G.H. RAISONI COLLEGE OF ENGINEERING,
NAGPUR
DEPARTMENT OF CIVIL ENGINEERING
Question Bank: Strength of Material
UNIT – 1 :- (Simple stresses & strains)
1) Draw the stress-strain curve for tension test on a M.S. specimen
and mark the significant points on it.
2) The Composite bar shown in figure is subjected to a tensile force of
30 KN. The extension observed is 0.372mm. Find the Young Modulus
of brass, If Young Modulus of steel is 2 X 105 N/mm2.
30mm O
20mm O
Steel
400mm
Brass
P=30KN
300mm
3) The steel flat shown in figure has uniform thickness of 20mm. Under
an axial load o 80 KN, its extension is found to be 0.17mm.
Determine the Young’s Modulus of the material.
b2=40mm
P
P=80KN
b1=80mm
500mm
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4) Find the force P acting at C in the bar as shown in figure. Find the
extension of the bar if E = 2X105 Mpa.
20mm=O
15mm=O
15mm=O
30KN
60KN
A
P
80KN
300mm
D
C
B
300mm
400mm
5) A rigid bar ABCD is connected to steel bar at A and B and is having
hinged support at C. At free end a load of 40KN is acting as shown in
figure. Find the forces developed in the bars and deflections of free
end if E = 2 X 105 N/mm2, diameter of rod at A=30mm and at B is
25mm.
40KN
A
B
C
d
300mm
400mm
200mm
200mm
400mm
6) A steel tube of 50mm outer diameter and 10mm thick is fitted into a
copper tube of inner diameter 50mm and 10mm thick. They are
connected by using 20mm diameter pins at the ends. If the length of
compound bar is 600mm find the stresses produced in the tubes and
pins when temperature is raised by 250C.
Take: αs = 12 x 10-6/0 C,
αc = 17.5 x 10-6/0 C,
5
2
Ec = 1.2 x 105 N/mm2,
Es = 2 x 10 N/mm ,
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7) In figure a steel bar of cross-sectional area 250 mm2 held firmly by
the end supports and loaded by an axial force of 25KN.
Determine:
i)
Reactions at L and M.
ii)
Extension of the left portion.
E=200GN/m2
L
30mm O
N
25KN
RL
0.25m
M
RM
0.6m
8) For the bar as shown in figure calculate the reaction produced by the
lower support on the bar. Take E = 200GN/m2. Find also the stresses
in the bars.
R1
L
1.2m
A 1 = 110
M
2.4m
55KN
A2 = 220
N
1.2 m m
R2
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9) The following data relate to a bar subjected to a tensile test:
Diameter of the bar, d = 30mm
Tensile load, P = 54KN
Gauge length, ℓ = 300mm
Extension of the bar, δℓ = 0.112mm
Change in diameter, δℓ = 0.00366
Calculate : i) Poisson’s ratio ii) The value of three moduli
10) Composite section made up of copper tube of 150-mm dia enclosed
with steel tube 150-mm internal diameter and 12 mm thick. Length
of assembly is 50 cm is fastened at both ends. Now temperature of
assembly is raised by 75º C. find the stress develop in each material
and change in length of assembly.
Take Es = 2 x 105 Mpa
Ec = 1 x 105 Mpa
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-: UNIT – 2 :- (Bending Moments & Shear Forces)
1)
Draw the shear force and bending diagrams for the beam shown
in figure. Clearly mark the position of the maximum bending
moment and determine its value.
150N−m
C
x1
2.0m
m
2)
B
Draw the B.M. S.F. diagrams for the beam shown in figure
150N−m
C
B
x1
2.0m
m
BEAM
3)
As shown in figure a beam AB of length 4m acted upon by the
forces and moments. Draw the B.M. and S.F. diagrams
300KN
x
150N−m
C
4.0m
4)
x1
B
2.0m
A loaded beam as shown in figure, a) sketch the B.M. and S.F.
diagrams giving the important numerical values.
b) Calculate the maximum bending moment and the point at
which it occurs.
