4778-2-56P
AID: 1825 | 24/10/2014
For the case (a),
Sketch the temperature distribution for initial condition
t
t 0
and two intermediate times at mid plane wall in
T x
, steady state condition
coordinates as in Figure
(1).
From the above figure states

4778-2-33P
AID: 1825 | 24/10/2014
Express the general form of one dimensional heat conduction equation for Cartesian
coordinate.
(1)
&
2T q 1 T
x 2 k t
Here, second order temperature gradient at x direction is
conductivity is k, thermal diffusivity is

4846-6-10P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
50

4846-6-23P
AID: 1825 | 07/02/2014
Draw the diagram of forces acting on a small segment of the shaft as shown in Figure (1).
(a)
Express the stress acting along the x direction of the shaft.
4P
x
d2
Here, stress along the x direction is
x
, axial load is

4846-6-24P
AID: 1825 | 14/03/2014
Express the stress along the x direction.
3LP
x
8tc 2
Here, stress along the x direction is
length of beam is L, vertical load is P, thickness is
x
t, and depth is 2c.
Substitute 0.50 m for L, 40kN for P, 40 mm for t, an

4846-6-12P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
for

4846-6-27P
AID: 1825 | 07/02/2014
Draw the diagram of the stresses acting on a small segment of the thick walled tube as
shown in Figure (1).
(a)
Express the radial stress on the internally pressurized thick-walled tube.
(1)
pr 2 r 2
r 2 1 2 22 1
r2 r1

4846-6-6P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
30 M

4846-4-37P
AID: 1825 | 14/03/2014
From the graph of load-displacement graph for three-pont bending test of alumina,
write the fracture load and displacement at fracture load as 192 N and 0.091 mm.
Express the bend strength of alumina.
3L
fb 2 Pf
8tc
Here

4846-6-3P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
xy
, stress along the x plane is
Substitute 50 M

4846-6-2P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
xy
, stress along the x plane is
Substitute 60 M

4846-5-37P
AID: 1825 | 31/01/2014
From the table of elastic constants and density for epoxy reinforced with 60%
unidirectional fibers, take the elastic constants and Poissons ratio constant for T-300
graphite fiber reinforced epoxy composites. Tabulate th

4846-6-22P
AID: 1825 | 07/02/2014
Calculate the shear stress along the xy plane.
16T
xy 3
d
Here, shear stress along the xy plane is
Substitute
1.5 kN m
xy
, torque is T, and diameter is d.
xy
for T and 50 mm for
d
.
1, 000 mm
1m
16 1.5 103 N m
50

4846-6-26P
AID: 1825 | 14/02/2014
Draw the diagram of the stresses acting on a small segment of the thick walled tube as
shown in Figure (1).
(a)
Express the radial stress on the internally pressurized thick-walled tube.
(1)
pr12 r22
r 2 2 2 1
r2 r1 R

4846-6-25P
AID: 1825 | 07/02/2014
Draw the diagram showing the stresses acting on a segment of the thick-walled spherical
vessel as shown in Figure (1).
(a)
Express the radial stress on the internally pressurized thick-walled spherical vessel.
(1)
pr13 r

4846-6-14P
AID: 1825 | 31/01/2014
Express the first principal normal stress.
2
y
y
2
1 x
x
xy
2
2
Here, first principal normal stress is
Substitute
7.58 MPa
for
1
.
,
x 163.34 MPa
for
, and
y
24.59 MPa
7.58 MPa 163.54 MPa
7.58 MPa 163.34 MPa
2
1

4846-6-21P
AID: 1825 | 07/02/2014
Draw the diagram of forces acting on a small segment of the shaft as shown in Figure (1).
(a)
Express the stress acting along the x direction of the shaft.
32 M
x
d3
Here, stress along the x direction is
x
, bending mome

4846-6-19P
AID: 1825 | 31/01/2014
Calculate the inner radius of the pipe.
r1 r2 t
Here, outer radius is
r2
Substitute 40 mm for
, inner radius is , and thickness is t.
r1
r2
and 2 mm for t.
r1 40 mm 2 mm
38 mm
Calculate average radius of the pipe.
r r
ra

4846-6-18P
AID: 1825 | 31/01/2014
Calculate the inner radius of the pipe.
r1 r2 t
Here, outer radius is
r2
Substitute 40 mm for
, inner radius is
r2
and thickness is t.
r1
and 2 mm for t.
r1 40 mm 2 mm
38 mm
Calculate average radius of the pipe.
r r
ravg

4846-6-17P
AID: 1825 | 07/02/2014
Calculate the radius of the inner diameter of the spherical vessel.
d
r1 1
2
Here, inner radius is
r1
Substitute 150 mm for
and inner diameter is
d1
d1
.
.
150 mm
2
75 mm
r1
Express the circumferential stress of the sph

4846-6-16P
AID: 1825 | 07/02/2014
Calculate the radius of the inner diameter of the vessel.
d
r1 1
2
Here, inner radius is
and inner diameter is
r1
Substitute 300 mm for
d1
d1
.
.
300 mm
2
150 mm
r1
Express the circumferential or hoop stress of the vess

4846-6-15P
AID: 1825 | 31/01/2014
Express the first principal normal stress.
2
y
y
2
1 x
x
xy
2
2
Here, first principal normal stress is
Substitute
532.3 MPa
for
x
,
1
.
for
211.4 MPa
y
, and
31.74 MPa
for
xy
.
2
532.3 MPa 211.4 MPa
2
532.3 MPa 211

4846-6-11P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
50

4846-6-13P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
50

4846-6-9P
AID: 1825 | 21/03/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
100

4846-6-7P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
70 M

4846-5-42P
AID: 1825 | 31/01/2014
From the table of elastic constants for various materials, take the value of elastic constant
and Poissons ratio for titanium (matrix) as 120 GPa and 0.361 respectively. Similarly,
take the value of elastic constant and P

4846-5-34P
AID: 1825 | 31/01/2014
From the table of elastic constants and density for epoxy reinforced with 60%
unidirectional fibers, take the elastic constant and Poissons ratio for Kevlar 49 fiber as
124 GPa and 0.35 respectively. Similarly, take the e

4846-6-8P
AID: 1825 | 31/01/2014
(a)
Express the rotation angle for maximum and minimum values of stress.
2 xy
tan 2 n
x y
Here, rotation angle for maximum and minimum values of stress is
the xy plane is
Substitute
xy
, stress along the x plane is
50 M

4846-5-13P
AID: 1825 | 31/01/2014
(a)
Write the genralized Hookes law for strain in each direction for the three-dimensional
case.
1
x x y z
E
1
y y z x
E
1
z z x y
E
Here, the axial strain in x, y ,z directions are
in x ,y,z directions are
E
x , y