GATE ME Mechanics of Materials PYQs & Answers — Page 6

Questions 51–60 of 90. Imported answers require independent review unless marked reviewed.

Uniaxial compression test data for a solid metal bar of length 1 m is shown in the figure.

Diagram for Mechanical Engineering question 38

The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is ______ mm (round off to one decimal place).

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Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus

MPa and Poisson’s ratio

are given. The principal strains in the plane of the sheet are

Your answerChoose one option.

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A cylindrical rod of diameter 10 mm and length 1.0 m is fixed at one end. The other end is twisted by an angle of 10° by applying a torque. If the maximum shear strain in the rod is

, then p is equal to ______ (round off to two decimal places).

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A solid cube of side 1 m is kept at a room temperature of 32 °C. The coefficient of linear thermal expansion of the cube material is

/°C and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly to 42 °C, then the magnitude of volumetric (mean) stress (in MPa) induced due to heating is ______

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The state of stress at a point in a component is represented by a Mohr’s circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ______ MPa.

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During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of −70 MPa. The R-ratio (minimum stress to maximum stress) for this cyclic loading is ______ (round off to one decimal place)

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A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ______ MPa.

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Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the specimen was unloaded to point R, where the stress is zero. If the same specimen is reloaded in tension from point R, the value of stress at which the material yields again is ______ MPa.

Diagram for Mechanical Engineering question 25

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Consider two concentric circular cylinders of materials M and N in contact with each other at

, as shown below. The interface at

is frictionless. The composite cylinder system is subjected to internal pressure

. Let

and

denote the radial and tangential displacement and stress components, respectively, in material M. Similarly,

and

denote the radial and tangential displacement and stress components, respectively, in material N. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:

Diagram for Mechanical Engineering question 30

Your answerChoose one option.

and

only

and

only

and

only

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A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is

, Young’s modulus

, and area moment of inertia

, the magnitude of the maximum deflection is

Diagram for Mechanical Engineering question 31

Your answerChoose one option.

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GATE ME Mechanics of Materials PYQs

Question 38

Question 6

Question 20

Question 21

Question 21

Question 22

Question 22

Question 25

Question 30

Question 31