# Questions & Answers of Bending and Shear Stresses

A simply-supported beam of length 3L is subjected to the loading shown in the figure.

It is given that $P = 1 N, L = 1$ m and Young’s modulus $E=200\;\mathrm{GPa}.$ The cross-section is a square with dimension 10 mm × 10 mm. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $I_1$, while the circular cross-section has flexural rigidity $I_2$. Both sections have the same cross-sectional area. The ratio $I_1/I_2$ is

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, ${\theta }_{s}$ is the twist and ${\tau }_{s}$ is the maximum shear stress in the solid shaft, whereas is the twist and ${\tau }_{H}$ is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gage pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is

In a plane stress condition, the components of stress at a point are , and . The maximum shear stress (in MPa) at the point is

A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) is____________

Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are ${\tau }_{1}$ and ${\tau }_{2}$. If R2/ R2=2, then ${\tau }_{2}$/${\tau }_{1}$ is _______