Practical Worst-Case Collision Force: Q CT

The objective of developing pier protection guidelines is to minimize the chance of bridge collapse due to heavy-vehicle collisions with pier components. The most vulnerable type of pier components are generally pier columns. It is necessary to estimate the probable range and distribution of extreme event impact forces in heavy-vehicle impacts with pier components. Appendix D: Lateral Impact Loads on Pier Columns provides a discussion of the finite element modeling of tractor-trailer truck impacts with bridge columns as well as a comparison to the tractor-trailer rigid-pole tests conducted by Buth et al. [Buth 2011].

The force–time history in Figure 14 shows the origin of the 600-kip design load used in the eighth edition of the LRFD

Bridge Design Specifications. The engine impact with the rigid

pole created a peak force of just over 600 kips. The particular magnitude of this peak force is dependent on the filter strategy used in analyzing the data; the 10-ms average first peak was over 900 kips, and the 25-ms average was just over 600 kips. Buth et al. chose the 25-ms average acceleration as being

essentially equivalent to the quasi-static design load, and this was adopted in the eighth edition.

The results of the analyses described in Appendix D and summarized in Figure 14 show that the peak impact force is not a function of the total mass and speed of the vehicle but, rather, the impact is actually a series of loosely coupled impact events. The first major event is the collision of the essentially rigid engine block with the pier, followed by the crushing of the tractor cabin and eventually the impact with the front of the trailer. While the trailer load could potentially subject the pier to a large loading if it were massive and rigid, the first practical worst-case impact force (QCT) was found to

be directly related to the impact between the truck engine and the pier column. The engine is the first large essentially rigid mass that is encountered in a head-on impact, and it domi- nates the impact force–time history. In other words, the total kinetic energy of the vehicle is not predictive of the practical worst-case impact force (QCT).

The structural design of bridges and bridge piers is accom- plished primarily in the force domain, whereas collisions occur in the energy and momentum domains. It is necessary, there- fore, to transform the dynamic impact force–time response into an equivalent quasi-static load that can be used as a design criterion. An approach to estimating the peak impact load was developed by assuming that the early phases of the impact can be represented by two square wave impulses: one caused by the frame and body structures between the column and the front of the engine, and the second caused by the engine–column impact. The following simple equation provided good and slightly conservative predictions of the finite element analy- sis (FEA) impact force at impact velocities between 35 and 50 mph. i i i i i i 32.2 1000 32.2 1000 CT 1 Q W V T W V T d V e e f e =    + _ + _         φSU SC=

Value Superstructure Cross-Section Type

0.80-0.96 Continuous steel I-girder with non-compact negative bending sections [see Ghosn 2014, Appendix A, Table 1.3.6.1-1].

0.80-1.20 All other simple span and continuous I-girder bridges [see Ghosn 2014, Appendix A, Table 1.3.6.1-1]. 0.83-0.97 Simple span box-girder bridges ≤

≤

24 ft wide [see Ghosn 2014, Appendix A, Table 1.3.6.1-2]. 0.80-1.20 Simple span box-girder bridges >24 ft wide

[see Ghosn 2014, Appendix A, Table 1.3.6.1-2]. 0.80-1.20 Continuous box-girder bridges 24 ft wide

[see Ghosn 2014, Appendix A, Table 1.3.6.1-2].

0.80-1.20 Continuous steel box-girders w/non-compact negative bending sections [see Ghosn 2014, Appendix A, Table 1.3.6.1-2].

0.80-1.20 Continuous box-girder bridges with compact negative bending sections [see Ghosn 2014, Appendix A, Table 1.3.6.1-2].

0.80 Single-cell box-girder bridge [see Ghosn 2014, Appendix A, Table 1.3.6.1-3]. 1.00 Multicell box-girder bridge [see Ghosn 2014, Appendix A, Table 1.3.6.1-3].

Table 6. System factors for superstructure continuity (eSU SC) [adapted from Ghosn 2014].

where

We= effective weight of engine (lb),

Wf= effective weight of structure

in front of the engine (lb),

Te= period of the engine pulse (s),

d1= distance from front bumper to front of engine (ft),

V = impact velocity (ft/s), and

QCT= practical worst-case impact force (kips).

All of the variables in this equation for QCT are normal ran-

dom variables. Typical values based on the dimensions and masses of commonly used crash-test vehicles are shown to the right of the equation’s where list. The impact velocity in particular is expected to have an important effect on the dis- tribution of impact forces.

