Civil Engineering Reference
In-Depth Information
If a motion ∆
jz
is imposed, there is resistance and therefore forces. The
free-body diagram of the deflected shape is shown in Figure 5.3. The
conjugate beam will be the same as shown in Figure 5.2. The resulting
forces are derived using conjugate beam. Note that the direction of
P
iz
in
Figure 5.3 will be the opposite of that in Figure 5.2, so all the values will
be the opposite of those from ∆
iz
.
M
jy
M
iy
=0
∆
jz
P
iz
P
jz
Figure 5.3.
Example 5.2
q
iy
end release.
3
EI
L
y
P
=−
∆
iz
jz
3
3
EI
L
y
k
=−
∆
39
,
jz
3
3
EI
L
y
MP L
=−
=
∆
jy
iz
jz
2
3
EI
y
k
=
∆
,
L
PP
EI
L
11 9
jz
2
3
y
=− =
∆
jz
iz
jz
3
3
EI
L
y
k
=
∆
99
,
jz
3
If a motion
q
iy
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 ∆
iz
:
PMPM
k
====
====
0
0
iz
iy
jz
jy
k
k
k
35
,
55
,
95
,
11 5
,
If a motion
q
jy
is imposed, there is resistance and therefore forces. The
free-body diagram of the deflected shape is shown in Figure 5.4. The
