Civil Engineering Reference
In-Depth Information
0 2150
0 5202
0 6524
.
.
.
y
y
y
1
inches
=
2
3
The exact solution at the center is
y
3
=
0
.
6284 inches, which is a 3.81%
error. This is more error than the deflection found in Example 3.10,
even though a more accurate operator was used. This is due to the
fact that this physical model has more variation in deflection than
that of the simply supported beam. The relationship for rotation is as
follows:
′ ==
−+ −
y
8
y
8
y
+
y
i
+
2
i
+
1
i
−
1
i
−
2
y
q
i
12
h
0000
8181
1818
0000
y
y
y
y
q
q
q
q
0
0
−
−
−−
1
12
1
1
=
h
2
2
3
3
0000
y
y
y
y
q
q
q
q
0
0
−
8181
1818
0000
−
−−
1
2
1
1
=
L
2
2
3
3
0
q
q
q
q
0
−++−
−−+
8
yyyy
8
1
2
0
1
2
3
1
=
L
y
8
y
y
8
y
0
1
2
3
2
0
3
0 0000
.
q
q
q
q
0
0.0052
1
radians
=
0 0041
0 0000
.
.
2
3
The solution at the end is
q
0
=
0
.
00000
radians
, which is exact, while
the value in the center is also exact. The relationship for moment is as
follows:
′′ =− =
−+ −+ −
M
EI
y
16
y
30
y
16
y
y
i
+
2
i
+
1
i
i
−
1
i
−
2
y
i
12
h
2
