1
THE CAPACITY DESIGN OF REINFORCED CONCRETE
HYBRID STRUCTURES FOR MULTISTOREY BUILDINGS
T. Paulay and W. J. Goodsir
1
2
SYNOPSIS
T o c o m p l e m e n t e x i s t i n g c a p a c i t y d e s i g n p r o c e d u r e s used in N e w
Zealand for r e i n f o r c e d c o n c r e t e b u i l d i n g s in w h i c h e a r t h q u a k e
r e s i s t a n c e is p r o v i d e d by d u c t i l e f r a m e s or d u c t i l e s t r u c t u r a l
walls,
an a n a l o g o u s m e t h o d o l o g y is p r e s e n t e d for the d e s i g n
of d u c t i l e h y b r i d s t r u c t u r e s .
M o d e l l i n g and types of s t r u c t u r e s
in w h i c h the m o d e of w a l l c o n t r i b u t i o n is d i f f e r e n t are b r i e f l y
described.
A step by step d e s c r i p t i o n of a c a p a c i t y d e s i g n
p r o c e d u r e for a s t r u c t u r a l system in w h i c h fixed base d u c t i l e
f r a m e s and w a l l s , b o t h of i d e n t i c a l h e i g h t , i n t e r a c t , is
presented.
T h e r a t i o n a l e for e a c h step is o u t l i n e d and, w h e r e
n e c e s s a r y , e v i d e n c e is offered for t h e s e l e c t i o n of p a r t i c u l a r
d e s i g n p a r a m e t e r s and their m a g n i t u d e s .
A n u m b e r o f issues
w h i c h r e q u i r e further study are b r i e f l y o u t l i n e d . T h e s e r e l a t e
to i r r e g u l a r i t y in l a y o u t , t o r s i o n a l e f f e c t s , d i a p h r a g m
f l e x i b i l i t y , shortcomings in the p r e d i c t i o n s for d y n a m i c shear
d e m a n d s in w a l l s , and to l i m i t a t i o n s of the p r o p o s e d d e s i g n
procedure.
It is believed t h a t the m e t h o d o l o g y is l o g i c a l ,
r e l a t i v e l y s i m p l e and that it should e n s u r e , w h e n combined with
appropriate detailing, excellent seismic structural response.
INTRODUCTION
W h e n l a t e r a l load r e s i s t a n c e is p r o v i d e d by
the c o m b i n e d c o n t r i b u t i o n s of d u c t i l e m u l t i storey f r a m e s and s t r u c t u r a l w a l l s , the
s y s t e m is o f t e n r e f e r r e d t o as a "hybrid
structure".
In N o r t h A m e r i c a , the t e r m
"dual s y s t e m " is u s e d .
These s t r u c t u r e s
c o m b i n e t h e a d v a n t a g e s o f their c o n s t i t u e n t
components.
B e c a u s e of the large s t i f f n e s s
o f w a l l s w h i c h are p r o v i d e d w i t h a d e q u a t e
r e s t r a i n t s a t the f o u n d a t i o n s , e x c e l l e n t
storey d r i f t c o n t r o l m a y be o b t a i n e d .
Moreo v e r , s u i t a b l y d e s i g n e d w a l l s can e n s u r e t h a t
storey m e c h a n i s m s (soft s t o r e y s ) w i l l n o t
d e v e l o p in any e v e n t .
Interacting ductile
frames o n the o t h e r h a n d , w h i l e c a r r y i n g
the m a j o r p a r t o f the g r a v i t y l o a d , can
provide, when required, significant energy
d i s s i p a t i o n , p a r t i c u l a r l y in the upper
storeys.
D e s p i t e t h e a t t r a c t i v e n e s s and indeed
e x i s t e n c e o f m a n y such s t r u c t u r e s in N e w
Z e a l a n d , c o m p a r a t i v e l y little research
e f f o r t h a s b e e n d i r e c t e d to them.
The New
Z e a l a n d C o d e o f P r a c t i c e for D e s i g n of
Concrete S t r u c t u r e s draws designers'
a t t e n t i o n to the need for "special s t u d i e s "
when designing "ductile hybrid structures".
N o specific guidance i s , however, provided.
K n o w n s t u d i e s r e f e r p r i m a r i l y to e l a s t i c
r e s p o n s e , d e s p i t e t h e o b v i o u s i m p o r t a n c e of
the features of inelastic behaviour.
1
A s t u d y w a s i n i t i a t e d w i t h the a i m of
ultimately formulating a design procedure
for h y b r i d s t r u c t u r e s w h i c h w o u l d b e
a n a l o g o u s to t h o s e d e v e l o p e d in N e w Zealand
for d u c t i l e f r a m e s a n d d u c t i l e s t r u c t u r a l
walls .
It w a s h o p e d t h a t a s c h e m e c o u l d
b e f o r m u l a t e d w h i c h w o u l d p r o v i d e a smooth
t r a n s i t i o n b e t w e e n d e s i g n a p p r o a c h e s for
s p a c e f r a m e s * and those for b u i l d i n g s in
w h i c h seismic r e s i s t a n c e is p r o v i d e d by
structural walls o n l y * ' 2 .
To this e n d
n u m e r o u s a n a l y t i c a l studies of p r o t o t y p e
b u i l d i n g structures w e r e c o n d u c t e d '
to
p r o v i d e a p p r o p r i a t e c a l i b r a t i o n of the
principal design parameters.
This paper
r e p o r t s on the findings and c o n c l u s i o n s as
they relate to d e s i g n p r o c e d u r e s r a t h e r
t h a n on details of features of s t r u c t u r a l
behaviour.
1
1
3
4
The t r a d i t i o n a l p r o c e d u r e of d e s i g n i n g for
earthquake resistance, utilizing elastic
a n a l y s i s t e c h n i q u e s and e q u i v a l e n t l a t e r a l
s t a t i c l o a d s , is w e l l e s t a b l i s h e d .
The
r e s u l t i n g d i s t r i b u t i o n o f lateral load
r e s i s t a n c e o v e r the h e i g h t of b u i l d i n g s
w i t h d u c t i l e f r a m e s , or s t r u c t u r a l w a l l s ,
is g e n e r a l l y a c c e p t e d as m e e t i n g s a t i s f a c t o r i l y actual e a r t h q u a k e load d e m a n d s . T h e r e
w a s little e v i d e n c e to indicate t h a t this
w o u l d b e the c a s e also w i t h h y b r i d
structures.
O n e source of c o n c e r n for
possibly drastic differences between
"elastic s t a t i c " and " e l a s t o - p l a s t i c
dynamic" responses of hybrid structures
s t e m s from the r e c o g n i t i o n of f u n d a m e n t a l
d i f f e r e n c e s in the b e h a v i o u r of
D e t a i l s of the "capacity d e s i g n " of
r e i n f o r c e d c o n c r e t e s t r u c t u r e s are g i v e n
in N Z S 3101:1982 and the b a c k g r o u n d to
t h i s design p h i l o s o p h y is o u t l i n e d in
some d e t a i l in the c o m m e n t a r y o f the
code of p r a c t i c e .
1
1
2
P r o f e s s o r o f Civil E n g i n e e r i n g , U n i v e r s i t y of C a n t e r b u r y , N e w Z e a l a n d .
Engineer, Ove Arup Partnership, London,
England.
BULLETIN OF THE NEW ZEALAND NATIONAL SOCIETY FOR EARTHQUAKE ENGINEERING, Vol. 19, No. 1, March 1986
2
b e a m - c o l u m n frames and s t r u c t u r a l w a l l s .
T h e s e d i f f e r e n c e s stem from d i s s i m i l a r
d e f o r m a t i o n p a t t e r n s w h e n subjected to the
s a m e l a t e r a l load, as shown in F i g . 1.
F r a m e s and w a l l s , w h i l e sharing in the
r e s i s t a n c e of shear f o r c e s in the lower
s t o r e y s , o p p o s e e a c h other in the storeys
n e a r the top of the b u i l d i n g .
It w a s of
m a j o r i n t e r e s t to e x a m i n e the load sharing
b e t w e e n t h e s e two t y p e s of i n t e r a c t i n g
elements during inelastic dynamic response
to a m a j o r s e i s m i c e v e n t .
F o r the sake of c o m p l e t e n e s s , c e r t a i n
a s p e c t s of the "capacity d e s i g n " of
d u c t i l e frames are r e s t a t e d .
2.
T Y P E S OF H Y B R I D S T R U C T U R E S
THEIR MODELLING
In the f o l l o w i n g , some d i s t i n c t and
c o m m o n types of h y b r i d s t r u c t u r e s , in w h i c h
w a l l s and frames i n t e r a c t in a p a r t i c u l a r
m a n n e r , are d e s c r i b e d .
N o a t t e m p t is m a d e ,
h o w e v e r , t o c a t e g o r i z e all p o s s i b l e
c o m b i n a t i o n s in w h i c h t h e s e two s y s t e m s m a y
be u t i l i z e d .
Conventional modelling techn i q u e s , to b e u s e d for the p u r p o s e s of
a n a l y s i s , a r e b r i e f l y r e v i e w e d and s u g g e s t ions m a d e for choices of s u i t a b l e e n e r g y
d i s s i p a t i n g systems in h y b r i d s t r u c t u r e s .
2.1
Lateral
Load
Fig.
Frame Element
Walt Element
(Shear Model
(Bending Mode)
1
Coupled
Frame-Wall
Building
D e f o r m a t i o n P a t t e r n s of
L o a d e d F r a m e , W a l l s and
Wall-Frame Elements.
Laterally
Coupled
A s t e p by s t e p d e s i g n m e t h o d o l o g y is
proposed^ to m e e t the i n t e n t of the "capacity
design" philosophy.
The presentation
c o n c e n t r a t e s solely o n i s s u e s r e l e v a n t to
the largest expected seismic event envisaged
by the c o d e .
T h e e m p h a s i s is t h e r e f o r e o n
i s s u e s of d u c t i l i t y and the p r e v e n t i o n of
collapse.
E x i s t i n g p r o c e d u r e s , to s a t i s f y
d e s i g n c r i t e r i a for s t i f f n e s s and m i n i m u m
s t r e n g t h , b o t h r e l e v a n t p r i m a r i l y to d a m a g e
c o n t r o l , and c o n s i d e r e d to be e q u a l l y
a p p l i c a b l e to h y b r i d s t r u c t u r e s , are n o t
r e f e r r e d to in t h i s p a p e r .
5
Interacting Ductile Frames
Ductile Cantilever Walls
o
and
In the m a j o r i t y of r e i n f o r c e d c o n c r e t e
m u l t i s t o r e y b u i l d i n g s , lateral load
r e s i s t a n c e is a s s i g n e d to b o t h d u c t i l e s p a c e
frames and c a n t i l e v e r structural w a l l s .
F i g u r e 2(a) shows in p l a n the s o m e w h a t
i d e a l i z e d s y m m e t r i c a l d i s p o s i t i o n of f r a m e s
and w a l l s in a 12 storey e x a m p l e b u i l d i n g .
T h e p r o p e r t i e s of t h e s e two d i s t i n c t
structural elements may be conveniently
lumped into a single frame and a s i n g l e
c a n t i l e v e r w a l l , as shown in F i g . 2 ( b ) .
Instead of i n d i v i d u a l w a l l s , s h o w n in F i g .
2 ( a ) , tubular c o r e s , or coupled s t r u c t u r a l
w a l l s , are also u s e d f r e q u e n t l y .
Direction
1 •—-1
- h — H —
i
r j\
m! -,. I ^
IV' 1
Structural
wall
•
K
•
I
i,„
j
Main
frame
I
1
1
1
X
of
^
r
1
(a)
T h e d o m i n a n t f e a t u r e o f the c a p a c i t y d e s i g n
s t r a t e g y is the a p r i o r i e s t a b l i s h m e n t of a
r a t i o n a l h i e r a r c h y in s t r e n g t h b e t w e e n the
c o m p o n e n t s of the e n t i r e s t r u c t u r a l system.
A c c o r d i n g l y , the a p p r o a c h to the d e s i g n of
e a c h p r i m a r y l a t e r a l load r e s i s t i n g c o m p o n e n t w h i c h is to be p r o t e c t e d a g a i n s t y i e l d ing or b r i t t l e f a i l u r e , such as due to s h e a r ,
c a n b e d e s c r i b e d by the s i m p l e g e n e r a l
e x p r e s s i o n for the ideal strength
S., thus
S.
l
AND
. . 1
T
1
j
ALL
,
Secondary
beams
Transverse
frames
PLAN
Total
Shear
(1)
code
where
S
,
is the r e q u i r e d d e p e n d a b l e
s t r e n g t h o r t h e m e m b e r selected for e n e r g y
d i s s i p a t i o n , as d e t e r m i n e d by elastic
a n a l y s i s t e c h n i q u e s for a c o d e
specified
l a t e r a l s t a t i c load o n the s t r u c t u r e ;
<J>
is the r a t i o of the m a x i m u m s t r e n g t h ,
S , w h i c h can b e d e v e l o p e d in the s e l e c t e d
i n e l a s t i c c o m p o n e n t (as built) by large
d i s p l a c e m e n t s d u r i n g a severe s e i s m i c
e v e n t , to the strength r e q u i r e d ,
H '
for the same m e m b e r by the code s p e c i f i e d
l a t e r a l l o a d i n g ; and
w
is a d y n a m i c
m a g n i f i c a t i o n factor w h i c h q u a n t i f i e s
d e v i a t i o n s in s t r e n g t h d e m a n d s o n the
m e m b e r to be p r o t e c t e d , from d e m a n d s
i n d i c a t e d by e l a s t i c a n a l y s i s .
