CIVE 114001
This question paper consists
of 5 printed pages, each of
which is identified by
the Code Number...CIVE 114001
UNIVERSITY OF LEEDS
January/February 2000
Examination for the degree of
BEng/ MEng
Civil Engineering
FUNDAMENTALS OF MECHANICS
Time allowed: 2 hours
Attempt 5 questions including at least one question from section B
All questions carry equal marks
SECTION A
1.
The vertical sides of a square plate are subjected to a compressive direct stress of
2
2
380kN/m and an anti-clockwise shear stress of 40 kN/m , and the horizontal sides to a
2
2
compressive direct stress of 320 kN/m and a clockwise shear stress of 40 kN/m .
(a) Calculate the magnitude and direction of the principal stresses.
[12 marks]
(b) Calculate the maximum shear stress, and the orientation of the planes upon which it acts.
[8 marks]
1
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CIVE 114001
2.
Figure 1 shows a pin-jointed frame supporting a load of 100N. All the members of the
frame have the same cross-sectional area. What are the loads in each member?
D
C
B
l0
40° 40°
A
100 N
FIGURE 1.
[20 marks]
3.
What is the maximum allowable uniformly distributed load that can be applied to a
cantilever 6 metres long of the cross-section shown in Fig. 2?
3
Weight of steel is 7800 kg/m
2
Allowable stress in bending (tension or compression) is 165 N/mm .
[20 marks]
75 mm
15 mm
15 mm
270 mm
15 mm
250 mm
FIGURE 2.
2
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CIVE 114001
4.
Determine the forces in the members of the pin-jointed truss shown in Fig. 3.
[20 marks]
4m
E
2x2m
10 kN
10 kN
C
D
4m
30°
60°
60°
B
A
F
G
FIGURE 3.
3
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CIVE 114001
5.
Draw a bending moment diagram and a shear force diagram for the simply supported
beam shown in Figure 4 below. The critical values of bending moment and shear force
should be calculated and indicated on the sketches.
[10 marks for each diagram]
4m
Unif orm ly dist ribut ed load= 5 kN/ m
8m
FIGURE 4
6. (a) Derive expressions for the elastic and plastic moments of resistance of a rectangular
section (NB the derivation must be shown; it is not sufficient simply to quote the result).
[7 marks for each derivation]
(b) Sketch a diagram showing the change in moment with strain for a rectangular beam
section of width 100mm and depth 200mm if the material is perfectly elastic-plastic with
2
a yield strength of 400 N/mm in both compression and tension and a modulus of
2
elasticity of 200000 N/mm . The elastic and plastic moments of resistance should be
calculated and marked on the sketch.
[6 marks]
4
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CIVE 114001
SECTION B
2
7. (a) A car starts from rest and accelerates in a straight line at 3.0 m/s for 20s.
i.
ii.
What is its final speed?
How far has it travelled in this time?
If the brakes are then applied and it travels a further 50m before stopping
iii.
What is the retardation deceleration?
[10 marks]
(b) A hoist and its maximum load have a mass of 1000 kg. It starts at ground level and
2
accelerates at 2.0 m/s for 3s. It then moves with uniform speed for 5s and is finally
2
brought to rest at the top of a building with a deceleration of 2.0 m/s .
i
ii
iii
Draw the speed time graph of the motion
What is the height of the building?
During the period of uniform speed what is the power required if the frictional
resistance can be taken as 190N?
[10 marks]
8. (a) A lift with its load has a mass of 1000 kg. It is supported by a steel cable. Find the
tension in the cable when it:
i
ii
iii
iv
v
is at rest
moves downwards at a steady speed of 2 m/s
move upwards at a steady speed of 2 m/s
2
accelerates upwards uniformly at 2m/s
2
accelerates downwards with uniform acceleration of 2 m/s
[10 marks]
(b) A block with mass 10 kg will just slide along a level floor when pulled by a constant
force of 50N.
i
ii
If the block is pulled along a distance of 10 m in 20s, what is the power used?
What is the coefficient of (static) friction ?
[5 marks]
(c) A railway wagon of mass 10 tonnes travelling at 0.5m/s collides with another of mass 20
tonnes travelling in the opposite direction at 0.5m/s. The wagons become coupled on
impact. Find:
i
ii
their common velocity after impact
the loss of kinetic energy.
[5 marks]
5
END