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Sample Question Paper for 9210-130
Graduate Diploma in Mechanical Engineering
Mechanics of machines and strength of materials
Duration: three hours
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pen, pencil, ruler
General instructions
• This paper consists of nine questions over two sections A and B.
• Answer five questions, at least two questions from each section.
• All questions carry equal marks. The maximum marks for each section within a
question are shown.
• Use graph papers to answer Questions 1 and 5.
© The City and Guilds of London Institute
Section A
1
a
Define briefly the terms principal stress and principal plane in a two
dimensional stress system.
b
A structural member is loaded in such a manner that at a particular point
in the member a two dimensional stress system, consisting of
Vx
60 N / mm 2 , V y
40 N / mm 2 and W xy
(4 marks)
50 N / mm 2
exists.
2
i
Calculate the direct strain in the x and y directions and the shear
strain Ȗxy at the given point.
(6 marks)
ii
Calculate the principal strains at the point and determine the
positions of the principal planes.
(5 marks)
iii
Verify your answer using a graphical method. Take Modulus of
elasticity ‘E’ = 200 kN/mm2 and ȣ = 0.3.
Use attached worksheet WSQ1.
(5 marks)
a
Briefly explain the effect of change of temperature in a composite bar.
(3 marks)
b
Define stress, strain and elasticity.
(3 marks)
c
Derive a relation between stress and strain of an elastic body.
(3 marks)
d
A simply supported beam ABCD 4 m long is overhanging by 1 m and
carries loads as shown in Figure Q 2.
(11 marks)
4 kN
2 kN/m
B
A
1m
D
C
1m
2m
Figure Q2
Draw the shear force and bending moment diagrams for the beam and
locate the point of contraflexture.
3
a
State Castigliano’s first and second theorems for strain energy.
(4 marks)
b
Explain the application of these theorems.
(4 marks)
c
A simply supported beam of span 3 m, is carrying a uniformly distributed
load of 20 kN/m over the whole span. Using Castigliano’s theorem, obtain
the deflection at the center of the beam if section modulus ‘EI’ of the
material is 2.5 MNm2.
2
(12 marks)
4
a
What are the limitations of Euler formula?
(3 marks)
b
A long strut with both ends clamped is subjected to a compressive load P
as shown in Figure Q4
(7 marks)
P
MA
L
X
Y
P
MB
Figure Q4
Show that the critical buckling load Pcr is given by
Pcr
c
4S 2 EI
where L is length of the strut and EI is the flextural stiffness
L2
A steel bar with both ends pin jointed is compressed longitudinally until it
buckles. Length of the bar is 2.0 m and cross section is 20x5 mm2. Using
Euler’s formula estimate the maximum central deflection before the yield
point is reached.
(10 marks)
Take Modulus of elasticity, E = 210 GPa and yield stress = 330 MPa
3
See next page
Section B
a
Figure Q5(a) shows a link OA rotating about O with a uniform angular
velocity Ȧ and a block B sliding along OA with a linear velocity v. Express
the magnitude of the Coriolis component of acceleration of B relative to
OA and indicate its sense.
(4 marks)
A
B
v
Ȧ
O
Figure Q5(a)
b
Figure Q5(b) shows a quick return mechanism in which the crank OA
rotates clockwise at a uniform angular velocity of 10 rad/s about the fixed
point O. The crank makes the slotted lever BC rotate about the fixed point
Q. End C is connected to a slider D by a connecting rod CD. The slider D
reciprocates in fixed guides. The lengths of the links are, OA = 200 mm,
CQ = 150 mm and CD = 500 mm.
For the position shown determine :
C
Ɣ
D
100 mm
5
Q
Ɣ
Ɣ
ƔO
60o
A
Not to Scale
Ɣ
B
Figure Q5(b)
i
velocity of D
(8 marks)
ii
angular acceleration of slotted lever BC.
(8 marks)
Use attached worksheet WSQ5.
4
6
7
8
a
State and prove the belt friction formula for a flat belt with negligible mass
in contact with a cylindrical pulley.
b
An open belt 4 mm thick and 75 mm wide is used to transmit power
between two parallel shafts the axes of which are 2.5 m apart. The
diameter of the pulley on the driving shaft is 900 mm and it rotates at a
speed of 240 rev/min. The speed ratio between the driving and driven
shafts is 1.5. The belt material has a linear density of 2.5 kg/m and a
permissible stress of 4 N/mm2. The coefficient of friction between the belt
and the pulley is 0.2.
Determine,
(6 marks)
i
the angle of lap of the smaller pulley
(6 marks)
ii
the maximum power that can be transmitted through the belt drive
if the initial tension has been adjusted to 1100 N.
(8 marks)
a
Explain what is meant by an isochronous governor.
b
A Porter governor has all four arms of equal length of 250 mm. The upper
arms are pivoted on the axis of rotation and the lower arms are attached
to the sleeve at distances of 30 mm from the axis. The mass of each ball is
5 kg and the load on the sleeve is 40 kg. If the extreme radii of rotation of
the governor balls are 160 mm and 200 mm, determine the corresponding
equilibrium speeds.
(16 marks)
a
Why is it necessary to attach a flywheel to a machine which requires a non
uniform operating torque when it is driven by a constant torque motor?
(4 marks)
b
A constant torque motor running at a speed of 300 rev/min, drives a
machine that requires a torque increasing uniformly from 400 Nm to 1600
Nm in the first 180o of the cycle and it remains constant for the next 360o.
The torque then decreases uniformly to 400 Nm in the next 180o and
remains constant for the remaining 360o of the cycle. This cycle is
repeated. Determine the output power of the motor and the coefficient of
fluctuation of speed if the moment of inertia of the flywheel is 160 kgm2.
(16 marks)
5
(4 marks)
See next page
9
a
Figure Q9 shows a uniform rod AB of length L and mass m hinged at A and
supported at C by a spring of stiffness k. A dashpot of damping constant b
is fitted to the rod at D. The rod is horizontal in the static equilibrium
position. This system executes vibrations in the vertical plane. Derive the
equation of motion and obtain expressions for the damped natural
frequency and the logarithmic decrement of the motion assuming the
system to be underdamped.
b
If L = 2.4 m, m = 40 kg, k = 6250 N/m and b = 175 Ns/m, determine,
(12 marks)
0.5L
b

D
A
C
B
k
0.75L
L
Figure Q9
i
the frequency of free vibrations if the dashpot is disconnected,
(4 marks)
ii
the frequency of damped vibrations and the ratio of successive
amplitudes on the same side of the equilibrium position if the
dashpot is operative.
(4 marks)
6