Civil Engineering Reference
In-Depth Information
P.7.6
A vertical hanger supporting the deck of a suspension bridge is formed from a
steel cable 25m long and having a diameter of 7.5mm. If the density of the steel is
7850 kg/m
3
and the load at the lower end of the hanger is 5 kN, determine themaximum
stress in the cable and its elongation. Young's modulus
E
200 000N/mm
2
.
=
Ans
. 115.1N/mm
2
, 14.3mm.
P.7.7
A concrete chimney 40m high has a cross-sectional area (of concrete) of 0.15m
2
and is stayed by three groups of four cables attached to the chimney at heights of
15, 25 and 35m respectively. If each cable is anchored to the ground at a distance
of 20m from the base of the chimney and tensioned to a force of 15 kN, calculate
the maximum stress in the chimney and the shortening of the chimney including the
effect of its own weight. The density of concrete is 2500 kg/m
3
and Young's modulus
E
20 000N/mm
2
.
=
Ans
. 1.9N/mm
2
, 2.2mm.
P.7.8
A column of height
h
has a rectangular cross section which tapers linearly in
width from
b
1
at the base of the column to
b
2
at the top. The breadth of the cross
section is constant and equal to
a
. Determine the shortening of the column due to an
axial load
P
.
Ans.
(
Ph
/[
aE
(
b
1
−
b
2
)]) log
e
(
b
1
/
b
2
).
P.7.9
Determine the vertical deflection of the 20 kN load in the truss shown in
Fig. P.7.9. The cross-sectional area of the tension members is 100mm
2
while that
of the compression members is 200mm
2
. Young's modulus
E
205 000N/mm
2
.
=
Ans
. 4.5mm.
60
°
60
°
20 kN
60
°
60
°
3m
F
IGURE
P.7.9
P.7.10
The truss shown in Fig. P.7.10 has members of cross-sectional area 1200mm
2
and Young's modulus 205 000N/mm
2
. Determine the vertical deflection of the load.
Ans.
10.3mm.
