Page 149 - Handbook of Civil Engineering Calculations, Second Edition

1.132 STRUCTURAL STEEL ENGINEERING AND DESIGN

These results may be combined and expressed verbally thus: If a point is displaced
along a virtual circular arc, its displacement as projected on the u axis equals the displace-
ment angle times the length of the radius as projected on an axis normal to u.

GABLE-FRAME ANALYSIS BY USING
THE MECHANISM METHOD
For the frame in Fig. 31a, assume that plastic hinges form at D and F. Calculate the plas-
tic moment associated with this assumed mode of failure by applying the mechanism
method.

Calculation Procedure:

1. Indicate the frame configuration following a virtual displacement
During collapse, the frame consists of three rigid bodies: ABD, DF, and GF. To evaluate
the external and internal work performed during a virtual displacement, it is necessary to
locate the instantaneous center of rotation of each body.
In Fig. 33 indicate by dash lines the configuration of the frame following a virtual dis-
placement. In Fig. 33, D is displaced to D
and F to F
. Draw a straight line through A and
D intersecting the prolongation of GF at H.

FIGURE 33. Virtual displacement of frame.