Civil Engineering Reference
In-Depth Information
q
2
q
2
q
1
q
1
q
1
q
1
q
1
q
1
q
1
q
1
q
1
q
1
All beams equal
All beams equal
All columns equal
E I
H
E I
L
E I
L
E I
H
> 10
> 10
All columns equal
columns
beams
beams
columns
L
L
L
L
L
L
a. frame layout and loading condition
b. bending moment diagram in beams and columns
200
200
Strong Column-Weak Beam (Ext)
Weak Column-Strong Beam (Ext)
Strong Column-Weak Beam (Int)
Weak Column-Strong Beam (Int)
Strong Column-Weak Beam (Ext)
Weak Column-Strong Beam (Ext)
Strong Column-Weak Beam (Int)
Weak Column-Strong Beam (Int)
100
100
0
0
0.00
0
2
5
0.50
0.
7
5
1.00
0.00
0.25
0.50
0.75
1.00
-100
-100
-200
-200
-300
-300
Normalized Length (
x
/
L
)
Normalized Length (
x
/
L
)
c. bending moment diagram in the beams
Figure 2.16
Distribution of bending moments in strong column-weak beam (
left
) and weak column-strong beam
(
right
) multi-storey frames under gravity loads: beams at fi rst (
bottom left
) and sixth (
bottom right
) fl oor
displacements, because they are symmetric structures with symmetric loads. The relative stiffness of
beams and columns affects signifi cantly the distribution of bending moments especially in the beams
as shown in Figure 2.16; the values of the moments are normalized with respect to
qL
2
/12, where
q
is
the uniformly distributed load at each level and
L
the beam span. In SCWB frames, the large bending
stiffness of the columns reduces considerably the rotations at the ends of the beams. Consequently, the
