Determination of Actual Derailment Loads on Transit Bridges (2025)
Chapter: 5 Impact Analysis on Detailed Bridge Deck
CHAPTER 5
Impact Analysis on Detailed Bridge Deck
The dynamic response of a bridge cannot always be simplified as an SDOF system, as modeled in Chapter 4. Additional modes may be excited, especially if impact locations other than those at midspan are considered. To verify this assumption, a more complicated analysis on a detailed bridge model is warranted.
5.1 Approach and Methodology
The approach of the impact analysis on the detailed bridge deck follows the same methodologies employed in Chapters 3 and 4 to study derailment impact loads in non-idealized bridge conditions. The results of the detailed bridge model can be compared to the findings in Chapter 4 to better assess the adequacy of the simplified methods. Two representative bridges with distinct dynamic properties were chosen for this study: a prestressed concrete bulb-tee girder bridge with a 120-ft span and a concrete post-tensioned U-girder with a 100-ft span. The selection of these bridges and their model development is discussed in Section 5.1.1.
Because the increased model size resulted in long computational run times, a subset of derailment cases analyzed in Chapters 3 and 4 were selected for simulation on the detailed bridge model. Findings from Chapter 4 indicated a small variance between the different derailment scenarios for each train. Therefore, only the baseline single rail break derailment scenario was considered. Six distinct analysis cases were conducted, consisting of three different impact locations and two different train vehicles, to capture a reasonable range of parameters across the two distinct bridges. Table 5 shows the matrix of analyses; for each bridge, an analysis under gravity alone was performed to determine the baseline displacements without any static train load or derailment impact load.
5.1.1 Bridge Modeling
Two bridges were selected for the impact analysis. The first bridge consists of six prestressed concrete bulb-tee BT54 girders supporting a double track with 120-ft spans. This bridge represents a common type of railway bridge construction. The second bridge is a concrete post-tensioned U-girder supporting a double track with 100-ft spans. This bridge represents a type of railway bridge construction that is becoming increasingly common and is distinct from bulb-tee girders with stiffer dynamic properties. Figure 22 shows a cross section of both bridges. These two bridges are examples of new bridge construction, thus ensuring their relevance to the goal of this research to establish derailment load criteria to be primarily used in the design of new transit bridges.
The finite element models for both bridges are shown in Figures 23 and 24. To reduce the mesh size, only a single span for each bridge is fully modeled. For the bulb-tee girder bridge,
Long Description.
The table lists five column headers: Bridge Model, Train Vehicle, Load, Impact Location, and Initial Condition of Train. The rows read, Bulb Tee Girder Bridge with train vehicle NA, load Gravity Only, impact location None, initial condition as No Train. Bulb Tee Girder Bridge with train vehicle N slash A, load Single Rail Break Derailment AW0 Load, impact location Midspan, and initial condition as Run train across the entire bridge span in the model to capture and assess the importance of secondary dynamic effects before derailment. Bulb Tee Girder Bridge with train vehicle NA, load Single Rail Break Derailment AW0 Load, impact location Midspan, and initial condition as the Start analysis just before the rail break location. Bulb Tee Girder Bridge with train vehicle NA, load Gravity with Operating Train Load, impact location Midspan, and initial condition as the same horizontal location as above but on opposite track without any rail break. Bulb Tee Girder Bridge with train vehicle Low Floor LRV, load Single Rail Break Derailment AW0 Load, impact location Quarter Span, and initial condition as start analysis just before rail break location. Bulb Tee Girder Bridge with train vehicle Low Floor LRV, load Gravity with Operating Train Load, impact location Quarter Span, and initial condition as the same horizontal location as above but on opposite track without any rail break. Bulb Tee Girder Bridge with train vehicle Low Floor LRV, load Single Rail Break Derailment AW0 Load, impact location at Pier, and initial condition as Start analysis just before rail break location. Bulb Tee Girder Bridge with train vehicle Low Floor LRV, load Gravity with Operating Train Load, impact location at Pier, and initial condition at Same horizontal location as above but on opposite track without rail break. Bulb Tee Girder Bridge with train vehicle Bi Level Commuter, load Gravity with Operating Train Load, impact location Midspan, and initial condition as Just before rail break location. Bulb Tee Girder Bridge with train vehicle Bi Level Commuter, load Single Rail Break Derailment AW0 Load, impact location Midspan, and initial condition as Same horizontal location as above but on opposite track without any rail break. U Girder Bridge with train vehicle NA, load Gravity Only, impact location None, and initial condition as No Train. U Girder Bridge with train vehicle NA, load Gravity with Operating Train Load, impact location Midspan, and initial condition as Start analysis just before rail break location. U Girder Bridge with train vehicle Low Floor LRV, load Single Rail Break Derailment AW0 Load, impact location Quarter Span, and initial condition as Start analysis just before rail break location. U Girder Bridge with train vehicle Low Floor LRV, load Gravity with Operating Train Load, impact location Quarter Span, and initial condition as the same horizontal location as above, but on opposite track without any rail break.
