GTU Mechanical Engineering (Semester 3)
Mechanics of Solids
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1(a) Two unlike parallel forces, will form a_________. ( Couple, Bending Moment, Shear force).
1 M
1(b) A particle is said to be in _______when the resultant force acting on it is zero. (Equilibrium, Stable, Unstable).
1 M
1(c) The process of finding components of a force is called_________of forces. ( Resolution, Splitting, Composition)
1 M
1(d) Define Law of Transmissibility.
1 M
1(e) The Relation between shear force and Bending moment is__________.
1 M
1(f) A cylinder is a surface of revolution generated by revolving a _______line about a fixed axis. (Straight, circular)
1 M
1(g) Co-efficient of static friction will always be ________than the coefficient of kinetic friction. (greater, equal, lesser)
1 M
1(h) The maximum value of Poisson's ratio for most of the engineering material is _______. (0.5, 1, 1.5)
1 M
1(i) Young's modulus of elasticity for a perfectly rigid body is _______ .(zero, infinity)
1 M
1(j) The point where the shear force is maximum, slope of the bending moment is __________.(maximum, minimum,zero)
1 M
1(k) In a beam of I-section, the maximum shear stress is carried by the _________.(web, flange)
1 M
1(l) At the point of contraflexure _______ changes it's sign. (shear force, bending moment, axial force)
1 M
1(m) Shear stresses on principal planes are_________. (zero, maximum, minimum)
1 M
1(n) For an element in pure shear, principal planes are oriented at ________ to the axis. (45°, 90°)
1 M

2(a) State and explain Varignon's theorem.
3 M
2(b) Two tensile forces acting at an angle 120° between them. The bigger force is 50kN. The resultant is perpendicular to the smaller force Find the smaller force and the resultant force.
4 M
Solve any one question.Q2(c) &Q2(d)
2(c) Two smooth sphere of weight 100 N each and radius 20 cm are in equilibrium in horiziontal channel of width 72 cm as shown in figure 1. Find reaction at the contact surface A, B and C. Assume sides of channel smooth.
7 M
2(d) At a point a strained material the state of stress is as shown in figure 2. Determine i) Location of principal planes ii) Principal stresses. Iii) Maximum shear stress and location of plane on which it acts.
7 M

solve any one question Q.3(a,b,c) &Q4(a,b,c)
3(a) For pure bending. Prove that the neutral axis coincides with the centroid of the crosss section.
3 M
3(b) A circular pipe of 100 mm external diameter and 80 mm internal diametern is used as a Simply supported beam of span 4 m. Find the safe concentrated load that the beam can carry at the mid point, if the permissible stress in the beam is 120 N/mm2.
4 M
3(c) A solid steel shaft is subjected to a torque of 45 kN m. If the angle of twist is 0.5° per meter length of shaft and shear stress is not to exceed 90 N/mm2. Find i) Suitable diameter of shaft ii) Final maximum shear stress and angle of twist for diameter of shaft selected. Take G = 80 Gpa.
7 M

4(a) State assumptions made in theory of pure bending.
3 M
4(b) For a hollow circular section whose external diameter is twice the inernal diameter, find the ratio of maximum shear stress to average shear stress.
4 M
4(c) What should be the value of θ in figure 3 which will make the motion of 1000N block down the plane to impend? The coefficient of friction for alll contact surfaces is 1/3.
7 M

solve any one question Q.5(a,b,c) &Q6(a,b,c)
5(a) Define: i) Lateral strain ii) Poisson's ratio iii) Modulus of rigidity.
3 M
5(b) In a tension test, a bar of 20 mm diameter undergoes elongation of 14 mm in a gauge length of 150 mm and a decrease in diameter of 0.85mm at a tensile load of 6 kN. Determine the two physical constant's Poisson's ration and modulus of elasticity of the material.
4 M
5(c) Determine the cetroid of the plane area in which a circular part of 40 mm radius, has been removed as shown in Figure 4.
7 M

6(a) Determine the surfaces area and volume of a right circular cone with radius of base R and height h using Pappus-Guldinus theorem.
3 M
6(b) Derive expression of moment of inertia of triangle by first principal.
4 M
6(c) A 6 m long steel rod having 20 mm diameter is connected to two grips and each end at a temperature 20°C. Find i) pull exerted when temperature falls to 40°C and end do not yield. ii) pull exerted when temperature falls to 40°C and ends yield by 11 mm, iii) the shortening allowed for no stress at 40°C and iv) the minimum final temperature for shortening of 1.1 mm.Take Esteel = 205 Gpa, αsteel=11×10-6/sup>/°C.
7 M

solve any one question Q.7(a,b,c) &Q8(a,b,c)
7(a) Define: i) Coefficient of friction ii) Angle of friction
3 M
7(b) A solid circular steel shaft of diameter 75 mm can resist maximum shear stress of 75 N/mm2. If shaft is rotating at 150rpm, calculate the power transmitted by shaft. Also calculate the angle of twist for 1.4m long shaft if G=100Gpa.
4 M
7(c) Draw Shear Force and Bending Moment diagram for the beam as shown in figure 5.
7 M

8(a) Enlist various type of loads and type of supports.
3 M
8(b) A steel bar of rectangular cross section is 60 mm wide and 50 mm thickness is subjected to an axial pull of 85kN. Calculate Normal Tangential and Resultant stresses on an inclined plane at 30° to the cross section of bar.
4 M
8(c) A weight 750 N just starts moving down a rough inclined plane supported by a force of 250 N acting parallel to the plane and it is at the point of moving up the plane when pulled by a force of 350N parallel to the plane. Find the irrelination of the plane and the co-efficient of friction between the inclined plane and the weight.
!mage
7 M



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