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Revision - Tutorial Questions
1. For the framework given below in Fig. 1 determine the magnitude of the force in
each member and state whether each is a tie or a strut. (Note that it is not usual
to label the framework for you.)
Answers
R1= 2.75kN R2= 3.25kN
All of the following found by measurement:
hb = 3.75kN (strut) ch = 1.9kN (tie) fd = 1.6kN (tie) ef = 3.2kN (strut)
ag = 2kN (strut) fg = 0.85kN (tie) gh = 0.3kN (tie)
2. Use the method of resolution at joints to verify the forces in the members that
make up the top right hand joint of Fig. 1.
2kN
3kN
A
E
R1
All members are 1m
G
F
B
H
D
1kN
Fig. 1
C
R2
Answers
hb = -3.75kN hg = 0.286 kN ga = -2.018 kN
3. For the pin jointed frame shown in Fig. 2 solve all the forces and reactions in the
frame stating which members are tie and which are struts. The length of all
vertical and horizontal members are 3m.
A
F
E
D
G
C
15kN
H
B
30kN
Answers (These have not been verified by me)
R1=25kN R2=20kN
ha = 35.5kN (strut) bh = 25kN (tie) ed = 20kN (tie) ea = 29kN (strut)
cg = 25kN (tie) gf = 7.07kN (strut) fa = 20kN (strut) ef = 20kN (tie)
gh = 30kN (tie)
4. A load of mass 1350 kg lies on a gradient inclined at 60 o to the horizontal. For
static friction μ = 0.5, for kinetic friction μ 0.4. Calculate: (a) the pull parallel to
the gradient required to prevent the load sliding down; (b) the pull required to
pull the load up the gradient at constant speed.
(8.15 kN; 14.1 kN)
5. A body of mass m on a rough plane inclined at 20o to the horizontal is moved
steadily up the plane by a force of 200 N applied upward and parallel to the
plane. When the force is reduced to 75 N, the body slides steadily downwards.
Determine the values of m and μ.
(41 kg; 0.17)
6. For the loaded beam shown below produce neat sketches/drawings of the shear
force and bending moments.
x
10 kN
20 kN
UDL = 15 kN/m
1.5
A
B
2m
R1
C
D
2m
E
0.5 m
R2
7. Determine the resultant out of balance force at the centre of rotation 'O', when the
system shown below rotates at 10 rev/min and state its direction. What value of balance
weight would be required at 1m radius and where should it be placed?
(55.94N; 51kg 12o to vertical)
8. Calculate the second moment of area for the section shown below about an axis
X-X through the centroid.
(Centroid 33.7mm from top; I = 3.19 x 106mm4)
9. A load of 8 t is to be raised with a uniform acceleration of 1.1 m/s 2 by means of a
light cable passing over a hoist drum of 2 m diameter. The drum has a mass of 1
t and a radius of gyration of 750 mm. Find the torque required at the drum if
friction is neglected.
(87.8 kN)