Shear Stress Distribution In Rectangular Section

Draw typical shear stress distribution diagram for the symmetrical i section symmetrical about both the axes t section solid rectangular section and circular section.

Shear stress distribution in rectangular section. The maximum shear strain and stress occur at the centerline of the long sides of the rectangular cross section. τ shear stress n mm2 a area of section where shear stress is to be determined mm2 ȳ distance of c g of the area where shear stress is to be determined from neutral axis of the beam section m a. Where b 2 r o r i is the effective width of the cross section i c π r o 4 r i 4 4 is the centroidal moment of inertia and a π r o 2 r i 2 is the area of the cross section.

For this section the maximum stress is equal to. Shear stresses in i beams. We can say from equation of shear stress for a rectangular section that shear stress distribution diagram will follow parabolic curve and we have drawn the shear stress distribution diagram for a rectangular section as displayed in following figure.

It is clear from the above notes that for a beam subject to shear loading and bending the maximum shear stress is at the neutral axis and reduces to zero at the the outer surfaces wher y 1 c. The strain and stress variations on the cross section are primarily nonlinear. Draw the shear stress distribution diagram for t inverted c channel and i symmetrical and unsymmetrical section.

Q first moment of area section above area of interest i moment of inertia b width of section for the rectangular section shown above. The distribution of shear stress along the web of an i beam is shown in the figure below. It may be noted that the shear stress is distributed parabolically over a rectangular cross section it is maximum at y 0 and is zero at the extreme ends.

I section. ȳ moment of the whole shaded area about the neutral axis. The maximum shear stress occurs at the neutral axis and is zero at both the top.

The maximum shear stress is then calculated by. The maximum value of shear stress would obviously beat the location y 0. The shear strain and stress at the corners and center of the rectangular cross section are zero.