the top of the barrier is compared to the measured displacement of the barrier obtained by high- speed film analysis in Figure 3.12(c). The curves deviate from one another at approximately 0.07 sec. The reason is that, in the test, the soil fills the gap behind the moment slab and pre- vents the slab from returning to its initial position. This phe- nomenon is not captured in the finite element analysis. The acceleration of the end of the moment slab during the impact as calculated by the finite element analysis is compared to the measured acceleration of the moment slab in Figure 3.13(a). The comparison is also reasonably good. 3.4 Conclusions The following conclusions are based on and limited to the content of this chapter. 1. The design impact loads for traffic barriers have evolved over the last 50 years. There are two primary values in case: 44.5 kN (10 kips) and 240 kN (54 kips). The 44.5 kN (10 kips) is an equivalent static load typically used in con- junction with an elastic analysis while the 240 kN (54 kips) 35 (a) (b) (c) (d) Figure 3.20. Analytical solution for sliding: (a) force, (b) acceleration, (c) velocity, and (d) displacement.

36 (a) (b) Figure 3.22. Variations of (a) h and (b) l. (a) (b) (c) (d) Figure 3.21. Comparison of analytical simple solution and advanced solution for overturning: (a) impact force, (b) acceleration, (c) velocity, and (d) displacement.

is a dynamic load and is used in conjunction with an ulti- mate strength analysis. It is not proper to use the 240 kN (54 kips) as an equivalent static load when designing a moment slab as the results are excessively conservative. 2. Current practice uses an ASD approach. The LRFD approach is not complete yet. 3. A set of static and dynamic analytical calculations represent- ing increasing levels of complexity are developed. One static load test and two impact tests were performed on a full-scale barrier. Comparison between the analytical results and the results of three full-scale barrier tests show good agreement. 4. In this project, overturning occurred before sliding. This was shown analytically and confirmed by the full-scale static and dynamic test results. However, both criteria should be checked. 5. There is a significant ratio between the static load and the dynamic load that the barrier can resist. For the 3.05 m (10 ft) barrier tested, the ultimate static load was 40.5 kN (9.1 kips). For the same barrier, the maximum dynamic load in a 20.9 km/h (13 mph) impact test was 189 kN (42.5 kips) for a dynamic to static ratio of 4.7. The maximum dynamic load in an 18 mph impact test was 240 kN (54 kips) for a dynamic to static ratio of 5.9. This ratio is due to the iner- tial resistance of the system. 6. These ratios use a static load and a dynamic load which do not correspond to the same amount of displacement. If a tolerable displacement of 25 mm (1 in.) is targeted, then the static load is still 40.5 kN (9.1 kips), but the dynamic load drops to 170 kN (38.2 kips) for the 13 mph impact test (dynamic to static ratio of 4.2) and to 210 kN (47.2 kips) for the 18 mph impact test (dynamic to static ratio of 5.2). 7. Since the static load resisted by the dead weight alone of the 3.05 m (10 ft) long barrier is 22.8 kN (5.1 kips) for a rota- tion point A, for a barrier to resist an equivalent static design load of 44.5 kN (10 kips) with a factor of safety of 1.5, it needs to be at least 9.15 m (30 ft) long. 37 (a) (b) Figure 3.23. Finite element model for overturning (a) at rest and (b) at impact.