Simulate Early, Simulate Often... In Rhino
NOTE: This is an engineering exercise looking at the FIU Bridge as an interesting application of Scan&Solve ONLY. We are not bridge designers. Theories presented here must be tempered by the limitations inherent in the geometric detail, material assumptions, and mathematical models being used.
On March 15, 2018, a bridge in Florida collapsed during construction killing 6 people with 9 people also injured. The bridge was designed to be 274 feet in length with a tower splitting the bridge into 175 and 99-foot sections. The bridge, being constructed for Florida International University, was built using a new technique in bridge design called Accelerated Bridge Construction (ABC). In this case, the main span and supports were first constructed before the main span was rotated from the staging zone to the supports over the roadway. This was meant to decrease the construction time and increase safety because the construction would not take place over the top of the roadway. Power lines also played a role in using the technique as they were present at one end of the bridge making it difficult to use cranes for the process . Shortly after the 175-foot section was positioned, it collapsed onto the roadway crushing both cars and people.
Figure 0: Rendered image of the planned FIU bridge
A key aspect in the design was the aesthetic features of the truss members and cables. The members were aligned to be colinear with their respective cables that were to be attached to the tower. This caused an asymmetrical arrangement of the trusses along the length of the bridge. The cables and tower were not a main support structure for the bridge since the main span was designed to meet the loading of its own weight and pedestrians without needing the cables. Their main purpose was to handle vibrations from the loads the bridge would experience from pedestrians and to provide a view in the skyline for residents around the bridge.
Materials and Design:
The 175-foot section of the bridge collapsed after it was positioned over the roadway and standing alone on the supports at both ends. We wish to test why the bridge collapsed, considering it was claimed to have been able to support its own weight once it was positioned. With a simulation, we will be able to look at where the structure is weak to find some critical areas. To do this, the bridge needs to be modeled to size and our material needs to be chosen. The bridge was made of mostly concrete with some steel reinforcement. Since plain concrete is much stronger under compression than tension, reinforcement steel is added to increase the overall strength and hold the concrete in compression. Although the density of the steel is greater than concrete, which increases the weight of the structure when it is added, the elastic modulus of the steel makes a much larger impact. This makes the structure stiffer overall and the bridge will experience a smaller deformation under loading despite being heavier.
Fairly high strength concrete without reinforcement was simulated along with 2.5% and 5% steel reinforcement by volume on the main span. For this simulation, it is estimated that the actual amount of steel is somewhere between those percentages. Custom materials were made in Scan&Solve Pro to replicate the reinforced materials <link to customizing materials>. Material properties for the reinforced concrete were calculated based on the volume fraction of steel to concrete along with their respective material properties.
Table 0: Material Properties Used
Since the company chose to make a bridge with uneven trusses, we also wish to test if creating a uniform structure would have been more advantageous. Considering that the main purpose of the bridge is not for it to be a landmark, but to allow people to walk over the road, it makes sense to design a stronger bridge at the expense of aesthetics if the structure requires it. These designs were modeled with the walkway and overhead of the bridge remaining the same. The truss members are at 45-degree angles and it is expected that the new arrangements will strengthen the bridge by decreasing the stresses in some of the members.
Figure 1: Designs of alternate bridges tested
Another setup to test is how the bridge reacted during the transportation process. The self-propelled modular transporters that moved the bridge into place were located under the bridge just like the permanent supports, except they were closer to the center of the structure. The images below show the permanent structure and the transporters where the bridge was supported during movement.
Figure 2: Entire design proposed not including the pylon and cables
Figure 3: Photograph of the FIU bridge being positioned with self-propelled modular transporters
Scan&Solve Pro was used to run all the simulations using the bridge models created in Rhino 5. First, under the components section, the model that was desired to be simulated was selected. Then fairly high strength concrete or one of the custom materials added was chosen as the material of the structure. The restraints varied between the final position simulations and the transported case. When simulating the final case, each side of the walkway was selected and the restraints were edited to only be in the z direction. At only one end of the bridge, small edges were used to restrain it in the x and y directions so that the restraints act like a pin and a roller. The only load applied in the simulations was gravity because the bridge collapsed under its own weight. The same set up was used for the transportation simulations. Except this time restraints were moved from the outside surfaces to edges that were created in the position of the transporters.
Figure 4: Final bridge design with restraints and restraint editor showing the settings used
Figure 5: Restraints on the underside of the transported case design
The data in Table 1 follows a trend that we would expect. As the material contains more steel, we expect it to get stiffer while the maximum deflection should decrease. This occurred in all the designs tested even though a slight increase in the maximum principal tension and compression stress was generally observed as the percentage of steel increases. All the tensile stress values are of concern in that column because they are all larger than the tensile strength of fairly high strength concrete. This means that concrete alone will not be strong enough for the structure. It gets a little harder to directly judge the reliability of the reinforced concrete because the tensile strength is unknown. This will lead to us looking at the stress in each individual member along with the pre-tensions added to them.
Table 1: Overall Bridge Simulation with Designated Materials
The member numbers and pre-tensioning data in Table 3 correlate to the numbers given in the diagram shown below it. Although the concrete materials containing steel have pre-tension, the simulation gives us the results as if there was no pre-tension. The maximum principal tension and compression stress columns in Table 2 show these values. The positive numbers highlighted in red denote tension and the negative numbers in green show a member in compression. The pre-tension stresses can later be analyzed by comparing them with the stresses from the simulation.