Extreme
d e m a n d s are e x p e c t e d to occur during t h e
i n e l a s t i c d y n a m i c r e s p o n s e of the s t r u c t u r e .
5
Q
s
C
O
e
Krode, total'
(hi STRUCTURAL
Fig.
2
MODELLING
(c) STOREY
SHEAR
FORCES
M o d e l l i n g of and L a t e r a l L o a d
Sharing in a T y p i c a l W a l l - F r a m e
System.
It is c u s t o m a r y to assume t h a t floor slabs
at all l e v e l s h a v e i n f i n i t e i n p l a n e r i g i d i t y .
Such d i a p h r a g m s w i l l then e n s u r e t h a t storey
d i s p l a c e m e n t s for frames and w a l l s a r e the
same o r that in the c a s e of storey t o r s i o n ,
a simple linear relationship exists between
the storey d i s p l a c e m e n t s of v e r t i c a l
e l e m e n t s . W h e n d i a p h r a g m s are r e l a t i v e l y
slender and w h e n l a r g e c o n c e n t r a t e d l a t e r a l
s t o r e y f o r c e s need to be i n t r o d u c e d to
3
r e l a t i v e l y stiff w a l l s , p a r t i c u l a r l y w h e n
t h e s e are spaced far a p a r t , the f l e x i b i l i t y
o f floor d i a p h r a g m s m a y need to b e taken
into account.
T h i s issue is b r i e f l y
r e v i e w e d in S e c t i o n 4.3.
The e x t e n s i o n a l l y i n f i n i t e l y r i g i d h o r i z o n tal c o n n e c t i o n b e t w e e n lumped f r a m e s and
w a l l s at e a c h f l o o r , shown in F i g . 2 ( b ) ,
e n a b l e s the a n a l y s i s of such laterally
loaded e l a s t i c s t r u c t u r e s to b e carried o u t
speedily.
T y p i c a l r e s u l t s are shown in
Fig. 2 (c).
Here the s h a r i n g b e t w e e n w a l l s
and frames o f the t o t a l storey shear forces
is i l l u s t r a t e d .
The r e l a t i v e p a r t i c i p a t i o n s
w h i c h r e f l e c t the b e h a v i o u r of the two
d i f f e r e n t s y s t e m s , as shown in F i g . 1,
i n d i c a t e a r a p i d d e c l i n e w i t h h e i g h t of the
c o n t r i b u t i o n o f t h e w a l l s to shear r e s i s t ance . F i g u r e 2 ( c ) a l s o shows h o w the two
s y s t e m s o p p o s e e a c h o t h e r in the top
storeys.
T h e d i s t r i b u t i o n of m a g n i t u d e s of
s h e a r f o r c e s w i t h h e i g h t for each system
w i l l d e p e n d p r i m a r i l y on the r e l a t i v e s t i f f n e s s e s of t h e w a l l s and f r a m e s . T h i s e x a m p l e
s t r u c t u r e , s h o w n in F i g . 2,will b e s u b s e q u e n t l y u s e d to i l l u s t r a t e typical
d i s t r i b u t i o n s of forces a n d m o m e n t s for
b o t h w a l l s a n d f r a m e s , as a c o n s e q u e n c e of
i n e l a s t i c d y n a m i c r e s p o n s e to seismic
excitations.
A s t h e f l e x u r a l r e s p o n s e of w a l l s is i n t e n d ed to c o n t r o l d e f l e c t i o n s in h y b r i d s t r u c t ures , the d a n g e r of d e v e l o p i n g "soft
storeys" should not arise.
The d e s i g n e r
may t h e r e f o r e freely choose t h o s e m e m b e r s
o r l o c a l i t i e s in frames w h e r e e n e r g y d i s s i p a t i o n s h o u l d take p l a c e w h e n r e q u i r e d .
A
p r e f e r a b l e a n d p r a c t i c a l m e c h a n i s m for the
frame of F i g . 2 is shown in F i g . 4 ( a ) .
In
this frame, p l a s t i c h i n g e s , w h e n required
d u r i n g a l a r g e e x p e c t e d s e i s m i c e v e n t , are
m a d e to d e v e l o p in all the b e a m s and at the
b a s e of all v e r t i c a l e l e m e n t s .
A t roof
level, p l a s t i c h i n g e s m a y f o r m in e i t h e r the
beams or the columns.
The m a i n a d v a n t a g e
of t h i s s y s t e m is in the d e t a i l i n g of the
potential plastic hinges.
G e n e r a l l y it is
e a s i e r to d e t a i l b e a m r a t h e r than c o l u m n
e n d s for p l a s t i c r o t a t i o n .
M o r e o v e r , the
a v o i d a n c e o f p l a s t i c h i n g e s in columns
a l l o w s l a p p e d s p l i c e s to be c o n s t r u c t e d a t
the b o t t o m e n d r a t h e r than a t m i d h e i g h t of
c o l u m n s in e a c h u p p e r s t o r e y .
W h e n l o n g span b e a m s are u s e d , and in
particular when gravity rather than earthq u a k e l o a d i n g g o v e r n s the s t r e n g t h of b e a m s ,
it m a y b e p r e f e r a b l e to a d m i t the d e v e l o p m e n t o f p l a s t i c h i n g e s at b o t h e n d s of all
c o l u m n s o v e r the full h e i g h t of the s t r u c t ure , as shown i n F i g . 4 ( c ) .
D u c t i l e F r a m e s and W a l l s C o u p l e d
Beams.
2.2
S t r u c t u r a l w a l l s , instead of b e i n g i s o l a t e d
as free standing c a n t i l e v e r s , may b e
c o n n e c t e d by c o n t i n u o u s b e a m s in t h e i r p l a n e
to a d j a c e n t f r a m e s .
The m o d e l o f such a
s y s t e m is shown in F i g . 3 ( a ) . B e a m s w i t h
span l e n g t h s ij_ and £ are r i g i d l y c o n n e c t ed to t h e w a l l s . A p o s s i b l e m e c h a n i s m t h a t
c a n b e u t i l i z e d in this type of s y s t e m is
shown in Fig. 4 ( b ) . B e a m h i n g e s at or c l o s e
to t h e w a l l edges m u s t d e v e l o p . H o w e v e r , at
c o l u m n s , the d e s i g n e r m a y d e c i d e to a l l o w
p l a s t i c h i n g e s to form in either the b e a m s
or the c o l u m n s , above and b e l o w e a c h f l o o r ,
,as s h o w n in Fig. 4(c)
2
Plastic
hinges
Wall
(a)
lb)
let
Fig. 4 Complete Energy Dissipating Mechanisms
Associated with Different Hybrid
Structural Systems.
This type of s y s t e m c o u l d be u t i l i z e d a l s o
in t h e b u i l d i n g of F i g . 2(a) if t h e w a l l s
w e r e t o be connected to the a d j a c e n t c o l u m n s
by p r i m a r y lateral load r e s i s t i n g b e a m s .
In
that case the e n t i r e s t r u c t u r a l s y s t e m w o u l d
c o n s i s t of 7 ductile f r a m e s , shown in F i g .
2(b) and two coupled f r a m e - w a l l s of the
type g i v e n in F i g . 4 (b) .
T h e d e s i g n p r o c e d u r e d e s c r i b e d in c o n s i d e r able d e t a i l in S e c t i o n 3, is r e l e v a n t to
t h i s type o f s t r u c t u r a l s y s t e m and its
p r e f e r r e d e n e r g y dissipating m e c h a n i s m s .
(a)
Fig.
(b)
3
by
(c)
M o d e l l i n g of D i f f e r e n t T y p e s of Hybrid
(d)
Systems.
4
S i m p l i f i e d a n a l y s i s t e c h n i q u e s , u s e f u l at
l e a s t for p r e l i m i n a r y d e s i g n , h a v e b e e n
d e v e l o p e d for such a m i x t u r e of i n t e r a c t i n g
f r a m e s and w a l l s ^ .
The structural
i d e a l i z a t i o n u s e d in s h o w n in F i g . 3 ( b ) . T h e
s t i f f n e s s of all w a l l s , as q u a n t i f i e d by the
s e c o n d m o m e n t of a r e a , are lumped i n t o a
s t i f f n e s s , I , of a s i n g l e w a l l . W h e r e
a p p r o p r i a t e Allowance for shear d i s t o r t i o n s
in the w a l l s should a l s o b e m a d e .
The
b e a m s framing d i r e c t l y into w a l l e d g e s , i.e.
t h o s e w i t h span l e n g t h s
and
in F i g .
3 ( a ) , are lumped a t each floor into a s i n g l e
b e a m h a v i n g a m e a n second m o m e n t of a r e a ,
I , and s p a n
I , as shown in F i g . 3 ( b ) . A l l
o t h e r b e a m s , suSh as span
in F i g . 3(a)
and the b e a m s of the f r a m e s in F i g . 2 ( a ) ,
a r e also l u m p e d and r e p l a c e d a t each floor
w i t h b e a m s h a v i n g the m e a n p r o p e r t i e s of 1^
2
and &
b
shown in F i g . 3 ( b ) . T h e aim is to
o b t a i n r e p r e s e n t a t i v e m e a n I/£ r a t i o s for
the beams.
F i n a l l y all t h e c o l u m n s of the
b u i l d i n g s are l u m p e d into two i d e n t i c a l
c o l u m n s , each h a v i n g o n e half of the m o m e n t
i n e r t i a , 0.51 , of the sum of the m o m e n t of
i n e r t i a of al5 c o l u m n s of the real
s t r u c t u r e . S t a n d a r d s o l u t i o n s for a r a n g e
of r e l a t i v e s t i f f n e s s e s h a v e b e e n p r e s e n t e d
for this t y p e (Fig. 3(b)) of s t r u c t u r e ^ .
A n o t h e r u s e f u l t e c h n i q u e r e p l a c e s all f r a m e s
w i t h a s i n g l e e q u i v a l e n t "shear" c a n t i l e v e r
and c o n n e c t s t h i s c o n t i n u o u s l y over the
h e i g h t of the b u i l d i n g to a s i n g l e e q u i v a l e n t
"bending" cantilever w a l l .
T h e m e t h o d is
s i m i l a r to that u s e d in t h e "laminar
a n a l y s i s " of c o u p l e d structural w a l l s . It is
limited to regular structures with vertically
constant geometric properties.
7
B e f o r e the d e s i g n of i n d i v i d u a l m e m b e r s can
b e f i n a l i s e d , it is n e c e s s a r y to i d e n t i f y
c l e a r l y the l o c a t i o n s in beams and c o l u m n s
a t w h i c h p l a s t i c h i n g e s are intended in
o r d e r to e n a b l e the c a p a c i t y d e s i g n
p r o c e d u r e to b e a p p l i e d .
2.3
Frames Interacting with Walls
Partial Height
of
A l t h o u g h in m o s t b u i l d i n g s s t r u c t u r a l w a l l s
extend o v e r the full h e i g h t , t h e r e are
c a s e s w h e n for a r c h i t e c t u r a l or o t h e r
r e a s o n s , w a l l s are t e r m i n a t e d b e l o w the
level of the top f l o o r . A m o d e l of such
a s t r u c t u r e is shown in F i g . 3 ( c ) .
B e c a u s e of the a b r u p t d i s c o n t i n u i t y in total
s t i f f n e s s e s a t the level w h e r e w a l l s
t e r m i n a t e , the s e i s m i c r e s p o n s e of t h e s e
s t r u c t u r e s is v i e w e d w i t h some c o n c e r n .
G r o s s d i s c o n t i n u i t i e s are expected to r e s u l t
in p o s s i b l y c r i t i c a l f e a t u r e s of d y n a m i c
r e s p o n s e w h i c h are d i f f i c u l t to p r e d i c t . It
is s u s p e c t e d that the r e g i o n s of d i s c o n t i n u i t y m a y s u f f e r p r e m a t u r e d a m a g e and that
l o c a l d u c t i l i t y d e m a n d s during the l a r g e s t
e x p e c t e d s e i s m i c e v e n t s m i g h t e x c e e d the
a b i l i t y of a f f e c t e d c o m p o n e n t s to d e f o r m in
the plastic range without significant loss
of r e s i s t a n c e .
O n the o t h e r h a n d , e l a s t i c a n a l y s e s for
l a t e r a l s t a t i c l o a d s show that s t r u c t u r a l
w a l l s in the u p p e r s t o r e y s m a y s e r v e n o
useful structural purpose.
Figure 2
s u g g e s t s t h a t the t e r m i n a t i o n of w a l l s b e l o w
t h e top floor m a y b e n e f i c i a l l y a f f e c t
overall behaviour.
T h e r e s p o n s e of such s t r u c t u r e s h a s also
b e e n studied r e c e n t l y ! . A limited n u m b e r
of case s t u d i e s , u s i n g the 1 9 4 0 El C e n t r o
earthquake record, suggested no features
t h a t could n o t b e r e a d i l y a c c o m m o d a t e d in
currently used design procedures.
The
f i n d i n g s of this s t u d y , t o g e t h e r w i t h the
a p p r o p r i a t e a p p l i c a t i o n of the c a p a c i t y
design approach, will be reported separately.
1
2.4
Hybrid Structures with Walls
Deformable Foundations
on
It is c u s t o m a r y to a s s u m e t h a t c a n t i l e v e r
w a l l s are fully r e s t r a i n e d a g a i n s t r o t a t i o n s
at the b a s e .
