# Mechanics of Solids

EXAMINATIONS FOR DEGREES AND DIPLOMAS October-November 2008

Mechanics of Solids

First and only paper

Time Allowed: THREE (3) hours

Instructions:

Answer all questions.

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Question 1

Figure 1

Two circular A-36 steel1 rods are connected as shown in Figure 1. The rod CD has a diameter of 30mm. Both members are pin connected together at C (see figure detail). You are asked to determine: a b Identify what kind of structural member are AB and CD respectively. The maximum force P that can be applied to the handle of so the member CD does not fail. The shear force and bending moment diagrams for member AB for this load. The required diameter for the round member AB to resist only the bending action of the force P (use a factor of safety F.S.=2). The diameter of the pin C, also made of A-36 steel, so it acts as a fail-safe mechanism to limit the loading of the member CD to 75% of its critical load (assume the τallow=125 MPa). [20 marks]

c d

e

Continued…

A table providing the material properties of common engineering materials can be found at the end of this exam paper. 1

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Question 2

Figure 2

For the 304 Stainless steel2 beam shown in Figure 2 you are required to: a Calculate the reactions and create the shear force and bending moment diagrams for the beam. Select the lightest weight steel wide-flange beam3 that will safely support the bending load (use a factor of safety, FS=2). Do not include the weight of the beam for this calculation. Derive and graph the equation of, slope and elastic curve by integration. (Ignore the weight of the beam for this calculation.) Determine the magnitude and location of the maximum deflection of the beam. (Ignore the weight of the beam for this calculation.) [20 marks]

b

c

d

Continued…

A table providing the material properties of common engineering materials can be found at the end of this exam paper. 2

A table providing geometrical properties of structural shapes can be found at the end of this exam paper. 3

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Question 3

Figure 3

The A-36 steel4 square bar shown in Figure 3 is constrained to just fit between to fixed walls when T1=30°C. If the temperature is raised to T2=60°C, determine a The reactions at ends A and B respectively b The average normal stress developed in the bar c The displacement of the end A if the wall A were removed d The edge length of a square support plate to be located under the bar to resist bearing if the allowable stress of the fix walls is σallow=30 MPa.

[20 marks]

Continued…

A table providing the material properties of common engineering materials can be found at the end of this exam paper. 4

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Question 4

Figure 4

The titanium bicycle pedal crank AB has the rectangular cross section shown in Figure 4. If the crank is fully fixed to the gear (chain ring) at point B and does not rotate while subjected to a force of 600N (Assume that the force is applied at the shear centre of the crank). You are asked to: a Construct the shear and bending moment diagrams of the crank. b Create an element that describes the state of stress at point C of plane X-X. c Calculate the orientation of the plane and the magnitude of principal stresses and maximum in-plane shear stress at point C. d Construct the Mohr Circle that represents this case.

[20 marks]

Continued…

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Question 5

Answer the following questions concisely (no more than half a page per question): a What do you understand by strength, stiffness and stability in the Mechanics of Solids context? b What is the importance of the shear centre of a bending member and how can it be determined analytically and experimentally? c Describe three ways of improving load carrying capacity of a pinned-pinned column of a given length L. d Explain mathematically why the skin of sausage will normally fail longitudinally (i.e. with a crack running on the...

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