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Assignment, Engineering and Construction Strength of materials- torsion

Project description
i will attach the questions

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1
of
2
C&ENVENG 2025
Strength of Materials IIA
Semester 1, 2014
Assignment 2: Torsion
Due: 4pm Monday, 7 April 2014
The assignment should be done by students individua
lly. Solution should start with a clear statement o
f the
problem, a summary of the given information, what i
s to be solved for, and then a clear and easy to fo
llow
solution with diagrams where appropriate and highli
ghting any assumptions made along the way. If you b
elieve
that a parameter or an important piece of informati
on has been inadvertently omitted, assume a suitabl
e value,
clearly stating it, and continue with the solution.
Each question will be marked using criteria as sho
wn below

Correct working and answer: 100% mark

Correct working but wrong answer (including wrong u
nit): 70% mark

Incorrect working and answer but demonstrate a cert
ain level of understanding: 30% mark

Incorrect working and answer, and demonstrate no un
derstanding: 0% mark
Assignment must be submitted to the course submissi
on box in front of the School of Civil, Environment
al &
Mining Engineering Office (Eng. North N136). Late s
ubmission will be penalised at the rate of 10% per
day
until the assignments are returned within a week. N
o credit will be given for assignments submitted af
ter they
have been marked and returned to the class.
Question 1 (30 marks total)
While an oil well is being drilled at a depth of 20
00m, it is observed that the top of the 20cm-diamet
er steel drill
pipe rotates though two complete revolutions before
the drilling bit starts to rotate. Using G=90GPa,
determine
the maximum shearing stress in the pipe caused by t
orsion.
2000m
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2
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2
Question 2 (70 marks total)
(a)
From the torsion test 1 video (torsion test, small
strain in “Course Material / Videos of experiments”
),
calculate the shear modulus G of the steel material
of the specimen.
The specimen is made of structural steel with Young
modulus E=200 GPa and Poisson’s ratio
?
=0.3. Use
the relationship between E and
?
(see slide 29, Ch02_Stress_strain), determine G an
d compare it with the
value that you have just calculated above. What cau
ses the difference in your opinion?
Note:

Use the incremental relationship
?
t
=
?
?
G for the calculation of shear modulus G. This is
due to the
rigid body rotation (very small torque and large ro
tation at the beginning of the test) of the specime
n
before the torsion loading taking effects. See figu
re below.

Cross section is circular with an averaged diameter
determined from 3 measurements.
(b)
From the torsion test 2 video (torsion test, large
strain), determine the shear stress at yield
t
y
and estimate
the ultimate shear stress
t
ult
(assuming the whole cross section reaches the same
ultimate stress). Same
length L and averaged diameter in (a) can be used.
Use the above material properties (shear modulus G,
shear yield stress
t
y
)
for the design of steel rods under torsion:
(c)
For a solid cross section, determine the diameter d
of the steel rod so that
the maximum shear stress in the rod is equal to
t
y
. Calculate the angle of
twist at H.
(d)
To save material, a hollow circular cross section i
s used. Given the inner
radius c
1
=6mm, determine the outer radius c
2
so that the angle of twist at
H does not exceed that calculated above in (c) AND
the material does not yield. How much (in terms of
material volume) can be saved compared to (c)?
(e)
Find the inner radius c
1
and outer radius c
2
of a hollow tube so that when subjected to the abo
ve torque of
250 Nm (Figure above):

the angle of twist is equal to that calculated in (
c)

and the maximum stress in the tube is equal to the
yield stress
t
y
.
length L on which rotation
angle
f
(or angle of twist)
is measured
?
t
and
?
?
to be calculated from corresponding
?
T
(Torque) and
?
f
(Rotation)
based on 2 points on the
red dashed line.
1.5m
d
250 Nm
Question 2
H

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