It is r e c o g n i s e d , h o w e v e r ,
t h a t full b a s e fixity for such l a r g e
s t r u c t u r a l e l e m e n t s is v e r y d i f f i c u l t , if
n o t i m p o s s i b l e , to a c h i e v e .
Foundation
c o m p l i a n c e m a y r e s u l t from soil d e f o r m a t i o n s
b e l o w f o o t i n g s a n d / o r from d e f o r m a t i o n s
occurring within the foundation structure,
such as p i l e s .
B a s e r o t a t i o n is a v i t a l
c o m p o n e n t of w a l l d e f o r m a t i o n s . T h e r e f o r e
it m a y s i g n i f i c a n t l y a f f e c t t h e s t i f f n e s s
of c a n t i l e v e r w a l l s and h e n c e p o s s i b l y their
share in the lateral load r e s i s t a n c e w i t h i n
elastic hybrid structures.
The reluctance
to a d d r e s s the p r o b l e m m a y b e a t t r i b u t e d to
o u r l i m i t a t i o n s in b e i n g a b l e to e s t i m a t e
r e l i a b l y s t i f f n e s s p r o p e r t i e s of s o i l s .
M o r e o v e r , soil s t i f f n e s s is g e n e r a l l y v e r y
d i f f e r e n t for static and d y n a m i c l o a d i n g .
F o r the l a t t e r , f r e q u e n c y and a m p l i t u d e are
also p a r a m e t e r s w h i c h a f f e c t soil r e s p o n s e .
T o g a u g e the s e n s i t i v i t y of h y b r i d s t r u c t u r e s
of the type shown in F i g . 2(b) w i t h r e s p e c t
to f o u n d a t i o n c o m p l i a n c e of t h e w a l l e l e m e n t s
o n l y , p a r a m e t r i c studies w e r e c o n d u c t e d .
T h e m a j o r v a r i a b l e s in the s t r u c t u r e s c h o s e n
for a n a l y s e s w e r e :
1 1
(1)
V a r i a t i o n of w a l l r e s t r a i n t b e t w e e n
the extreme l i m i t s of full r o t a t i o n a l
fixity and a h i n g e a t the b a s e .
(2)
V a r i a t i o n in the n u m b e r of storeys in
a building.
P r e d o m i n a n t l y 6 a n d 12
storey structures w e r e s t u d i e d .
(3)
T h e r e l a t i v e c o n t r i b u t i o n of w a l l s to
total lateral load r e s i s t a n c e w i t h i n
the s t r u c t u r e w e r e v a r i e d . • T h i s w a s
achieved with a p p r o p r i a t e v a r i a t i o n of w a l l
lengths,
shown in F i g . 2 ( a ) .
(4)
E l a s t i c r e s p o n s e to code s p e c i f i e d
l a t e r a l static load w a s c o m p a r e d w i t h
the e l a s t o - p l a s t i c d y n a m i c r e s p o n s e of the
s t r u c t u r e to the 1940 EI C e n t r o e a r t h q u a k e
record.
D e t a i l s of this study are to b e r e p o r t e d .
T h o s e aspects of the c o n c l u s i o n s w h i c h are
p a r t i c u l a r l y r e l e v a n t to the i s s u e s
e x a m i n e d in this p a p e r are as f o l l o w s :
(a)
A b o v e t h e first f l o o r , the static
r e s p o n s e of the s t r u c t u r e w i t h w a l l s
w i t h m o d e r a t e s t i f f n e s s is n o t s i g n i f i c a n t l y
a f f e c t e d by the d e g r e e of b a s e r e s t r a i n t .
A s a c o r o l l a r y , the s t i f f e r a w a l l t h e m o r e
p r o f o u n d is the i n f l u e n c e of f o u n d a t i o n
compliance.
(b)
In pinned b a s e w a l l s , as e x p e c t e d ,
v e r y l a r g e and r e v e r s e d b a s e shear
forces are p r e d i c t e d by e l a s t i c a n a l y s e s
for static l a t e r a l load.
This points
to the n e e d for studying the t r a n s f e r of
t h e s e l a r g e forces t o the d i a p h r a g m at
5
first floor level.
T h e w a l l shear r e v e r s a l s
i n the f i r s t storey n e c e s s i t a t e d d r a m a t i c
i n c r e a s e s in c o l u m n shear f o r c e s in that
storey.
In the first storey t h e sum of the
c o l u m n s h e a r f o r c e s exceed t h e r e f o r e the
t o t a l s t a t i c b a s e shear for the e n t i r e
structure.
In t h e analysis for the e l a s t i c a l l y
r e s p o n d i n g s t r u c t u r e , d u e a l l o w a n c e should
b e m a d e for the e f f e c t s of c r a c k i n g o n the
s t i f f n e s s of b o t h f r a m e m e m b e r s and w a l l s .
B o t h f r a m e s and w a l l s m a y g e n e r a l l y b e
a s s u m e d to be fully r e s t r a i n e d a t t h e i r
base.
Load e f f e c t s are r e f e r r e d to as E .
(c)
Step 2 - S u p e r i m p o s e the b e a m b e n d i n g
m o m e n t s o b t a i n e d in S t e p 1 u p o n c o r r e s p o n d i n g
b e a m m o m e n t s w h i c h a r e d e r i v e d for
a p p r o p r i a t e l y factored g r a v i t y l o a d i n g o n
the structure..
The single most important parameter
a f f e c t i n g the s e i s m i c d y n a m i c r e s p o n s e
of such h y b r i d s t r u c t u r e s w a s found to be
t h e p e r i o d s h i f t b r o u g h t a b o u t by the
r e d u c t i o n of w a l l s t i f f n e s s e s w h e n c o m p l e t e
l o s s of r o t a t i o n a l r e s t r a i n t a t the b a s e
was assumed.
(d)
This superposition corresponds with the
c o m b i n a t i o n s of f a c t o r e d loads U = D + 1.3L
± E , w h e r e D is the dead load a n d L
is
t h e l i v e load r e d u c e d as the t r i b u t a r y
area i n c r e a s e s ^ .
(e)
Step 3 - If a d v a n t a g e o u s ,
r e d i s t r i b u t e d e s i g n m o m e n t s o b t a i n e d in
S t e p 2 h o r i z o n t a l l y at a f l o o r b e t w e e n any
or all b e a m s in e a c h b e n t , and v e r t i c a l l y
b e t w e e n b e a m s of the same span a t d i f f e r e n t
floors.
E x t r e m e l e v e l s of shear f o r c e s ,
p r e d i c t e d b y e l a s t i c a n a l y s e s for
c o l u m n s a n d w a l l s , did n o t e v e n t u a t e d u r i n g
t h e time h i s t o r y a n a l y s i s for the E l C e n t r o
event.
In t h e u p p e r s t o r e y s i m p o r t a n t d e s i g n
q u a n t i t i e s for the e x a m p l e h y b r i d
s t r u c t u r e s , such as d r i f t s , c o l u m n and w a l l
m o m e n t s , and r o t a t i o n a l d u c t i l i t y d e m a n d s in
p l a s t i c h i n g e s of b e a m s , w e r e only
insigniciantly affected when walls were
modelled with pinned bases.
(f)
F u l l w a l l b a s e fixity is n o r m a l l y
a s s u m e d in d e s i g n , a l t h o u g h it is
known to b e generally unavailable.
These
parametric studies indicated, however, that
e r r o r s d u e to q u i t e s i g n i f i c a n t r e l a x a t i o n
in b a s e r e s t r a i n t , are n o t l i k e l y to
seriously affect elasto-plastic dynamic
response.
B r i e f c o m p a r i s o n s of a few f e a t u r e s of the
a n a l y t i c a l l y p r e d i c t e d r e s p o n s e of p r o t o t y p e h y b r i d s t r u c t u r e s w i t h fixed or p i n n e d
b a s e d w a l l s , a r e m a d e in S e c t i o n 3.
3.
D E T A I L S OF A C A P A C I T Y
PROCEDURE
DESIGN
In the f o l l o w i n g s e c t i o n s a c a p a c i t y d e s i g n
a p p r o a c h for h y b r i d s t r u c t u r e s is d e s c r i b e d
in a s t e p - b y - s t e p m a n n e r .
The presentation
f o l l o w s t h e p a t t e r n o f , and is similar t o ,
the d e s i g n p r o c e d u r e suggested for
r e i n f o r c e d c o n c r e t e d u c t i l e f r a m e s in the
C o m m e n t a r y of N Z S 3 1 G 1 .
Where necessary,
t h e p r e s e n t a t i o n of a d e s i g n step is
followed by comments, sometimes extensive.
T h e s e a r e r e l e v a n t t o t h e p u r p o s e of and
i n t e n d to e x p l a i n t h e j u s t i f i c a t i o n for t h a t
particular step.
F r e q u e n t r e f e r e n c e is m a d e
to F i g . 2, w h i c h shows a p r o t o t y p e f r a m e wall structure.
1
R
In t h e p r o c e s s of m o m e n t r e d i s t r i b u t i o n ,
the p e a k v a l u e s of beam m o m e n t s , r e s u l t i n g
from the load c o m b i n a t i o n s U = D + 1.3L
± E , m a y b e reduced b y up to 3 0 % . H o w e v e r ,
the c u r t a i l m e n t of the beam f l e x u r a l
r e i n f o r c e m e n t along a beam m u s t b e such that
at l e a s t 7 0 % of the m o m e n t o b t a i n e d from
e l a s t i c a n a l y s e s in S t e p 2 can b e r e s i s t e d .
Final moments obtained after redistribution
should be checked to e n s u r e that no l o s s in
the total lateral load r e s i s t a n c e of the
structure r e s u l t s .
A l s o c o m b i n a t i o n s for
g r a v i t y load a l o n e , U = 1.4D + 1.7L , m u s t
b e e x a m i n e d b e f o r e the p r o p o r t i o n i n g of
beams commences.
1
1
8
T h e p r i n c i p l e s of r e d i s t r i b u t i o n of m o m e n t s
at a level among d i f f e r e n t spans of b e a m s
w i t h i n frames are w e l l e s t a b l i s h e d > .
O n e o f the a d v a n t a g e s w h i c h m a y r e s u l t is
the r e d u c t i o n of the peak beam n e g a t i v e
m o m e n t at an e x t e r i o r c o l u m n w h i c h is
associated^_with the load c o m b i n a t i o n U = D
+ 1 . 3 L + E . T h e r e d u c t i o n is a c h i e v e d
at the e x p e n s e of i n c r e a s i n g the (usually
n o n - c r i t i c a l ) p o s i t i v e m o m e n t at the same
s e c t i o n associated w i t h the c o m b i n a t i o n
U = D + 1. 3 L + E .
In the latter c a s e the
1
8
R
D
K
o Factored
gravity
moments
only
• Gravity and earthquake
moments
from elastic
analysis
x After horizontal
redistribution
I After
vertical
redistribution,
T h e p r o c e d u r e o u t l i n e d in the following 19
s t e p s is r e l e v a n t to the t y p e s of s t r u c t u r e s
s h o w n in F i g s . 4(a) and ( b ) . In t h e s e
c o l u m n s in u p p e r s t o r e y s a r e i n t e n d e d to b e
protected against significant plastic
deformations.
Thereby various concessions
w i t h r e s p e c t t o their d e t a i l i n g for
ductility
may be utilised.
S t e p 1 - D e r i v e the b e n d i n g m o m e n t s
and shear f o r c e s for all m e m b e r s of t h e
f r a m e - s h e a r w a l l system s u b j e c t e d to the
c o d e s p e c i f i e d e q u i v a l e n t l a t e r a l static
e a r t h q u a k e load o n l y .
T h e s e a c t i o n s are
subscripted "code".
-800
Fig.
5
-400
0
400
800
(kNm)
T h e R e d i s t r i b u t i o n of D e s i g n M o m e n t s
A m o n g B e a m s of a H y b r i d S t r u c t u r e .
6
g r a v i t y and e a r t h q u a k e m o m e n t s , s u p e r i m p o s e d
in S t e p 2, o p p o s e each o t h e r . A n e x a m p l e
in F i g . 5 s h o w s m a g n i t u d e s of b e a m d e s i g n
m o m e n t s at each floor at an e x t e r i o r
c o l u m n a t v a r i o u s s t a g e s of the a n a l y s i s .
T h e g r a v i t y m o m e n t s (always n e g a t i v e ) ,
s h o w n b y c i r c l e s , are changed b y the_^
a d d i t i o n of e a r t h q u a k e m o m e n t s E or E , to
v a l u e s shown b y solid c i r c l e s .
r e d i s t r i b u t i o n d i s c u s s e d h e r e are similar
to t h o s e u s e d in t h e d e s i g n of coupling
b e a m s of c o u p l e d s t r u c t u r a l w a l l s .
B e c a u s e near their b a s e , w a l l s m a k e v e r y
s i g n i f i c a n t c o n t r i b u t i o n s to the r e s i s t a n c e
of both h o r i z o n t a l shear (Fig. 2) and
o v e r t u r n i n g m o m e n t , the f l e x u r a l d e m a n d s o n
the b e a m s of h y b r i d s t r u c t u r e s a r e
r e l a t i v e l y small in t h e lower s t o r e y s . T h e
d i s t r i b u t i o n of b e a m and w a l l m o m e n t d e m a n d s
w i t h the h e i g h t of the e l a s t i c s t r u c t u r e
d e p e n d s on the r e l a t i v e s t i f f n e s s of w a l l s
and f r a m e s ^ .