To determine the cumulative distribution of impact forces that are likely given that a heavy-vehicle impact occurs with a pier system component, this equation was used in a Monte Carlo simulation to generate data for a cumulative distribu- tion. In a Monte Carlo simulation, a random number is gen- erated and used to choose a particular value for each random variable according to the known statistical parameters of that distribution; for a normal distribution, the mean and the

Tractor Trailer Single-Unit Truck 4,500 1,965 3,000 1,310 0.0241 0.0241 1.146 2.210

standard deviation are sufficient. Monte Carlo simulations using 25,000 cases per category were performed for speeds of between 35 and 75 mph in 5 mph increments for each of the four functional classes to be used in the guidelines (i.e., rural Interstate, rural collector, urban Interstate, and urban collec- tor). The cumulative distributions created using these Monte Carlo simulations are shown in Figure 15 through Figure 18, which plot the nominal lateral resistance (RCPC) on the x-axis

and the probability of the impact force (QCT) exceeding the

nominal lateral resistance (RCPC) on the y-axis. For example,

the probability of exceeding a nominal lateral resistance (RCPC)

of 600-kip on a 55-mph rural Interstate is shown by Figure 15 to be 0.50, whereas the probability of exceeding a nominal lateral resistance (RCPC) of 600-kip on a 45-mph urban col-

lector is 0.0140, as shown in Figure 18.

Figure 15 through Figure 18 show several interesting features. First, as expected, for a nominal lateral resistance (RCPC), the probability of exceeding that force increases as

the posted speed limit (PSL) increases. Second, all four fig- ures have a unique “S” shape where the smaller nominal lateral resistances (RCPC) are primarily associated with the

lighter single-unit trucks, and the higher nominal lateral resistances (RCPC) are associated with heavier tractor-trailer

trucks. The nature of the “S” is controlled by the proportion of each type of truck on each functional class of roadway.

Figure 14. Force–time history for Test 429730-2 and finite element analysis (FEA) results indicating key impact events.

Figure 15. Cumulative distribution of expected impact force – rural Interstates/primaries.

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Figure 17. Cumulative distribution of expected impact force – urban Interstates/primaries.

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These figures indicate that large impact forces are primarily associated with tractor trailers, as expected. This is also con- firmed by Table 3 and Table 4, where all but two of the 24 real- world crashes found in the literature involved tractor trailers. Of the two non–tractor-trailer trucks, one was an intercity bus that did not cause the pier column to fail, and the other was a single-unit truck that caused the column to fail but did not cause the bridge to collapse. There were 16 cases where a truck caused the pier column to fail, and all but one was a tractor- trailer truck. Table 3 also lends support to the idea that the total weight of the truck is not determinative of pier column failure. While some cases did involve very heavy vehicles haul- ing heavy, rigid loads, at least one (e.g., Buth #19 [Buth 2010]) was an unloaded tractor-trailer that was still able to cause a pier column to fail.

Figure 15 through Figure 18 are shown in guideline form in Table 7. The user enters the table for the appropriate func- tional classification of the roadway of interest with nominal lateral load capacity of the column (RCPC) and reads over to

the column corresponding to the PSL of interest. The value tabulated is the probability that the impact force (QCT) will

exceed the nominal lateral load capacity of the column (RCPC).

In Table 7, the probability of exceeding the nominal lat- eral resistance increases in each row as the PSL increases, as expected. Similarly, the probability of exceeding the nominal lateral resistance decreases in each column as the nominal lat- eral resistance increases, which is also as expected. If the prob- ability of exceeding a nominal lateral resistance of 600 kips on a 65-mph roadway is examined in Table 7, the highest prob- ability of exceed the lateral resistance is 0.76 (rounded) on a rural primary route. Rural primary roadways have the high- est percentage of tractor trailers of the four functional class categories, and the long-distance movement of goods is one of the primary functions of rural primary routes. The prob- ability of exceeding 600 kips on a 65-mph rural collector is much less (i.e., 0.32 rounded) because there are fewer tractor- trailer trucks, and the weight distribution on those roads is not as heavy. Similarly, a pier located on a 65-mph urban primary highway would have a probability of 0.65 (rounded) of exceeding 600 kips, a little lower than the rural primary roads because the percentage of trucks is somewhat lower. Like the rural collectors, a bridge pier on a 65-mph urban collector would have a probability of exceeding 600 kips of only 0.22 (rounded) because the heavy-vehicle mix is domi- nated by smaller, lighter, single-unit trucks. In other words, the data summarized in Figure 15 through Figure 18 and Table 7 make intuitive sense. The most at-risk piers are those on high-speed rural Interstates, whereas those on low-speed urban collectors are at relatively low risk, all other character- istics being equal.