one full-span length at the abutment is modeled, and the model is terminated at the midpoint of the next span. For the U-girder bridge, an interior span was modeled, and the model is truncated at the midpoint of each adjacent span with symmetry boundary conditions at these midspan cutoff points. Given the configuration of the pier and abutment supports, soft layers of soil provide little vertical support (e.g., side friction and pile cap bearing at grade); therefore, only lateral boundary conditions are imposed along the length of the piles and caissons. The soil is assumed to provide sufficient confinement to the caissons and piles to prevent the piles and caissons from buckling. Vertical boundary conditions are applied to the bottom of the piles and caissons where they bear on rock.
On both bridges, the concrete plinths were modeled with full nodal connectivity with the deck. The rail is connected to the plinths in a manner resembling direct fixation fastening, with merged nodes at regular intervals along the edges of the rail base and frictional contact between the bottom of the rail and the concrete surface.
Long Description.
The illustration contains two labeled bridge cross sections. The left section includes six equally spaced beams supporting a deck with four rail tracks positioned above. Each track is labeled, and the deck includes emergency walkway zones and pedestrian fences on both sides. Dimensions are labeled along the base and sides. The right section shows a U girder profile with labeled girder walls and transverse drainage openings positioned between rail tracks. It includes dimensioned widths and heights of structural parts. Drainage openings are labeled as 300 over 150 millimeters and girder layout includes transverse ribs marked at specific intervals. Labels indicate section view B with scale noted as the ratio of 1 and 50.
Long Description.
The illustration displays a 3D model of a prestressed concrete bulb tee girder bridge and a section view labeled AA. The bridge deck includes multiple long girders arranged side by side, supported by a central column and a set of vertical elements at one end. The section view AA shows a cross section of the bridge, highlighting the arrangement of girders, support columns, and layered structural components. A 3D axis marker is placed at the bottom left of both views to show spatial orientation. The deck and supports are divided into rectangular segments, indicating a mesh or model layout. Each structural part is colored differently and separated.
Long Description.
The illustration displays a prestressed concrete U girder bridge model and its cross section labeled as view AA. The 3D model shows a bridge with two main U shaped girders supporting a deck containing multiple rail tracks. The bridge rests on vertical support columns. Several braces connect the girders across the span. The section view AA on the right shows the U shaped profile with rail tracks resting on the inner base, supported by mesh layers representing the structural composition. A 3D axis indicator is placed at the bottom of both views to indicate spatial orientation. Each component of the bridge is color coded and segmented for modeling clarity.
5.1.2 Derailment Scenarios
For the bulb-tee girder bridge, the derailment of both the low-floor LRV and the bi-level commuter car was simulated to capture two distinct train load distributions. The low-floor LRV was derailed at three different locations corresponding to impact at midspan, quarter span, and the pier. For the bi-level commuter car, the derailment occurred at the midspan impact location. The four analysis cases regarding the bulb-tee girder bridge are shown at the moment of impact in Figure 25. For all four derailment scenarios, the train stayed on the plinth and did not drop the additional height of the plinth onto the deck.