In the e x a m p l e f r a m e s , the
b e a m m o m e n t s at the e x t e r i o r c o l u m n c o u l d
b e r e d i s t r i b u t e d so as to r e s u l t in
m a g n i t u d e s shown b y c r o s s e s in F i g . 5. It
is s e e n that the n e g a t i v e and p o s i t i v e
m o m e n t d e m a n d s are now c o m p a r a b l e in
magnitudes.
S t e p 4 - D e s i g n all c r i t i c a l beam
s e c t i o n s so as to p r o v i d e the r e q u i r e d
d e p e n d a b l e f l e x u r a l s t r e n g t h s , and detail
t h e r e i n f o r c e m e n t for all b e a m s in all
frames.
T o o p t i m i z e the p r a c t i c a l i t y of b e a m d e s i g n ,
w h e r e b y b e a m s of i d e n t i c a l strength are
preferred over the largest possible number
of a d j a c e n t f l o o r s , some v e r t i c a l
r e d i s t r i b u t i o n of b e a m d e s i g n m o m e n t s
should a l s o b e c o n s i d e r e d .
In the e x a m p l e
of F i g . 5, t h e d e s i g n m o m e n t s s h o w n b y
c r o s s e s m a y b e r e d i s t r i b u t e d u p and d o w n the
f r a m e s so as t o r e s u l t in m a g n i t u d e s s h o w n
b y t h e c o n t i n u o u s stepped l i n e s .
It is
s e e n t h a t b e a m s of the same f l e x u r a l s t r e n g t h
c o u l d b e u s e d over 6 f l o o r s . :The' stepped
l i n e h a s b e e n c h o s e n i n such a w a y t h a t the
a r e a e n c l o s e d by it is a p p r o x i m a t e l y the
s a m e as that w i t h i n the c u r v e formed by the
crosses.
T h i s c h o i c e m e a n s t h a t the
c o n t r i b u t i o n of the frames to the r e s i s t a n c e
of o v e r t u r n i n g m o m e n t s is only i n s i g n i f i c a n t l y
a l t e r e d by v e r t i c a l m o m e n t r e d i s t r i b u t i o n .
It m a y b e n o t e d t h a t h o r i z o n t a l r e d i s t r i b u t ion of b e a m m o m e n t s a t a p a r t i c u l a r level
w i l l c h a n g e the m o m e n t i n p u t to i n d i v i d u a l
columns.
H e n c e the shear d e m a n d a c r o s s
i n d i v i d u a l c o l u m n s w i l l also c h a n g e w i t h
r e s p e c t to t h a t i n d i c a t e d by the e l a s t i c
a n a l y s i s u s e d in Step 1. H o w e v e r , the total
shear d e m a n d o n c o l u m n s o f a b e n t m u s t n o t
change.
T h i s is r e f e r r e d to as
r e d i s t r i b u t i o n of d e s i g n shear f o r c e s
between columns.
W h e n v e r t i c a l r e d i s t r i b u t i o n of b e a m m o m e n t s
is c a r r i e d o u t , the total m o m e n t i n p u t to
some or all c o l u m n s at a floor w i l l a l s o
change.
H e n c e the total shear d e m a n d o n
c o l u m n s of a p a r t i c u l a r storey m a y d e c r e a s e
(the 5th storey in F i g . 5 ) , w h i l e in o t h e r
s t o r e y (the 2nd storey in F i g . 5) it w i l l
increase.
T o ensure that t h e r e is no
d e c r e a s e in t h e t o t a l storey shear r e s i s t a n c e i n t e n d e d by the c o d e s p e c i f i e d
lateral loading, there must be a horizontal
r e d i s t r i b u t i o n of s h e a r f o r c e s b e t w e e n the
v e r t i c a l e l e m e n t s of the s t r u c t u r e , i.e.
c o l u m n s and w a l l s .
It w i l l b e s h o w n
s u b s e q u e n t l y t h a t the u p p e r r e g i o n s of w a l l s
w i l l b e p r o v i d e d w i t h s u f f i c i e n t shear a n d
f l e x u r a l s t r e n g t h to a c c o m m o d a t e a d d i t i o n a l
s h e a r f o r c e s shed b y u p p e r storey c o l u m n s .
T h e p r i n c i p l e s involved in v e r t i c a l load
2
T o safeguard a g a i n s t p r e m a t u r e y i e l d i n g in
b e a m s d u r i n g small e a r t h q u a k e s , t h e
r e d u c t i o n of b e a m m o m e n t s r e s u l t i n g from
c o m b i n e d h o r i z o n t a l and v e r t i c a l m o m e n t
r e d i s t r i b u t i o n should n o t e x c e e d 3 0 % .
T h e s e r o u t i n e steps r e q u i r e the d e t e r m i n a t i o n of the size and n u m b e r of r e i n f o r c i n g
b a r s to b e u s e d to r e s i s t m o m e n t s along all
b e a m s in a c c o r d a n c e w i t h t h e d e m a n d s of
m o m e n t e n v e l o p e s o b t a i n e d after m o m e n t
redistribution.
It is i m p o r t a n t a t this
stage to l o c a t e the two p o t e n t i a l p l a s t i c
h i n g e s in each span (Fig. 4(a)) for each
d i r e c t i o n of e a r t h q u a k e a t t a c k . In l o c a t i n g
p l a s t i c h i n g e s w h i c h r e q u i r e the b o t t o m
(positive) f l e x u r a l r e i n f o r c e m e n t to y i e l d
in t e n s i o n , b o t h load c o m b i n a t i o n s U = D +
1 . 3 L + E and U = 0.9D + E , should b e
c o n s i d e r e d , as each c o m b i n a t i o n may i n d i c a t e
a different hinge position.
D e t a i l i n g of
the b e a m s should t h e n b e c a r r i e d out in
c o n f o r m i t y w i t h the r e l e v a n t c o d e
provisions.
5
R
1
Step 5 - In each b e a m d e t e r m i n e the
flexural o v e r s t r e h g t h of each of the two
potential plastic hinges corresponding with
each of t h e two d i r e c t i o n s of e a r t h q u a k e
attack.
T h e p r o c e d u r e , i n c o r p o r a t i n g a l l o w a n c e s for
strain h a r d e n i n g of t h e steel and the
p o s s i b l e p a r t i c i p a t i o n in f l e x u r a l r e s i s t a n c e
of all r e i n f o r c e m e n t p r e s e n t in the s t r u c t u r e
as b u i l t , is the same as t h a t used in the
d e s i g n of b e a m s of d u c t i l e f r a m e s .
The
primary aim is to e s t i m a t e the m a x i m u m
m o m e n t i n p u t from b e a m s to a d j a c e n t c o l u m n s
a s s o c i a t e d w i t h the l a r g e s t seismic e v e n t .
1
S t e p 6 - D e t e r m i n e the lateral
d i s p l a c e m e n t induced shear f o r c e , V
,
a s s o c i a t e d w i t h the d e v e l o p m e n t of °
flexural o v e r s t r e n g t h at the two p l a s t i c
h i n g e s in each beam span for each d i r e c t i o n
of e a r t h q u a k e a t t a c k .
T h e s e shear forces are r e a d i l y o b t a i n e d from
the f l e x u r a l o v e r s t r e n g t h s of p o t e n t i a l
p l a s t i c h i n g e s , d e t e r m i n e d in Step 5, w h i c h
w e r e located in Step 4.
W h e n combined w i t h
gravity induced shear f o r c e s , the d e s i g n
shear e n v e l o p e for each b e a m span is
o b t a i n e d , and the r e q u i r e d shear r e i n f o r c e m e n t can then b e d e t e r m i n e d .
The
d i s p l a c e m e n t induced m a x i m u m b e a m shear
forces, V
, are u s e d s u b s e q u e n t l y t o
determine°She m a x i m u m l a t e r a l d i s p l a c e m e n t
induced axial c o l u m n load input a t each
floor.
1
Step 7 - D e t e r m i n e the b e a m f l e x u r a l
o v e r s t r e n g t h f a c t o r , <j> , at the c e n t r e l i n e
of each c o l u m n at each
f l o o r for b o t h
d i r e c t i o n s of e a r t h q u a k e a t t a c k .
Fixed
v a l u e s of
<f)
are:
(a) A t groun8 level <f> = 1.4
(b) A t roof level
<f>° = 1.1.
T h i s f a c t o r is s u b s e q u e n t l y u s e d to e s t i m a t e
t h e m a x i m u m m o m e n t w h i c h could b e
i n t r o d u c e d to c o l u m n s by fully p l a s t i f i e d
beams.
The beam overstrength factor, $ ,
a t a c o l u m n , is the r a t i o of t h e sum of
t h e f l e x u r a l o v e r s t r e n g t h s d e v e l o p e d by
a d j a c e n t b e a m s , as d e t a i l e d , t o the sum of
t h e f l e x u r a l s t r e n g t h s r e q u i r e d in the
g i v e n d i r e c t i o n by the code specified
l a t e r a l e a r t h q u a k e loading a l o n e , b o t h sets
of v a l u e s b e i n g t a k e n at the centre line
o f the r e l e v a n t c o l u m n .
T h e b e a m m o m e n t s at c o l u m n c e n t r e lines can
b e r e a d i l y o b t a i n e d g r a p h i c a l l y from the
d e s i g n b e n d i n g m o m e n t e n v e l o p e s , after the
f l e x u r a l o v e r s t r e n g t h m o m e n t s at the e x a c t
l o c a t i o n s of the t w o p l a s t i c h i n g e s along
the b e a m h a v e b e e n p l o t t e d .
where
=
(D
<TJ)
c o
V
_
code
c
col
U
col
where M
M
+ 1.3$ M
- )
o code
+ 0. 5 h )
e
Step 10 - D e t e r m i n e the t o t a l d e s i g n
axial load on each c o l u m n for each of the
two d i r e c t i o n s of e a r t h q u a k e attack from
code
and
P
LR
+ P
(6)
eq
17)
= 0.9P^ - P^
D
eq
Step 11 - O b t a i n the d e s i g n m o m e n t s
for c o l u m n s a b o v e and b e l o w each floor
from
(3)
col
b
m
i e
v
a
l
u
e
o
£
n
2
o
code
°-
and
R
1 + 0.55(a) - 1) (10
b col>
V
f' A
c
g
h
is a d e s i g n m o m e n t r e d u c t i o n
able w h e n
1
D y n a m i c a n a l y s e s of e x a m p l e h y b r i d
structures
indicated t h a t shear forces
induced in the b o t t o m and top storey columns
m a y exceed b y a l a r g e m a r g i n the m a g n i t u d e s
p r e d i c t e d by e l a s t i c (Step 1) a n a l y s e s ,
V
a ^
It m a y b e n o t e d , h o w e v e r , that
in h y b r i d s t r u c t u r e s , as F i g . 2 s u g g e s t s ,
t h e computed static c o l u m n shear f o r c e s ,
V
^
are o f t e n v e r y small in these two
storeys.
3 h
( 8 )
the b e a m o v e r s t r e n g t h factor a p p l i cable to the floor and the d i r e c t i o n
of lateral l o a d i n g under c o n s i d e r ation
the d e p t h of the beam w h i c h frames
into the column
M
=
column
k
~ t h e d e p t h of the first
floor beam
T h e p r o c e d u r e for the e v a l u a t i o n of column
d e s i g n shear forces is v e r y similar to that
u s e d in the c a p a c i t y d e s i g n of d u c t i l e
frames- -.
It r e f l e c t s a h i g h e r d e g r e e of
c o n s e r v a t i o n b e c a u s e of the intent to avoid
a c o l u m n shear f a i l u r e in any e v e n t .
Case
s t u d i e s show t h a t in spite of the a p p a r e n t
s e v e r i t y o f E q s . (2) and ( 3 ) , shear r e q u i r e m e n t s v e r y s e l d o m g o v e r n the a m o u n t of
t r a n s v e r s e r e i n f o r c e m e n t to be used in
columns.
Y
w h e r e OJ = the d y n a m i c m o m e n t m a g n i f i c a t i o n
f a c t o r , the value of w h i c h is
given in F i g . 6.
c
I
.
e,mm
+ P
where P
and P
are axial forces d u e to
d e a d ana reduced live l o a d s • r e s p e c t i v e l y .
toy ^
^
for the
'
^ c o l u m n at the
re line
of the first floor b e a m s .
= the clear h e i g h t of the
t
P
*D
e,max
y
= the flexural o v e r s t r e n g t h
of the c o l u m n base section
c o n s i s t e n t w i t h the axial
load and shear w h i c h are
a s s o c i a t e d w i t h the d i r e c t i o n
d i r e c t i o n of e a r t h q u a k e
attack.
col
(5)
T h e m a g n i t u d e s of the m a x i m u m l a t e r a l
d i s p l a c e m e n t induced beam shear f o r c e s ,
V , at each f l o o r , w e r e o b t a i n e d in S t e p 6.
T n e p r o b a b i l i t y of all b e a m s above a
p a r t i c u l a r level d e v e l o p i n g s i m u l t a n e o u s l y
p l a s t i c h i n g e s at flexural o v e r s t r e n g t h
d i m i n i s h e s w i t h the number of floors a b o v e
that level. The reduction factor, R ,
m a k e s an a p p r o x i m a t e a l l o w a n c e for tXis.
(2)
w h e r e c o l u m n d y n a m i c shear m a g n i f i c a t i o n
f a c t o r , w , is 2 . 5 , 1.3 and 2.0 for the
b o t t o m , i n t e r m e d i a t e and top storeys
respectively.
