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School of Civil, Environmental & Mining Engineering
Practice test 1: Axial loading & Torsion (Chapters 1-3)
CEME 2001: Strength of Materials
Important note: This is a practice test to prepare for Test 1 on 9 April 2021. There should be no
assumptions that the same types of questions will be asked in Test 1.
INSTRUCTIONS TO CANDIDATES
1. This is an OPEN book test.
2. This is a 60-min test (including the reading time). 30 minutes are added to take into account
the time (and any potential minor issues) for downloading questions, scanning and uploading
solutions on MyUni.
3. All questions carry equal marks.
4. Clearly state your procedure and show all the calculations. A correct answer without any
details will not result in any marks.
5. If you believe that additional information is required, clearly state your assumption and
proceed with your solution.
6. Solutions should be uploaded as a single PDF file on MyUni. You can use CamScanner to
convert photos taken using your smart phone (either Android or iPhone) to a single PDF file
with good quality. The free version is sufficient for this purpose. Please install and try it a few
times before the quiz.
Each question will be marked following the below criteria:
x Correct approach and answer: 100% mark
x Correct approach and answer but wrong unit: 81% - 90%
x Correct approach but wrong answer: 31% - 80% mark
x Incorrect approach and answer but demonstrating a certain level of understanding: 1% - 30% mark
x Incorrect approach and answer, and demonstrating no understanding: 0% mark
Formulae you may find useful:
Axial Loading:
A
P V ,
L
GH ,
EA
PL G
Torsion:
T
J
UW , GW J ,
L
UIJ ,
JG
TL I
,
For a solid circular cross-section with radius r:
2
4rJ S
For a hollow circular cross section: 4 41 outside inside2J r rS
Page 2 of 2
Question 1 (50 marks total):
The rigid beam ACE is subjected to the load P and
suspended at points A, C, and E by three suspender bars
AB, CD, and EF (see Figure 1). These three suspender bars
are made of the same steel and have the same circular cross
section with the same diameter of d=30 mm. The ultimate
stress of steel is Vu=450 MPa and Young modulus is E=200
GPa.
(a) Using a factor of safety FS=1.5, determine the
maximum allowable load P so that the stresses in all
three suspender bars will not exceed the allowable
stress Vall (Vall = Vu / FS) AND the maximum deflection
will not exceed 2 mm. (40 marks).
(b) If bars AB, CD, and EF have different diameters, what should you do to determine the maximum
allowable load P? Explain without calculation. (10 marks).
Question 2 (50 marks total):
An engineer is in charge of the design of a cylinder (length L=150mm; Figure 2) under torsion. The
cylinder is fully fixed at one end and subjected to a torque T = 5 kNm at its free end (Figure 2). The
shear modulus of the material is G = 200 GPa and its ultimate shear stress is Wu=280 MPa.
Preliminary design: At first a solid circular cylinder
with radius of 25mm is used (Figure 2). Could you
help the engineer determine:
(a) the maximum shearing stress, and the maximum
angle of twist in the cylinder. Determine the
factor of safety (FS=Wu/Wmax). Sketch the
variation of angle of twist, and shear strain along
the length of the cylinder. (15 marks).
(b) the shearing stress at point A (see Figure 2: point
A lies on a 10-mm-radius circle drawn on the
free end of the cylinder). (5 marks).
(c) the percent of the torque carried by the portion
of the cylinder within the 10mm radius. (10
marks).
Optimisation:
(d) The engineer realises that the factor of safety in question 2(a) is still relatively high and hence
he (she) wants to reduce it to an acceptable value of FS=1.1 to save material, by using a hollow
circular cylinder with the same outer radius of 25mm. Could you help the engineer determine
the inner radius? How much stress increase (in percentage) compared to the percentage of
material saving? What are your conclusions? (15 marks).
(e) Still not happy with the material saving, the engineer wants to use a different hollow circular
cylinder with different outer radius, so that when subjected to the above torque of 5 kNm the
maximum angle of twist and maximum shearing stress are still equal to those calculated in
question 2(a). Is it possible? Explain without calculation. (5 marks).