Project description

i will attach the questions

Page

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

Page

2

of

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