Civil Engineering Reference
In-Depth Information
becomes a rectangle in which
α
=
90
◦
(Fig. 2.5) and, clearly
F
2
=
R
cos
θ
F
1
=
R
sin
θ
(2.3)
It follows from Fig. 2.5, or from Eqs (2.1) and (2.2), that
F
1
F
2
R
2
F
1
+
F
2
=
tan
θ
=
(2.4)
We note, by reference to Fig. 2.2(a) and (b), that a force does not induce motion in a
direction perpendicular to its line of action; in other words a force has no effect in a
direction perpendicular to itself. This may also be seen by setting
θ
90
◦
in Eq. (2.3),
=
then
F
1
=
RF
2
=
0
and the component of
R
in a direction perpendicular to its line of action is zero.
THE RESULTANT OF A SYSTEM OF CONCURRENT FORCES
So far we have considered the resultant of just two concurrent forces. Themethod used
for that case may be extended to determine the resultant of a system of any number
of concurrent coplanar forces such as that shown in Fig. 2.6(a). Thus in the vector
diagram of Fig. 2.6(b)
R
12
=
F
1
+
F
2
A
C
R
F
1
R
sin
u
a
90
°
F
IGURE
2.5
Resolution of a
force into two
components at
right angles
u
O
B
F
2
R
cos
u
y
R
F
2
F
3
u
F
4
F
3
a
R
123
b
x
O
F
1
g
F
2
R
12
R
F
IGURE
2.6
Resultant of a
system of
concurrent forces
F
4
F
1
(a)
(b)
