Civil Engineering Reference
In-Depth Information
F
6
F
6
F
5
F
5
F
4
F
4
F
3
F
3
F
2
F
2
F
1
F
1
All beams equal
E I
H
E I
L
All beams equal
All columns equal
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
Figure 2.17
Distribution of bending moments in strong column-weak beam (
left
) and weak column-strong beam
(
right
) multi-storey frames under horizontal loads
latter behave like members fi xed at both ends, particularly in the lower storeys of high- rise frames.
Bending moments at the beam- to - column connections are
qL
2
/12; at mid-spans the moment is
qL
2
/24.
On the other hand, when WCSBs are utilized, beam response is similar to simply supported members.
Under gravity loads, bending moments and shear forces on columns are often small. Values of axial
loads in columns depend on tributary areas at each fl oor.
Action distribution in frames with SCWBs and WCSBs subjected to horizontal loads is shown in
Figure 2.17. The distribution of bending moments, especially in columns, is signifi cantly affected by
the relative stiffness of the frame members.
In frames with SCWBs, the relatively low fl exural stiffness of beams causes a shift upwards of the
point of contra- fl exure in columns as shown in Figure 2.17. This is typically observed at lower storeys.
High values of bending moments can be expected in the columns at ground level. By increasing the
fl exural stiffness of beams, buildings behave like shear frames, as shown in Figure 2.15. The points of
contra - fl exure in the columns of shear frames are located at mid-height for both exterior and interior
columns.
The distribution of moments caused by the combined effects of vertical and horizontal loads is shown
in Figure 2.18 for SCWBs and WCSBs frames. By comparing such distributions with those provided
in Figures 2.16 and 2.17, it is noted that, especially for systems with WCSBs, bending moments may