The same derailment simulations of the low-floor LRV with impact at midspan and quarter span were performed on the U-girder bridge, as shown in Figure 26, to compare the dynamic amplification across the two bridges.
5.1.3 Initial Conditions
The explicit transient nature of the analysis requires the bridge to be initialized under gravity before the derailment event occurs. For computational efficiency, global damping is prescribed to the structure at critical damping based on the natural frequency of the primary vertical mode
Long Description.
The illustration shows four simulation cases on a bulb tee girder bridge. The top case depicts a low floor LRV derailment at midspan with a front view of the train on the bridge. The second case shows a low floor LRV derailment at the quarter span, with a line pointing to a corresponding front view of the vehicle and bridge cross section. The third case presents a low floor LRV derailment near the pier, also linked to its front view section. The fourth case at the bottom shows a bi level commuter car derailment at midspan, with its front view showing a wider train body on the same bridge type. All bridge decks are supported by columns and are consistent in profile. Each derailment location is annotated, and the front views are shown in rectangular boxes to the right. A 3D axis marker appears at the bottom of each simulation view to show spatial orientation.
Long Description.
The illustration depicts two derailment simulations on a U girder bridge. The top section presents a low floor LRV derailment at midspan with the train centered between two support columns. The bottom section shows a low floor LRV derailment at the quarter span, with the train positioned closer to the right support. Arrows from both scenarios point to a common section view on the right, which displays a front cross section of the U girder bridge. The section includes the train on top, rail tracks, interior girder walls, and the girder base. Structural layers are highlighted in contrasting blocks, and a 3D axis indicator is included at the lower left corner of each scenario view to show orientation.
of the bridge. Critical damping is applied over the course of the first period and is gradually removed over the subsequent period, such that any vibrations due to initial gravity are damped out. After the bridge equilibrates under gravity with no kinetic energy, a horizontal velocity of 40 km/h is applied to the train (Figure 27).
5.1.4 Postprocessing
In Chapter 4, DAFs were determined as a ratio of the peak dynamic derailment impact force to the static operational train force. In the detailed bridge model, bridge displacement can be used
Long Description.
The illustration displays a 3 D schematic of a train on a bulb tee girder bridge with a labeled rail break location. The train travels at a speed of 40 kilometers per hour toward the midspan region of the bridge. A labeled arrow marks the approximate distance from the front of the train to the rail break based on previous analyses. The bridge includes structural support columns and multiple girders beneath the track. Below the main schematic is a section view of the track with the train, showing the rail, sleeper arrangement, and bridge support under the vehicle. Mesh elements divide the train and track components for modeling detail. A 3 D axis marker in the corner indicates spatial orientation.
as an equivalent measure of impact force. Note that in Chapter 4, the term impact force referred to the peak force in the bridge spring rather than the contact force between the bridge deck and the rail car wheels. Since the detailed bridge models use linear–elastic materials, the displacement of the bridge is proportional to the static equivalent impact force used in Chapter 4. This approach is also consistent with the AASHTO LRFD Guide. The peak total displacement is determined by extracting the maximum displacement on the bridge at the impact location. The total displacement includes the effects of bridgeʼs self-weight and the static weight of the train. To isolate the effects of the dynamic derailment impact load, corresponding analyses were performed to calculate bridge displacements at the impact location due to the self-weight of the bridge alone and the normal operation of the train. For the normal operation of the train, both a static case with the train positioned at the impact location and a dynamic case with the train moving across the bridge were run. The DAF for derailment impact is calculated using Equation 5.1:
|
(5.1) |
Long Description.
The equation reads: DAF equals total displacement with derailment minus total displacement with no derailment over total displacement with no derailment minus total displacement with bridge only.
