Civil Engineering Reference
In-Depth Information
so that
L
2
+
2
w
2
Hh
wL
HD
−
=
0
(5.14)
Equation (5.14) is a quadratic equation in
H
and may be solved for a specific case
using the formula.
Alternatively,
H
may be determined by considering the moment equilibrium of the
lengths AC and CB about A and C, respectively. Thus, for AC
w
L
1
2
H
(
D
−
h
)
−
=
0
which gives
wL
1
2(
D
H
=
(5.15)
−
h
)
For CB
wL
2
2
HD
−
=
0
so that
wL
2
2
D
H
=
(5.16)
Equating Eqs (5.15) and (5.16)
wL
1
2(
D
wL
2
2
D
h
)
=
−
which gives
D
−
h
L
1
=
L
2
D
But
L
1
+
L
2
=
L
therefore
D
1
h
D
+
−
L
2
=
L
from which
L
D
−
h
D
L
2
=
1
(5.17)
+
Then, from Eq. (5.16)
wL
2
2
D
D
−
h
D
H
=
(5.18)
1
2
+