T h e d e s i g n shear force in
t h e b o t t o m s t o r e y c o l u m n s should n o t be
less than
> 0.7
is a r e d u c t i o n factor w h i c h t a k e s t h e
n u m b e r of f l o o r s , n, above the s t o r e y u n d e r
c o n s i d e r a t i o n , into a c c o u n t .
Step 8 - E v a l u a t e the c o l u m n d e s i g n
shear f o r c e s in e a c h storey from
col
(1 - n/67)
0.15
<
f
1
<
A
c
1) < 1
(9)
factor a p p l i -
0.10
g
where P
is to b e taken n e g a t i v e
causing axial tension.
e
when
T h e s e r e q u i r e m e n t s are very s i m i l a r to those
r e c o m m e n d e d for c o l u m n s of d u c t i l e f r a m e s .
1
1 1
Step 9 - E s t i m a t e in e a c h storey the
m a x i m u m likely l a t e r a l d i s p l a c e m e n t induced
a x i a l load on e a c h c o l u m n from
P
eq
=
R
v
EV
oe
(4)
—
"i
- 1-0
J
5
Fig. 6 Dynamic Moment Magnification Factor
for C o l u m n s in H y b r i d S t r u c t u r e s .
8
T h e steps in the d e r i v a t i o n of t h e c o l u m n
design moment, M
^, a r e g i v e n in F i g . 7 as
follows.
T h e v a r i a t i o n of c o l u m n m o m e n t s
d u e to c o d e l o a d i n g (Step 1 ) , M
, , above
and b e l o w a floor is s h o w n w i t h § n i d e d l i n e s .
T h e s e m o m e n t s a r e m a g n i f i e d t h r o u g h o u t the
h e i g h t of the c o l u m n to § M
, when beams
a d j a c e n t to the c o l u m n d e v e J o p f l e x u r a l
o v e r s t r e n g t h s a t t h e i r p l a s t i c h i n g e s . It
is a s s u m e d t h a t the m a x i m u m m o m e n t input
from the t w o b e a m s ,
^ , as s h o w n in
F i g . 7, c a n n o t b e e x c e e d e d d u r i n g a n
earthquake.
However,
the
distribution
of
this
total
moment
imput
between
the
columns
above
and
below
the
floor,
during
the
dynamic
r e s p o n s e , is
Moment gradient
with 0.6V
y
with V
' M ode
C
y
*o
cof
M
code
coly
c
uncertain.
A l l o w a n c e for d i s p r o p o r t i o n a t e
d i s t r i b u t i o n is m a d e b y the d y n a m i c m a g n i f i c a t i o n f a c t o r OJ ^ 1.2.
For e x a m p l e the
e s t i m a t e d m a x i m u m m o m e n t for the u p p e r
c o l u m n in F i g . 7, m e a s u r e d at t h e b e a m c e n t r e
l i n e , is t h u s w <J> M
.
At the t o p of the
b e a m , at the c r i t i c a l s e c t i o n o f t h i s c o l u m n ,
t h e m o m e n t is l e s s .
The r e d u c t i o n d e p e n d s
o n the m a g n i t u d e of the c o l u m n s h e a r force
generated simultaneously.
For t h i s p u r p o s e a
c o n s e r v a t i v e a s s u m p t i o n is m a d e , w h e r e b y
0
6
V
6
2
v
v
S t e
0
3
h
v
a
s
W h e n the a x i a l load o n the c o l u m n p r o d u c e s
small compression / i » e . p
< o . 1 f£ A , or
r e s u l t s ifn n e t a x i a l t e n s i o n , some y i e l d i n g
of the c o l u m n is n o t u n a c c e p t a b l e .
Such
c o l u m n s should e x h i b i t s u f f i c i e n t d u c t i l i t y
even without special confining reinforcement
in the e n d r e g i o n s .
H e n c e for this s i t u a t i o n
the d e s i g n m o m e n t s are r e d u c e d b y the f a c t o r
Rjp g i v e n in
Eq. (9) . T h i s e x p r e s s i o n w i l l
give the same v a l u e s t h a t have b e e n r e c o m m e n d e d for c o l u m n s o f d u c t i l e f r a m e s , p r o v i d e d t h a t t h e v a l u e o f w is not t a k e n larger
than 1.2.
The m i n i m u m v a l u e o f 1 ^ is 0.72.
T h i s w i l l e n a b l e the a m o u n t of r e q u i r e d
t e n s i o n r e i n f o r c e m e n t in e x t e r i o r c o l u m n s ,
w h e r e this s i t u a t i o n a r i s e s , to b e r e d u c e d .
e
a
1
B e c a u s e the v a l u e o f the d y n a m i c m o m e n t
m a g n i f i c a t i o n factor for c o l u m n s in h y b r i d
s t r u c t u r e s is r e l a t i v e l y s m a l l , i.e.ui
£ 1.2,
the a b o v e r e d u c t i o n of c o l u m n d e s i g n m o m e n t s
w i l l seldom exceed 2 0 % . T o s i m p l i f y c o m p u t a t ions , the d e s i g n e r m a y p r e f e r to u s e
= 1.0.
W h e n the r e d u c t i o n f a c t o r , R , is used in
d e t e r m i n i n g the a m o u n t o f c o l u m n r e i n f o r c e m e n t , the d e s i g n shear V
, o b t a i n e d in
Step 8, may a l s o b e r e d u c e d p r o p o r t i o n a l l y .
m
c
o
l
H a v i n g o b t a i n e d the c r i t i c a l d e s i g n q u a n t ities for e a c h c o l u m n , i . e . M j _ f r o m Step
11 and V i f r o m Step 8, the r e q u i r e d
f l e x u r a l and s h e a r r e i n f o r c e m e n t a t e a c h
c r i t i c a l s e c t i o n can b e found.
B e c a u s e the
design quantities have been derived from
b e a m o v e r s t r e n g t h s i m p u t , the a p p r o p r i a t e
strength r e d u c t i o n f a c t o r for t h e s e c o l u m n s
is cj) = 1 . 0 .
End r e g i o n s of c o l u m n s n e e d
further b e c h e c k e d to e n s u r e t h a t t h e t r a n s verse reinforcement provided satisfies the
c o d e requirements for confinement, stabi l i t y of v e r t i c a l r e i n f o r c i n g b a r s and
lapped s p l i c e s .
c o
c o
1
1
overstrength
™beam
Fig.
7 The D e r i v a t i o n of D e s i g n M o m e n t s
Columns.
for
C O ( i e
V n
°*
max = °'
col <
P 8> •
Hence
the m o m e n t r e d u c t i o n a t the top of the b e a m
b e c o m e s 0.5 h>
b min =
- b col
shown
in F i g . 7.
=
two beams at
The d e s i g n of c o l u m n s at the b a s e , w h e r e
the d e v e l o p m e n t of a p l a s t i c h i n g e in e a c h
c o l u m n m u s t b e e x p e c t e d , is the same as for
c o l u m n s of d u c t i l e f r a m e s .
1
Step 12 - D e t e r m i n e the a p p r o p r i a t e
g r a v i t y and e a r t h q u a k e i n d u c e d a x i a l forces
on w a l l s .
In the e x a m p l e s t r u c t u r e (Fig. 2 ) , it w a s
i m p l i c i t l y a s s u m e d t h a t l a t e r a l load on the
b u i l d i n g does n o t i n t r o d u c e a x i a l f o r c e s to
the c a n t i l e v e r w a l l s . F o r this s i t u a t i o n the
d e s i g n axial forces o n the w a l l s are
P§ = P p
LR
e
nGenerally the l a t t e r , w h e n c o n s i d e r e d t o g e t h e r
w i t h l a t e r a l load i n d u c e d m o m e n t s , g o v e r n s
t h e a m o u n t of v e r t i c a l w a l l r e i n f o r c e m e n t
to b e u s e d .
+
l
s
3
p
o
r
p
=
0
,
9
p
If w a l l s are c o n n e c t e d to c o l u m n s v i a r i g i d ly c o n n e c t e d b e a m s , as s h o w n for e x a m p l e in
F i g . 3 ( a ) , the l a t e r a l load i n d u c e d a x i a l
forces o n the w a l l s are o b t a i n e d from the
i n i t i a l e l a s t i c a n a l y s i s of the s t r u c t u r e
(Step 1 ) .
S i m i l a r l y this a p p l i e s w h e n ,
instead of^cantilever walls,coupled structu r a l w a l l s share with frames in l a t e r a l
load r e s i s t a n c e .
z
Step 13 - D e t e r m i n e the m a x i m u m
b e n d i n g m o m e n t at the b a s e of e a c h w a l l and
d e s i g n the n e c e s s a r y f l e x u r a l r e i n f o r c e m e n t ,
t a k i n g into a c c o u n t the m o s t a d v e r s e
c o m b i n a t i o n w i t h a x i a l forces on t h e w a l l .
This simply i m p l i e s t h a t t h e r e q u i r e m e n t s
of s t r e n g t h d e s i g n b e s a t i s f i e d .
The
a p p r o p r i a t e c o m b i n a t i o n of a c t i o n s is M
=
^ode
3 P = P • B e c a u s e the w a l l should
meet the additional seismic requirements
s p e c i f i e d by t h e c o d e , t h e a p p r o p r i a t e
s t r e n g t h r e d u c t i o n f a c t o r t o b e u s e d is
cj) = 0 . 9 , i r r e s p e c t i v e o f the level of
axial compression.
The e x a c t a r r a n g e m e n t
of b a r s w i t h i n the w a l l s e c t i o n a t the
b a s e , as b u i l t , is to b e d e t e r m i n e d to
a l l o w the f l e x u r a l o v e r s t r e n g t h o f t h e
s e c t i o n to b e e s t i m a t e d .
u
a n <
u
e
1
1
Ideal
moment
strength
to be
provided
Elastic
moment
pattern
• provided
Fig.
at base
8 D e s i g n M o m e n t E n v e l o p e for W a l l s
Hybrid Structures.
of
Step 14 - W h e n c u r t a i l i n g the
v e r t i c a l r e i n f o r c e m e n t in the u p p e r s t o r e y s
of w a l l s , p r o v i d e f l e x u r a l r e s i s t a n c e n o t
less t h a n g i v e n b y the m o m e n t e n v e l o p e in
F i g . 8.
e n v e l o p e s given in F i g . 8.
T h r e e 12 storey
b u i l d i n g s , in p l a n as shown in F i g . 2 , w i t h
w a l l s of 3.0, 3.6 and 7.0 m e t r e s l e n g t h ,
w e r e studied.
All buildings were designed
in a c c o r d a n c e w i t h this c a p a c i t y d e s i g n
procedure.
W h i l e the e n v e l o p e s a p p e a r to
provide considerable reserve flexural
s t r e n g t h in the upper s t o r e y s d u r i n g the
El C e n t r o r e c o r d , at v a r i o u s i n s t a n t s of
the e x t r e m e (and u n r e a l i s t i c ) P a c o i m a D a m
e v e n t the a n a l y s i s p r e d i c t e d the a t t a i n m e n t
of the ideal f l e x u r a l s t r e n g t h in m o s t
storeys.
Analyses showed, however, that
c u r v a t u r e ductility d e m a n d s , e v e n d u r i n g
this e x t r e m e e v e n t , w e r e very small in the
upper storeys.
A s p a r t of the study of the
e f f e c t s of foundation c o m p l i a n c e , d i s c u s s e d
in S e c t i o n 2 . 4 , these s t r u c t u r e s , w i t h p i n ned base w a l l s , b u t o t h e r w i s e i d e n t i c a l
w i t h the p r o t o t y p e s t r u c t u r e s , w e r e a l s o
a n a l y s e d for the El C e n t r o r e c o r d .
It is
s e e n in Fig. 9, that w a l l m o m e n t d e m a n d s for
the El C e n t r o event in the u p p e r storeys are
very similar to those e x p e r i e n c e d w i t h
fixed base w a l l s .
Step 15 - D e t e r m i n e the m a g n i t u d e of
the flexural o v e r s t r e n g t h f a c t o r <j> , for
each wall.
This is the r a t i o of the flexural o v e r s t r e n g t h of the w a l l , M , as
d e t a i l e d , to the m o m e n t r e q u i r e d to r e s i s t
the code specified lateral l o a d i n g , M
;
b o t h m o m e n t s taken at the b a s e s e c t i o n of' a
wall.
n w
The e n v e l o p e s h o w n is similar to b u t n o t the
same as t h a t r e c o m m e n d e d for c a n t i l e v e r
walls .
It s p e c i f i e s slightly larger
f l e x u r a l r e s i s t a n c e in the top s t o r e y s .
Its c o n s t r u c t i o n from the i n i t i a l m o m e n t
d i a g r a m , ^ o b t a i n e d from the e l a s t i c a n a l y s i s
in Step 1, m a y b e r e a d i l y followed in F i g . 8.
It is i m p o r t a n t to note that the e n v e l o p e is
r e l a t e d to the ideal f l e x u r a l s t r e n g t h of a
w a l l at its b a s e , as b u i l t , rather than the
m o m e n t r e q u i r e d a t that section by the
a n a l y s i s for lateral load.
The e n v e l o p e
r e f e r s to e f f e c t i v e ideal f l e x u r a l s t r e n g t h .
H e n c e v e r t i c a l b a r s in the w a l l m u s t e x t e n d
b y at least full d e v e l o p m e n t length b e y o n d
l e v e l s i n d i c a t e d b y the e n v e l o p e .
1
The aim o f t h i s a p p a r e n t l y c o n s e r v a t i v e
a p p r o a c h is to e n s u r e that s i g n i f i c a n t
y i e l d i n g w i l l n o t o c c u r b e y o n d the a s s u m e d
height, \
of t h e p l a s t i c h i n g e at the
base.
