Civil Engineering Reference
In-Depth Information
0
0
0
0
0
0
0
0
0
0
0
0
1 2036
.
1 2036
.
0
0
0
0
0 1018
.
0
−
0
0
0
0 1018
.
∆
∆
∆
P
P
P
M
M
M
P
P
P
M
M
M
L
L
ix
iy
iz
θ
x
iy
iz
jx
jy
jz
jx
jy
jz
ix
iy
iz
ix
iy
iz
jx
jy
jz
jx
jy
jz
1 2036
.
1 2036
001018
.
0
0
001018
−
.
0
0
0
−
−
.
0
L
L
0
0
0
0
0
0
0
0
0
0
0
0
θ
θ
0
0
−
0 1018 001379
.
.
L
0
0
0
0 1018 000361
.
−
.
L
0
001018
.
0
0
0
0 1379 001018
.
L
−
.
0
0
0
−
0 0361
.
L
P
=
ix
∆
∆
∆
0
0
0
0
0
0
0
0
0
0
0
0
1 2036
.
1 2036
.
0
−
0
0
0
−
0 1018 0
.
0
0
0
−
0 1018
.
L
L
1 2036
.
1 2036
001018
.
θ
θ
θ
0
0
−
001018
.
0
0
0
.
0
L
L
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−
0 1018 000361
.
−
.
L
0
0
0
0 1018 001379
.
.
L
0
001018
.
0
0
0
−
0 0361 001018
.
L
−
.
0
0
0
0 1379
.
L
(5.32)
If more digits are desired for accuracy, the following substitutions can be made:
1.2036 = 1.20362445
0.1018 = 0.1018122226
0.1379 = 0.1378809597
0.0361 = 0.03606873710
5.11
gEOMEtRic AnD SHEAR StiffnESS
The effect of both the geometric and shear stiffness could be included in
the flexural stiffness derivations. This matrix was derived by Karl J. Blette
(Blette 1985). The procedure to derive the stiffness matrix would be to
include the shear stiffness contribution used in Sections 5.5 and 5.6 in
the geometric stiffness of Sections 5.8 and 5.9.
Equation 5.33 shows the
elastic and shear member stiffness in the 3-D Cartesian coordinate system.
Equation 5.34 shows the elastic geometric and shear member stiffness in
the 3-D Cartesian coordinate system.
The terms
a
and
b
are defined as follows:
3
L
EI
a
=
y
12
y
3
L
EI
L
GA
L
GA
a
=
z
12
z
b
=
y
z
b
=
z
y
