Mechanics of Solids — Winter 2023

Find magnitude and direction of resultant of force system shown in Fig.1

Explain principle of transmissibility and superposition

State and explain parallelogram law of forces

Two shafts Aof 700 kN and Bof 400 kN are supported as shown in fig. 4 Neglecting friction at the contact surfaces P, Q, Rand S, determine the reactions at all contact surfaces.

Differentiate moment and couple

Find the moment of all the forces about point Ogiven in fig. 2 Consider size of the square as 1 cm x 1 cm.

Determine support reaction for the given beam shown in Fig.3

Arectangular block of 525mm x 230mm x 115mm is subjected to following load

Explain (a) Homogeneous material (b) Yield strength (c) Prismatic section

Acircular brass rod of 2m length is subjected to axial pull of 15kN. What should be the diameter of the rod so that stress should not be more than 120 N/mm2 and elongation should not be more than 6mm. Take E = 120 GPa.

Draw shear force and bending moment diagram of the beam shown in Fig. finding values at all important points on the beam.

Illustrate stress Vs strain graph for a standard mild steel bar. Show all the salient points on the graph.

In a standard tensile test, a bar of 20mm diameter undergoes elongation of 14mm in a gauge length of 150mmand a decrease in diameter of 0.85mm at a tensile load of 6 kN. Determine the Poisson’s ratio.

on 230 x 115mm face 1550 kN tensile (ii) on 525 x 230 mm face 2575 kN tensile (iii) on 525 x 115mm face 2100 kN compressive. Find the strain on all directions. Take Poisson’s ratio as 0.25 and E = x105 N/mm2.

Locate the Centre of Gravity of composite 3d object shown in fig.7 (all dimensions are in mm)

Differentiate centroid and center of gravity.

Explain laws of friction1

Find moment of inertia of a given section in fig. 6 about its centroidal axis

Explain different types of supports with their reactions.

Determine the horizontal force on block required to cause (i) impending motion downward and (ii) impending motion upward. Refer fig. Take  = 0.55.

Write assumptions made in theory of pure torsion.

Draw shear stress distribution diagram for following sections (i) rectangle (ii) Hollow circular (iii) hollow rectangular (iv) Lsection.

Asimply supported beam of 3m span is subjected to central load ‘W’ and having rectangular cross section 275mm x 425mm. If permissible shear stress is 3 N/mm2 Calculate maximum permissible load on beam in bending and shear.

Write the assumptions made in the theory of pure bending.

Ashaft is required to transmit 1MW at 240 rpm. If the shear stress is not to exceed 55 N/mm2 determine the required diameter of the shaft.

Amaterial is stressed by shear 5 N/mm2, axial compression N/mm2 in X-direction and axial tension 7 N/mm2 in Ydirection. Calculate (i.) Normal and tangential stress on plane making 60º with X-axis. (ii) Maximum normal stress with their locations. Fig. 1 Fig. Fig. Fig. 42 Fig. Fig. Fig. Fig.