Civil Engineering Reference
In-Depth Information
Elastic
strength
V
e
R =
V
e
/
V
d
=
R
·
Ω
Δ
m
d
(R
=
V
e
/
V
y
)
m
Idealized bilinear
envelope
Actual capacity
envelope
(
Ω
=
V
y
/
V
e
)
i
Actual
strength
V
y
0.75
V
y
(
=
V
y
/ V
d
)
Ω
V
fy
First local yield
d
Design
strength
V
d
V
Δ
Δ
Top Displacement
y
max
(
m
=
max
/
Δ
Δ
y
)
Figure 2.44
Relationship between strength, overstrength and ductility
V
y
V
e
V
e
Idealized
V
y
V
d
Actual
V
d
Top Disp.
Δ
Δ
Δ
Δ
y
max
max
y
Figure 2.45
Different levels of inherent overstrength
Ω
i
: ductile response,
Ω
i
<
1.0 (
left
), and elastic response
under design earthquake
Ω
i
≥
1.0 (
right
)
Key
:
V
d
= design base shear strength;
V
e
= elastic base shear strength;
V
y
= actual base shear strength;
Δ
= roof
displacement
Experimental and numerical research on the performance of buildings during severe earthquakes
have indicated that structural overstrength plays a very important role in protecting buildings from
collapse (e.g. Whittaker
et al
., 1990, 1999; Jain and Navin, 1995; Elnashai and Mwafy, 2002 , among
others). Similarly, high values of Ω
d
-factors are generally essential for the survivability of bridge
systems (Priestley
et al
., 1996). Structural overstrength results from a number of factors (Uang, 1991 ;
Mitchell and Paulter, 1994; Humar and Ragozar, 1996; Park, 1996). The most common sources of
overstrength include:
(i)
Difference between actual and design material strengths, including strain hardening;
(ii)
Effect of confi nement in RC, masonry and composite members;
