Jawaharlal Nehru Technological University Hyderabad B.Tech II MECHANICS OF SOLIDS Previous Question Paper (May/June - 2019 - R16)

A beam AB 5 m long is simply supported at A and B. It is loaded with point loads of 20 kN, 30 kN and 40 kN at distances of 1 m, 3 m and 4 m respectively from the support A, and a uniformly distributed load at the rate of 20 kN/m over the length of 2 m, the beginning of the uniformly distributed load being at the of 2 m from A. Draw the shear force and bending moment diagrams.

A I-section has flanges of size 200 × 12 mm and its overall depth is 360 mm. Thickness of web is also 12 mm. It is used as a simply supported beam over a span of 4 m to carry a load of 60 kN/m over its entire span. Determine the bending and shear stress at various critical points of the section. Draw the variation of bending and shearing stresses.

A shaft as shown in Figure 2 is subjected to a bending load of 3 kN, pure torque of 1000 Nm and an axial pulling force of 15 kN. Determine (a) Maximum principal stress at points A and B, (b) Minimum principal stress at points A and B, (c) Maximum shear stress at points A and B, (d) Von Mises Equivalent stress at both the points.

A plane stress condition exists at a point on the surface of a loaded structure such as shown in Figure 3. Determine the stresses acting on an element that is oriented at a clockwise angle of 15° with respect to the original element, the principal stresses, the maximum shear stress and the angle of inclination for the principal stresses. Draw the Mohr’s circle and indicate the points on it.

A hollow steel shaft has outer diameter of 150 mm and inner diameter of 100 mm. The steel has shear modulus of elasticity 75 GPa. For an applied torque of 16 kN m, determine the following quantities: (a) Shear stress at the outer surface and inner surface of the shaft. Represent them graphically. (b) Rate of twist (degrees per unit of length). (c) What diameter d is required for a solid shaft to resist the same torque with the same maximum stress? (d) What is the ratio of the weight of the hollow tube to the weight of the solid shaft?

A thin cylinder 75 mm internal diameter, 250 mm long with walls 2.5 mm thick is subjected to an internal pressure of 7 MPa. Determine the change in internal diameter and the change in length. If, in addition to the internal pressure, the cylinder is subjected to a torque of 200 N m, find the magnitude and nature of the principal stresses set up in the cylinder. Young’s Modulus = 200 GPa. Poisson’s = 0.3.