Civil Engineering Reference
In-Depth Information
Figure 14.3
14.4
LIMIT DESIGN
It can be clearly shown that a statically indeterminate beam or frame normally will not
collapse when its ultimate moment capacity is reached at just one section. Instead, there is
a redistribution of the moments in the structure. Its behavior is rather similar to the case
where three men are walking along with a log on their shoulders and one of the men gets
tired and lowers his shoulder just a little. The result is a redistribution of loads to the other
men and thus changes in the shears and moments throughout the log.
It might be well at this point to attempt to distinguish between the terms
plastic de-
sign
as used in structural steel and
limit design
as used in reinforced concrete. In structural
steel, plastic design involves both (a) the increased resisting moment of a member after
the extreme fiber of the member is stressed to its yield point and (b) the redistribution or
change in the moment pattern in the member. (Load and resistance factor design [LRFD]
is a steel design method that incorporates much of the theory associated with plastic de-
sign.) In reinforced concrete the increase in resisting moment of a section after part of the
section has been stressed to its yield point has already been accounted for in the strength
design procedure. Therefore, limit design for reinforced concrete structures is concerned
only with the change in the moment pattern after the steel reinforcing at some cross sec-
tion is stressed to its yield point.
The basic assumption used for limit design of reinforced concrete structures and
for plastic design of steel structures is the ability of these materials to resist a so-called
yield moment while an appreciable increase in local curvature occurs. In effect, if one
section of a statically indeterminate member reaches this moment, it begins to yield
but does not fail. Rather, it acts like a hinge (called a
plastic hinge
) and throws the ex-
cess load off to sections of the members that have lesser stresses. The resulting behav-
ior is much like that of the log supported by three men when one man lowered his
shoulder.
