8

FIGURE 2.105 Analysis chart for pinned-base gable frame.
FIGURE 2.106 Analysis chart for fixed-base gable frame.

evaluated and the corresponding value of Mp/(lwL2) can be read directly from the appropriate chart. The required value of Mp is obtained by multiplying the value of Mp/(lwL2) by AwL2.

2.11.11 Grillages

A grillage is a type of structure consisting of straight beams lying on the same plane, subjected to loads acting perpendicular to the plane. An example of such a structure is shown in Figure 2.107. The grillage consists of two equal simply supported beams of span length 2L and full plastic moment Mp. The two beams are connected rigidly at their centers where a concentrated load W is carried.

The collapse mechanism consists of four plastic hinges formed at the beams adjacent to the point load as shown in Figure 2.107. The work equation is

WL0 = 4Mp0

where the collapse load is

4Mp L

2.11.11.1 Six-Beam Grillage

A grillage consisting of six beams of span length 4L each and full plastic moment Mp is shown in Figure 2.108. A total load of 9W acts on the grillage, splitting into concentrated loads W at the nine nodes. Three collapse mechanisms are possible. Ignoring member twisting due to torsional forces, the work equations associated with the three collapse mechanisms are computed as follows:

Mechanism 1 (Figure 2.109a)

Work equation:

where

12 Mp 4Mr

0 0

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