This document contains instructions for Assignment No. 3 and No. 4 to be submitted by September 31st, 2015 for the Mechanics of Solids course. Assignment No. 3 contains 6 questions related to deformation of conical bars, deflection of cantilever beams, stresses and strains in beams, design of shafts based on allowable stresses, and derivation of Poisson's ratio from other material properties. Assignment No. 4 contains 5 questions on deflection and stresses in beams, relationship between principal and shear stresses, design of bolts, design of rotating shafts, and stresses in beams with T-sections. Students are to attempt the questions and problems in the assignments.

1. Assignment No. 3 ( To Be submitted by 31/9/15)
NME-302 (Mechanics of Solids)
(2nd
Yr., 3rd
Sem Mechanical Engg. )-Section A & B
1) Derive an expression for deformation of conical bar hung to a ceiling having diameter ‘D’
& height ‘L’, weight density of bar ρ & Young’s modulus is E.
2) Find the free end deflection in Cantilever beam with uniformly distributed load by
Moment Area Method & Macaulay’s Method.
3) Attempt any one question :
Determine the deflection at the mid & slope at the end of the beam in terms of “EI” for a
beam as shown in figure 1.
Figure 1
4) A solid shaft is subjected to a bending moment of 2.3kN/m & a twisting moment of 3.45
kN/m . Find the diameter of the shaft if the allowable tensile & shear stresses for shaft
material are limited to 703 MPa & 421.8 MPa respectively.
5) Attempt any four question :
(A) Define Principal Plane & Principal stress.
(B) Draw the Mohr’s Circle for pure shear.
(C) Define Neutral Axis.
(D)What do you understand by section modulus?
(E) Name any four theories of failure.
(F) Explain impact load & Impact stress.
(G) What do you mean by “strength of a shaft”, torsional rigidity & torsional stiffness?
(H) Define Neutral Axis.
(I) State Mohr’s theory for beams.
6) Show that if “E” is assumed correct, an error of 1% in the determination of “G” will
involve an error of about 5% in the calculation of Poisson’s ratio when its correct value is
0.25.
4m 3m 1m
2 kN/m
A B

2. Assignment No. 4 ( To Be submitted by 31/9/15)
NME-302 (Mechanics of Solids)
(2nd
Yr., 3rd
Sem Mechanical Engg. )-Section A & B
1) Find deflection at point B & C of beam given below(figure 1): E=200 GPa, , I= 19802.8
cm4
Figure 1
2) Prove that the maximum shear stress in a body is half of the difference between maximum
principal & minimum principal stress.
3) The load on a bolt consists of an axial pull of 20 kN together with a transverse shear of 10
kN . Calculate the diameter of bolt according to :
(1) Maximum Principal stress theory.
(2) Maximum Principal strain theory.
(3)Maximum shear stress theory .
(4) Maximum Strain Energy theory
(5) Maximum shear strain energy theory . (Take μ= 0.3, Elastic limit in tension 280 MPa &
Factor of safety = 3)
4) A solid shaft rotating at 500 rpm transmits 300 kW. The maximum torque is 20% more
than the mean torque. Material of shaft has the allowable shear stress of 65 MPa & modulus
of rigidity of 81GPa, the angle of twist in the shaft should not exceed 1⁰ in 1 m length.
Determine the diameter of the shaft.
5) A beam having T section is shown in figure 2 below with its flanges of (180mm * 10mm)
& a web of (220 mm * 10 mm) is subjected to sagging bending moment of 15 kN-m.
Determine the maximum tensile stress & maximum compressive stress.
Figure 3
Figure 2
1m 3m 1m
30 kN/m
A D
B
C1m
m
60 kN
E
180 mm
220 mm
10 mm
10 mm