An elevated walkway will connect a pair of facilities on one side of a street to a single building on the other side. As a result, it was decided that the walkway will be wider at one end and narrower at the other. The resulting idealized dead load is trapezoidal. Our job is to determine the peak moment in the girder due to the dead load.
a. Guess the location of the peak moment.
b. Estimate the peak moment by replacing the linear distributed load by an equivalent uniform distributed load. Will this provide an upper bound, a lower bound, or just an approximation for the actual peak moment? Justify your answer.
c. Derive the equations for the shear and moment for the beam with the trapezoidal load.
d. Construct the shear and moment diagrams for the beam. Label values and locations.
e. Identify at least two features of the shear diagram that suggest you have a reasonable answer.
f. Identify at least two features of the moment diagram that suggest you have a reasonable answer.
g. Determine the peak moment due to the dead load and its location.
h. Make a comprehensive argument that the peak moment found in part (g) is reasonable.
i. Comment on why your guess in part (a) was or was not close to the solution in part (g).