Complex multi-degree-of-freedom systems, such as the bridge models analyzed in this research, respond dynamically at a range of frequencies. Therefore, different structural components may have different DAFs. Displacement at the point of impact was used to calculate DAF since bridge displacement correlates with the primary bridge design demands, such as bending moment.
5.2 Results
5.2.1 Bulb-Tee Girder Bridge
Results were presented for dynamic amplification at midspan, quarter span, and pier impaction locations on the bulb-tee girder bridge.
5.2.1.1 Impact at Midspan
The first analysis case was the single rail break derailment of the low-floor LRV impacting the bridge at the midspan of the bridge. First, the midspan deflection due to the self-weight of the bridge alone was determined with and without the train placed on the bridge with the front truck
wheelset centered at midspan using a quasi-static, damped gravity initialization analysis. The results are shown in Figure 28; the midspan deflection is 21.6 mm without any train load and 24.5 mm with a stationary train.
In addition, a simulation of the train moving across the bridge without derailment was performed. The initial position of the train was located just shy of the rail break. This simulation was performed over a duration of 2 s after gravity initialization. An initial longitudinal velocity of 40 km/h was applied to the train after gravity initialization. This simulation was performed to gauge the dynamic effects of the moving train (without derailment) so that they could be isolated from the dynamic effects of the derailment impact.
Derailment was then simulated in a similar manner. The derailment simulation was performed over a duration of 2 s after gravity initialization, with the train positioned just shy of the rail break (note that the same initial positioning was used in the previous simulation). Like the previous simulation, an initial longitudinal velocity of 40 km/h was applied to the train after gravity initialization. The midspan deflections from all four analyses (two quasi-static and two dynamic) are plotted in Figure 29.
The peak midspan deflection after derailment impact occurs 0.93 s after the start of the derailment and is 29.5 mm. At the same analysis time in the non-derailment simulation, the midspan deflection is 24.6 mm, meaning that the derailment impact results in an additional 4.9 mm of displacement. This value is nearly identical to the quasi-static analysis, with a stationary train placed at midspan. Using Equation 5.1, a derailment impact DAF of 160% was calculated from these results.
5.2.1.2 Full-Span Simulation
For the low-floor LRV, an additional analysis was performed, starting the train at the boundary of the bridge model before moving nearly 100 ft until it reached the rail break location and
Long Description.
The graph plots quasi static gravity loading results with midspan deflection in millimeters on the vertical axis from negative 35 to 0, and analysis time in seconds on the horizontal axis from 0.0 to 1.0. Two curves are plotted. The first curve, labeled self weight without train, starts at 0 and deflects to nearly negative 23 millimeters by 0.4 seconds, then levels off. The second curve, labeled, stationary train at midspan, begins similarly but drops further, reaching approximately negative 28 millimeters around 0.4 seconds before also stabilizing. The self weight curve remains consistently above the stationary train curve, showing reduced deflection without the train. Both curves flatten beyond 0.6 seconds, indicating equilibrium.
Long Description.
The graph plots midspan deflection in millimeters on the vertical axis from negative 35 to 0, and analysis time in seconds on the horizontal axis from 0.0 to 2.0. Four curves are plotted. The self weight without train curve is a horizontal dotted line at approximately negative 22 millimeters. The stationary train at midspan curve is a dashed line just below it, around negative 24 millimeters. The regular operational train curve follows a smooth path slightly above the derailment curve, representing normal load fluctuations. The derailment at midspan curve shows large dynamic deflection changes with oscillations starting after 0.7 seconds. The peak deflection from normal train load is around negative 25 millimeters, and the lowest deflection from dynamic derailment impact drops to negative 30 millimeters. Arrows highlight the differences between these two deflection levels. The graph illustrates the contrast between static, operational, and impact loading effects on the bridge.
impacting the plinth at midspan. The initial position of the train is located off the modeled portion of the bridge while the bridge initializes under gravity. An initial longitudinal velocity of 40 km/h is then applied to the train, which then travels to the rail break location and derails at midspan, as shown in Figure 30.
