Compare the results of Problem P13.20 (a) and (c) with Problem P13.21(a) and (c).
Computer Study—comparison of approximate analysis with an exact analysis.
(a) Use approximate analysis to compute the reactions and draw the moment diagrams for
column AB and girder BC of the frame in Figure P13.20, and draw the deflected shape.
Consider column bases are fixed. (b) Repeat the computations with pinned column bases at
A and D. (c) Compare the results with the exact analysis using a computer software.
Computer Study—comparison of approximate analysis with exact analysis.
Consider the structure in Figure P13.21. (a) Use approximate analysis to compute the
reactions and draw moment diagram for the column AB and draw the approximate deflected shape of the frame. (b) Determine truss bar forces. All truss joints are pinned. (c) Compare the results with the exact analysis using a computer software. Truss member properties are A
Comparison of pinned base frames for problems P13.20 and P13.21 generate the same
moment at joints B of 75 ft-k in both approximate and exact methods. Though the truss
appears to be a very different structural system with it’s depth and moment of inertia
significantly higher than the girder in P13.20 I truss = 3,600 and I girder = 1350, the analysis approach is the same. Both structures have same boundary conditions of pinned bases, and both are symmetric in geometric and material properties, the same assumption applied to both: lateral load is divided equally to the columns. Their analysis results are exactly the same because lateral load is distributed based on the flexural stiffnesses of the columns, not the girders or trusses.
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