GATE ME topic:solid-mechanics PYQs & Answers — Page 5

Questions 41–50 of 90. Imported answers require independent review unless marked reviewed.

A right solid circular cone standing on its base on a horizontal surface is of height

and base radius

. The cone is made of a material with specific weight

and elastic modulus

. The vertical deflection at the mid-height of the cone due to self-weight is given by

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A plane frame

(fixed at

and free at

) is shown in the figure. Both members (

and

) have length,

, and flexural rigidity,

. Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end,

, is

Diagram for Mechanical Engineering question 31

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An overhanging beam

is subjected to uniformly distributed load 20 kN/m as shown in the figure.

Diagram for Mechanical Engineering question 51

The maximum bending stress developed in the beam is ______ MPa (round off to one decimal place).

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A cantilever beam with a uniform flexural rigidity (

N.m²) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 1000 N.m². The magnitude of the slope of the beam at its free end is ______ micro radian (round off to the nearest integer).

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A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The modified endurance, yield and ultimate strengths of the material are 200 MPa, 500 MPa and 600 MPa, respectively.

Diagram for Mechanical Engineering question 54

The factor of safety of the beam using modified Goodman criterion is ______ (round off to one decimal place).

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The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ − τ plane is 1 MPa, the Mohr’s circle representation of the state-of-stress is given by

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a circle with a radius equal to principal stress and its center at the origin of the σ − τ plane

a point on the σ axis at a distance of 10 units from the origin

a circle with a radius of 10 units on the σ − τ plane

a point on the τ axis at a distance of 10 units from the origin

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Bars of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

Diagram for Mechanical Engineering question 28

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Tensile and compressive load specimens

Torsional load specimen

Bending load specimen

None of the specimens

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A cantilever of length

, and flexural rigidity

, stiffened by a spring of stiffness

, is loaded by a transverse force

, as shown. The transverse deflection under the load is

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The truss shown in the figure has four members of length

and flexural rigidity

, and one member of length

and flexural rigidity

. The truss is loaded by a pair of forces of magnitude

, as shown in the figure.

The smallest value of

, at which any of the truss members will buckle is

Diagram for Mechanical Engineering question 30

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A thin-walled cylinder of radius

and thickness

is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.

The material of the cylinder has Young’s modulus

, Poisson’s ratio

, and coefficient of thermal expansion

. What is the minimum rise in temperature

of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of

above the atmosphere?

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GATE ME topic:solid-mechanics PYQs

Question 31

Question 31

Question 51

Question 53

Question 54

Question 7

Question 28

Question 28

Question 30

Question 30