Once the cross-section is fully plasticized, it can rotate with no additional moment applied.

**Plastic “Hinges”**

Once the cross-section
is fully plasticized, it can rotate with no additional moment applied. Thus for
a beam subjected to pure moment (with a constant moment diagram), the entire
beam plasticizes simultaneously and there is unrestrained plastic flow. In the
normal situation where the moment diagram varies, this is not the case.

Consider for example the EPS cantilever beams of
rectangular cross-section with a concentrated load, *P*, at its free end
shown in Figure 11.3a. Assume that the cross-section at the wall is on the
verge of full plastification

the* *stress distribution will be as shown in
Figure 11.3d where the elastic zone extends *y _{e}* from the
neutral axis. Therefore

. Since *M _{A}* is a known function of

As long as the elastic
core remains, plastic flow is constrained. However, when *P* increases
such that *PL = **M _{P}* ,
the cross-section becomes fully plastic and the curvature can increase without
limit but contained within the plas-tic zone. The beam rotates like a rigid
body about a “plastic hinge” holding the ultimate plastic moment

On the other hand, the effect of axial load *N*
combined with bending moment *M *in the plastic range is straightforward.
Suppose* N *and* M *combine to give the* *stress state at yield
shown in Figure 11.4b. The maximum stress in the bottom fiber is

as the elastic
interaction curve for yield shown in Figure 11.4d. When *N*_{1} is
zero, *M*_{1}* *=* M _{Y} *and similarly when

If we call *N _{u}* and

This interaction
relationship plotted in Figure 11.4d gives all combinations of *N* and *M*
for full plastification.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Civil : Principles of Solid Mechanics : One Dimensional Plasticity for Design : Plastic “Hinges” |

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