T h e r e b y t h e shear strength o f the
w a l l in the upper s t o r e y s is also i n c r e a s e d , and h e n c e r e d u c e d a m o u n t s of h o r i z o n t a l shear r e i n f o r c e m e n t may be used.
1
5
w
15
20 MNm
0
fO
WALL
Fig. 9
P
n
H
Q
The m e a n i n g and p u r o o s e of this f a c t o r ,
<f>o.w = ( M ° / M
,
base\
the same as t h a t
e v a l u a t e d for b e a m s in Step 7.
Strictly,
for w a l l s there are two l i m i t i n g v a l u e s of
o v e r s t r e n g t h , M ° , which could be c o n s i d e r e d .
T h e s e are the m o m e n t s d e v e l o p e d in the
p r e s e n c e of two d i f f e r e n t a x i a l load i n t e n s i t i e s , i.e. P
and P
However,
it is considered to be s u f f i c i e n t for the
i n t e n d e d p u r p o s e to e v a l u a t e f l e x u r a l o v e r s t r e n g t h developed with axial c o m p r e s s i o n
on c a n t i l e v e r w a l l s due to dead load a l o n e .
Step 16 - C o m p u t e the w a l l shear
ratio,
This is the r a t i o of the sum of
the shear forces at the b a s e of all w a l l s ,
IV
,-j
, , p r e d i c t e d by the a n a l y s i s for
, w a l l , code ±
- r - r—r—i—s
= —r-^ ~r
d e s i g n load, to the total d e s i g n b a s e shear
for the entire s t r u c t u r e , V
, . . .
code,total
The relative c o n t r i b u t i o n of all w a l l s to
the required total lateral load r e s i s t a n c e
is expressed as a m a t t e r of c o n v e n i e n c e by
c o d e
l
m
a
x
s
e
m
i
i
r
2
] t
Figure 9 compares wall moment demands,
e n c o u n t e r e d d u r i n g the a n a l y s i s for the
E l C e n t r o and the 1971 P a c o i m a Dam
e a r t h q u a k e r e c o r d s , w i t h the m o m e n t
u
1940
20
BENDING
30
iOMNm
0
20
W
MOMENT
Wall Moment Demands Encountered During Earthquake Records.
60
80 MNm
10
t h e shear r a t i o
n
i> = a
v ,
i , w a l l , code
i=l
code,total
base
(10)
It a p p l i e s s t r i c t l y to the b a s e of t h e
structure.
A s F i g . 2(c) s h o w s , such a shear
r a t i o w o u l d r a p i d l y r e d u c e w i t h h e i g h t , and
n e a r the top it could b e c o m e n e g a t i v e .
This
i n d i c a t e s t h a t the p a r a m e t e r
^ is a c o n v e n i e n t b u t n o t unique m e a s u r e to q u a n t i f y the
s h a r e o f w a l l s in the total l a t e r a l l o a d
resistance.
D e s i g n c r i t e r i a for shear strength
will
o f t e n b e found to b e c r i t i c a l .
A t the b a s e
the t h i c k n e s s of w a l l s m a y n e e d to b e
i n c r e a s e d on a c c o u n t of Eq. ( 1 1 ) , and
b e c a u s e of the m a x i m u m s h e a r stress l i m i t ations of NZS 3 1 0 1 .
T y p i c a l l y w h e n using
Grade 380 v e r t i c a l w a l l r e i n f o r c e m e n t in a
12 storey h y b r i d s t r u c t u r e , w h e r e the w a l l s
have b e e n assigned 6 0 % of the total b a s e
shear r e s i s t a n c e , it w i l l be found that w i t h
1.7,
= 0.6 and w* = 1 . 4 2 ,
*p,w." - ' v
t
he"i
the
i d"e a l shear s t r e n g t h w i l l n e e d to b e
X
6
w
^wall
2.27 V
.
In c o m p a r i s o n , the
ideal shear strength of a w a l l , p r o p o r t i o n e d
w i t h strength rather than c a p a c i t y d e s i g n
p r o c e d u r e s , w o u l d be V
= code/° *
1.18 V
.
Thus Eq. (11) implies very
large a p p a r e n t r e s e r v e s t r e n g t h in s h e a r .
A n a l y s e s in cases s t u d i e d
consistently
p r e d i c t e d , h o w e v e r , shear forces w h i c h are
o f t e n 3 0 % larger than t h o s e r e q u i r e d by
E q n . ( 1 1 ) . Of all the a s p e c t s of t h i s
p r o p o s e d design s t r a t e g y , the e s t i m a t i o n of
w a l l shear forces w a s found to be the l e a s t
satisfactory.
Some r e l e v a n t i s s u e s are
d i s c u s s e d s u b s e q u e n t l y in Section 4.4.
=
C
Step 1 7 - E v a l u a t e for each w a l l
d e s i g n shear force at the b a s e f r o m
the
Q
d
e
v
w
V
wall,base
K
=
*o,w
V
C
wall,code
Q
d
a
l
8 5
=
l
e
1 1
and
1 +
U
1H-
(12)
w h e r e u\ is the d y a n m i c shear m a g n i f i c a t i o n
f a c t o r r e l e v a n t to c a n t i l e v e r w a l l s , o b t a i n e d
from
T
OJ
or
= 0.9
v
+ n/10
a) = 1 . 3 +
n/30
when
n
< 1.8
< 6
when
(13a)
n
> 6
w h e r e n is the n u m b e r o f storeys above
base.
the
(13b)
V
Step 18 - In each storey of each w a l l ,
p r o v i d e shear r e s i s t a n c e n o t less than t h a t
given by the shear d e s i g n envelope of F i g . 1 0 .
O'SKvoli.bose
The approach d e v e l o p e d for the shear d e s i g n
of w a l l s in h y b r i d structures is an e x t e n sion o f the two stage m e t h o d o l o g y u s e d for
cantilever w a l l s ' .
1
9
In the first s t a g e , the d e s i g n shear force is
increased from the initial (Step 1) v a l u e to
t h a t c o r r e s p o n d i n g w i t h the d e v e l o p m e n t of a
p l a s t i c h i n g e at f l e x u r a l o v e r s t r e n g t h at the
b a s e of the w a l l .
This is a c h i e v e d w i t h t h e
i n t r o d u c t i o n of the flexural o v e r s t r e n g t h
f a c t o r , <j> , o b t a i n e d in Step 1 5 .
In the
n e x t s t a g e a l l o w a n c e is m a d e for the
a m p l i f i c a t i o n of the b a s e s h e a r force d u r i n g
the i n e l a s t i c d y n a m i c r e s p o n s e of the
structure.
While a plastic hinge develops
at the b a s e o f a w a l l , due to the c o n t r i b u t i o n of h i g h e r m o d e s of v i b r a t i o n , the
c e n t r o i d of i n e r t i a forces o v e r the h e i g h t of
the b u i l d i n g m a y b e in a s i g n i f i c a n t l y lower
p o s i t i o n than that p r e d i c t e d by the c o n v e n t i o n a l a n a l y s i s for l a t e r a l l o a d s .
The
larger the n u m b e r of s t o r e y s , the m o r e
i m p o r t a n t is the p a r t i c i p a t i o n of h i g h e r m o d e s .
The d y n a m i c shear m a g n i f i c a t i o n for c a n t i lever w a l l s , oo , given in Eq. ( 1 3 ) , m a k e s
a l l o w a n c e for this p h e n o m e n o n .
The v a l u e s
so o b t a i n e d a g r e e w i t h those r e c o m m e n d e d i n
NZS 3101.
Q w
9
v
9
It h a s also b e e n f o u n d , that for a g i v e n
e a r t h q u a k e r e c o r d , the d y n a m i c a l l y i n d u c e d
base shear f o r c e s in w a l l s of h y b r i d s t r u c t ures i n c r e a s e d w i t h an increased p a r t i c i p a t i o n of such w a l l s in the r e s i s t a n c e o f
the t o t a l b a s e shear for the e n t i r e s t r u c t ure . W a l l p a r t i c i p a t i o n is q u a n t i f i e d b y
the "shear r a t i o " ,
o b t a i n e d in Step 1 6 .
The e f f e c t of t h e "shear r a t i o " upon the
m a g n i f i c a t i o n the m a x i m u m w a l l s h e a r force
is e s t i m a t e d b y E q . ( 1 2 ) . It is seen t h a t
w h e n i|i = 1,
= w .
3
v
F i g . 10 Envelope for Design Shear Forces
Walls of H y b r i d S t r u c t u r e s
for
As F i g . 2(c) s h o w s , shear demands p r e d i c t e d
by a n a l y s e s for static load may b e q u i t e
small in the upper half of w a l l s .
As can
be e x p e c t e d , during the r e s p o n s e of the
b u i l d i n g to vigorous seismic e x c i t a t i o n s ,
m u c h larger shear forces may be generated at
these upper l e v e l s .
A linear scaling up of
the shear force d i a g r a m drawn for static
load, in a c c o r d a n c e w i t h Eq. ( 1 1 ) , w o u l d
give an e r r o n o u s p r e d i c t i o n of shear d e m a n d s
in the upper s t o r e y s .
T h e r e f o r e from case
studies the shear d e s i g n e n v e l o p e shown in
F i g . 10 w a s d e v e l o p e d .
It is seen that the
e n v e l o p e gives the r e q u i r e d shear strength
in terms of the base shear for the w a l l ,
w h i c h w a s o b t a i n e d in Step 1 7 .
F i g u r e 11 p r e s e n t s some r e s u l t s of the
relevant s t u d y
of a 12 storey b u i l d i n g .
It is seen that the shear d e s i g n e n v e l o p e is
satisfactory when structures with relatively
s l e n d e r w a l l s , w i t h ip < 0 . 5 7 , w e r e s u b j e c t e d
1 1
11
- 8 - 5 - 4 - 2
0
2
WALL SHEAR FORCE
i
6 MN
WALL SHEAR FORCE
Fig.
11 P r e d i c t e d
S h e a r D e m a n d s for D i f f e r e n t W a l l s in a 12 Storey
to the El C e n t r o e x c i t a t i o n .
The shear r e s p o n s e o f t h e structure w i t h 7 m w a l l s is less
s a t i s f a c t o r y in the lower s t o r e y s .
As may
b e e x p e c t e d , the p r e d i c t e d demand for s h e a r
in p i n b a s e d w a l l s * is l e s s , p a r t i c u l a r l y as
t h e length of the w a l l s , £ , increases . S h e a r
l o a d s p r e d i c t e d for the P a c o i m a e v e n t w e r e
found to c o n s i s t e n t l y exceed the s u g g e s t e d
design values.
w
W i t h the aid of the shear design e n v e l o p e ,
t h e r e q u i r e d a m o u n t of h o r i z o n t a l (shear)
w a l l r e i n f o r c e m e n t at any level m a y b e
readily found.
In t h i s , a t t e n t i o n m u s t b e
p a i d to t h e d i f f e r e n t a p p r o a c h e s u s e d
to
e s t i m a t e the c o n t r i b u t i o n of the c o n c r e t e to
s h e a r s t r e n g t h , v , in the p o t e n t i a l p l a s t i c
h i n g e and t he e l a s t i c r e g i o n s of a w a l l .
In
the p o t e n t i a l p l a s t i c h i n g e r e g i o n , e x t e n d ing
a b o v e the b a s e , as shown in F i g . 1 0 ,
t h e m a j o r p a r t of the d e s i g n s h e a r , V ^ ^ ,
w i l l n e e d to b e a s s i g n e d to s h e a r r e i n f o r c e ment.
In the upper (elastic) p a r t s of the
w a l l , h o w e v e r , the c o n c r e t e m a y b e relied
on
to c o n t r i b u t e s i g n i f i c a n t l y to shear
resistance, allowing considerable reduction
in the d e m a n d for s h e a r r e i n f o r c e m e n t .
1
c
w a
1
S t e p 19 - In the end r e g i o n s of e a c h
w a l l , o v e r the a s s u m e d length of the p o t e n t ial plastic hinge, provide adequate trans-
Hybrid
Structure.
verse r e i n f o r c e m e n t to supply the r e q u i r e d
c o n f i n e m e n t to p a r t s of the f l e x u r a l comp r e s s i o n zone and to p r e v e n t p r e m a t u r e
b u c k l i n g of v e r t i c a l b a r s .
These d e t a i l i n g r e q u i r e m e n t s for d u c t i l i t y
are the s a m e as those r e c o m m e n d e d for c a n t i lever and c o u p l e d s t r u c t u r a l w a l l s .
Recent
experimental s t u d i e s i n d i c a t e d , however,
that current code r e q u i r e m e n t s , r e l e v a n t to
the region of c o n f i n e m e n t w i t h i n w a l l
s e c t i o n s , should be a m e n d e d .
For t h i s
r e a s o n , although p r e s e n t e d e l s e w h e r e , the
s u g g e s t e d improvement in the p r o c e d u r e is
restated here.
1
1 1
1 0
The p r o p o s e d approach to t h e c o n f i n e m e n t of
w a l l sections rests on the p r e c e p t that
c o n c r e t e should be laterally c o n f i n e d w h e r e wherever compression strains, corresponding
w i t h the e x p e c t e d c u r v a t u r e d u c t i l i t y d e m a n d
on the relevant s e c t i o n , e x c e e d 0.004.
