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```									                                      CN213 Strength of Materials

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School of Environment & Technology

Semester 1 Examinations 2007-2008

CN213

STRENGTH OF MATERIALS

Instructions to Candidates

Time allowed: TWO hours

Answer ALL questions from Section A
Answer TWO questions from Section B

All questions carry equal marks

January 2008

Page 1 of 9
CN213 Strength of Materials 2007-08

SECTION A
Answer BOTH questions from this section

Question 1

(a)   A steel shaft with a diameter of d = 60 mm is subjected to a torque of
T= 3000 Nm and an axial force of F = 100 kN as shown in Figure 1.

(i)     Determine the normal stress and in-plane shear stress that act on a point
on the surface of the shaft. Sketch the stress state in a typical plane
element on the bar surface.
(4 marks)

(ii)    Determine the principal stresses and the maximum in-plane shear stress
that act at a point on the surface of the shaft.
(4 marks)

(iii)   Determine the angles p and s corresponding with the maximum principal
stresses and maximum shear stresses.
(4 marks)

F

T

y

x

T

F

Figure 1

Question 1 continues on next page 

Page 2 of 9
CN213 Strength of Materials 2007-08

Question 1 (continued from previous page)

(b)   A channel section with a cross section as shown in Figure 2 is subjected to a
load P = 4 kN acting vertically at point A.
(i)     Determine the position of the shear centre of the channel section
(5 marks)
(ii)    Determine the torque that is applied to the section by the load P
(2 marks)
(iii)   Assuming the section is used to construct a cantilever beam of length
L = 1.5 m and that the load P is applied at the free end of the beam,
determine the angle of twist if G = 75 GPa.
(6 marks)
P

A
y

b/2          tf = 6 mm

h = 100 mm                                z

tw = 10 mm

b = 60 mm

Figure 2

Page 3 of 9
CN213 Strength of Materials 2007-08

Question 2
(a)   A piece of steel as shown in Figure 3 is subjected to a load P.

(i)    Determine the radius r of the fillets so that the maximum stress in vicinity
of the fillets is equal to the maximum stress in the vicinity of the hole with
diameter d = 20 mm.
(Use the graphics provided in the aide memoire to solve this question)
(12 marks)
(ii)   Determine the maximum allowable load P if the allowable normal stress is
80 MPa.
(3 marks)
15 mm

r

20 mm            50 mm           P

80 mm

Figure 3

(b)   Figure 4 shows a strain gauge rosette attached to the surface of a structural
member. The following strains have been measured by the strain rosette:
A = 25010-6, B = -10010-6, C = 32010-6.
Determine the largest in-plane normal strain.
(10 marks)

Figure 4

Page 4 of 9
CN213 Strength of Materials 2007-08

SECTION B

Answer ANY TWO questions from this section

Question 3
(a)   A wooden member is subjected to plane stress as shown in Figure 5. The grain
forms an angle of 35 with the horizontal. Use Mohr’s circle to determine the in-
plane shearing stress parallel to the grain and the normal stress perpendicular
to the grain.
(15 marks)

-4.5 MPa

3 MPa

2 MPa
35

Figure 5

Question 3 continues on next page 

Page 5 of 9
CN213 Strength of Materials 2007-08

Question 3 (continued from previous page)

(b)   A tube is made of aluminium and has a rectangular hollow cross-section as
shown in Figure 6. The tube is subjected to the torque T. The tube is fixed at D.
The shear modulus G= 26 GPa.

(i)    Determine the average shear stress in the tube at points A and B.

(5 marks)

(ii)   Determine the angle of twist at end C in degrees.

(5 marks)

fixed
8mm
A

T = 50 Nm                    B         D
5mm                             A
50 mm

B
5mm
8mm
L = 2.5 m
C
35 mm

Figure 6

Page 6 of 9
CN213 Strength of Materials 2007-08

Question 4
(a)   Find the strain energy stored in bars (i), (ii) and (iii) with applied torques as
shown in Figure 7. Use TB = 100 Nm, TC = 150 Nm, L = 1.6m,
G = 80 GPa and diameter of the bars d= 30mm.
(12 marks)
A                            B
(i)                                          TB

L

A             C             B
(ii)                           TC

L/2

A             C             B
(iii)                          TC            TB

L/2           L/2

Figure 7

Question 4 continues on next page 

Page 7 of 9
CN213 Strength of Materials 2007-08

Question 4 (continued from previous page)

(b)   A beam is made of wide flange section with a cross section as shown in
Figure 8 (all dimensions a are equal, flanges and web have the same thickness
t = 5mm). The beam is fixed at one end and subjected to a torque of
T = 100 Nm at the free end.
(i)    Determine the length a that is required if the maximum allowable shear
stress in the section is allow = 50 MPa.
(7 marks)
(ii)   Determine the length a that is required if the maximum allowable angle of
twist at the free end of the beam is allow = 5. (Length of the beam is
L = 2 m, G = 78 GPa).
(6 marks)

a

t = 5 mm

a
t = 5 mm

a

Figure 8

Page 8 of 9
CN213 Strength of Materials 2007-08

Question 5
(a)   The concrete pier shown in Figure 9 is subjected to a load P = 500 kN applied
at position a = 0.8 m and b = 1.0 m from the centroid of its cross section.

(i)    Determine the normal stress at the corners A and C indicating if these are
compressive or tensile. Neglect the weight of the pier.          (12 marks)

(ii)   Determine the angle between the neutral axis and the z-axis in the y-z
plane. Draw a sketch of the y-z plane showing the neutral axis.
(3 marks)

P = 500 kN
z

1.6 m
b     a
y
1.6 m
A
2.5 m        2.5 m

C

Figure 9

(b)   The plane stress state shown in Figure 10 occurs in a structural element with
yield stress Y = 450 MPa. Determine whether yield will occur in the element. If
yield does not occur, determine the factor of safety.

(i)    Use the maximum principal stress criterion                          (5 marks)

(ii)   Use the maximum distortional energy criterion                       (5 marks)

y = 250 MPa

xy = 50 MPa

x = 200 MPa

Figure 10

Page 9 of 9

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