All 40 Chapters & Laboratory Exercises Covered
,Part 2: Solutions to Tutorial Questions
Introduction
This part of the instructor’s manual presents the solutions to the tutorial questions which are at the
end of the book. All of the solutions to the questions at the end of the individual chapters are given
with the questions.
The majority of these questions were originally set in exams. Typically in a two hour exam five
questions are set and the students are required to answer three of them. In a three hour exam they
answer five out of eight. An able student can often complete their solutions in far less time than this
but some, in particular those whose first language is not English, need all the time.
Solutions to essay questions should typically be about 600 words. Students are advised that there is
no need for an introduction (e.g. copying out the question) or conclusions. Marks are simply
awarded for each valid point made. Obviously the notes given here do not constitute a full essay
solution; they are only intended to give guidance on the directions the discussions should take.
Knowledge of material from other chapters has been assumed in some questions. For example, the
concept of the proof stress from chapter 30 is needed in some of the chapter 2 questions.
Chapter 1
1 How many m are there in a m?
…………….106
2 How many Pa are there in a MPa?
………….106
3 How many Pa are there in a GPa?
……………….109
4 How many ns are there in one second?
…………………109
5 If 1017 is written in non-scientific notation how many zeros are there after the 1?
………………..17
6 If 10-14 is written in non-scientific notation how many zeros are there between the decimal
point and the 1?
…………………..13
7 How many g are there in 107 kg
………………….1010
8 How many s are there in 10-2 s
…………………..104
9. The force required to make a mass m kg accelerate with an acceleration a is ma Newtons.
a. What are the units of acceleration ?
,b. What are the units of force when expressed in metres, kilogrammes and seconds ?.
c. If the force is 3.2 102 kN and the mass is 2 106 kg what is the acceleration ?
d. If the force is 4.3 103 MN and the mass is 3 g what is the acceleration ?
e. If the force is 2.7 107 N and the mass is 20 mg what is the acceleration ?
…………………………………………..
a m/s2
b kg m/s2
c 0.16 m/s2
d 1.43E12 m/s2
e 1.35E12 m/s2
10. The force on a mass m kg due to gravity is mg Newtons where g = 9.81 m/s2
a. If the force is 3.5 103 kN what is the mass ?
b. If the mass if 35700 kg what is the force ?
c. If the mass is 2 1013 g what is the force ?
…………………………..
a 3.57E5 kg
b 3.5E5 N
c 1.96E11 N
11. The energy needed to apply a force F Newtons over a distance L metres is FL Joules.
a. What are the units of energy when expressed in metres, kilogrammes and seconds ?
b. If the force is 3.5 108 N and the distance is 5 km what is the energy ?.
c. If the force is 2.7 105 kN and the distance is 20 mm what is the energy ?
d. If the energy is 2 104 MJ and the distance is 2 107 m what is the force ?
……………………………….
a kg m2/s2
b 1.75E12 J
c 5.4E6 J
d 1000 N
12. The stress on an area A m2 due to a force F Newtons is F/A Pascals.
a. What are the units of stress when expressed in metres, kilogrammes and seconds ?
b. If the force is 3 GN and the stress is 20 GPa what is the area ?
c. If the force is 5 105 N and the stress is 10 kPa what is the area?
d. If the force is 2.2 103 N and the area is square with side 100 mm what is the stress ?
e. If the force is 20 MN and the stress is 20 mPa on a square area what is the length of the side ?
f. If the force is 3.2 107 N and the stress is 2 1015 Pa on a square area what is the length of the side ?
a kg/(m s2)
b 0.15m2
c 50m2
d 2.2E5 Pa
e 3.16E4 m
f 1.26E-4 m
Chapter 2
1.
, a. The following observations are made when a 100mm (3.94 in.) length of 10mm (0.394 in.)
diameter steel bar is loaded in tension:
Extension extension
Load kN
mm Load kip in.
0 0 0.00 0.0000
1.57 0.01 0.35 0.0004
4.71 0.03 1.06 0.0012
7.85 0.05 1.77 0.0020
9.42 0.06 2.12 0.0024
15.7 0.1 3.53 0.0039
18.84 0.12 4.24 0.0047
21.98 0.14 4.95 0.0055
23.55 0.15 5.30 0.0059
24.5 0.2 5.51 0.0079
25.5 0.3 5.74 0.0118
25.9 0.365 5.83 0.0144
26.5 0.5 5.96 0.0197
28.5 1 6.41 0.0394
31.5 1.9 7.09 0.0748
Calculate the following:
a. the Young's modulus
b. the 0.2% proof stress
c. the yield stress
d. the ultimate stress
e. Explain which of these measurements is used for specification of steel and why it is used.
…………………………………………………..
MKS solution
The student should plot the points
cross sectional area of bar = 0.01 0.01 PI/4 = 0.000078 m2
a. The points are linear up to 0.15 mm thus E = 23.55 100 /(0.15 area) = 201 GPa
b. A line drawn parallel to the linear portion at 0.2mm greater extension intersects the curve at 25.905
kN. Thus Stress = 25.905/area = 332 MPa
c. Yield is at 23.55 Kn thus stress = 23.55/area = 302 MPa
d. Ult load = 31.4 kN thus stress = 31.4/area = 402 MPa
US unit solution
The student should plot the points
cross sectional area of bar = 0.394 0.394 PI/4 = 0.122 in2
,Part 2: Solutions to Tutorial Questions
Introduction
This part of the instructor’s manual presents the solutions to the tutorial questions which are at the
end of the book. All of the solutions to the questions at the end of the individual chapters are given
with the questions.
