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B.Sc. (Eng.), B.Eng and M.Eng degrees by course unit

Friday 2nd May 2008 14:30 17:00

DEN102 Stress Analysis Duration: 2 hours 30 minutes

YOU ARE NOT PERMITTED TO START READING THIS QUESTION PAPER UNTILINSTRUCTED TO DO SO BY AN INVIGILATOR.

Answer THREEof the Four Questions.

Total 100 Marks.

NON-PROGRAMMABLE CALCULATORS ARE PERMITTED IN THIS EXAMINATION. PLEASE

STATE ON YOUR ANSWER BOOK THE NAME AND TYPE OF MACHINE USED.

COMPLETE ALL ROUGH WORKINGS IN THE ANSWER BOOK AND CROSS THROUGH ANYWORK WHICH IS NOT TO BE ASSESSED.

Examiners:

Dr P. Dabnichki

Dr. P.H. Wen

Queen Mary, University of London, 2008

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Page 2 DEN102 (2008)

Question 1

A beam of constant cross-section is subjected to vertical and horizontal loads as shown inFig. Q1.

2.5 m 3 m

40 kN/m 50 kN

4 m 2 m2 m

40 kN

Figure Q1

a) Determine the reactions at the supports.

[8 marks]

b) Plot the shear force diagram .

[10 marks]

c) Plot the bending moment diagram.

[10 marks]

d) Calculate the maximum bending stress if the cross-section is a hollow circle withexternal radius of 0.6 m and internal one of 0.3m. Clearly indicate at what point of thebeam and where exactly in relation to the cross-section the maximum shear stressis.

[5.33 marks]

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DEN102 (2008) Page 3

Question 2

A cantilever made out of steel (Youngs modulus E=195 GPa) is subjected to onedistributed and one point load as seen in Fig. Q2.

a) Determine the reactions at the built-in end.[5 marks]

b) Sketch the shear force and bending moment diagrams.

[16 marks]

c) Discuss and calculate which of the following cases will give the greatest bending stress if the beam is a hollow cylinder with diameter of 0.5 m and wall thickness of 0.2m anda solid cylinder with the same external diameter.

[6 marks]

d) Discuss whether the inclusion of the weight is needed to make a correct choice. Is thisgoing to make a difference to the analysis and consequent selection?

[6.33 marks]

80kN/m 150kN

2 m 2.5 m 1.5 1.5 m

Figure Q2

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Page 4 DEN102 (2008)

Question 3

The structure shown in Figure Q3 consists of pin-jointed bars. The frame is attached to thepinned and roller supports

Figure Q3

a) Calculate the horizontal and vertical components of the reaction forces at the supportpoints.

[8 marks]

b) Calculate the internal forces in all members.

[18 marks]

c) Produce a sketch that shows all the internal forces clearly indicating whether they aretensile or compressive.

[7.33 marks]

100kN

63

1

74

2A B

5

C

D E

F

4m

3m

8 9

3m 3m 3m

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DEN102 (2008) Page 5

Question 4

A stress tensor for the plane stress elasticity is given by:

=

2040

4060

(MPa).

The Youngs modulus and Poissons ratio of this material are GPa200=E and 3/1= respectively.

a) Draw a square element with the above stress components acting on its sides;

[6 marks]

b) Calculate the strain tensor in matrix form;

[10 marks]

c) Determine the principal stresses and their directions;

[10 marks]

d) Fine the stresses (normal and shear) acting on the plane orientated at angle 600tothe x-axis.

[7.33 marks]

End of Paper