Shear
Shear stress (τ) is the internal resistance to sliding between adjacent layers of a material. For beams, shear stress varies across the cross-section and is maximum at the neutral axis. The average shear stress is τ_avg = V/A, but the actual distribution depends on the section shape. Shear flow (q) is used in thin-walled sections.
Knowledge Check
1.What is the average shear stress in a circular rod of diameter 20 mm subjected to a shear force of 30 kN?
2.For a rectangular beam, the shear stress distribution is:
3.In a rectangular beam, the maximum shear stress is what multiple of the average shear stress?
4.Where is the shear stress maximum in a solid circular cross-section?
5.What is the formula for shear stress in a beam at a point using the shear formula?
6.The shear flow (q) at a point in a thin-walled section is given by:
7.A 200 mm wide and 300 mm deep rectangular beam carries a shear force of 150 kN. What is the maximum shear stress?
8.At the top surface of a beam, the shear stress is:
9.The first moment of area (Q) about the neutral axis for a rectangular section is maximum at:
10.A bolt in single shear with a diameter of 12 mm carries a load of 20 kN. What is the shear stress in the bolt?