Question 1
Figure Q1 shows a system of forces with different magnitudes and directions. The
squares have sides of 1m.
Figure Q1a
a) Calculate the resultant R and its direction.
(4 marks)
b) Calculate the resulting moment of the forces about the axis of rotation passing
through A and state its direction.
(4 marks)
c) Calculate the resulting moment about the axis of rotation passing through B and
state its direction.
(4 marks)
Question 2
For the beams of Figure Q2a and Figure Q2b, determine the reactions at the supports.
Figure Q2a
(10 marks)
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Mechanics A
Page 3 of 4
Figure Q2b
(10 marks)
Question 3
For the loaded truss of Figure Q3:
a) Determine the reactions at the supports.
(5 marks)
b) Use the method of joints to determine the forces in members AB, BC, BJ, BH
and BI. Indicate whether the members are in tension or compression.
(15 marks)
c) Use the method of sections to determine the forces in members DE, DL and KL.
Indicate whether the members are in tension or compression.
(10 marks)
Figure Q3
Question 4
For the beam and loading shown in Figure Q4:
Figure Q4
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Mechanics A
Page 4 of 4
a) Calculate the reactions at the support.
(4 marks)
b) Draw the shear force and bending moment diagrams giving salient values.
(10 marks)
c) If the beam, made of steel, has a rectangular cross section with 275mm in
width and uniform depth of 650 mm, calculate the maximum bending stress in
the beam. The Young’s modulus of the beam material is E = 200GPa.
(6 marks)
d) Find the minimum equivalent diameter of a circular steel section to carry the
bending stress calculated in part c.
(4 marks)
Question 5
A mass of 120kg is on a spring of stiffness 7500N/m.
a) What is the natural frequency?
(2 marks)
b) If the mass is initially displaced 0.25m and released what is its displacement
after 5s?
(4 marks)
c) At what time will it first come to rest?
(5 marks)
d) Explain what happens if a forcing vibration, very close to the natural frequency,
is imposed on the system. Give examples of such situations.
(3 marks)