# SOM GATE 2019, Set-2

• 1. 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 E = 200 MPa and Poisson’s ratio ν = 0.3 are given. The principal strains in the plane of the sheet are

(A) (0.35, −0.15)

(B) (0.5, 0.0)

(C) (0.5, −0.15)

(D) (0.5, −0.5)

2. 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.

3. 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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• 4. A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity EI = 200 N·m2 is subjected to an applied moment MA = 1.0 N·m at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is _______ mm (round off to one decimal place).

5. A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

(A) qL4 / 15EI

(B) qL4 / 30EI

(C) qL4 / 10 EI

(D) qL4 / 60EI