Figure 6: Principal tensile/compression stress comparison among models with the given slider settings in lb/ft^2. From top to bottom: FIU Design, FIU Design Transported, Trusses at 45˚, Trusses at opposite 45˚
Figure 7: Deflection diagrams of the designs tested. From top to bottom: FIU Design, FIU Design Transported, Trusses at 45˚, Trusses at opposite 45˚
Table 2: Original FIU Bridge Design: Data of Each Member Without P.T. Considered
Member numbers are given in Figure 10 and the stress values for each member were found using the point marking tool in Scan&Solve Pro. This can be used after the simulation by going to the “View” tab and clicking on “Point” in the section labeled “Mark”. Points of interest on the model can now be clicked on to show the stress. This can also be verified by placing a small range on the legend to isolate a member from the structure and view the stress distribution in the truss. In this case, any stress above the maximum value is red and any value below the minimum is blue. Since tension is of more concern than compression, the value of -333.20KIPS/ft^2 was used as the critical value because it was the most positive value in the member.
Figure 8: Value displayed using the point tool and stress range colored on the individual member in lb/ft^2
A large part of the analysis is finding out where and why the bridge collapsed. Looking at the bridge from the view below, you can see the highlighted member, number 10, consistently contains the highest tensile stress through all the simulations conducted when the bridge is in its final position.
Figure 9: Full FIU bridge design
This is the same end of the bridge that appears to break first during the collapse. Even though this is the case, it might not actually contain as much tensile stress as the simulation indicates because the steel pre-tensioning helps hold the concrete in compression.
In the real bridge design, the designers defined the number of bars in each member and the pre-tension in each bar. As you can see in Table 3, members 3, 8, and 10, were all specified to have much larger total pre-tension forces on them than the other members in the truss. Designing it that way makes sense because those three also need to hold the largest tensile forces out of all the members. These along with the other pre-tensions all seem to do their job and keep the concrete in compression since these forces are larger than any of the forces felt from the tension loads in the simulation. This is noticed in Tables 4 and 5 where the maximum stresses with the pre-tension accounted for are all negative. This means that any tensile forces acting on the members are still less than the compressive force from the steel and that the material at these locations should still be safe.
Table 3: Pre-Tension in each truss member
Figure 10: P.T. loading designated to each member
Table 4: Analysis of each member in FIU 2.5 and 5% Steel: Transporting Bridge
Table 5: Analysis of each member in FIU 2.5 and 5% Steel: Final Position
In the simulations where the bridge is being moved into position, the bridge is supported toward the center of the structure more than when it is in its final position. Since this is the case, there is less deflection and smaller maximum principal stresses from tension and compression. This can also be seen in Table 1 where it is confirmed that smaller deflections and stresses take place relative to the final design. If the bridge is designed to stand in its final position, there should be no issues during transportation if the positioning process goes smoothly. Since there is a different support system here, it is possible that some structures are now in tension that are usually in compression when the bridge is in place. If this happens to a member with little reinforcement it could potentially cause a problem since the concrete is so much weaker in tension than compression. This happens in both members 2 and 11 during the simulation of the process where the bridge is moved. The only difference between the two is that number 2 was given enough pre-tension to effectively keep it in compression where member 11 was not given any. Even though this happens, the tensile strength of the non-reinforced concrete is still larger than the stress seen in the member. This means that the bridge appears strong enough when looking at the individual members for both the transported and final reinforcement cases.
We also wanted to analyze the more traditional truss layout structures with the members located at 45-degree angles. They are similar except for the fact that the first member on the left design goes upward whereas the one on the right starts downward. In Table 1, you can see that both designs behaved better than the final design because they both had smaller maximum stresses and deflections. It seems the final design could have been based off these initially and altered to satisfy the visual goal they had.
Since we previously saw that the pre-tensions were large enough to keep all the members in compression or under the tensile strength of concrete, it seems like it was reasonable for them to use the design they ultimately went with even though some strength was given up. All the simulations and analysis done point to the possibility of a mishap during the construction process. It was reported that at the same location where the bridge collapsed, work was being done to strengthen it. It was also stated that cracks had been found near the same edge of the structure which could explain some testing and strengthening that was being conducted. The cracks were specifically located at the bottom of truss element number 11. Ongoing investigations are focusing on the cracks even though the design engineer stated that they caused no safety concerns . The Miami Herald reported that support rods in numbers 2 and 11 were kept tight during the transportation process to support the ends of the bridge and were to be loosened once it was resting on the final supports where this tension was no longer needed. This directly correlates with the analysis of those members because the simulations showed they were in tension when the bridge was moving but only compression afterwards. They also reported that a possibility of the collapse is because number 11 shattered while the support rods were being tightened . In the analysis conducted, I used the pre-tension numbers given in the technical proposal of the design as seen in Figure 10. One surprising thing is that the rods were specified in member 2 but none were given for number 11 in the proposal despite the report claiming they were tightening rods in member 11. Although the simulations pointed to member 11 being safe without any rods, it seems like either reinforcement was not documented in the proposal or the plans changed somewhere down the line and it was added.
Since the bridge appears to fail near members 10 and 11, it is reasonable to conclude that the investigations are correct to analyze number 11 extensively considering the high number of concerns that arose. Having the reports claim that the bridge failed during the process of tightening the rods even though no rods were planned in the report, and adding the cracks into the equation, makes it believable that a mistake could have been made with either the design or the adjusting process. As investigations continue, everybody will have to wait to see what details emerge and if they can pin down the actual cause of the collapse.