ENGINEERING FACULTY
DEPARTMENT OF MECHANICAL ENGINEERING
COURSE:
National Diploma in Mechanical Engineering
(D3MCHE)
SUBJECT:
STRENGTH OF MATERIALS II - STL261S
Assignment 1: Stress & Strain and Torsion of Shafts
DATE:
04 May 2021
DUE DATE:
18 May 2021
WEIGHTING:
20%
EXAMINER:
MODERATOR:
M. LUDICK…………………………………
S. MAKHOMO / W. BOSHOFF…………………….
INSTRUCTIONS
1.
2.
3.
4.
5.
6.
7.
DOCUMENT TO BE TYPED OR NEATLY HANDWRITTEN.
NO LATE SUBMISSIONS WILL BE ACCEPTED.
DRAW SKETCHES TO ASSIST IN SOLVING THE PROBLEMS.
DRAWINGS MUST BE DONE IN PENCIL.
CALCULATIONS CAN BE TYPED OR HANDWRITTEN NEATLY IN INK
(BLUE \ BLACK) ONLY.
YOU MAY WORK INDIVIDUALLY OR IN GROUPS OF UP TO FIVE (5)
MEMBERS MAXIMUM.
ANY FORM OF COPYING WILL RESULT IN ALL INVOLVED GROUPS
TO GET ZERO MARKS!
SURNAME & INITIALS
STUDENT NUMBER
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2…………………………………
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STL261S – Assignment 1: Stress & strain and Torsion of Circular Shafts
Question 1
A bicycle chain consists of a series of small links, where each is 12 mm long between the
centres of the pins (see figure). You might have to observe a bicycle chain and observe its
construction. The pedal crank arm has a length L = 162 mm centre to centre as shown and the
sprocket (toothed gearwheel) radius R = 90 mm.
1.1
1.2
Calculate the tensile force T in the chain due to a force F = 800 N applied to one of the
pedals.
/4/
Calculate the average shear stress τ in the pins.
/6/
[10]
Question 2
A force P of 70 N is applied by a rider (cyclist) to the front handbrake of his bicycle. (P is the
resultant of an evenly distributed hand pressure). As the handbrake pivots at A, a tension T
develops in the 460 mm long brake cable (cross-sectional area = 1.075 mm2), which
elongates by 0.214mm.
2.1 Determine the stress in the cable.
/3/
2.2 Determine the strain in the cable.
/2/
2.3 Determine the modulus of elasticity of the cable.
/3/
2.4 What material is used to manufacture the cable? Motivate your answer.
/2/
[10]
Question 3
A uniform beam, 1 metre long, is suspended in a horizontal position by two vertical support
rods as shown in the figure below. Rod A has a diameter of 12 mm and manufactured from
steel with Esteel = 200GPa. Rod B has a diameter of 16 mm and is made from copper with
Ecopper = 100 GPa. This simply supported beam is to carry a motor vehicle engine and
gearbox weighing 10 kN.
3.1 Determine the distance ‘x’ from the left-hand support ‘A’ in order for the beam to remain
in a horizontal position.
/7/
3.2 Calculate the stress in each rod due to the applied load.
/4/
3.3 Calculate the movement (extension) of the support wires under this 10 kN load.
/2/
3.4 Will the rods be able to withstand the applied load? Motivate your answer.
/2/
500 mm
300 mm
A
B
x
10 kN
1000
mm
[15]
Question 4
Two solid shafts, 50 mm in diameter, are connected by a rigid flange coupling. The coupling has
a pitch circle diameter of 95 mm and the coupling bolt diameter is 11 mm. The bolts and the shafts
are to have the same maximum shear stress.
4.1 Calculate the number of bolts required.
/4/
4.2 If the maximum working shear stress is limited to 55 MPa, calculate the maximum power that
can be transmitted by the coupling at 700 r/min.
/4/
4.3 If the overall angle of twist is not to exceed 10, what must be the length of the shaft assembly?
(Ignore the effects of the coupling).
/2/
[10]
Question 5
A transmission shaft has gears attached to it and is subjected to the torques as shown below.
The shaft has a diameter of 40 mm and is made from steel with G = 80 GPa.
5.1 Calculate the maximum shear stress in the shaft.
.
5.2 Determine the angle of twist of end B with respect to end A.
/10/
/5/
[15]
TOTAL = [60]
STL261S: Stress & Strain and Torsion
MARKING CRITERIA – 2021: Assignment 1
1.1
1.2
2.1
2.2
2.3
2.4
Question 1
Tensile force T
Shear stress τ
4
6
Question 2
Stress in cable
Strain in cable
ECable
Cable material
Motivation
3
2
3
1
1
Question 3
3.1
3.2
3.3
3.4
x - distance
Stress in each rod
Wire extension Δl
Load carrying capability of rods
Motivation
7
4
2
1
1
Question 4
4.1
4.2
4.3
No. of Bolts
Max Power transmitted
Overall shaft assembly length
4
4
2
5.1
5.2
Question 5
Max shear stress τ in shaft
Overall angle of twist θ
10
5
Graduate Attribute
GA1 Problem solving
TOTAL
%
5
65