Civil Engineering Reference
In-Depth Information
PMPM
k
====
====
0
0
iz
iy
jz
jy
k
k
k
33
,
53
,
93
,
11 3
,
If a motion ∆
jz
is imposed, there is no resistance and therefore no forces.
The resulting forces are the stiffness values due to the motion. The follow-
ing are forces and stiffness due to ∆
jz
:
PMPM
k
====
====
0
0
iz
iy
jz
jy
k
k
k
39
,
59
,
99
,
11 9
,
If a motion
q
iy
is imposed, there is resistance and therefore forces. The
resulting forces are derived using conjugate beam.
ML
EI
iy
Σ
F
=− =
q
0
z
iy
y
EI
L
y
M
=
q
iy
iy
EI
L
y
k
=
q
55
,
iy
From statics on the real beam:
Σ
MMM
MM
EI
L
=+=
0
y
iy
jy
y
=− =−
q
jy
iy
iy
k
EI
L
PP
k
y
=−
q
11 5
,
iy
==
=
0
iz
jz
k
95
=
0
35
,
,
From symmetry of the stiffness matrix, the following terms can be
found:
k
=
k
511
,
115
,
EI
L
y
k
=−
q
511
,
jy