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150N−m
C
x1
B
2.0m
4.0m
BEAM
5)
Draws shear force and bending diagram for the beam shown in
figure. Locate point of Contra flexure if any.
6)
A beam of span 6m has one support at the left and the other
support at a distance of 2m from the right end. The beam carries
a UDL of 10kN/m over the entire span. Draw the SFD and BMD
and prove that the middle point of the beam is the point of contra
flexure.
7)
A beam 10 m long has supports at it’s A & B. It carries a point
load of 2.5 KN at 3m from A and a point load of 2.5 KN at 7m
from A and a uniformly distributed load of -.5Kn/m between the
point loads. Draw the shearing force and bending moment
diagrams for the beam.
-: UNIT – 3 (a) :- (Bending Stresses in Beams)
1) Derive the simple bending of a beam formula
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M
f
E
= =
I
y R
with usual notation. Give the assumption in theory of pure bending.
2) A cast iron water main 12 meters long, of 500mm inside diameter
and 25mm wall thickness runs full of water and is supported at its
ends. Calculate the maximum stress in the metal if density of cast
iron is 7200kg/m3 and that of water is 1000kg/m3.
Cast iron
water main
WATER
500mm
25mm
25mm
3) A hollow circular bar having outside diameter twice the inside
diameter is used as a beam. From the bending moment diagram of
of the beam, it is found that the bar is subjected to a bending
moment of 40KN/m. if the allowable bending stress in the beam is
to be limited to 100MN/m2, find the inside diameter of the bar.
4) Two wooden planks 150mm x 50mm each are connected to form a
T-section of a beam. If a moment of 3.4 kNm is applied around the
horizontal neutral axis, inducing tension below the neutral axis, find
the stresses at the extreme fibres of the cross section. Also
calculate the total tensile force on the cross-section.
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150mm
1
2
50mm
150mm
50mm
5) A beam simply supported at ends and having cross-section as
shown in figure is loaded with a U.D.L., over whole of its span. If
the beam is 8m long, find the U.D,L, if maximum permissible
bending stress in tension is limited to 30N/m and in compression to
45MN/m2. What are the actual maximum bending stresses set up in
the section.
100mm
30mm
30mm
200mm=d
120mm
50mm
120mm
BEAM
6) A flitched timber beam consists of two joists 100 mm wide and 300
mm deep with a steel plate 200 mm deep and 15 mm thick placed
symmetrically in between and clamped to them. Calculate
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the total moment of resistance of the section if the allowable stress
in joint is 9MN/m2.
300mm
200mm
100mm
15mm
100mm
Timber Beam
7) A flitched beam consists of a wooden joist 12cm wide and 20cm
deep strengthened by steel plate 1cm thick and 18cm deep, one on
either side of the joist. If the stresses in wood and steel are not to
exceed 7.5 MN/ m2 and 127.5 MN/ m2 find the moment of
resistance of the section of the beam. Take Es = 20 Ew.
1.0cm
20cm
18cm
1.0cm
12.0 cm
Flitched Beam
-: UNIT – 3 (b) :- (Shearing Stresses in Beams)
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1) An I-Section as shown in figure, beam 340 mm x 200 mm has a
web thickness of 10mm and flange thickness of 20 mm. It carries a
shearing force of 100 KN. Sketch the shear stress distribution
across the section.
200mm
20mm
Web
T=10mm
340mm=d
300mm
Flange
20mm
BEAM
2) A T-shaped cross-section of a beam shown in figure is subjected to
a vertical shear force of 100KN. Calculate the shear stress at the
neutral axis and at the junction of the web and the flange. Moment
of inertia about the horizontal neutral axis is 0.0001134 m4.
200mm
Flange
Web
50mm
50mm
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200mm
3) A beam of channel section 120mm x 60mm has uniform thickness
of 15mm. Draw diagram showing the distribution of shear stress for
a vertical section where shearing force is 50KN. Find the ratio
between maximum and mean shear stresses.
