JNTU B.Tech II MECHANICS OF SOLIDS Previous Question Paper (December - 2017 - R15)

Differentiate between Elasticity and plasticity.

Determine modulus of rigidity and bulk modulus if Poisson’s ratio = 0.3 and Young’s modulus E = 200 MPa.

Present the sign conventions for shear force and bending moment diagrams.

Derive the relationship between load intensity, shear force and bending moment.

State the bending equation. Give the meaning of each term and a set of consistent units for the terms.

Draw the variation of shear stresses across the depth of a beam of triangular section, indicating the values at critical depths.

The sum of the normal stresses on mutually perpendicular planes is a constant. Justify.

Why the Von-Mises distortion energy theory is more suitable for ductile materials?

A shaft transmits 20 kW of power at 200 rpm. What is the torque transmitted?

Compare the nature of stresses induced in thin cylinder and thin spherical vessel.

A tapering rod has diameter d₁ at one end and it tapers uniformly to a diameter d₂ at the other end in a length L. If the modulus of elasticity is E, find the change in length when subjected to an axial tensile force P. What are the stresses induced at sections L/4, L/2 and 2L/3 from the d₁ end?

The figure 1 shows a cantilever beam A loaded by point force F and pinned to a beam BD at B. Beam BD is loaded by couple C and is supported at D. Sketch the shear-force and bending-moment curves.

A beam ABCD, 10 m in length, is simply supported at B and C, which are 5 m apart, and overhangs the support B by 3 m. The overhanging part AB carries a total load of 180 KN, uniformly distributed, and the part BD carries a total load of 210 kN uniformly distributed. D is a point at the other end of the beam. Draw to scale the Shear Force and Bending Moment diagrams for the beam. Calculate the position and magnitude of the least value of the B.M. between the supports.

Prove that the strength of a square section used as a beam to bend about a diagonal can be increased by flattening the corners in the plane of loading and that the maximum strength is obtained by removing one-ninth of the diagonal length, equally divided at the top and bottom.

A timber beam, 240 mm deep by 100 mm wide, has a steel plate 10 mm thick and 100 mm wide bolted firmly to its lower edge. The beam is freely supported on a span of 4 m and is loaded uniformly. Find the load it will carry when the maximum compressive stress in the timber is 8.5 MPa and calculate the maximum stress in the steel under this load. The ratio of the elastic moduli of steel and timber is 18.

At a point in a stressed material the direct stresses on two perpendicular planes are 140 MPa tension and 90 MPa compression respectively, and the shearing stress on these planes is τ. The yield stress for the material is 250 MPa. Find the value of τ at which failure may be expected, according to each of the following theories of failure: (a) maximum principal stress theory; (b) maximum shearing stress theory; and (c) maximum shear strain energy theory.

The state of stress at a point is as shown in Figure 2. Determine the principal stresses, principal planes and the maximum shear stress. Determine normal and tangential stresses on plane AC.

For the shaft shown in Figure 3, find the stresses in the two materials and the angle of twist between A and B. The modulus of rigidity G = 85 GPa for steel and 28 GPa for aluminium.

A thin spherical shell has a diameter of 1.2 m, and is subjected to an internal pressure of 2.5 MPa. Determine the minimum thickness required if the stress is not exceeding 40 MPa. Find the increase in the diameter of the sphere, and the change in volume. E = 200 GPa and poisson’s Ratio = 0.3.