Civil Engineering Reference
In-Depth Information
2
2
cos
b
−
sin cos
b
b
cos
b bb
sincos
2
2
AE
L
−
sincos
bb b
sin
sin cos
b
b
−
sin
b
=
K
g
2
2
cos
b
sin cos
b
b
cos
b bb
−
sincos
2
sin
2
b
sincos
bb b
−
sin
−
sin cos
b
b
Members 1 and 2 have the same orientation. Selecting the bottom
end as the
i
-end, the rotation is −90° or 270°. The axial stiffness is
555.6 k/in.
0
0
0
0
0
55560555 6
.
−
.
KK
KK
KK
KK
=
=
[
]
=
[
]
=
11
14
33
35
KK
14
35
0
0
0
0
41
44
53
55
0
−
55560 555 6
.
.
Member 3 does not need rotations since it is already in the global system
orientation. The global stiffness will be the same as the member stiffness.
Selecting the left end as the
i
-end, the rotation is 0°. The axial stiffness is
416.7 k/in.
4167041670
0 0 0 0
41670 41670
0
.
−
.
KK
[
]
=
44
4
5
K
=
45
−
.
.
KK
54
55
0
0
0
Members 4 and 5 have the same orientation. Selecting the bottom-left end
as the
i
i-end, the rotation is −36.87° or 323.13°. Instead of using angles, in
this case it is easier to use trigonometry directly. The cosine is 0.8 and the
sine is −0.6. The axial stiffness is 666.7 k/in.
426 7
.
320 0
.
−
426 7
.
−
320 0
.
320 0
.
240 0
.
−
320 0
.
−
240 0
.
K
KK
K
1
[
]
=
[
]
=
1
12
KK
12
=
25
−
4
26 7
.
−
320 0
.
426 7
.
320 0
.
21
22
−
320 0
.
−
240 0
.
320 0
.
240 0
.
KK
KK
=
22
25
52
55
