9y h 13 5C Mp [f f y y c c

FIGURE 2.103 Vertical load and horizontal force interaction curve for collapse analysis of gable frame.

FIGURE 2.103 Vertical load and horizontal force interaction curve for collapse analysis of gable frame.

Substituting values of C and f and simplifying, we have

The hinge rotations and displacements corresponding to this mechanism are shown in Figure 2.102d. The rotation of all hinges is 0. The horizontal load moves by 13.50 but the horizontal load has no vertical displacement. The work equation becomes

The interaction equations corresponding to the three mechanisms are plotted in Figure 2.103. By carrying out moment checks, it can be shown that mechanism 1 is valid for the portion AB of the curve, mechanism 2 for portion BC, and mechanism 3 is valid only when V = 0.

2.11.10 Analysis Aids for Gable Frames 2.11.10.1 Pin-Based Gable Frames

Figure 2.104a shows a pinned-end gable frame subjected to a uniform gravity load IwL and a horizontal load 11H at the column top. The collapse mechanism is shown in Figure 2.104b. The work equation is used to determine the plastic limit load. First, the instantaneous center of rotation, O, is determined by considering similar triangles:

From the horizontal displacement of D

hl hl

FIGURE 2.104 Pinned-base gable frame subjected to combined uniform distributed load and horizontal load.

0 0

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