STEEL & CONCRETE STRUCTURES

Steel & Concrete Structures



Steel & Concrete Structures

Task 1

a)

Slabs with continuous drop panels between column lines facilitate formwork, make long spans possible in addition to increase punching shear resistance around supports and provide unobstructed spans with minimum structural floor depth resulting in lower floor-to-floor heights. The moment distribution in such slabs is different from that in conventional flat plates or slabs with drop panels systems. Dimensioning according to the current provisions in CSA A23.3-94 is problematic because the continuous drop panels are subject to moments exceeding the minimum values allowed by the Code for conventional slab systems.

b)

Moment redistribution is a term that describes the behavior of an indeterminate concrete member after first yielding occurs at some cross-section of the member. As applied load is increased on an indeterminate member, the response is initially elastic (deflections, moments, shears are linearly proportional to applied load and can be calculated by elastic indeterminate theory) up to the load where yielding first occurs in any cross-section. The applied load producing first yielding at any cross-section is called wJ" Incremental applied load w2 greater than Wj is assumed to produce inelastic rotation at the yielded section, but no change in applied moment. Since w 2 produces no incremental moment at the yielded cross-section, incremental moments resisting w 2 are developed at sections other than the initially yielded section. Thus after first yielding, moments are redistributed to other cross-sections of the member which are still elastic. As w2 increases, eventually other sections will yield and develop hinges. When enough hinges have developed in any span of the member to make it unstable (a mechanism rather than a flexural member), the member is considered to have failed. The load at which a mechanism forms in any span is called the "limit" load in that span.

The inelastic behavior of a continuous member depends on whether yielding first occurs in a negative moment region (at a support) or in the field of the member in the positive moment region. ACI 318 code requirements permit first yielding in either positive or negative moment regions, although this is not immediately obvious.

Moment redistribution is used in the design of continuous con-crete members by providing a flexural capacity (!JM" at the negative or positive moment regions of the member (or both) that is less than the moment at the same point calculated by elastic theory. The reduced moment capacities must be statically consistent with moments at other sections of the member under the same loading condition.

c)

To demonstrate the mechanics of moment redistribution, a twospan beam model on pinned supports will be used, since it is the simplest indeterminate member available that illustrates all of the necessary aspects of moment redistribution. In order to demonstrate the effects of "secondary moments" through the entire range of loading, the beam model will be assumed to contain both prestressed and non-prestressed reinforcement. Additional factors such as more spans, support width, support stiffness, etc., albeit realistic, add only mathematical complexity to this basic model without ...