Civil Engineering Reference
In-Depth Information
The Collapse Mechanism
To understand moment redistribution in steel or reinforced concrete structures, it is neces-
sary first to consider the location and number of plastic hinges required to cause a struc-
ture to collapse. A statically determinate beam will fail if one plastic hinge develops. To
illustrate this fact, the simple beam of constant cross section loaded with a concentrated
load at midspan shown in Figure 14.6(a) is considered. Should the load be increased until
a plastic hinge is developed at the point of maximum moment (underneath the load in this
case), an unstable structure will have been created, as shown in Figure 14.6(b). Any fur-
ther increase in load will cause collapse.
The plastic theory is of little advantage for statically determinate beams and frames,
but it may be of decided advantage for statically indeterminate beams and frames. For a
statically indeterminate structure to fail, it is necessary for more than one plastic hinge to
form. The number of plastic hinges required for failure of statically indeterminate struc-
tures will be shown to vary from structure to structure, but may never be less than two.
The fixed-end beam of Figure 14.7 cannot fail unless the three plastic hinges shown in the
figure are developed.
Although a plastic hinge may be formed in a statically indeterminate structure, the
load can still be increased without causing failure if the geometry of the structure permits.
The plastic hinge will act like a real hinge insofar as increased loading is concerned. As
the load is increased, there is a redistribution of moment because the plastic hinge can re-
sist no more moment. As more plastic hinges are formed in the structure, there will even-
tually be a sufficient number of them to cause collapse.
The propped beam of Figure 14.8 is an example of a structure that will fail after two
plastic hinges develop. Three hinges are required for collapse, but there is a real hinge at the
right end. In this beam the largest elastic moment caused by the design-concentrated load is at
the fixed end. As the magnitude of the load is increased, a plastic hinge will form at that point.
The load may be further increased until the moment at some other point (here it will
be at the concentrated load) reaches the plastic moment. Additional load will cause the
Figure 14.6
