Civil Engineering Reference
In-Depth Information
2m
15 mm
1m
A
5mm
5mm
B
20 mm
C
5mm
15 mm
20 N
F
IGURE
P.13.11
P.13.12
The simply supported beam shown in Fig. P.13.12 supports a uniformly dis-
tributed load of 10N/mm in the plane of its horizontal flange. The properties of
its cross section referred to horizontal and vertical axes through its centroid are
I
z
=
10
6
mm
4
. Determine the
magnitude and direction of the deflection at the mid-span section of the beam. Take
E
10
6
mm
4
,
I
y
=
10
6
mm
4
and
I
zy
=−
1
.
67
×
0
.
95
×
0
.
74
×
70 000N/mm
2
.
Ans.
52
.
3mm at 23.9
◦
below horizontal.
=
80 mm
10 mm
100 mm
10 mm
2m
F
IGURE
P.13.12
P.13.13
A uniform cantilever of arbitrary cross section and length
L
has section prop-
erties
I
z
,
I
y
and
I
zy
with respect to the centroidal axes shown (Fig. P.13.13). It is loaded
in the vertical plane by a tip load
W
. The tip of the beam is hinged to a horizontal
link which constrains it to move in the vertical direction only (provided that the actual
deflections are small). Assuming that the link is rigid and that there are no twisting
effects, calculate the force in the link and the deflection of the tip of the beam.
Ans. WI
zy
/
I
z
(compression if
I
zy
is positive),
WL
3
/
3
EI
z
(downwards).
