Strength of Materials (CE-305) - Important Questions

A steel rod 25 mm in diameter and 3 m long is subjected to an axial tensile load of 40 kN. Calculate the stress, strain and axial deformation (elongation). Take E = 200 GPa.

Explain Mohr's circle of stresses and explain how principal stresses, principal planes and maximum shear stresses are obtained from it with a neat sketch.

Draw the shear force and bending moment diagrams for a simply supported beam of span 6 m carrying a uniformly distributed load of 10 kN/m over the entire span and a concentrated load of 20 kN at mid-span. Determine the values of maximum shear force and maximum bending moment.

A rectangular beam 60 mm wide and 150 mm deep is simply supported over a span of 4 m and carries a uniformly distributed load of 5 kN/m over the entire span. Determine the maximum bending stress induced in the beam.

Using Macaulay's method, for a simply supported beam of span l carrying a concentrated load W at a distance a from the left support, find the slopes at the supports, deflection under the load and maximum deflection.

State and explain Mohr's first and second moment-area theorems for determination of slope and deflection of beams.

A T-section 150 mm x 120 mm x 20 mm is used as a strut 4 m long with both ends hinged. Calculate the Euler crippling load and the safe load taking factor of safety as 3. Take E = 2.0 x 10^5 N/mm2.

Explain Rankine's formula for intermediate columns, including its basis, expression and limitations.

A solid steel shaft is required to transmit a torque of 10 kN-m. If the allowable shearing stress is not to exceed 45 MPa, determine the required minimum diameter of the solid shaft.

A hollow shaft of diameter ratio 3/8 is required to transmit 600 kW at 110 r.p.m., the maximum torque being 20% greater than the mean. Determine the inside and outside diameters of the hollow shaft satisfying both allowable shear stress of 63 MN/m2 (strength) and allowable angle of twist of 1 degree per metre length (stiffness). Take G = 84 GPa.

At a point the normal stresses are sigma_x = 80 MPa (tensile) and sigma_y = 40 MPa (compressive) with shear stress tau = 30 MPa. Determine the principal stresses, maximum shear stress and the location/orientation of principal planes.

Explain the shear stress distribution across a rectangular beam section and show that it is parabolic in nature with neat sketches, indicating maximum and mean values.

Derive the differential relations between intensity of loading, shear force and bending moment (dV/dx = -w and dM/dx = V) for a loaded beam.

Write the assumptions made in the theory of simple bending.

Explain any three theories of failure with their graphical representation.

Explain pure torsion and derive the torsion equation (T/J = tau/r = G*theta/L), stating the assumptions made.