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GEO5

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Verification of Spread Footing for Punching Shear

The program allows us to verify spread footing for punching shear. The critical section loaded in shear Ucr is distant from the column edge by one half of the footing thickness. It is loaded by the prescribed moments Mx, My and by the shear force V* provided by:

where:

A

-

area of footing

V

-

assigned vertical force developed in column

At

-

hatched area in fig.

Dimensioning of shear reinforcement area At

The program computes the maximal shear force V* developed in the critical section, the shear force transmitted by concrete with no shear reinforcement Vuc as a minimum of values (Art. 9.3.3):

where:

where βc is the ratio of the longest overall dimension of the effective loaded area, Y, to the overall dimension, X, measured perpendicular to Y.

and the maximal allowable force Vumax (Art. 9.3.4):

where:

u

-

critical cross-section span

x

-

short dimension of cross section

y

-

long dimension of cross section

a

-

the dimension of the critical shear perimeter measured parallel to the direction of M*v

M*v

-

the bending moment transferred from the slab to support in the direction being considered

For V* < Vuc no shear reinforcement is needed.

For V* > Vuc and V* < Vumax the shear reinforcement must be introduced. The ultimate shear force is given by (Art. 9.3.4):

Area of reinforcement must satisfy condition (Art. 9.3.4):

For V* > Vumax the shear reinforcement cannot be designed. It is therefore necessary to increase the cross-section height.

The analysis is carried out independently in directions x and y, as the decisive one the lower value of Vu is accepted.

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