The
s t r a i n p r o f i l e shown shaded in F i g . 12
i n d i c a t e s the u l t i m a t e c u r v a t u r e , <j>, w h i c h
m i g h t be necessary to e n a b l e the e s t i m a t e d
d i s p l a c e m e n t d u c t i l i t y , y/\ for a p a r t i c u l a r
h y b r i d structure to be s u s t a i n e d , w h e n the
c o n c r e t e strain in the e x t r e m e c o m p r e s s i o n
fibre theoretically r e a c h e s the m a g n i t u d e
of 0 . 004 . This strain p r o f i l e is a s s o c i a t e d
w i t h a neutral axis d e p t h , c .
An e s t i m a t e
for this c r i t i c a l n e u t r a l axis d e p t h , c , may
be m a d e with
u
f
c
c
1
*Note that the shear r a t i o , K
g i v e n by E q .
"(10), is n o t a p p l i c a b l e to p i n b a s e d w a l l s .
c
c
= 0.10
4>* S £
w
(14)
12
systems.
The v a r i e t y of w a y s in w h i c h w a l l s
and frames may be c o m b i n e d may p r e s e n t
p r o b l e m s to w h i c h a s a t i s f a c t o r y solution
w i l l r e q u i r e , as in m a n y other s t r u c t u r e s ,
the a p p l i c a t i o n of e n g i n e e r i n g j u d g e m e n t .
This may n e c e s s i t a t e some r a t i o n a l a d j u s t m e n t s in the o u t l i n e d 19 step p r o c e d u r e .
In the f o l l o w i n g , a few situations are
m e n t i o n e d w h e r e such j u d g e m e n t in the
a p p l i c a t i o n of the p r o p o s e d design m e t h o d ology w i l l b e n e c e s s a r y .
Some d i r e c t i o n s
for p r e m i s i n g a p p r o a c h e s are also s u g g e s t e d .
ac
4.1
Fig.
where
12 S t r a i n P r o f i l e s for W a l l
&
Sections.
= length of w a l l ,
S = s t r u c t u r a l type f a c t o r , and
(p* = global o v e r s t r e n g t h f a c t o r , w h i c h
is the ratio of the total r e s i s t a n c e of the
h y b r i d structure to o v e r t u r n i n g m o m e n t ,
i n c l u d i n g the c o n t r i b u t i o n s of a x i a l forces
in c o l u m n s and w a l l s and those o f p l a s t i c
h i n g e s at the b a s e of all c o l u m n s and w a l l s ,
e v a l u a t e d at levels of f l e x u r a l o v e r strength , to the c o r r e s p o n d i n g o v e r t u r n i n g
m o m e n t due to code specified l a t e r a l static
l o a d i n g / W h e n the total s t r e n g t h p r o v i d e d
by y i e l d i n g r e g i o n s of the s t r u c t u r e m a t c h e s
very closely that r e q u i r e d by the l a t e r a l
code l o a d i n g , the value of <J>* w i l l n o t be
less than 1.4.
w
2
To a c h i e v e in a w a l l the same u l t i m a t e
curvature w h e n the c o m p u t e d n e u t r a l a x i s
d e p t h , c, is larger than the c r i t i c a l v a l u e ,
c , as F i g . 12 s h o w s , the length of w a l l
section s u b j e c t e d to c o m p r e s s i o n s t r a i n s
larger than 0.004 , b e c o m e s a c .
It is this
length over w h i c h the c o m p r e s s e d c o n c r e t e
n e e d s to b e c o n f i n e d .
F r o m the g e o m e t r y
shown in F i g . 1 2 , a = 1 - c / c .
c
c
B e c a u s e it h a s b e e n found in t e s t s
that,
after reversed cyclic loading, observed
n e u t r a l axis depths tend to be larger than
those p r e d i c t e d by c o n v e n t i o n a l s e c t i o n
a n a l y s e s , it is s u g g e s t e d that the l e n g t h of
c o n f i n e m e n t , a c , be derived from
1 0 , 1 1
a = 1 - 0.7 c / c
c
> 0.5
(15)
w h e n e v e r c / c < 1.
W h e n c is only a l i t t l e
larger than c , a very small and i m p r a c t i c a l
value of a w o u l d be o b t a i n e d .
In line w i t h
c u r r e n t r e q u i r e m e n t s , it is s u g g e s t e d t h a t
in such cases at least one h a l f of the
t h e o r e t i c a l c o m p r e s s i o n zone be c o n f i n e d .
c
c
1
The tests q u o t e d
a l s o i n d i c a t e d t h a t the
a m o u n t of c o n f i n i n g r e i n f o r c e m e n t s p e c i f i e d
in the c o d e is likely to be a d e q u a t e .
1 0
1
4.
ISSUES R E Q U I R I N G F U R T H E R
STUDY
The p r o p o s e d c a p a c i t y d e s i g n p r o c e d u r e and
the a c c o m p a n y i n g d i s c u s s i o n of the
b e h a v i o u r of h y b r i d s t r u c t u r e s , p r e s e n t e d
in the p r e v i o u s s e c t i o n , are by n e c e s s i t y
r e s t r i c t e d to simple and r e g u l a r s t r u c t u r a l
Gross I r r e g u l a r i t i e s in the
Load R e s i s t i n g S y s t e m .
Lateral
It is generally r e c o g n i s e d that the larger
the departure from symmetry and regularity
in the a r r a n g e m e n t o f lateral load r e s i s t ing s u b s t r u c t u r e s w i t h i n a b u i l d i n g , the
less c o n f i d e n c e should the d e s i g n e r have in
p r e d i c t i n g likely s e i s m i c r e s p o n s e .
Examples of i r r e g u l a r i t y are w h e n w a l l
dimensions change d r a s t i c a l l y o v e r the
h e i g h t of the b u i l d i n g or w h e n w a l l s t e r m inate at d i f f e r e n t h e i g h t s , and w h e n s e t backs occur.
S y m m e t r i c a l p o s i t i o n i n g of
w a l l s in p l a n m a y lead to gross e c c e n t r i cities of applied l a t e r a l load with respect
to c e n t r e s of r i g i d i t y .
4.2
Torsional
Effects
Codes m a k e simple and r a t i o n a l p r o v i s i o n s
for t o r s i o n a l e f f e c t s .
The severity of
torsion is commonly q u a n t i f i e d by the
d i s t a n c e b e t w e e n t h e c e n t r e of rigidity
(or s t i f f n e s s ) of the lateral load r e s i s t i n g
structural system and the centre of m a s s .
In reasonably regular and s y m m e t r i c a l
b u i l d i n g s this d i s t a n c e (horizontal e c c e n t r i c i t y ) , does n o t s i g n i f i c a n t l y c h a n g e from
storey to storey.
E r r o r s due to inevitable
v a r i a t i o n s of e c c e n t r i c i t y over b u i l d i n g
h e i g h t are t h o u g h t to b e c o m p e n s a t e d for by
code s p e c i f i e d a m p l i f i c a t i o n s of the
computed (static) e c c e n t r i c i t i e s .
The
c o r r e s p o n d i n g a s s i g n m e n t of a d d i t i o n a l
lateral load to r e s i s t i n g e l e m e n t s , p a r t i c ularly those s i t u a t e d at g r e a t e r d i s t a n c e s
from the centre o f r i g i d i t y (centre of
h o r i z o n t a l t w i s t ) , are i n t e n d e d to c o m p e n sate for t o r s i o n a l e f f e c t s .
Because minimum
and m a x i m u m e c c e n t r i c i t i e s , at least w i t h
r e s p e c t to the t w o p r i n c i p a l d i r e c t i o n s of
e a r t h q u a k e a t t a c k , n e e d to be c o n s i d e r e d ,
the s t r u c t u r a l s y s t e m , as d e s i g n e d , w i l l
p o s s e s s increased t r a n s l a t i o n a l r a t h e r than
torsional resistance.
It w a s e m p h a s i s e d that the c o n t r i b u t i o n s of
w a l l s to lateral load r e s i s t a n c e in h y b r i d
structures usually change d r a m a t i c a l l y over
the h e i g h t of the b u i l d i n g .
An e x a m p l e w a s
shown in F i g . 2 ( c ) . For this r e a s o n the
p o s i t i o n of the c e n t r e of rigidity may also
c h a n g e s i g n i f i c a n t l y f r o m floor to f l o o r .
For the p u r p o s e of i l l u s t r a t i n g the v a r i ation of e c c e n t r i c i t y w i t h h e i g h t , c o n s i d e r
the e x a m p l e s t r u c t u r e shown in F i g . 2 ( a ) ,
but slightly modified.
B e c a u s e of s y m m e t r y ,
torsion due to v a r i a t i o n in the p o s i t i o n of
the centre of r i g i d i t y , does n o t a r i s e .
A s s u m e , h o w e v e r , t h a t i n s t e a d of the two
s y m m e t r i c a l l y p o s i t i o n e d w a l l s shown in
F i g . 2 ( a ) , two 6 m long w a l l s are p l a c e d
side by side at 9.2 m from the left hand end
13
Wails
F i g u r e 14 shows p l a n s o f a b u i l d i n g w i t h
three different positions of identical
walls.
The b u i l d i n g is similar to t h a t
shown in F i g . 2 ( a ) . T h e c o n t r i b u t i o n of t h e
two w a l l s to t o t a l l a t e r a l load r e s i s t a n c e
is a s s u m e d to b e the same in e a c h of t h e s e
three cases.
Diaphragm deformations associ a t e d w i t h each case a r e shown a p p r o x i m a t e l y
to scale by the d a s h e d l i n e s .
Diaphragm
d e f o r m a t i o n s in the case o f F i g . 14(a) w o u l d
be n e g l i g i b l y small in c o m p a r i s o n w i t h t h o s e
o f the other two c a s e s .
In d e c i d i n g w h e t h e r
such d e f o r m a t i o n s are s i g n i f i c a n t , the
following aspects might be considered:
(a)
F i g . 13 The V a r i a t i o n o f C o m p u t e d T o r s i o n a l
E c c e n t r i c i t i e s in an U n s y m m e t r i c a l
12 Storey H y b r i d S t r u c t u r e .
o f the b u i l d i n g , as shown in F i g . 1 3 , and
t h a t the r i g h t h a n d w a l l is r e p l a c e d b y a
standard frame.
B e c a u s e the two w a l l s , w h e n
d i s p l a c e d laterally b y the same a m o u n t as
the f r a m e s , w o u l d in this e x a m p l e s t r u c t u r e
r e s i s t 7 4 % of t h e total shear in the first
s t o r e y , the centre of r i g i d i t y w o u l d b e
19.5 m f r o m the c e n t r e of the (mass) b u i l d ing.
In the 8th storey the two w a l l s
b e c o m e r a t h e r i n e f f e c t i v e , as they r e s i s t
o n l y a b o u t 1 2 % of the storey shear i.e.
a p p r o x i m a t e l y as m u c h as one f r a m e .
At
this l e v e l the e c c e n t r i c i t y b e c o m e s n e g l i gible.
A s F i g . 13 s h o w s , the computed
s t a t i c e c c e n t r i c i t i e s w o u l d vary c o n s i d e r a b l y in this e x a m p l e b u i l d i n g b e t w e e n l i m i t s
a t the b o t t o m and top s t o r e y .
Note a l s o the
different senses*
T o r s i o n a l e f f e c t s on
i n d i v i d u a l c o l u m n s and w a l l s w i l l d e p e n d on
the t o t a l t o r s i o n a l r e s i s t a n c e of the s y s t e m ,
i n c l u d i n g the p e r i p h e r y frames along the
long s i d e s of the b u i l d i n g .
4.3
Diaphragm
Flexibility.
F o r m o s t b u i l d i n g s , floor d e f o r m a t i o n s
a s s o c i a t e d w i t h d i a p h r a g m a c t i o n s are
negligible.
However, when structural walls
r e s i s t a m a j o r f r a c t i o n of the s e i s m i c a l l y
i n d u c e d i n e r t i a f o r c e s in long and n a r r o w
b u i l d i n g s , the e f f e c t s of inplane f l o o r
d e f o r m a t i o n s upon the d i s t r i b u t i o n of
r e s i s t a n c e to frames a n d w a l l s m a y n e e d to
be examined.
If e l a s t i c r e s p o n s e is c o n s i d e r e d ,
the a s s i g n m e n t of l a t e r a l load to
some frames (Figs. 14 (b) and (c)) w o u l d b e
c l e a r l y u n d e r e s t i m a t e d if d i a p h r a g m s w e r e
to b e assumed to be i n f i n i t e l y r i g i d .
Inp l a n e d e f o r m a t i o n s of f l o o r s , e v e n w h e n
d e r i v e d w i t h c r u d e a p p r o x i m a t i o n s , s h o u l d be
c o m p a r e d w i t h interstorey d r i f t s p r e d i c t e d
by standard elastic analyses.
Such a
c o m p a r i s o n w i l l then i n d i c a t e t h e r e l a t i v e
i m p o r t a n c e of d i a p h r a g m f l e x i b i l i t y .
(b)
In ductile s t r u c t u r e s , s i g n i f i c a n t
inelastic storey d r i f t s are to be
expected.
The larger the i n e l a s t i c d e f o r m a t i o n s the less i m p o r t a n t are d i f f e r e n t i a l
e l a s t i c d i s p l a c e m e n t s b e t w e e n frames w h i c h
w o u l d result from d i a p h r a g m d e f o r m a t i o n s .
(c)
A s F i g . 2(c) i l l u s t r a t e d , the c o n t r i b u t i o n of w a l l s to l a t e r a l load
r e s i s t a n c e in h y b r i d s t r u c t u r e s
diminishes
w i t h the distance m e a s u r e d from the b a s e .
