# 12083 - Mechanics of Structures

Mechanics

Jul 18, 2012 (6 years and 2 days ago)

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Scheme – E

Sample Question Paper

Course Name : Civil Engineering Groups
Course Code : CE/CS/CR/CV
Semester : Fourth
Subject Title : Mechanics of Structures
Marks : 100 Time: 3 Hours
Instructions:
1. All questions are compulsory.
3. Figures to the right indicate full marks.
4. Assume suitable data if necessary.
5. Preferably write the answers in sequential order.
6. Use of Non Programmable scientific calculator is permissible

Q. 1] A] Attempt SIX of the following: [6x2=12]
a] Define Elastic body & Plastic body.
b] Define shear stress & shear strain.
c] Define Poisson’s ratio? Give its expression.
d] Define bulk modulus along with expression.
e] Draw bending stress distribution diagram for a rectangular beam used as a
Cantilever.
f] State relation between average & maximum shear stress for circular section.
g] Draw shear stress distribution diagram for a T beam showing details on it.
h] Define modulus of resilience and state its unit.

B] Attempt TWO of the following: [2x4=08]
a] Calculate the shear stress induced in a rivet used for double riveted lap joint,
having 20mm as diameter & subjected to a load of 200kN.
12083

b] A bar of 30 mm diameter is subjected to a pull of 60 kN. The measured extension
on a gauge length of 200 mm is 0.09 mm and change in diameter is 0.039 mm.
Calculate the poison’s ratio and modules of elasticity.
c] A steel bar 2.5m long is at a temperature of 20
0
c. Find the free expansion of the bar
when the temperature of the bar is raised to 65
0
c. Also find the magnitude &
nature of stress developed if the expansion is fully prevented.

Q. 2 ] Attempt FOUR of the following: [4x4=16]
a] A RCC column of 230 mm x 230 mm is reinforced with 4 bars of 12 mm
dia. Determine the stresses induced in concrete and steel if it is subjected to
an axial Load of 250kN. Take E
c
= 12GPa and E
s
= 200GPa.
b] Determine the total elongation of the bar shown in below figure If E= 200GPa.

c] A bar of 20 mm in diameter is tested in tension on UTM .The loads at
yield point, ultimate point and breaking points are 120kN, 200kN, and 160kN
respectively. Final diameter of bar is 12 mm. Determine the yield stress, ultimate
stress, nominal breaking stress and actual breaking stress.
d] A bar is having dimensions 10 mm x 20 mm x 1000 mm. It is subjected to an axial
load of 10kN. Determine change in length & width of the section if Poisson’s
ratio=0.28. Take E=2 X10
5
N/mm
2
.
e] A cube of 100 mm size is subjected to a direct load of 50kN on all its
faces. Find the change in volume if K= 1.3GPa.
f] Calculate the strains induced in a cube of 500mm side in X, Y & Z direction if it is
subjected to stress of 1200 N/mm
2
(compressive) in X direction, 800N/mm
2

(tensile) in Y direction & 600 N/mm
2
(compressive) in Z direction.

10 kN 10 kN
12mm Ø
8mm Ø
20mm Ø
1000mm
500mm
800mm
Fig.1 [Q:2(b)]

Q. 3 ] Attempt FOUR of the following: [4x4=16]
a] A simply supported beam of a span 5.8 m is having a cross section of 200 mm wide
and 500 mm deep. Calculate the intensity of uniformly distributed load the beam
can carry if the bending stress is not to exceed 25 N/mm
2
.
b] A cantilever beam of a building having span of 3m is subjected to a udl of 20kN/m
over entire span. Determine the maximum bending stresses if the c/s of beam
is 200mm x 400mm. Take E= 1.4GPa.
c] A beam having hollow rectangular section with outer and inner dimensions of
250mm x 250 mm and 150mm x 150mm respectively is subjected to a shear force
of 180kN. Calculate the ratio of maximum to average shear stress.
d] A bar of 32 mm diameter is subjected to a load of 100kN which is dropped
from a height of 300mm on to the collar attached at the other end of a bar.
Determine the instantaneous stress induced due to this impact load. Take E =
200GPa.
e] A bar of 120 x 80mm & 2.5m long is subjected to a load of 80kN. Calculate the
strain energy stored in it if the load is applied suddenly.

Q. 4 ] Attempt TWO of the following: [2x8=16]
a] Draw SF and BM diagrams for the simply supported beam loaded as shown
in below figure indicating all the values at important points.

b] Draw SF and BM diagrams for an overhanging beam as shown in below figure.
Locate the point of contra flexure if any.

5kN/m

10k
N

20k
N

3
m

2
m

3
m

A
B
D
A

C
A

Fig.2 [Q:4(a)]
10 kN/m
5 kN

4m 1m
A
C B
Fig.3 [Q:4(b)]

c] Draw SF & BM diagrams for the cantilever beam loaded as shown in below
figure. Indicate the values at important points.

Q. 5 ] Attempt TWO of the following: [2x8=16]
a] Calculate the Ixx and Iyy for the unsymmetrical I section as shown in below
figure.

b] Calculate the MI of the section about the axis AB as shown in below figure.

5 kN 2 kN 2 kN
2 kN/m
2m 2m 2m
A
D
C
B
Fig.4 [Q:4(c)]
A
B

400mm
800mmm
Fig no 6 [Q5(b)]
200mm
300mm
270mm
10mm
20mm
10mm
Fig.5 [Q:5(a)]

c] Calculate the MI of a circular section having 400mm diameter about its tangent. Also
calculate polar moment of inertia & radius of gyration of it.

Q. 6 ] Attempt TWO of the following: [2x8=16]
a] Determine the forces in the members AB, AF, AG & BG along with their nature
for the frame subjected to loads as shown in below figure. Tabulate your results.
Use method of joints.

b] Determine the forces along with their nature in the members CD,CF and CG of
the cantilever frame loaded as shown in fig no. 8. Tabulate your results. Use
method of section.

c] Determine the forces in the members CB, CI, HG & HC along with their nature
for the frame subjected to loads as shown in fig .no. 7 .Tabulate your results.
5 kN
10 kN
5 kN
A
C
B
E D
I H
A

G
F
J
2 m
2 m
2 m
2 m
2 m
Fig.7 [Q:6(a & c)]
2m 2m 2m 2m
2m
4m
6m
8m
A
F
E
D
C
B
I
H
G
5 kN
5 kN
2 kN
Fig.8 [Q:6(b)]