The majority of these questions were originally set in exams. Typically in a two hour exam five
questions are set and the students are required to answer three of them. In a three hour exam they
answer five out of eight. An able student can often complete their solutions in far less time than this
but some, in particular those whose first language is not English, need all the time.
Solutions to essay questions should typically be about 600 words. Students are advised that there is
no need for an introduction (e.g. copying out the question) or conclusions. Marks are simply
awarded for each valid point made. Obviously the notes given here do not constitute a full essay
solution; they are only intended to give guidance on the directions the discussions should take.
Knowledge of material from other chapters has been assumed in some questions. For example, the
concept of the proof stress from chapter 30 is needed in some of the chapter 2 questions.
Chapter 1
1 How many m are there in a m?
…………….106
2 How many Pa are there in a MPa?
………….106
3 How many Pa are there in a GPa?
……………….109
4 How many ns are there in one second?
…………………109
5 If 1017 is written in non-scientific notation how many zeros are there after the 1?
………………..17
6 If 10-14 is written in non-scientific notation how many zeros are there between the decimal
point and the 1?
…………………..13
7 How many g are there in 107 kg
………………….1010
8 How many s are there in 10-2 s
…………………..104
9. The force required to make a mass m kg accelerate with an acceleration a is ma Newtons.
a. What are the units of acceleration ?
,b. What are the units of force when expressed in metres, kilogrammes and seconds ?.
c. If the force is 3.2 102 kN and the mass is 2 106 kg what is the acceleration ?
d. If the force is 4.3 103 MN and the mass is 3 g what is the acceleration ?
e. If the force is 2.7 107 N and the mass is 20 mg what is the acceleration ?
…………………………………………..
a m/s2
b kg m/s2
c 0.16 m/s2
d 1.43E12 m/s2
e 1.35E12 m/s2
10. The force on a mass m kg due to gravity is mg Newtons where g = 9.81 m/s2
a. If the force is 3.5 103 kN what is the mass ?
b. If the mass if 35700 kg what is the force ?
c. If the mass is 2 1013 g what is the force ?
…………………………..
a 3.57E5 kg
b 3.5E5 N
c 1.96E11 N
11. The energy needed to apply a force F Newtons over a distance L metres is FL Joules.
a. What are the units of energy when expressed in metres, kilogrammes and seconds ?
b. If the force is 3.5 108 N and the distance is 5 km what is the energy ?.
c. If the force is 2.7 105 kN and the distance is 20 mm what is the energy ?
d. If the energy is 2 104 MJ and the distance is 2 107 m what is the force ?
……………………………….
a kg m2/s2
b 1.75E12 J
c 5.4E6 J
d 1000 N
12. The stress on an area A m2 due to a force F Newtons is F/A Pascals.
a. What are the units of stress when expressed in metres, kilogrammes and seconds ?
b. If the force is 3 GN and the stress is 20 GPa what is the area ?
c. If the force is 5 105 N and the stress is 10 kPa what is the area?
d. If the force is 2.2 103 N and the area is square with side 100 mm what is the stress ?
e. If the force is 20 MN and the stress is 20 mPa on a square area what is the length of the side ?
f. If the force is 3.2 107 N and the stress is 2 1015 Pa on a square area what is the length of the side ?
a kg/(m s2)
b 0.15m2
c 50m2
d 2.2E5 Pa
e 3.16E4 m
f 1.26E-4 m
Chapter 2
1.
, a. The following observations are made when a 100mm (3.94 in.) length of 10mm (0.394 in.)
diameter steel bar is loaded in tension:
Extension extension
Load kN
mm Load kip in.
0 0 0.00 0.0000
1.57 0.01 0.35 0.0004
4.71 0.03 1.06 0.0012
7.85 0.05 1.77 0.0020
9.42 0.06 2.12 0.0024
15.7 0.1 3.53 0.0039
18.84 0.12 4.24 0.0047
21.98 0.14 4.95 0.0055
23.55 0.15 5.30 0.0059
24.5 0.2 5.51 0.0079
25.5 0.3 5.74 0.0118
25.9 0.365 5.83 0.0144
26.5 0.5 5.96 0.0197
28.5 1 6.41 0.0394
31.5 1.9 7.09 0.0748
Calculate the following:
a. the Young's modulus
b. the 0.2% proof stress
c. the yield stress
d. the ultimate stress
e. Explain which of these measurements is used for specification of steel and why it is used.
…………………………………………………..
MKS solution
The student should plot the points
cross sectional area of bar = 0.01 0.01 PI/4 = 0.000078 m2
a. The points are linear up to 0.15 mm thus E = 23.55 100 /(0.15 area) = 201 GPa
b. A line drawn parallel to the linear portion at 0.2mm greater extension intersects the curve at 25.905
kN. Thus Stress = 25.905/area = 332 MPa
c. Yield is at 23.55 Kn thus stress = 23.55/area = 302 MPa
d. Ult load = 31.4 kN thus stress = 31.4/area = 402 MPa
US unit solution
The student should plot the points
cross sectional area of bar = 0.394 0.394 PI/4 = 0.122 in2
