A footbridge over a stretch of road on a college campus has a span of approximately 1216 inches and a mass of approximately 610 metric tons. It is a truss bridge, but as a first approximation it can be considered to have the cross section shown below and it is made of a combination of structural steel and concrete. All vibrational modes on the bridge have an approximate damping ratio of 0.05. A strange man jumped up and down on the bridge at three points, shown in the diagram, and accelerometers mounted at each location recorded the frequency spectra of the bridge. You have been tasked with the following: 1. Examine the frequency spectra of the bridge and determine the first three modal frequencies. 2. Construct a five degree of freedom lumped mass model of the bridge. A lumped mass model, as discussed in lecture, approximates a continuous system as a series of point masses connected by massless springs. 3. Calibrate your model to fit the spectral data collected on the bridge. The first three modal frequencies of a successfully calibrated model will be within 10% of the first three experimentally determined modal frequencies. a. Calibration can be achieved by tweaking material and section properties in the model and recomputing modal frequencies. Remember that the section dimensions are an approximation and that the effective material properties of the bridge lie somewhere between steel and concrete. b. Calibrating a model is often a tedious process and involves tweaking masses and stiffnesses to fit the model to the data. You may wish to use a Matlab script or Excel to speed up the process. 4. From the accelerometer data, it was determined that the strange man jumping up and down imparted a velocity of 0.0673 m/s to the middle point of the bridge. If all other locations on the bridge start from rest, plot the first 10 seconds of the position of the midpoint using your calibrated model. 5. Propose a minor modification to the bridge to alter the bridge's response to jumping at the midpoint. You may propose selectively stiffening certain parts of the bridge, you may propose the addition of further modal damping, or something else entirely. Explain the reasoning behind your choice. Plot the first 10 seconds of the position of the midpoint if your modification were to be implemented and compare the results for your improved design to the results for the original. Your submission should be in Homework format. Plots should be made on a computer and may be attached as separate image files. Also attach any Matlab scripts or Excel sheets used for this work. 12.16 A B -203"-| -405 608" Figure 1 - Bridge span with locations of each measurement K 6" 84" -170" Figure 2 - First approximation of bridge section dimensions A footbridge over a stretch of road on a college campus has a span of approximately 1216 inches and a mass of approximately 610 metric tons. It is a truss bridge, but as a first approximation it can be considered to have the cross section shown below and it is made of a combination of structural steel and concrete. All vibrational modes on the bridge have an approximate damping ratio of 0.05. A strange man jumped up and down on the bridge at three points, shown in the diagram, and accelerometers mounted at each location recorded the frequency spectra of the bridge. You have been tasked with the following: 1. Examine the frequency spectra of the bridge and determine the first three modal frequencies. 2. Construct a five degree of freedom lumped mass model of the bridge. A lumped mass model, as discussed in lecture, approximates a continuous system as a series of point masses connected by massless springs. 3. Calibrate your model to fit the spectral data collected on the bridge. The first three modal frequencies of a successfully calibrated model will be within 10% of the first three experimentally determined modal frequencies. a. Calibration can be achieved by tweaking material and section properties in the model and recomputing modal frequencies. Remember that the section dimensions are an approximation and that the effective material properties of the bridge lie somewhere between steel and concrete. b. Calibrating a model is often a tedious process and involves tweaking masses and stiffnesses to fit the model to the data. You may wish to use a Matlab script or Excel to speed up the process. 4. From the accelerometer data, it was determined that the strange man jumping up and down imparted a velocity of 0.0673 m/s to the middle point of the bridge. If all other locations on the bridge start from rest, plot the first 10 seconds of the position of the midpoint using your calibrated model. 5. Propose a minor modification to the bridge to alter the bridge's response to jumping at the midpoint. You may propose selectively stiffening certain parts of the bridge, you may propose the addition of further modal damping, or something else entirely. Explain the reasoning behind your choice. Plot the first 10 seconds of the position of the midpoint if your modification were to be implemented and compare the results for your improved design to the results for the original. Your submission should be in Homework format. Plots should be made on a computer and may be attached as separate image files. Also attach any Matlab scripts or Excel sheets used for this work. 12.16 A B -203"-| -405 608" Figure 1 - Bridge span with locations of each measurement K 6" 84" -170" Figure 2 - First approximation of bridge section dimensions
