A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?

A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?

Solution

The formula for shear stress at any point of the beam’s cross-section is

                                                    τ=VQ/Ic b

where: V$V$ - shear force, Q$Q$ - first moment of the area bounded by the point of interest and the extreme fiber of the cross-section, I$I$ - centroidal moment of inertia of the cross-section, b$b$ - width of the cross-section at the level of the point of interest.

All these terms apart from b$b$ will be the same whether we calculate the stress in the web or in the flange at their junction. For the former case b$b$ will be equal to 20 mm$20mm$ while for the latter case it will be equal to 200 m$200m$. Thus, the shear stress in the flange will be 10 times lower than in the web: q/10$q/10$.