Civil Engineering Reference
In-Depth Information
V
V
y
e
e
=
(2.28.2)
ΔΔ
y
Therefore, it follows that:
V
V
e
u
e
uy
V
=
Δ
=
(2.28.3)
y
y
Δ
ΔΔ
The inelastic (or design) base shear
V
y
of the new system is therefore given by:
V
e
(2.29)
V
=
y
μ
and lateral displacement Δ
u
can be computed using equation (2.28.1) .
For the intermediate period systems, the displacement Δ
u
increases with decreasing yield action
V
y
.
Here, a criterion based on 'constant (or equal) energy' proves useful. By equating the energy absorbed
by the elastic and inelastic systems, the following ensues (Figure 2.51 ):
1
2
1
2
(
)
V
Δ
=
V
Δ
+
V
Δ
−
Δ
(2.30.1)
ee
yy
y u
y
which leads to:
V
e
2
2
V
=
(2.30.2)
y
(
)
2
ΔΔΔ
−
u
y
y
The inelastic (or design) base shear
V
y
and lateral displacement Δ
u
of the new system are therefore
given by:
V
e
V
=
(2.31.1)
y
21
μ
−
μ
μ21
Δ
=
Δ
(2.31.2)
u
e
−
0.5 seconds, there is no reduction in design forces, i.e.
V
y
=
V
e
,
which corresponds to elastic design. The ductility required to reduce elastic base shears
V
e
is extremely
high and seismic detailing is often impractical.
The above expressions, especially equations (2.30.1) , (2.30.2) , (2.31.1) and (2.31.2) , point towards
the following relationship:
For short - period structures, e.g.
T
<
V
V
e
y
R
=
Ω
(2.32)
d
where Ω
d
is the observed overstrength factor defi ned in Section 2.3.4, while
V
e
and
V
y
are the elastic
and the actual strength, respectively, as also displayed in Figure 2.51. In turn, the inherent overstrength
Ω
i
is related to the
R
- factor supply and Ω
d
as given below:
