# Questions & Answers of Bending and Shear Stresses

## Weightage of Bending and Shear Stresses

Total 14 Questions have been asked from Bending and Shear Stresses topic of Mechanics of Materials subject in previous GATE papers. Average marks 1.50.

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta=30^\circ$ as shown in the figure.

The glue used at the interface fails if

Criterion 1: the maximum normal stress exceeds 2.5 MPa.

Criterion 2: the maximum shear stress exceeds 1.5 MPa.

Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

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A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).

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A cantilever beam of length L and flexural modulus EI is subjected to a point load P  at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is

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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.)

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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

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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

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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?

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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

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

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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____________

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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?

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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 _______

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Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

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The transverse shear stress acting in a beam of rectangular cross-section, subjected to a transverse shear load, is