Civil Engineering Reference
In-Depth Information
00 000000 0000
0
6
5
1
10
6
5
1
10
000
0
−
000
L
L
00
6
5
1
10
000
6
5
1
10
− − − 0
00 000000 0000
00
1
10
0
0
∆
∆
∆
P
P
P
M
M
M
P
P
P
M
M
M
L
L
ix
iy
iz
ix
iy
iz
jx
jy
jz
jx
jy
jz
ix
iy
iz
ix
iy
iz
jx
jy
jz
jx
jy
jz
2
15
L
1
10
L
−
0
000
0
−
0
q
q
q
30
L L
30
00 000000 0000
0
1
10
2
15
1
10
000
0
000
0
−
−
P
=
ix
∆
∆
∆
6
5
1
10
6
5
1
10
−
000
−
0
000
−
L L
L L
0
00 000000 0000
00
1
10
00
6
5
1
10
6
5
1
10
q
q
q
−
0
000
0
L
1
10
2
15
L
−
0
−
30
000
0
0
1
10
L
1
10
000
2
L
15
0
000
−
0
−
30
(5.31)
The geometric stiffness of a member can also be derived based on a gen-
eral transcendental equation. The full derivation is published by Blette
(1985).
ya
n
p
+
n
p
++
=
sin
b
cos
cx d
2
L
2
L
The particular solution for ∆
iy
is as follows:
2
−
p
x
L
p pp
x
L
x
L
y
=
∆
sin
+ +−
cos
iy
4
−
p
2 222
The particular solution for
q
iz
is as follows:
4
L
pp pp
x
L
x
L
x
L
y
=
q
1
−
sin
2 22
1
+
cos
+
−
iz
2
4
pp
−
2
These two relationships can be used to develop the geometric stiffness
matrix.
