(Detailed solution)GATE ME | Strength of Materials | Bending questions

GATE ME solved Questions on Bending stress (Strength of Materials)

Question #1

Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.

(A) $d/2$

(B) $\pi d/2$

(C) $d$

(D) $\pi d$

[GATE 2017 Set 1, 1 mark]

Solution

$\large Z=\frac{I}{y}$

where,

Z=section modulus of the beam

I=Area moment of inertia of the beam about the neutral axis

In case of a circular section,

$\large y=\frac{d}{2}$

Therefore,

$\large \frac{I}{Z}=\frac{d}{2}…….(Answer)$

Question #2

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

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 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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