Unformatted text preview: 4608
Semester 1, 2008
page 1 of 10
________________________________________________________________________________ SEAT NUMBER: .....................................
FULL NAME: ...........................................
SID: ……………….................................... Faculty of ENGINEERING
School of Civil Engineering CIVL2110: Materials
Duration: 3h
Reading time: 10 mins INSTRUCTIONS TO CANDIDATES:  Closedbook exam
Programmable calculators allowed
Do not remove paper from exam room 4608
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________________________________________________________________________________
This exam is composed of three distinct parts that all need to be answered:
Part A: Metals (100 marks)
Part B: Soils (40 marks)
Part C: Concrete (100 marks)
On the last page of this exam, you will find the equation sheet previously circulated to all of you. PART A: METALS by Dr. Gwénaëlle Proust
This part contains 6 problems. The value of each problem is indicated for your information.
Problem 1: (18 marks)
a) The following table gives the composition of two steel alloys. Determine and explain which
of the two alloys will be easier to weld.
Alloys
1010
4130 %C
0.13
0.33 % Si
0.35
0.35 % Mn
0.60
0.70 %P
0.04
0.04 %S
0.04
0.04 % Cr
1.20 % Mo
0.25 b) For the less weldable alloy, give two measures that can be taken to improve its weldability.
c) Name regions A, B and C of the weld joint shown in Figure 1. Explain how and why the
microstructure has been modified during the welding process in each region of the joint. A B Figure 1: Weld joint. C 4608
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________________________________________________________________________________
Problem 2: (18 marks)
a) A cylindrical steel pressure vessel of 7.5 m diameter and 40mm wall thickness is to operate
at a working pressure of 5.1 MPa. The design assumes that a surface crack in the inside wall
will gradually extend through the wall by fatigue.
If the fracture toughness of the steel is 200 MPa m1/2 would you expect the vessel to fail in
service by leaking (when the crack penetrates the thickness of the wall) or by fast fracture?
Assume Y = 1 for the fast fracture equation.
Given: the hoop stress of a cylindrical vessel σ= pr
2t where p is the internal pressure, r the radius of the cylinder and t the wall thickness.
b) During service the growth of a flaw by fatigue is given by: da
4
= A(∆K )
dN where A = 2.44 x 1014 MPa4m1 If the initial length of the crack is 5mm, what is the pressure to which the vessel must be
subjected for failure to occur after 3000 loading cycles from zero to full load and back?
Problem 3: (16 marks)
The data shown in the following table were obtained for a carbon steel and an aluminium alloy (the
data has also been plotted on Figure 2).
a) Show that the yield strengths of this steel and aluminium alloy obey the HallPetch
relationship. Determine 0 and ky for each material.
b) Certain microalloyed steels contain small additions of vanadium or niobium that permit the
grain size to be reduced to about 2 m if the processing of the steel is carefully controlled.
Likewise, advanced aluminium alloys containing special types of particles can be processed
to have a grain size of about 2 m. Suppose we reduce the grain size to steel and aluminium
from 150 m to 2 m by such processing. Would a substantial increase in the strengths of
these materials result? Comment on your answer
Carbon Steel
Grain size
Yield Strength
d ( m)
y (MPa)
406
93
106
129
75
145
43
158
30
189
16
233 Aluminium alloy
Grain size
Yield Strength
d ( m)
y (MPa)
42
223
16
225
11
225
8.5
226
5.0
231
3.1
238 4608
Semester 1, 2008
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________________________________________________________________________________ 250 y (MPa) 200
150
100
50 Steel
Aluminium 0
0 0.2 0.4 0.6 d1/2 ( m1/2)
Figure 2: relation between grain size and yield strength for a carbon steel
and an aluminium alloy. Problem 4: (18 marks)
Describe why, how and where the corrosion occurs for the three following forms of corrosion. For
each of these three forms of corrosion cite two measures that can be taken to prevent and control it.
