Civil Engineering Reference
In-Depth Information
P.11.6
The thin-walled box section beam ABCD shown in Fig. P.11.6 is attached at
each end to supports which allow rotation of the ends of the beam in the longitudinal
vertical plane of symmetry but prevent rotation of the ends in vertical planes perpen-
dicular to the longitudinal axis of the beam. The beam is subjected to a uniform torque
loading of 20Nm/mm over the portion BC of its span. Calculate the maximum shear
stress in the cross section of the beam and the distribution of angle of twist along its
length
G
70 000N/mm
2
.
=
0
.
36
◦
,
θ
at mid-span
0
.
72
◦
.
Ans.
71
.
4N/mm
2
,
θ
B
=
θ
C
=
=
4mm
D
C
350 mm
6mm
6mm
B
A
4mm
1m
4m
1m
200 mm
F
IGURE
P.11.6
P.11.7
Figure P.11.7 shows a thin-walled cantilever box-beam having a constant width
of 50mm and a depth which decreases linearly from 200mm at the built-in end to
150mm at the free end. If the beam is subjected to a torque of 1 kNm at its free end,
plot the angle of twist of the beam at 500mm intervals along its length and determine
the maximum shear stress in the beam section. Take
G
25 000N/mm
2
.
=
33
.
3N/mm
2
.
Ans.
τ
max
=
200 mm
150
mm
1kNm
2.0 mm
50 mm
F
IGURE
P.11.7
P.11.8
The cold-formed section shown in Fig. P.11.8 is subjected to a torque of
50Nm. Calculate the maximum shear stress in the section and its rate of twist.
G
25 000N/mm
2
.
=
220
.
6N/mm
2
,d
θ
/d
x
Ans.
τ
max
=
=
0
.
0044 rad/mm.