In Figure 31, the midspan deflection time history is plotted for the full-length simulation and compared to the original analysis, in which the train was initially located at the rail break position and immediately derailed. The peak midspan deflection and dynamic response are nearly
Long Description.
The graph plots midspan deflection in millimeters on the vertical axis from negative 35 to 0, and analysis time after gravity initialization in seconds on the horizontal axis from 0.0 to 5.0. Four curves are plotted: self weight without train, stationary train at midspan, derailment at midspan, and derailment at midspan for full span duration. The self weight without train is a horizontal dotted line near negative 22 millimeters. The stationary train at midspan is a dashed line around negative 25 millimeters. The immediate derailment at midspan curve starts at about negative 22 millimeters and begins to fluctuate after 3.5 seconds with several deflection peaks between negative 25 and negative 32 millimeters. The full-span derailment curve follows a similar trend with slightly deeper deflection between 4.0 and 5.0 seconds. Both derailment cases show oscillating behavior, contrasting with the steady lines of static load conditions.
identical in both cases (2% difference). After the peak response occurred, more divergence was observed between the responses of the two models.
Running a full-span simulation of the train approaching the rail break location changes the initial conditions of the dynamic impact that follows. This change does not significantly affect the peak dynamic impact displacement of the bridge, which is driven by the impulse load from the derailment impact. However, dynamic systems with multiple degrees of freedom are sensitive to even slight changes in initial conditions. Therefore, it is logical that some relatively minor divergence is observed in the displacement time histories after derailment impact. Since the research team is primarily interested in the peak dynamic displacement due to impact, the abbreviated analysis was determined to be adequate.
In addition to derailing an articulated low-floor LRV, the same single rail break derailment simulation was also performed with a bi-level commuter car. The truck model in the bi-level commuter car was simplified, with the axles, wheels, and truck frame all rigidized together as one part. Using Equation 5.1, a DAF of 251% was calculated for this derailment scenario.
5.2.1.3 Impact at Quarter Span
The same analysis with the low-floor LRV was repeated; however, the initial position of the train was moved such that the impact location is at the quarter span (i.e., 30 ft from the pier) to evaluate the effect of the impact location on dynamic amplification. Figure 32 shows the displacement time histories at quarter span, along with the corresponding static displacements with and without the train. The self-weight of the bridge alone produces a deflection at the
Long Description.
The graph plots quarter span deflection in millimeters on the vertical axis from negative 18 to 0, and analysis time after gravity initialization in seconds on the horizontal axis from 0.0 to 2.0. Four curves are shown: self weight without train, stationary train at quarter span, regular operational train, and derailment at quarter span. The self weight without train curve is a horizontal dotted line around negative 12 millimeters. The stationary train at quarter span is a dashed line near negative 13.5 millimeters. The regular operational train curve fluctuates slightly above and below the dashed line. The derailment at quarter span curve begins near the same point but dips sharply at 0.9 seconds to nearly negative 16.5 millimeters and oscillates afterward. Two labeled arrows mark deflection from normal operational load and dynamic derailment impact, showing the difference in response under both conditions.
quarter span of 12.3 mm and increases to 13.3 mm with regular operational train load. Derailment impact causes the girder to displace an additional 2.7 mm at the quarter span. Using Equation 5.1, a DAF of 254% was calculated for this derailment scenario, which is higher than the amplification for a midspan impact location.
5.2.1.4 Impact at Pier
The last impact location considered was at the pier of the bulb-tee girder bridge. Figure 33 shows the displacement time history at the deck above the pier for regular train operation and with derailment impact, along with a reference horizontal line for the static deflection due to the self-weight alone. Using Equation 5.1, a DAF of 161% was calculated for this derailment scenario. It should be noted that the DAF calculated based on displacement (i.e., with Equation 5.1) is more sensitive at the pier than at the midspan since the displacements are smaller. This comparison is discussed in more detail in Section 5.3.
