Hall Ticket No Question Paper Code: ACE004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech IV Semester End Examinations (Supplementary) June, 2018
Regulation: IARE R16
Strength of Materials II
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Derive the basic differential equation for deflection curve of a simply supported beam using double
integration method.
A beam ABC of length has one support at the left end and the other support at a distance
from the left end. The beam carries a point load W at the right end. Find the slopes over
each support and at the right end. Find also the deflection at the right end and the maximum
deflection between supports.
2. Derive the expression for finding out deflection for a cantilever beam subjected to UDL over
whole span using Mohr's theorems.
Using conjugate beam method find slopes at ends and central deflection for a simply supported
beam shown in Figure 1. Plot SFD and BMD.
Figure 1
UNIT II
3. Determine the rotation at supports and deflection at mid span of the simply supported beam as
shown in the Figure 3. Use moment area method.
Figure 2
Page 1 of 3
Determine the horizontal displacement and rotation at roller support in the frame shown in
Figure 2. by unit load method. Flexural rigidity EI is constant throughout.
Figure 3
4. Calculate the central deflection and slope at the ends of a simply supported beam carrying UDL
per unit length over the whole span. Use unit load method.
Determine the vertical and horizontal displacement at the free end D in the frame shown in the
Figure 4. Take EI= 12 X 103 N mm2. Use Castigliano's theorem.
Figure 4
UNIT III
5. A shell 3.25m long, 1m in diameter is subjected to an internal pressure of 1 N/mm2. If the
thickness of the shell is 10mm, find the circumferential and longitudinal stresses. Find also the
maximum shear stress and the changes in the dimensions of the shell. Take 2X105 N/mm2
and 0.3.
A cylindrical shell 1 meter long, 180mm internal diameter, thickness of metal 8mm is filled with
a fluid at atmospheric pressure. If an additional 20000 mm3 of the fluid is pumped into the
cylinder, find the pressure exerted by the fluid on the wall of the cylinder. Find also the hoop
stress induced. Take 2 X 105 N/mm2 and 0.3.
6. Derive the Lame's equation for radial pressure and circumferential stress c.
A pipe of 400 mm internal diameter and 100mm thickness contains a fluid at a pressure of 8
N/mm2. Find the maximum and minimum hoop stress across the section. Also, sketch the
radial pressure distribution and hoop stress distribution across the section.
Page 2 of 3
UNIT IV
7. Analyze a cantilever beam propped at end and subjected to UDL of w/unit length covering entire
span of length L. Draw S.F.D and B.M.D.
Two cantilever beams 1 and 2 respectively are propped by a hinge as shown in Figure 5. Beam
1 carries a central concentrated load of 30 kN. Draw the SFD and BMD. EI is constant for both
cantilevers.
Figure 5
8. A fixed beam of 6m span is subjected to a clockwise concentrated couple of 150 KN.m applied
at a section 4m from the left end. Find the end moments. Draw SFD and BMD.
A propped cantilever beam AB is subjected to a uniformly distributed load of 15 kN/m throughout
the length of 10 m. Draw bending moment diagram and shear force diagram by consistent
deformation method. Assume that flexural rigidity of beam is constant throughout its length.

UNIT V
9. Derive the clapeyorn's equation of three moment for a continuous beam carrying UDL.
A continuous beam ABCD covers three spans AB= 1.5L, BC= 3L and CD=L. It carries UDL
of 2W, W and 3W per meter run on AB, BC and CD respectively. If the beam is of same cross
section throughout, Find B.M at supports B C and pressure on each support. Also plot the
BMD and SFD.
10. Derive the three moment equation for a continuous beam which is fixed at both the end. Consider
the beam carries a uniformly distributed load of w per unit length.
A three span continuous beam ABCD has different moment of inertia and is loaded as shown in
figure. Find reactions and support moments and draw the S.F.D and B.M.D.