# Mechanics

Mechanics

Faculty of Science and Engineering, School of Engineering
ASSESSMENT BRIEF
Module Title:    Engineering Mechanics II
Module Code:    5ET002
Component Number:    1 of 2    Element Number:    1of 2
Weighting:    30%
This assessment covers LO1 and LO2 as specified in the module guide
Learning Outcomes to be assessed:
Knowledge and Understanding:
Simple torsion, stresses and strains in thin shells, biaxial stresses, principal stresses and planes, maximum shear stresses, buckling analysis, vibration analysis, stress concentrations and stress in thick-walled cylinders.
Subject Specific Skills:
Evaluate the performance of mechanical systems and the strength of components through the use of engineering mechanics.
Intellectual Skills
Apply appropriate quantitative engineering mechanics tools to the analysis of mechanical components.

Students are expected to produce an individual written report demonstrating reasonable knowledge and understanding of the issues involved.
In order to successfully complete this component, the student need to achieve a minimum of 40%.
You should make it very clear what sources of information have been used; where material/information from these sources is quoted it must be clearly referenced using the Harvard Referencing System. (Details can be obtained from Learning Centres).

Note:  For the following questions, letter groups ABC, AB or BC represent numbers derived from your student number. For example: If your student number is 0924514, this corresponds to OABCDEF.

Student Number     1    4    2    4    9    8    7
Letters    O    A    B    C    D    E    F
Example     0    9    2    4    5    1    4
Then ABC = 924             AB = 92                 BC = 24

Question 1
A solid circular shaft is used to transmit a torque of ABC kNm. The shaft material has a Young’s Modulus of 180 GPa and Modulus of Rigidity of 85GPa.
a)    What is the diameter of the shaft if the shear stress is not to exceed 125MPa?
[10%]
b)    What is the angle of twist in a 2 m length of shaft?
[5%]
Question 2
What would be the external diameter of a hollow shaft needed to transmit a torque of AB kNm if the shear stress is not to exceed 100MPa and the shaft has an external diameter 1.3 times the internal diameter?
[10%]
Question 3
Calculate the Euler buckling load for a slender member 3.5 m long made from steel, with the cross-section shown in Fig. Q3. The ends may be considered to be pinned. Use the Young’s Modulus for the material as 200 GN/m2 and Modulus of Rigidity as 79 GPa.
[10%]

Fig. Q3
Question 4
A strut with the hollow cross-section shown in Fig. Q4 is 2.5 m long. If both ends can be pinned, calculate the buckling load. Young’s Modulus = 210 GN/m2 and Shear Modulus = 80 GN/m2.
[10%]

Fig. Q4

Question 5
A circular shaft shown in Fig. Q5 is subjected to an axial compressive force ABC N, and a torque AB Nm at the right end. Assuming a reasonable shaft diameter:
a) Evaluate the principal stresses on the surface of the shaft.
[5%]
b)    Evaluate the maximum shear stress on the surface of the shaft.
[5%]

Fig. Q5

Question 6
A stress differential element shown in Fig. Q6 is subject to the stresses indicated below, what are the stresses acting on the element in a direction at the angle to the y-direction indicated?
a) ?x = AB MPa, ?y = 0, ?xy=?yx= 30 MPa, ?=45?
[5%]
b) ?x = 40 MPa, ?y = -BC MPa, ?xy=?yx= 20 MPa, ?=30?
[5%]

Fig. Q6

Question 7

An engineer proposed that a steel hydraulic cylinder under internal pressure of 50 MPa, can be reinforced by shrinking on an outer cylindrical liner as shown in Fig. Q7. If the ‘Maximum Tensile Strength’, ‘Young’s Modulus’ and ‘Shear Modulus’ of steel are 100 MPa, 205000 MPa and 72000 MPa respectively:

a)    Help the engineer to calculate the required shrinkage (the difference between the outside radius of the inner cylinder and the inside radius of the outer cylinder).
[5%]
b)    Justify the proposed design by evaluating the tangential stress after shrink-fit and comparing it to a thick cylinder of internal radius r1 and external radius r3.
[5%]
c)    Compare and discuss the stress values using an ‘Excel type’ graph plotting the variation in tensile stress at 5 mm intervals along the radius.
[10%]

Fig. Q7
Question 8
With reference to the following paper:
Whittle, J. and Ramseyer C. (2009) Buckling capacities of axially loaded, cold-formed, built-up C-channels, Journal of Thin-Walled Structures, 47, pp. 190-201.
a)    Discuss the factors which affect the buckling load of a slender member subject to an axial compression load.
[10%]
b)    Discuss how to predict the buckling load accurately.
[10%]
c)    Discuss the effect of the set-up of testing rig on the measured buckling load.
[10%]
Question 9

A machine has mass of ABC kg and is supported by a spring of stiffness AB kN/m.  If the damping ratio for the vibrations produced by the system is known to be 0.5. Determine:
a)    The natural frequency.
[5%]
b)    The damped frequency.
[5%]
c)    The natural frequency when the same spring is added parallel to the original spring.
[5%]
d)    The natural frequency when the same spring is added in series to the original spring.
[5%]

Question 10
A viscously damped vibrating system consists of a mass of 3 Kg and a spring of stiffness of AB N/cm. Two consecutive positive peak amplitudes are found to be 1.0 and 0.95 respectively. Calculate:
a)    The natural frequency (in Hz) of the system.
[5%]
b)    The system’s logarithmic decrement.
[5%]
c)    The system damping factor.
[5%]
d)    The system damping coefficient.
[5%]
e)    The damped frequency (in Hz) of the system.
[5%]

Question 11
With reference to the following paper:
Curadelli, R.O. Ambrosini R.D. and Danesi R.F. (2004) Vibration control by attaching masses to a plate excited by rotating machinery, Journal of Sound and Vibration, 273, pp. 1087-1100.
a)    Discuss vibration control methods mentioned in the paper.
[20%]
b)    Discuss the paper’s main conclusions, and how the authors reached these.
[20%]

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