Civil Engineering Reference
In-Depth Information
250400 225
400700 400
450800 475
.
.
.
1
1
1
y
y
y
1
qh
EI
4
.
.
.
=
2
.
.
.
3
When the value of
h
=
L
/6 is substituted in and the matrix multiplication
is performed, the following is a general solution for a simply supported
beam with a uniformly distributed load:
875
15 00
17 25
.
y
y
y
1
qL
4
.
.
=
2
1296
EI
3
The particular solution for
q=
4
k/ft,
L=
25
ft,
E=
40
,
000
ksi,
and
I=
1000
in
4
is then obtained. The exact solution at the center is
y
3
=
0
.
87891
inches,
which is a 2.22% error.
0 44573
0 78125
0 89855
.
.
.
y
y
y
1
inches
=
2
3
Once the deflections are found, the other three desired values,
q
,
M
, and
V
,
can each be found from the corresponding central difference operators
using the same order of error. The procedure is the same as the operator
is laid upon each of the values that are unknown then the corresponding
equation may be written. The relationship for rotation is as follows:
′ ==
−
y
y
i
+
1
i
−
1
y
q
i
2
h
0200
1010
0101
0000
y
y
y
y
q
q
q
q
0
0
−
1
2
1
1
=
h
−
2
2
3
3
0200
1010
0101
0000
y
y
y
y
q
q
q
q
0
0
−
3
1
1
=
L
−
2
2
3
3
2
y
q
q
q
q
1
0
−
+
−+
y
y
yy
3
0
2
1
=
L
1
3
2
0
3
