s
ME202 1 / 8
UNIVERSITY OF BRIGHTON
SCHOOL OF ENGINEERING
MODULAR HONOURS DEGREE COURSE
LEVEL 2
SEMESTER 1
2001/2002
Examiners Dr M Philip/Dr E Sazhina
Attempt 5 questions only. Time allowed : 3 hours
Total number of questions = 8
All questions carry equal marks.
The figures in brackets indicate the relative weightings of parts of a question.
Special requirements :
Graph paper
Equations List

ME202 2 / 8
1) A single rivet of 16mm diameter is used to join two plates of the in coupling single shear as shown in Figure Q1a. The coupling is loaded in tension by
P = 8 kN. a) What is the average shear stress developed in the rivet? b) If the maximum allowable shear stress in the rivet is 80 MN/m
2
, what force is required to cause the rivet to fail in shear? c) If the coupling is constructed from three steel plates joined together by the
(4)
(3) rivet in double shear as shown in Figure Q1b, what is the average shear stress in the rivet? (4) d) What force is required to cause the coupling shown in Fig 1b to fail in shear? (3) e) Estimate the safety factor based on Tresca failure theory if the yield strength of the rivet material is
 yield
= 300 MN/m
2
. (3) f) Estimate the safety factor based on Von Mises failure theory assuming that an element is in pure shear and

= 80 MN/m
2
. Yield strength of the rivet material is
 yield
= 300 MN/m 2 . (3)
P
P
Figure Q1a: Two plates in single shear
P
P
Figure Q1b: Three plates in double shear

ME202 3 / 8
2) A steel cylinder in a Diesel engine has an inside diameter 100 mm. It is designed for a maximum pressure of 8 MN/m
2
. The thickness of the cylinder wall is 5mm. a) Describe the nature of the principal stresses in elements in the wall of the cylinder. b) Calculate the hoop and longitudinal stresses by thin cylinder theory c) Calculate the hoop and radial stresses by thick cylinder theory d) Determine the maximum shear stress in the cylinder wall
3) During a static test of an airplane wing the strain gauge readings from a 45
 rosette (see Figure Q3) were found to be as follows: gauge A:

A
= 420

10
-6
; gauge B:

B
= 350

10
-6
; gauge C:

C =
-70

10
-6
. a) Describe the role of the strain gauge in experimental stress analysis. b) Determine the principal planes. c) Determine the principal strains. d)
Determine the principal stresses if Young’s modulus, E = 207 GN/m 2
and
Poisson’s ratio, 
= 0.30. e) Determine the factor of safety according to the Tresca criterion if yield stress
 yield
= 360 MN/m
2
.

C

B

A x
Figure Q3: A 45

strain gauge rosette
(4)
(5)
(6)
(5)
(4)
(4)
(4)
(4)
(4)

ME202 4 / 8
4) An overhead crane travelling along guide rails is used to transport equipment along a corridor. Consider one section between two supports A and B fixing the rail to the ceiling, as illustrated in Figure Q4.
Treating this as a simply supported beam of length, L = 3 m between supports A and B, calculate the deflection due to a single concentrated load W = 10 kN acting at point C.
The beam is made of steel having a modulus of elasticity E = 200 GN/m 2 . The flexural rigidity of the beam is constant. Assume that I = 5800 cm 4 . a) Calculate the flexural rigidity of the beam b) Calculate the strain energy due to bending of the beam c) Using Castigliano’s theorem, determine the deflection at the point C, where the load is applied.
W
A a=2m
C b=1m
B x
1 x
2
Figure Q4: Supports for overhead crane
(4)
(8)
(8)

ME202 5 / 8
5) A torque T = 8500 Nm rotates a propeller shaft for a small ship at 100 rev/min.
The shaft is made of solid steel bar 120 mm in diameter. Figure Q5 illustrates the arrangement where the element ABCD is perpendicular to the radius from the central axis of symmetry of the cylinder. a) Describe the stresses acting on an element ABCD and their dependence on radial distance from the shaft axis b) Calculate the stresses acting on the element ABCD on the shaft surface. c)
Construct Mohr’s circle of stress and describe the stresses acting on an element rotated by 45

to the element ABCD . d) Calculate the power transmitted by the shaft. e) Determine the maximum torque that can be applied to the shaft if the allowable angle of twist is 2

over 3 m of length and G = 80 GN/m
2
.
A B
C D
Figure Q5: Propeller shaft in torsion
(3)
(3)
(5)
(4)
(5)

ME202 6 / 8
6) A beam of rectangular cross-section 200

300 mm is supported at points B and C as shown on Figure Q6a. The beam is loaded by two end loads W = 9 kN each.
The overall beam length AD is L = 3m. In addition, the overhangs AB and CD are each of length, 0.5 m. a) Describe the normal and shear stresses in a cross-section of the beam and the location of their maximum and minimum values as function of distance from the neutral axis . b) Construct shear force and bending moment diagrams for the beam
(4)
(6) c) Determine the maximum bending stress at the midpoint of the beam (point E) (5) d) Determine the maximum shear stress at a point F located 0.3 m from point A. (5)
A F B E
W y x
Figure Q6a: Schematic view of beam
under load
C D
W y z
200mm
Figure Q6b: View of cross-section of beam

ME202 7 / 8
7) Syndiotactic polypropylene is a semicrystalline polymer with the following properties:-
Density = 905 kg/m
3
Glass transition temperature, T
G
= - 10 o
C
Maximum operating temperature, T
Op
= 105 o
C
Physical properties at T = 21 o
C :-
Tensile strength = 33 MN/m
2
Flexural modulus = 1.5 GN/m
2
Elongation at break = 150 %
(a) Sketch and describe the load / extension characteristics of such a polymer at T = 21 o
C when subjected to a tensile test at a relatively low strain-rate.
(b) How is this behaviour changed if the test is repeated at a higher strain-rate while keeping the temperature constant?
(c) Sketch the load/extension behaviour for mild steel subjected to a tensile test, describe its features and compare the characteristics with those observed in (a).
(10)
(4)
(6)

ME202 8 / 8
8) (a) Describe the essential features of the Standard Linear Solid model when used to describe the viscoelastic behaviour of solid polymers. Although a derivation is not required, the description should include the model components and relevant equations.
(b) For the applied stress profile shown in Figure Q8, sketch the strain behaviour predicted from (a), over a time span from t = t
0 to t > t
1
if the Boltzmann superposition principle is assumed to apply.
Stress,

(10)
(6) t
0 t
1 time, t
Figure Q8: Stress profile for creep test
(c) What are the limitations of the Kelvin-Voigt model when used to explain stress relaxation as well as creep behaviour? (4)