B Tech III Semester Odd Semester Back Paper Examination – 2016

TME-303 – Solid Mechanics

TIME: 3 HOURS MM: 100

NOTE: Attempt all questions. Each question carries equal marks.

1. Answer Any Four (4x5=20)

a) Explain the formation of Mohr’s Circle and also explain the sign conventions used with Mohr’s

Circles.

b) A bar of cross section 850 mm2 isacted upon by axial tensile force of 60 kN applied at each end of

the bar. Determine the normal and shearing stresses on a plain inclined at 30o to the direction of

loading.

c) Define principal stress and principal plane. What is stress invariant?

d) Write the expressions of radius and center of a Mohr’s circle.

e) A plain element is subject to the stress σx= 82.74 MPa and σy = - 82.74 MPa. Determine analytically

the maximum shearing stress existing in the element.

2. Answer Any Four (4x5=20)

a) What is creep test and relaxation test?

b) Consider a carefully conducted experiment where an aluminum bar of 50 mm diameter is stressed in

a testing machine as shown in the figure. At a certain instant the applied force P is 100 kN, while the

measured elongation of the rod is 0.219 mm in a 300 mm gauge length and the diameter’s dimension

is decreased by 0.01215 mm. Calculate the constant ν ( Poisson’s ratio).

c) What are constitutive relations? Why they are considered more realistic in nature?

d) What is engineering stress- strain curve and true stress-strain curve?

e) Define the following material behaviours:

i. Homogeneous

ii. Heterogeneous

iii. Isotropic

iv. Transversely isotropic

v. Monolithic

3. Answer Any Two (2x10=20) a) Consider a cantilever beam loaded by a concentrated force at the free end together with a uniform load

distributed over the half of the beam. Find shearing force and bending moment at any point in the beam and plot

the shear and bending moment diagram.

b) Draw the torsional shear stress distribution in a solid and in a hollow shaft.

c) Draw the torsional shear stress distribution for a circular bar made of two different materials bonded together.

4. Answer Any Two (2x10=20) a) A simple beam supports a concentrated downward force ‘P’ at a distance ‘a’ from the left support. The flexural

rigidity EI is constant. Find the equation of the elastic curve by the successive integration.

b) Derive expressions for first and second moment area theorems.

c) Determine the deflection at every point of the cantilever beam subject to the single concentrated force P applied

at the free end. The length of the cantilever beam is L.

5. Answer Any Two (2x10=20)

a) Explain Castigliano’s theorem.

b) Derive expressions for strain and energy due to axial torsion and bending shear.

c) i) Explain strain energy due to transverse shear. ii) What is reciprocity theorem? Explain.

P

L/2 L/2

w/ unit length

P

P