Subject: STRENGTH OF MATERIALS
Date : 2071 – 10 – 14
Assume appropriate data if required.
Civl and rural II year
QN. 1a. discuss dynamic load ,imposed load and temperature load.
b. a bar of 1000mm length is attached rigidly at ends and applied forces as shown in the figure.
Calculate reactions at ends. If diameter of the bar is 30mm calculate stresses and changes in length
in each segment.
10kN
400
20kN
600
400
OR
QN.1a. Discuss different types of loads.
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 by 50°C.
steel
copper
Copper
A = 60mm2
α = 15x 10-6/°C
E = 180 kN/mm2
steel
A = 40mm2
α = 12x 10-6/°C
E = 220 kN/mm2
OR
QN1a. Explain different types of supports and symbolic representation.
b. Calculate change in dimension and volume in the following element due to applied forces. Take
E= 200kN/mm2 and Poisson’s ration = 0.3.
100mm
m
m
10kN
50
50mm
20kN
30kN
2.a Derive an equation of elongation of a bar of uniform section due to self weight.
8
b. Find principal moment of inertia with respect to centroidal axes of the following plane figure. Also
calculate orientation of principal axis and show it on figure.
6
3
OR
8
Ci
rc
ul
R ar c
= ur
3 ve
2a. derive an equation of elongation of tapering circular bar due to applied force P.
b. Find principal moment of inertia with respect to centroidal axes of the following plane figure.
Also calculate orientation of principal axis and show it on figure.
6
3
OR
2a. derive an equation of elongation of tapering bar of uniform thickness t due to applied load P
attends.
b. Find principal moment of inertia with respect to centroidal axes of the following plane figure.
Also calculate orientation of principal axis and show it on figure.
190
10
200
10
3.a Draw AFD, SFD and BMD of the following structure.
5m
2m
2m
9kN
2m
10kN
b. Derive an expression for buckling of slender column having both ends hinged.
OR
3.a Draw AFD, SFD and BMD of the following structure.
2m
5m
2m
2m
9kN
2m
10kN-m
b. calculate minimum slenderness ratio for a column to fail in buckling if crushing stress is
250N/mm2. Take E = 200kN/mm2.
OR
3.a. Draw AFD, SFD and BMD of the following structure.
2m
5m
2m
9kN
2m
10kN-m
b. A slender solid circular column of diameter 150mm has to be replaced by hollow circular column
of same strength, same material and same end conditions. Calculate diameter of the hollow column
if internal diameter is ¾ th of the outer diameter.
4. An element is acted by plane stresses as shown in the figure. Calculate ,
a. Normal and shearing stresses on a plane inclined at an angle of 25°
b. Principal stresses and its orientation
c. Maximum shearing stresses and corresponding plane.
d. Verify the result by Mohr’s circle.
10MPa
50°
10MPa
OR
An element is acted by plane stresses as shown in the figure. Calculate ,
a. Normal and shearing stresses on a plane inclined at an angle of 25°
b. Principal stresses and its orientation.
c. Maximum shearing stresses and corresponding plane.
d. Verify the result by Mohr’s circle.
10MPa
50°
10MPa
OR
An element is acted by plane stresses as shown in the figure. Calculate ,
a. Normal and shearing stresses on a plane inclined at an angle of 25°
b. Principal stresses and its orientation
c. Maximum shearing stresses and corresponding plane.
10M
20°
20°
Pa
10 M
10M
10 M
Pa
Pa
Pa
5.a Derive torsion equation for shaft having radius r, length l, Young’s modulus of elasticity E, shear
modulus G, polar moment of inertia J and applied torque T.
b Derive bending equation and write down the assumptions made in the derivation.
OR
5a. 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
relative to the other end. Take G = 80kN/mm2.
b. A simply supported T – beam having cross section as shown in the figure is 4.5m long. If it carries
bending moment on 35kN-m, calculate maximum bending stresses in tension and in compression.
190
10
200
10
OR
5a. Determine the diameter of solid shaft which will transmit 440kW at 280rpm. The angle of twist
must not exceed one degree per meter length and the maximum torsional shear is to be limited to
40N/mm2. Assume G = 84kN/mm2.
b. A beam having cross section of150mm wide and 300mm deep is simply supported over 3.5m
span. If it carries an uniformly distributed load of 5kN/m, calculate maximum bending stress
developed and maximum shearing stress developed in the beam.
6.a A cylindrical vessel is 2m long with 1m diameter and 20mm thick wall. It was filled with fluid in
atmospheric pressure. If 500000mm3 volume of fluid is injected, calculate pressure exerted on wall
by the fluid, hoop stress and longitudinal stress developed in the vessel.
b A laminated steel spring, simply supported at the ends and centrally loaded, with a span of 0.75m,
is required to carry a proof load of 750kg, and the central deflection is not to exceed 50mm; the
bending stress must not exceed 380N/mm2. Plates are available in multiples of 1mm for thickness
and 4mm for width. Determine suitable values for width, thickness, and number of plates, and
calculate the radius to which the plates should be formed. Assume width = 12 x thickness; E =
208000N/mm2.
OR
6.a. A spherical vessel of 1.5m internal diameter and 5mm thick is filled with a fluid under pressure
until its volume is increased by 250cm3. Calculate the pressure exerted by the fluid o the vessel.
Take E = 210 kN/mm2, µ = 0.3.
b. A close coiled helical spring has to absorb 50Nm of energy when compressed 5cm. the coil
diameter is eight times the wire diameter. If there are ten coils, estimate the diameter of coil and
wire and the maximum shear stress. G = 80000N/mm2.
OR
6.a. A cylindrical vessel is 3.5m long with 1m diameter and 20mm thick wall. It was filled with fluid
in atmospheric pressure. If 500000mm3 volume of fluid is pumped out, calculate pressure exerted
on wall by the fluid, hoop stress and longitudinal stress developed in the vessel. Final dimension of
the vessel.
b. derive an expression for deflection of axially loaded close coiled helical spring.
7. Write short notes on any two
a. Mohr’s circle construction for plane stress condition
b. Elasto plastic behavior in axial loading
c. Shear stress variation in I beam section.
d. Slenderness ratio
e. Spring in series and in parallel
f. Composite beam
g. Power transmission by a shaft
h. Static determinacy and indeterminacy
i. Section modulus
j. Relation between elastic constants
k. Relation between load shear force and bending moment.