FORCES IN STRUCTURES 55
Assignment 1
This assignment covers the material
contained in Chapters 1 to 4.
The marks for each question are shown
in brackets at the end of each question.
- A metal bar having a cross-sectional area
of 80 mm^2 has a tensile force of 20 kN
applied to it. Determine the stress in
the bar. (4)
- (a) A rectangular metal bar has a
width of 16 mm and can support
a maximum compressive stress of
15 MPa; determine the minimum
breadth of the bar when loaded
with a force of 6 kN
(b) If the bar in (a) is 1.5 m long and
decreases in length by 0.18 mm
when the force is applied, deter-
mine the strain and the percentage
strain. (7)
- A wire is stretched 2.50 mm by a
force of 400 N. Determine the force
that would stretch the wire 3.50 mm,
assuming that the elastic limit is not
exceeded. (5)
- A copper tube has an internal diame-
ter of 140 mm and an outside diame-
ter of 180 mm and is used to support a
load of 4 kN. The tube is 600 mm long
before the load is applied. Determine, in
micrometres, by how much the tube con-
tracts when loaded, taking the modulus
of elasticity for copper as 96 GPa. (8)
- The results of a tensile test are: diame-
ter of specimen 21.7 mm; gauge length
60 mm; load at limit of proportion-
ality 50 kN; extension at limit of
proportionality 0.090 mm; maximum
load 100 kN; final length at point of
fracture 75 mm.
Determine (a) Young’s modulus of elas-
ticity, (b) the ultimate tensile strength,
(c) the stress at the limit of proportion-
ality, (d) the percentage elongation.
(10)
- A force of 25 N acts horizontally to the
right and a force of 15 N is inclined at
an angle of 30°to the 25 N force. Deter-
mine the magnitude and direction of the
resultant of the two forces using (a) the
triangle of forces method, (b) the paral-
lelogram of forces method, and (c) by
calculation (12)
- Determine graphically the magnitude
and direction of the resultant of the
following three coplanar forces, which
may be considered as acting at a point.
ForceP, 15 N acting horizontally to the
right, forceQ, 8 N inclined at 45° to
forceP, and forceR, 20 N inclined at
120 °to forceP (7)
- Determine by resolution of forces the
resultant of the following three coplanar
forces acting at a point: 120 N acting at
40 ° to the horizontal; 250 N acting at
145 °to the horizontal; 300 N acting at
260 °to the horizontal. (8)
- Determine the unknown internal forces
in the pin-jointed truss of Figure A1.1.
(7)
R 2
H 1
H 2
1
30 °
2
3
2 kN
Figure A1.1
