A highway overpass is supported by a two-bay rigid frame. In order to perform preliminary design of the members and foundation, we want to perform an approximate analysis. The foundations are idealized as fixed, but the geotechnical engineer estimates that the point of fixity (i.e., the depth where the column actually behaves as fixed) is several feet below the ground surface. The dead weight from the bridge can be approximated as a uniform distributed load.
a. Guess the direction of each of the reactions for each of the column bases.
b. List the assumptions you make in order to perform an approximate analysis of the frame.
c. Use approximate analysis to determine the peak positive and negative moments for the beam.
d. Use approximate analysis to find the reactions at the base of each column.
e. To demonstrate the effectiveness of approximate analysis, use structural analysis software to find the peak positive and negative moments for the beam. Also find the reactions at the base of each column. In order to provide better corrosion resistance and quicker strength gain, you anticipate that the design will be based on a concrete strength of 6000 psi; that results in an estimated modulus of elasticity, E, of 4400 ksi. A more experienced member of the team estimates that the beam will be 8 ft deep and 6 ft thick (A = 48 ft2, I = 256 ft4) and the columns will be 6 ft by 6 ft square (A = 36 ft2,1 = 108 ft4).
f. Submit a printout of the displaced shape. Identify at least three features that suggest the displaced shape is reasonable. Verify equilibrium of the computer aided analysis results. Submit a printout of the moment diagram for the beam. Identify at least three features that suggest the moment diagram is reasonable. i. Are the results of your computer aided analysis reasonable? Make a comprehensive argument to justify your answer. Comment on why your guess in part (a) was or was not close to the solution in part (d).