60mm
Flange
15mm
120mm
Web
45mm
90mm
T=15mm
Flange
15mm
BEAM
4) A steel section shown in figure is subjected to a shear force 200KN.
Determine the shear stress at the important points and sketch the
shear distribution diagram.
300mm
300mm
200mm
15mm
100mm
Steel Section
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: UNIT – 5 :- (Deflection of Beams)
1) A steel girder of uniform section, 14 meters long is simply
supported at its ends. It carries concentrated loads of 90KN and
60KN at two points 3 meters and 4.5 meters from the two ends
respectively. Calculate
i)
The deflection of the girder at the points under the two
loads
ii)
Maximum deflection,
Take I = 64 x 10-4 m4 and E = 210x106 KN/m2
150N−m
C
x1
2.0m
4.0m
BEAM
2) A beam AB of 4 meters span is simply supported at the ends and is
loaded as shown in figure. Determine
i)
Deflection at C
ii)
Maximum deflection and
iii)
Slope at the end A
Given: E = 200x106 KN/m2 and I = 20x10-6 m4
x
150N−m
A
C
2.0m
4.0m
BEAM
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x1
B
3) A beam AB as of span 8m is simply supported at the ends A and B
and is loaded as shown in figure. If E=200x106 KN/m2 and
I=20x10-6m4
Determine
i)
deflection at the mid-span
ii)
maximum deflection
iii)
slope at the end A
10KN/m
A
C
2.0 m
B
D
2.0 m
4.0 m
8.0 m
BEAM
4) A beam 6 meters long is loaded as shown in figure. If the flexural
rigidity (EI) of the beam is 8x104 KN-m2 find the deflection at point
C.
300KN
150N−m
A
2.0m
4.0m
6.0m
BEAM
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C
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5) A simply supported beam 5m long carries concentrated loads of 10
KN each at points 1 m from the ends.
Calculate:
i)
maximum slope and deflection of the beam and
ii)
Slope and deflection under each load
Take: EI = 1.2 x 104 KN-m2
10KN
10KN
D
C
A
B
E
3.0 m
1.0 m
1.0 m
BEAM
6) A beam 6 meters long is loaded as shown in figure. If the flexural
rigidity (EI) of the beam is 8 x 104 KN-m2 find the deflection at
point C.
300KN
x
150N−m
A
C
2.0m
4.0m
BEAM
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x1
B
: UNIT – 6 :- (Principal Stresses and Strains)
1) A rectangular block of material is subjected to a tensile stress of 100
Mpa on one plane and tensile stress of 48 Mpa on a plane at right angles,
together with shear stresses of 65 Mpa on the same plane. Find:
i)
The magnitude of principle stress.
ii)
Magnitude of greatest shear stress.
iii)
The direction of principle plane.
iv)
The normal and tangential stresses on a plane at 20º
with the plane carrying greater stress.
2) A short metallic column of 500 mm2 cross-sectional area carries an
axial compressive load of 100kN. For a plane inclined at 60º with the
direction of load calculate:
i)
Normal stress
ii) Tangential stress
iii)
Resultant stress
iv)
Maximum shear stress and
v)
Obliquity of the resultant stress.
3) The principal stresses at point across two perpendicular planes are 75
MN/m2 (tensile) and 35 MN /m2 (tensile) Find the normal , tangential
stresses and the resultant stress and its obliquity on a plane 20º with the
major principal plane.
4) At a point in a stressed body the principal stresses are 100 MN/m2
(tensile)and 60 MN/m2 (compressive). Determine the normal stress and
the shear stress on a plane inclined at 50º to the axis of major principal
stress. Also calculate the maximum shear stress at the point
5) A point is subjected to perpendicular stresses of 50 KN/m2 and both
tensile, Calculate the normal tangential stresses and resultant stress and
its obliquity on a plane making an angle of 30º with the axis of second
stress.
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