Shear stress distribution in cross sections Assignment Help

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Shear stress distribution in cross sections:

Consider the width of beam at the level EF be b.

At the level EF, the intensity of the horizontal shear stress is τ.

 Then,

τ =  Unbalanced force / Shear area

971_Calculation of Shear Stress Distribution in Beams2.png

As we have seen earlier, dM/ dx = F, the shear force, and shear stress, 252_Calculation of Shear Stress Distribution in Beams3.png Where A is refer to the area of cross section of the beam above the level EF, &1587_Calculation of Shear Stress Distribution in Beams4.png is the distance of the centroid of the area above the level EF, through the neutral axis.

For a specific cross section of a beam, F remains constant for particular point along the depth of the beam. Thus, we can conclude that the shear stress at any point on a cross section is proportional to 1151_Calculation of Shear Stress Distribution in Beams5.pngFor sections of uniform width, the shear stress shall have maximum value at the neutral axis, since2408_Calculation of Shear Stress Distribution in Beams6.png is maximum at the neutral axis. The shear stress shall have zero value at top & bottom layers of the beam cross-section, As  is zero at these layers.

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