# Strength of Materials ```POKHARA UNIVERSITY
Level: Bachelor
Programme: BE
Semester - Spring
Year
2010
Full Marks : 100
Pass Mark : 45
: 3 hrs
Time
Course: Strength of Materials
Candidates are required to give their answers in their own words as far
as practicable.
The figures in the margin indicate full marh.
Attempt all the questions.
l.
a.
Find total, external and internal indeterminacy of the following
structure.
2
Internal
Hinge
2.
b. A spherical vessel of 1.5m internal diameter and 5rrun thick is
filled with a fluid under pressure until its volume is increased by
250cm3. Calculate the pressure exerted by the fluid on the
vessel. Take E = 210KN/mm2, &micro; = 0.3.
c. Derive Euler's formula for critical load for a column with one
end fixed and other end free. Also mention the assumption made
while deriving Euler's fonnula.
Calculate principal centroidal moment of inertia and its direction for
the given section.
l--1m--l
I
l
T
Im
l..
3m
T
Im
l..
3m
6
7
15
3.
a.
Draw shear force diagram, axial force diagram and bending
moment diagram of the following plane frame.
9
&middot;K
2m
+
2m
I--
3m
•I•
3m -+2m-,
b. Draw shear force diagram, axial force diagram and bending
moment diagram of the following frame.
6
8kN
A
j.-2m •+•
4.
20
2m
•I•
4m
&quot;I
a. Find change in length of the given bar (circular) after the
application of load as shown in figure. Take E =
220KN/mm2.
7
T
lOKN
.
10mm
20mm
,_I---'-----
20KN
l
b. Find stress in each of the given composite bar of length 100mm
and hence calculate the final length of the composite section if
temperature is decreased by100&deg;1 1-C-. c_;-:-e:-le_r
Copper
Steel
2
A= 60mm
A=40mm2
6
a =ISx10- !&deg;C a =12x10-61&deg;c
---lOOmtn ---------- &lt;
E=l 80KN/mm2 E=220KN/mm2
5. a. An infinitely small element consists of forces in two mutually
perpendicular plane as shown in figure. Determine the normal and
8
1
2
12
shearing stress on the inclined plane at an angle 30&deg; with the
vertical. Also calculate principal stresses their directions and
maximum shear stress.
30MPa
30MPa
50MPa ----- i,-+i
.---50MPa
30 1Pa
b. Verify the above result by constructing Mohr's Circle.
6.
a. A simply supponed T - beam having cross section as shown in
the figure is 3.5m long. If it carries bending moment of25kN-m,
calculate maximum bending stresses intension and in
compression.
7.
j-2ocm-J
b. A hollow circular shaft 10m long is required to transmit 130kW
power when running at a speed of 300rpm. If the maximum
shearing stress allowed in the shaft is 100N/mm2 and the ratio of
inner to the outer diameter is 0.5, find the dimensions of the
shaft and also the angle of twist of one end of the shaft relative
to the other end. Take G = 80kN/mm2.
Write shon notes on any two:
a. Relation between elastic constants
b. Flexure equation
c. Relation between load shear force and bending moment
3
3
8
7
```