## Capacity design of members against preemptive shear failure

5.6.4.1. Introduction

As already noted, a mechanism of force transfer dominated by shear does not provide energy Clause 5.2.3.3( I)

dissipation under cyclic loading. More importantly, once the shear reinforcement yields, the resistance degrades fast with cycling, leading to failure at relatively low deformations. So, this mechanism does not lend itself to ductile inelastic behaviour, and should be constrained in the elastic range. This is achieved by dimensioning concrete members in shear, not for their force demands from the analysis but for the maximum shear forces that may physically develop in them. This maximum value of the shear force is computed by expressing (through equilibrium) the shear force in terms of the bending moments at the nearest sections where plastic hinges may form and assuming that these bending moments are equal to the corresponding flexural capacities. As the bending moment in these sections cannot physically exceed the capacity in flexure, including the effect of strain hardening, the so-computed shear force is the maximum possible. Once dimensioned for this design force, a member will remain elastic in shear until and after the development of plastic hinges in the sections that affect the value of the shear force.

5.6.4.2. Capacity design shear force in beams and columns Clauses 5.4.2.3, The column of Fig. 5.4 may develop plastic hinges at the two end sections 1 and 2, unless at 5.5.2.2(3) one or both of these ends, plastic hinges develop first in the beams framing into the same joint as the end in question (as is normally the case in columns designed to fulfil equation (D4.23)). At the moment this happens the sum of column moments above and below the joint is equal to the total flexural capacity of the beam on opposite sides of that joint, XMRd b. It may be assumed that this sum is shared by the two column sections above and below the joint in proportion to their own flexural capacities. Then, the bending moment at the end section i (= 1, 2) of the column may be taken equal to the design value of the moment resistance of the column at that end, MRd ci, mutiplied by XMRd b/XMRd c, where EMR()i b refers to the sections of the beam on opposite sides of the joint at end i, and XMRd c to the sections of the column above and below the same joint. The sense of action of XMRd c on the joint is the same as that of MRd c„ while that of XMRd b is opposite. So, the design shear value of the column i is taken as

7Rd max V,

MRd cl min

1 ZMRd.b

+ MRd,c2min

In equation (D5.12) the factor 7Rd accounts for possible overstrength due to steel strain hardening, and is taken equal to 7Rd = 1.1 for columns of DCM and to 7Rd = 1.3 for those of DCH; ld is the clear length of the beam between the end sections. Clauses 5.4.2.2, The beam of Fig. 5.5 will develop plastic hinges at the two end sections 1 and 2, except in 5.5.2.1 (3) the rare case that at one or both of these ends, plastic hinges develop first in the column framing into the same joint as the end in question. With the same reasoning as for equation (D5.12), the design value of the maximum shear at a section* in the part of the beam closer to end i is taken as maxK,dW =

7Rd min

Rd,c

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