Civil Engineering Reference
In-Depth Information
Eq. (i)
R
A,V
=
3
.
7kN
The vertical reaction at D may now be found using
F
y
=
0 or by taking moments
about A, which would be slightly lengthier. Thus
5 sin 60
◦
=
R
D
+
R
A,V
−
3
−
0
so that
R
D
=
3
.
6kN
E
XAMPLE
2.3
Calculate the reactions at the support in the cantilever beam shown
in Fig. 2.21.
The beam has a fixed support at A which prevents translation in any direction and also
rotation. The loads applied to the beam will therefore induce a horizontal reaction,
R
A,H
, at A and a vertical reaction,
R
A,V
, together with a moment reaction
M
A
. Using
the first of Eqs. (2.10),
F
x
=
0, we obtain
2 cos 45
◦
=
R
A,H
−
0
whence
R
A,H
=
1
.
4kN
From the second of Eqs. (2.10),
F
y
=
0
2 sin 45
◦
=
R
A,V
−
5
−
0
which gives
R
A,V
=
6
.
4kN
y
5kN
2kN
A
B
C
45
°
x
R
A,H
M
A
R
A,V
F
IGURE
2.21
Beam of Ex. 2.3
0.4 m
0.6 m
