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# Punching shear

Punching shear arises when a concentrated load is applied to a small area of a slab or, most commonly, the reaction of a column against a slab. The resulting stresses are verified along defined control perimeters around the loaded area.

The shear force, V_{Ed} acts over an area *ud*_{eff}, where

*u *= the length of the perimeter. The basic perimeter, u_{1} is at 2d_{eff} from the column.

*d*_{eff }= the effective depth of the slab taken as the average of the effective depths in two orthogonal directions.

Design for punching shear should allow for the effects of moment transfer at the column/slab junction. For structures, the lateral stability of which do not rely on the frame action between the slab and columns and in which adjacent spans do not differ in length by more than 25%, the design punching shear may be obtained by enhancing V_{Ed} by 1.15 for internal columns, 1.4 for edge columns and 1.5 for corner columns.

At the column perimeter:

- Ensure that maximum punching shear stress is not exceeded, i.e.
*v*_{Ed}<*v*_{Rd,max}at the column perimeter - Determine whether punching shear reinforcement is required, i.e. whether
*v*_{Ed}>*v*_{Rd,c}at the basic perimeter, u_{1} - Determine whether punching shear reinforcement is required, i.e. whether
*v*_{Ed}>*v*_{Rd,c}at at successive perimeters to establish*u*= the length of the perimeter where_{out}*v*_{Ed}=*v*_{Rd,c}. Perimeters within 1,5 d from u_{out}need to be reinforced.

Where required provide reinforcement such that *v*_{Ed }≤ *v*_{Rd,cs}.

where

*v*_{Ed} = applied shear stress. The shear force used in the verification should be the effective force taking into account any bending moment transferred into the slab (see above)

*v*_{Rd,max }= design value of the maximum punching shear resistance, expressed as a stress (see Shear Table 7)

*v*_{Rd,c} = design value of punching shear resistance of a slab *without *punching shear reinforcement, expressed as a stress (see Shear Table 7)

*v*_{Rd,cs }= design value of punching shear resistance of a slab *with *punching shear reinforcement, expressed as a stress.

*v*_{Rd,cs} = 0.75 *v*_{Rd,c} + 1.5 (*d*/*s*_{r})*A*_{sw} *f*_{ywd,ef }(1/*u*_{1}*d*)sin a

where:

*A*_{sw} = area of shear reinforcement in one perimeter around the column (subject to *A*_{sw,min})

*s*_{r} = radial spacing of perimeters of shear reinforcement

*f*_{ywd,ef }= effective design strength of reinforcement (250 + 0.25*d*) ≤ *f*_{ywd}

*d *= mean effective depth in the two orthogonal directions (in mm)

*u*_{1} = basic control perimeter at 2*d *from the loaded area

sin a = 1.0 for vertical shear reinforcement

Where required each perimeter should have

*A*_{sw} = (*v*_{Ed} – 0.75 *v*_{Rd,c})*s*_{r} *u*_{1}/(1.5 *f*_{ywd,ef})

For further details see How to Design Concrete Structures using Eurocode 2: 7 Flat slabs and Concise Eurocode 2 Section 8.

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