5.2.2 U-Girder Bridge
For the U-girder bridge, a derailment analysis with the low-floor LRV was performed at midspan and impact locations.
5.2.2.1 Impact at Midspan
The deflection at midspan under the bridgeʼs self-weight alone is 8.4 mm and 9.8 mm under the regular operational train load. The derailment impact at midspan produces an additional 1.2 mm of deflection, equivalent to 91% DAF for the derailment impact, which is much smaller
Long Description.
The graph presents deflection at pier in millimeters on the vertical axis from negative 4 to 0, and analysis time after gravity initialization in seconds on the horizontal axis from 0.0 to 1.4. Three curves are shown: self weight without train as a horizontal dotted line between negative 2 and negative 2.5 millimeters, regular operational train as a slightly oscillating line below the dotted line, and derailment at the pier as a fluctuating curve with larger variations. The derailment curve dips sharply near 1.0 seconds to about negative 3.5 millimeters, then rises and continues to oscillate. Two labeled arrows mark deflection from normal train operational load and the lower deflection from dynamic derailment impact. The graph highlights the increase in deflection magnitude caused by derailment compared to regular operation.
than the corresponding DAF for the derailment impact at the midspan of the bulb-tee girder bridge. Displacement time histories at midspan are plotted in Figure 34.
5.2.2.2 Impact at Quarter Span
The derailment impact at quarter span produces a peak deflection of 8.5 mm, compared to 7.5 mm for normal operational train load. The deflection at the same location without any train load is 6.1 mm; therefore, the DAF for derailment impact in this scenario is 79%. Displacement time histories at quarter span are shown in Figure 35. It should be noted that amplification decreases at quarter span compared to midspan for the U-girder bridge, which contradicts the results found for the I-girder bridge. However, the research teamʼs modeling approach for impact at quarter span of the U-girder bridge differed from their approach for the bulb-tee girder bridge. For the bulb-tee bridge, the train traveled from the pier to the quarter span. When the front truck derailed and impacted, only the front truck was within the impacted bridge span; the other trucks were on the pier and the previous span. For the U-girder bridge, the train traveled from midspan to quarter span. When the front truck derailed and impacted, all three trucks landed on the impacted span. Therefore, the deflection of the U-girder bridge due to normal train operation (without impact) is relatively larger than the deflection that occurs when only one truck is on the span, which artificially reduces the DAF since deflection due to normal train operation (which is the denominator of DAF) includes the effects of two non-impacting trucks. If the increase in deflection at quarter span due to normal operation of the train with only the front truck on the span (i.e., a train traveling from pier to quarter span calculated based on the U-girder midspan analysis with no derailment) is used, then the DAF increases to 116%.
Long Description.
The graph presents midspan deflection in millimeters on the vertical axis from negative 12 to 0, and analysis time after gravity initialization in seconds on the horizontal axis from 0.0 to 2.0. Three curves are plotted: self weight without train as a horizontal dotted line near negative 8 millimeters, regular operational train as a slightly fluctuating line near the dotted line, and derailment at midspan as an oscillating line with larger variations. The derailment curve dips sharply around 1.25 seconds, reaching nearly negative 11 millimeters, then rises and continues with oscillations. Labeled arrows highlight deflection from normal train operational load and lower deflection from dynamic derailment impact. The comparison shows increased deflection from derailment relative to normal train loading.
Long Description.
The graph plots midspan deflection in millimeters on the vertical axis from negative 10 to 0, and analysis time after gravity initialization in seconds on the horizontal axis from 0.0 to 2.0. Three curves are displayed: self weight without train as a horizontal dotted line around negative 6 millimeters, regular operational train as a slightly fluctuating line below the dotted line, and derailment at quarter span as an oscillating curve with deeper variations. The derailment curve dips sharply around 1.25 seconds to below negative 8 millimeters before rising again. Two labeled arrows mark deflection from normal train operational load and deflection from dynamic derailment impact. The graph highlights the additional deflection caused by derailment compared to regular train loading at the quarter span of a U girder bridge.
