## Moment Redistribution

"I

w/unit length w/unit length

Load

Additional moments diagram (Hinges at A and C)

Collapse mechanism

Elastic BMD (Collapse loads) Final Collapse BMD

Load

Figure 3.28 Moment redistribution, one-span beam

Additional moments diagram (Hinges at A and C)

Collapse mechanism

Elastic BMD (Collapse loads) Final Collapse BMD

■I- :-; is the load to cause the first plastic hinge; thus the beam may carry a load of with redistribution.

m the design point of view, the elastic bending-moment diagram can be obtained la* required ultimate loading in the ordinary way. Some of these moments may then •. -.Juced; but this will necessitate increasing others to maintain the static equilibrium , structure. Usually it is the maximum support moments which are reduced, so • - - -niMtig in reinforcing steel and also reducing congestion at the columns. The : . - remenls for applying moment redistribution are;

Equilibrium between internal and external forces must be maintained, hence it is necessary lo recalculate the span bending moments and the shear forces for the load case involved.

2. The continuous beams or slabs are predominately subject to flexure.

3. The ratio of adjacent spans be in the range of 0.5 lo 2.

### 4. The column design moments must nol be reduced.

There are oilier restrictions on the amount of moment redistribution in order to ensure ductility of the beams or slabs. This entails limitations on the grade of reinforcing steel .ind of the areas of tensile reinforcement and hence the depth of the neutral axis as described in Chapter Four -'Analysis of the Section'._

EXAMPLE 3^9| Moment redistribution

In example 3.3, figure 3.13, it is required to reduce the maximum support moment of •Wra = 147 kN m as much as possible, but without increasing the span moment above the present maximum value of 118kNm.

Figure 3.29

Moments and shears after redistribution

Figure 3.29

Moments and shears after redistribution

(a) Original Moments (kN m) 140

108 Rn 102

(a) Original Moments (kN m) 140

108 Rn 102

(b) Redistributed Moments (kN m) 134

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