Advanced Solid Mechanics
Assignment - 8: End Torsion of Prismatic Bars
1. Knowing that the inner diameter of an annular cylinder is di = 30 mm
and that its outer diameter is do = 40 mm, determine the torque that
causes a maximum shearing stress of 52 MPa
Advanced Solid Mechanics
Assignment - 5: Constitutive Relations
1. A body in the form of a cube of side 10 cm is subjected to a deformation
of the form: x = (1+a1 )X +a2 Y , y = (1+a3 )Y , z = (1+a4 )Z, where ai s
are constants and (X, Y, Z) are the Carte
Advanced Solid Mechanics
Assignment - 7: Bending of Prismatic Straight
Beams
1. Find the displacement and stress elds in a cantilever beam with rectangular cross section of length 2l, depth 2c and width 2b subjected to
a pure bending moment by assuming th
Advanced Solid Mechanics
Assignment - 10: Beam on Elastic Foundation
1. A steel beam of a rectangular cross section, 180 mm wide and 280 mm
thick, is resting on an elastic foundation whose modulus of foundation
is 6.5 N/mm2 . This beam is subjected to a c
Advanced Solid Mechanics
Assignment - 9: Bending of Curved Beams
1. There are two beams - a straight beam and a curved beam - each of
which is subjected to a pure bending moment, M. Assuming that both
the beams are homogeneous and has a square cross secti
Advanced Solid Mechanics
Assignment - 3: Traction and Stress
1. Cauchy stress state corresponding to
(cfw_ex , ey , ez ) is as given below:
10 5
= 5 10
0
0
an orthonormal Cartesian basis
0
0 M P a.
0
For this stress state,
(a) Draw the stress cube
(b) Id
Advanced Solid Mechanics
Assignment - 6: Boundary Value Problems:
Formulation
1. A body in the form of an annular cylinder is pressurized from outside
as shown in gure 1. Obtain the stress and displacement eld for this
boundary value problem and show that
Advanced Solid Mechanics
Assignment - 2: Kinematics
1. A body in the form of a cube, B = cfw_(X, Y, Z)|0 X 1cm, 0 Y
1cm, 0 Z 1cm in the reference conguration, is subjected to the
following deformation eld: x = X, y = Y + A Z, z = Z + A Y ,
where A is a c
Advanced Solid Mechanics
Assignment - 4: Balance Laws
1. Determine which of the following Cauchy stress elds are possible within
a body at rest assuming that there are no body forces acting on it:
3 2 2
xy 3 0
2x y
1
4 y 4 0 ,
(a)
= xy 3
0
0
0
3yz z 2
Advanced Solid Mechanics
Assignment - 1: Mathematical Preliminaries
1. Give reasons for the following: (a) ii = 3, (b) ij ij = 3, (c) ij ai =
aj , (d) ij ajk = aik , (e) ij akj = aki , (f) ij aij = aii , (g) ij jk ik = 3,
(h) ik jm ij = km (i) kki = 0, (j