ME244_2011

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ME244_2011
Materials (ME244)
s
School of Computing, Engineering and Mathematics
Division of Engineering and Product Design
Semester-Two Examinations, June 2011
B.ENG. HONOURS DEGREE COURSE
MATERIALS (ME244)
EXAMINER: DR. S.H. LEE
Instructions to Candidates:
 The time allowed is TWO hours
 Attempt any FOUR questions only
 The total number of questions is SIX
 Each question carries 25 marks
 This is a CLOSED-BOOK examination
Special Requirements:
 Formulae Sheets (pages 5-6)
Page 1 of 7
Materials (ME244)
Question 1
Two rods A and B of equal free length hang vertically 60 cm apart and support a rigid
bar horizontally. The bar remains horizontal when carrying a load of 5000 kg at
20 cm from A as shown in Figure Q1. If the stress in B is 50 N/mm2:
(a) Find the stress in rod A.
(10 marks)
(b) Calculate the areas of rod A and B.
90,000 N/mm2.
EA = 200,000 N/mm2 and EB =
(15 marks)
60 cm
Rod B
Rod A
9m
20 cm
5000 kg
m
Figure Q1
Question 2
A solid phosphor-bronze shaft, 5 cm diameter, rotating at 400 r.p.m., is subjected to
torsion only. An electrical resistance strain gauge is mounted on the shaft with the
axis of the gauge at 45° to the axis of the shaft. Determine the power being
transmitted if the strain gauge reading is 4.17 x 10 -4. For phosphor-bronze E =
105,000 N/mm2.
(25 marks)
Page 2 of 7
Materials (ME244)
Question 3
The I-beam shown in Figure Q3 is simply supported at its ends over a 9 m span and
carries a concentrated load, W at a distance of 3 m from one support. Calculate the
concentrated load which can be carried when the maximum permissible stress is
75 N/mm2.
110 mm
W
12 mm
8 mm
230
mm
3
m
9m
Figure Q3
(25 marks)
Question 4
A girder 30 m long carrying a uniformly distributed load of 2 kN/m is supported on
two piers 18 m apart as shown in Figure Q4. Draw the shearing force and bending
moment diagrams and find the position and magnitude of the maximum bending
moment.
2 kN/m
5m
18 m
7m
Figure Q4
(25 marks)
Page 3 of 7
Materials (ME244)
Question 5
(a) What assumptions are made when analysing a pressure vessel as a thin-walled
vessel?
(4 marks)
(b) What is the limiting ratio of radius to wall thickness of a pressure vessel?
(4 marks)
(c) A cylindrical compressed-air drum is 1.9 m in diameter with plates 12.7 mm
thick. The efficiencies of longitudinal and circumferential joints are respectively
85% and 45%. If the tensile stress in the plating is limited to 100 N/mm 2, what is
the maximum safe air pressure?
(17 marks)
Question 6
An element in plane stress from the fuselage of an airplane is subjected to stresses
of σx = 60 MPa, σy = -35 MPa and xy = -38 MPa.
(a) Determine the stresses acting on an element rotated through an angle of 15°
anticlockwise from the x axis.
(15 marks)
(b) Calculate the principal stresses on the element.
(10 marks)
Page 4 of 7
Materials (ME244)
FORMULAE SHEET
Materials
Young’s modulus
ratio
Shear modulus
where  is Poisson’s
where  is the coefficient of expansion
Thermal strain
Safety factor,
Bending and Torsion
Axial loading:
Relationship between lateral and longitudinal (axial) strain:
Beam bending:
Second moment of area:
For a rectangle about N.A.:
For a circle about diameter:
where  is the shear stress produced by a torque T, J
Shear and torsion:
is the polar second moment of area, G is the shear modulus and
twist produced over a length .
where
is the angle of
is the shear strain
Polar second moment of area:
Solar circular shaft:
Hollow circular shaft:
Power in a shaft = torque  angular velocity (rad/s) = 2nT where n is the revolutions
per second
Page 5 of 7
Materials (ME244)
Thin-Walled Pressure Vessels
Cylindrical: Hoop stress
, longitudinal stress
Spherical:
Page 6 of 7
Materials (ME244)
Biaxial Stress (Plane stress)
Principal stresses
45 strain gauge rosette
Stress/strain transformation
Page 7 of 7

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