5.3 Discussion
Table 6 summarizes the results of the six analysis cases. The table shows that DAF values vary from as little as 91% to as much as 254%. This is a wider range of DAF values than what was found in the simplified analyses of trains impacting a simple SDOF representation of a bridge. In Chapter 4, DAF values for AW0 low-floor LRV trains only ranged from 119% to 140% for different derailment scenarios. Furthermore, when the stiffness of the SDOF bridge was increased so that the frequency would increase from 2.0 Hz to 3.0 Hz, the DAF increased from 126% to 163%. This result showed that an increase in the stiffness of the impacted structure had a greater effect on dynamic amplification than the type of derailment. The results of the impact analysis on the detailed bridge deck in this chapter are consistent with this finding in that they show that the dynamic properties (e.g., mass and stiffness) of the impacted structure significantly affect dynamic amplification.
The results of the impact analyses in the previous and current chapters also indicate that the dynamic properties of the rail car are important. The results from Chapter 4 showed that increasing the mass of the rail car by increasing the passenger load from AW0 to AW4 produced a higher DAF. The lighter low-floor LRV with more flexible suspension had a DAF of 160% for midspan impact on the bulb-tee girder bridge, while the heavier bi-level commuter car with stiffer suspension had a significantly higher DAF of 254%. The results also show that the impacts on the U-girder bridge have significantly lower DAF values than the corresponding impacts on the bulb-tee girder bridge. The U-girder bridge is stiffer than the bulb-tee bridge and has a higher frequency. Therefore, the research team was inclined to expect that the U-girder bridge would have higher DAF values based on the results of Chapter 4. However, the U-girder bridge is also heavier than the bulb-tee girder bridge, and increased bridge weight tends to reduce DAF.
As mentioned in Section 5.2.1.4, the DAF calculated based on displacement (Equation 2) varies more when displacements are small, such as at the pier. When DAF is calculated based on axial force in the pier, the DAF increases from 161% to 225%. This variation in DAF based on structural components and impact location is considered in the probabilistic evaluation of DAF in Section 6.5.
The findings from this chapter are summarized here:
- The dynamic properties of the impacted structure have a more significant effect on dynamic amplification than the derailment scenario.
- The dynamic properties of the train also significantly affect dynamic amplification.
- Running an abbreviated derailment simulation (with the train initially located adjacent to the rail break) does not significantly affect the peak dynamic impact displacement of the bridge when compared to a full-span simulation of the train approaching the rail break location.
(1)Value used in numerator of Equation 5.1, as described in Section 5.1.4.
(2)Value used in denominator of Equation 5.1, as described in Section 5.1.4.
Long Description.
The table includes five column headers: Bridge, Train Vehicle, Impact Location, Total Deflection in millimeters, and Derailment Dynamic Amplification. Under Total Deflection, three subscript-columns are listed: Bridge only, With Moving Train no Derailment, and With Derailment. For the bulb tee girder with low floor LRV, midspan deflection is negative 21.58 for bridge only, negative 24.64 with train, and negative 29.53 with derailment, with amplification of 160 percent. Quarter span values are negative 12.25, negative 13.32, and negative 16.05, with 254 percent amplification. Pier values are negative 2.25, negative 2.71, and negative 3.44, with 161 percent amplification. For the bulb tee girder with bi level commuter at midspan, deflection values are negative 21.58, negative 24.13, and negative 30.56, with 251 percent amplification. For the U girder with low floor LRV at midspan, values are negative 8.35, negative 9.76, and negative 11.03, with 91 percent amplification. At quarter span, the values are negative 6.14, negative 7.45 and negative 7.04 from two different footnotes, and negative 8.49 with derailment, showing 116 percent amplification.
