To verify our understanding of a new structural analysis tool, we should use it to find a known solution. This helps ensure that we are applying the tool properly. To be sure that we understand how to...

To verify our understanding of a new structural analysis tool, we should use it to find a known solution. This helps ensure that we are applying the tool properly. To be sure that we understand how to apply the Double Integration Method, let's find the expressions for the slope and vertical displacement of a simply supported beam with a triangular distributed load. We can compare those expressions with information inside the front cover of this text.

a. Guess the location of the peak vertical displacement.

b. Derive the expressions for the shear and moment for the beam.

c. Derive the expressions for the slope and displacement.

d. Calculate the slope at both ends of the beam. Determine the location and value of the peak vertical displacement. Note: the peak is not at midspan. Compare those values with the values from inside the front cover of this text.

e. Comment on why your guess in part (a) was or was not close to the solution in part (d).