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Shear stresses due to shear forces

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The shear stress due to shear force Vy action is given by:

               eq. (a)


tsy: average transverse shear at level y in section;

mp: the first moment, with respect to the neutral axis, of the the cross sectional area above the level y;

Iy: moment of inertia of the entire cross section, taken with respect to the neutral axis;

: the width of the cross section at level y.

The shear stress acts in the same direction as the resultant shear force V.

In the x direction we use the same equations by replacing x instead of y.





The reduced shear section area:





And, the section shear correction factors are given by:


     Ky=Ary/A in y direction

     Kx=Arx/A in x direction


The shear-stress formulas (a) may be applied to calculate the distribution of shear in a wide variety of beam shapes under a wide variety of loading. These formulas were based on the flexure formula. Therefore, the limitation on the applicability of the flexure formula (slender beam, linearly elastic behavior, etc.) apply to these shear formulas also. However, there are some additional limitations on the shape of the beam and on the load distribution. The shear stress formulas must be taken by more precaution when the width by, varies rapidly and in thin-wall beams cases

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