a) Galvanic corrosion
b) Pitting
c) Stress corrosion
Problem 5: (10 marks)
An aluminium bar 125mm long and having a square cross section 16.5mm on an edge is pulled in
tension with a load of 66,700 N, and experiences an elongation of 0.43 mm. Assuming that the
deformation is purely elastic, calculate the elastic modulus of that material. 4608
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________________________________________________________________________________
Problem 6: (20 marks)
A cylindrical cantilever beam of radius r and length L is subjected to a force F (see Figure 3). The
length L, the maximum displacement and the force F are fixed. Figure 3: Schematic of the cantilever showing its dimensions.
a) Write an expression for the mass of that cantilever as a function of the material density .
b) The beam end deflection is given by the following expression: FL3
δ=
where E is the elastic modulus and I the moment of inertia.
3 EI
For a cylindrical beam the moment of inertia is given by:
Derive an expression for the radius of the cantilever. I= π r4
4 . c) Using the equations derived in parts a) and b), derive a new expression for the mass of the
cantilever and determine the design parameter for a light and stiff cantilever.
d) Using the property chart shown on Figure 4 explain how to determine the materials with the
best combination of properties to obtain a light and stiff cantilever beam. Which material of
steel and aluminium alloys possesses the best design parameter for this particular
application? Explain. 4608
Semester 1, 2008
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________________________________________________________________________________ Figure 4: Elastic modulus – density material selection chart. 4608
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________________________________________________________________________________ PART B: SOILS by A/Prof David Airey
Answer all questions. Your answers should contain sufficient discussion, and sketches if
appropriate, to demonstrate an understanding of the issues.
a. Explain the physical basis for friction between two hard flat surfaces in contact
b. Would you expect the surface roughness to affect the friction coefficient and if so how and why?
c. A concrete foundation, shown schematically in Figure 1, is to be designed to resist normal force,
X and lateral force, Y. Three different designs have been proposed with contact areas with the soil
A1 > A2 > A3. Discuss what factors would affect the choice of footing area.
d. Discuss what properties affect the frictional resistance of a sandy soil.
e. If the foundation in Figure 1 was constructed on a sandy soil would you expect the coefficient of
friction between the sand and the concrete to be greater than, the same, or less than the friction
angle of the sand alone? Justify your answer.
X Foundation Soil
Figure 1 Y 4608
Semester 1, 2008
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________________________________________________________________________________ PART C: CONCRETE by Mr. Paul UNO !" #
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Semester 1, 2008
page 10 of 10
________________________________________________________________________________ Equation Sheet
Mechanical Properties of Metals E = 2 G (1 + ν ) Fire Consideration
σ y (T )
= 1 When 0°C < T
σ y (20 ) UTS (MPa) = 3.45 x HB
Dislocation and Strengthening Mechanisms σ y = σ 0 + k y d −1 / 2
% CW = A0 − Ad
×100
A0 215°C σ y (T ) 905 − T
=
When 215°C < T 905°C
σ y (20 )
690
E (T )
= 1.0 +
E (20 ) T
2000 ln T
1100 When 0°C < T Failure σ m = 2σ 0 600°C
T
690 1 −
E (T )
1000
=
E (20 )
T − 53.5 1/ 2 a ρt 2Eγs
σc =
πa 1/ 2 When 600°C < T 1000°C K c = Yσ c π a RambergOsgood Equation ∆K c = ∆σ c π a ε= da
= A ∆K m
dN σ
E0
ln Q
ε = K 2σ n exp − c
RT
LarsonMiller Parameter: n=
ln T (C + log t r ) + 0.002 0.002
0.0001 σ 0.002
σ 0.0001 Concrete P − B ratio = f 'cm = f 'c + 1.65s CPR = KW
ρ At Carbon Equivalent Formula
CE (% ) = %C + % Mn % Mo %Cr % Ni %Cu % P
+
+
+
+
+
6
5
5
15
15
3 n σ 0.002
ln(20) = Corrosion and Degradation of Materials AO ρ M
a AM ρ O σ ln σ 0.002
σ 0.0001 ...
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 Three '11
 various
 Civil Engineering, Friction, Aluminium, ........., Tensile strength

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