T h e r e f o r e at upper f l o o r s , l a t e r a l load w i l l
b e m o r e evenly d i s t r i b u t e d among i d e n t i c a l
frames.
This w i l l g r e a t l y reduce d i a p h r a g m
i n p l a n e shear and f l e x u r a l a c t i o n s .
Hence
d i a p h r a g m d e f o r m a t i o n s at u p p e r levels w o u l d
diminish.
(d)
H o r i z o n t a l i n e r t i a forces are e x p e c t e d
to i n c r e a s e w i t h the d i s t a n c e from
the b a s e , w h i l e inplane b e n d i n g and shear
e f f e c t s w i l l d i m i n i s h b e c a u s e of the
d e c r e a s i n g p a r t i c i p a t i o n of w a l l s at upper
floors.
Hence it may be c o n c l u d e d t h a t
d i a p h r a g m flexibility is o f lesser i m p o r t a n c e
in h y b r i d s t r u c t u r e s of the type shown in
F i g . 1 4 , than in b u i l d i n g s w h e r e lateral load
r e s i s t a n c e is p r o v i d e d e n t i r e l y by c a n t i l e v e r
w a l l s i.e. w i t h o u t the p a r t i c i p a t i o n of any
frames.
4.4
P r e d i c t i o n of Shear Demand in W a l l s .
A n u m b e r of case s t u d i e s for s t r u c t u r e s of
the type shown in F i g . 2 , t y p i c a l l y w i t h
3 . 0 , 3.6 and 7.0 long w a l l s , h a v e i n d i c a t e d t h a t the capacity design p r o c e d u r e set o u t in
S e c t i o n 3, led to s t r u c t u r e s in w h i c h :
1
fa)
Walls
(b) j-
(a)
Inelastic d e f o r m a t i o n s d u r i n g
Centro e v e n t r e m a i n e d w i t h i n
c u r r e n t l y e n v i s a g e d in N e w Zealand.
a l l y storey drifts did not e x c e e d 1%
storey heights.
(b)
(c)
t t t
F i g . 14 D i a p h r a g m
t
Flexibility.
the El
limits
Typicof
Plastic h i n g e s in the c o l u m n s o f
upper s t o r e y s w e r e n o t p r e d i c t e d .
Derived c o l u m n d e s i g n shear forces
p r o s c r i b e d shear failure w i t h o u t the
u s e of e x c e s s i v e shear r e i n f o r c e m e n t .
(c)
1
14
(d)
R o t a t i o n a l d u c t i l i t y d e m a n d s at the
b a s e of b o t h c o l u m n s and w a l l s ,
r e m a i n e d w e l l w i t h i n the l i m i t s r e a d i l y
a t t a i n e d in a p p r o p r i a t e l y d e t a i l e d l a b o r atory s p e c i m e n s .
3m Wall
1 0
PACOIMA
DAM
(e)
P r e d i c t e d s h e a r d e m a n d s in the u p p e r
s t o r e y s of w a l l s w e r e s a t i s f a c t o r i l y
c a t e r e d for by the e n v e l o p e shown in F i g . 1 0 .
H o w e v e r , m a x i m u m d y n a m i c shear f o r c e s at the
b a s e s e x c e e d e d t h e d e s i g n shear level
(Fig. 11) .
This latter f e a t u r e w a s i n i t i a l l y v i e w e d
with concern.
T h e r e f o r e a f u r t h e r study o f
the phenomenon, discussed previously with
the d e s c r i p t i o n of d e s i g n S t e p s 17 and 1 8 ,
was undertaken.
Some of the f i n d i n g s of
t h i s study are s u m m a r i s e d in the f o l l o w i n g .
F i r s t l y the i n c i d e n c e of the l a r g e s t w a l l b a s e
shear forces and m o m e n t s , a n a l y t i c a l l y
p r e d i c t e d for the El C e n t r o e v e n t , w a s
studied.
This was achieved by recording the
s t a t u s of a w a l l b a s e e v e r y 1/10 s e c o n d s
MOMENT
&
SHEAR
>a6 >0.7 >0.8 >09
i
(Q)
12 STOREY - EL
>Q6
>0.7 >08 >0.9
>0.6>0.7*a8>0.9
CENTRO
30
7.0m wolf
20
3.6m wall
W
3.0m wall
0
(b)
>0.6 >07 >0.8>0.9
>C6 >0.7>0.8>0.9
12 STOREY - PACOIMA DAM
>O6>0.7>0.8>0.9
F i g . 15 O c c u r r e n c e of H i g h Shear F o r c e s and
M o m e n t s D u r i n g the El C e n t r o E v e n t
at t h e Base of the W a l l s o f a 12
Storey H y b r i d S t r u c t u r e *
d u r i n g the first 10 s e c o n d s e x c i t a t i o n .
Figure 15 (a) shows for the El C e n t r o e v e n t the
frequency of o c c u r r e n c e d u r i n g t h e s e first
10 s e c o n d s o f the r e c o r d of r a n g e s of
n o r m a l i z e d h i g h s h e a r or m o m e n t i n t e n s i t i e s ,
as w e l l as t h e c o n c u r r e n t o c c u r r e n c e of b o t h .
I n t e n s i t i e s o f shear o r m o m e n t w e r e e x p r e s s e d
in terms of a b s o l u t e m a x i m a e n c o u n t e r e d
d u r i n g the r e c o r d and shown in F i g . 1 1 .
It
is seen for e x a m p l e t h a t w h e n 7 m w a l l s w e r e
u s e d , the b a s e shear in e x c e s s o f 6 0 % of the
a b s o l u t e m a x i m u m w a s e n c o u n t e r e d 19 t i m e s .
Similarly shear load on t h e 3 m w a l l l a r g e r
t h a n 9 0 % of the m a x i m u m , w a s e n c o u n t e r e d 3
times.
In the 3.6 m long w a l l s , b a s e m o m e n t s
in excess of 9 0 % of the m a x i m u m , w e r e
e n c o u n t e r e d 8 times d u r i n g the 10 s e c o n d s of
E l Centro r e c o r d .
>06 >0J >Q£ >0.9
NORMALIZED
12 STOREY
>06 >0J >0.8 >0.9
WALL SHEAR
FORCE
BUILDING
F i g . 16 D u r a t i o n of Large W a l l
Shear F o r c e s and B a s e
M o m e n t s in W a l l s of a 12
Storey Hybrid S t r u c t u r e
A s e x p e c t e d , such f r e q u e n c y d i s t r i b u t i o n s
are strongly d e p e n d e n t on the c h a r a c t e r i s t i c s
of the e a r t h q u a k e r e c o r d .
As F i g . 1 5 ( b )
s h o w s , the p a t t e r n is d i f f e r e n t for the
e x t r e m e l y severe P a c o i m a Dam r e c o r d .
While
m o m e n t d e m a n d s d u r i n g the two d i f f e r e n t
s e i s m i c e v e n t s w e r e c o m p a r a b l e , the
frequency of large shear f o r c e s and large,
c o n c u r r e n t s h e a r and m o m e n t d e m a n d s w e r e
s i g n i f i c a n t l y less d u r i n g the P a c o i m a e v e n t .
For r e a s o n s of c o m p u t a t i o n a l e c o n o m y ,
s a m p l i n g w a s at 1/10 s e c o n d s i n t e r v a l s , e v e n
though the time step used in the a n a l y s e s
w a s 1/100 s e c o n d s .
A s a m p l i n g at 1000
i n s t a n t s w o u l d h a v e y i e l d e d an i n c r e a s e in
the n u m b e r of o c c u r r e n c e s of shear levels
of c o n c e r n .
F i g u r e 16 p r o v i d e s a d d i t i o n a l u s e f u l
information.
Here the t o t a l time d u r i n g
w h i c h a c e r t a i n i n t e n s i t y of s h e a r , in t e r m s
of the m a x i m u m , w a s e x c e e d e d during the 10
s e c o n d s of two d i f f e r e n t e a r t h q u a k e r e c o r d s ,
is p r e s e n t e d .
This gives a more reassuring
picture.
W h e n c o m p a r e d w i t h F i g . 1 5 ( a ) , it
is seen for e x a m p l e that d u r i n g the El C e n t r o
e v e n t , the total time d u r i n g w h i c h the p r e d i c t e d shear in the 3 m w a l l s e x c e e d e d 9 0 %
of the m a x i m u m , (on three o c c a s i o n s ) w a s only
0.12 s e c o n d s .
S i m i l a r l y the p r e d i c t e d
d u r a t i o n of the 19 o c c u r r e n c e s of shear in
the 7 m w a l l s , l a r g e r than 6 0 % of m a x i m u m ,
w a s only 0.26 s e c o n d s .
The c o m p u t e d d u r a tion of s h e a r s l a r g e r than 9 0 % of the m a x i m u m , n e v e r e x c e e d e d 0.05 s e c o n d s d u r i n g the
El C e n t r o e v e n t .
A l t h o u g h it is s t r e s s e d t h a t the p r o h i b i t i o n
of shear f a i l u r e is of p a r a m o u n t i m p o r t a n c e
in seismic d e s i g n , it w a s c o n c l u d e d a t the
end of this study that the concern s t e m m i n g
from the less than s a t i s f a c t o r y c o r r e l a t i o n
b e t w e e n r e c o m m e n d e d d e s i g n shear force l e v e l s
for w a l l s w i t h m a x i m a o b t a i n e d from a n a l y t i cal p r e d i c t i o n s , could be d i s m i s s e d
because:
(a)
P r e d i c t e d p e a k shear forces w e r e of
very s h o r t d u r a t i o n s .
While there
w a s n o e x p e r i m e n t a l e v i d e n c e to p r o v e i t , it
w a s felt t h a t shear f a i l u r e s during r e a l
e a r t h q u a k e s could n o t o c c u r w i t h i n a few
hundredths of a second.
15
(b)
The p r o b a b l e s h e a r s t r e n g t h of a w a l l ,
w h i c h c o u l d b e u t i l i z e d d u r i n g such an
e x t r e m e e v e n t , is in e x c e s s of the ideal
s t r e n g t h (Eqn. (11)) u s e d in d e s i g n .
(c)
Some i n e l a s t i c shear d e f o r m a t i o n
d u r i n g the v e r y few e v e n t s of p e a k
shear should be acceptable.
W a l l s and c o l u m n s w e r e found n o t to
b e s u b j e c t e d s i m u l t a n e o u s l y to p e a k
shear demands.
T h e r e f o r e the d a n g e r of
shear f a i l u r e a t the b a s e , for the b u i l d i n g
as a w h o l e , should n o t a r i s e .
been established.
It is f e l t t h a t I|J = 0.33
m i g h t be an a p p r o p r i a t e l i m i t .
For h y b r i d
s t r u c t u r e s for w h i c h 0.1 <
< 0.33, a
l i n e a r interpolation of the r e l e v a n t p a r a m e t e r s , applicable to d u c t i l e f r a m e s and
ductile hybrid structures, seems approp r i a t e . These p a r a m e t e r s are w , u ) , oa* and
c
V
(d)
(e)
The s i m u l t a n e o u s o c c u r r e n c e d u r i n g an
e a r t h q u a k e r e c o r d of p r e d i c t e d peak
shear and peak f l e x u r a l d e m a n d s w a s found
to be a b o u t the same as the o c c u r r e n c e of
peak shear demands.
This m e a n s t h a t w h e n
m a x i m u m shear demand o c c u r r e d , it did
generally coincide with maximum flexural
demands.
Present code p r o v i s i o n s were
b a s e d on t h i s p r e c e p t .
W h i l e the r e l e v a n t
c o d e p r o v i s i o n s do n o t a f f e c t the a m o u n t of
shear r e i n f o r c e m e n t to b e u s e d , they e n s u r e
t h a t w a l l t h i c k n e s s is large e n o u g h to k e e p
s h e a r s t r e s s e s d u r i n g such e v e n t s at
moderate levels.
1
4.5
V a r i a t i o n s in the C o n t r i b u t i o n of
W a l l s to E a r t h q u a k e R e s i s t a n c e ^
The study of the seismic response of h y b r i d
s t r u c t u r e s h a s s h o w n , as w a s to be e x p e c t e d ,
t h a t the p r e s e n c e o f w a l l s s i g n i f i c a n t l y
r e d u c e d t h e d y n a m i c m o m e n t d e m a n d s on
columns.
This is b e c a u s e the m o d e shapes
of r e l a t i v e l y stiff w a l l s , do n o t p e r m i t
e x t r e m e d e f o r m a t i o n p a t t e r n s in the
i n h e r e n t l y m o r e flexible c o l u m n s .
Therefore
m o m e n t i n c r e a s e s in c o l u m n s above or b e l o w
b e a m s , due to h i g h e r m o d e e f f e c t s , as shown
in F i g . 7, are m u c h s m a l l e r .
This w a s
r e c o g n i s e d by the i n t r o d u c t i o n of a smaller
dynamic moment magnification factor, w = 1.2,
at i n t e r m e d i a t e f l o o r s , as d i s c u s s e d in
d e s i g n Step 11 and shown in F i g . 6.
The
a p p l i c a b i l i t y of a p p r o p r i a t e v a l u e s for us
w a s s u p p o r t e d w i t h a n u m b e r of case
s t u d i e s ^ , 1 1 , in w h i c h w a l l s made a s i g n i f i c a n t c o n t r i b u t i o n to the resistance o f
design base shear.
The c o n t r i b u t i o n of all w a l l s to lateral
load r e s i s t a n c e w a s e x p r e s s e d by the w a l l
shear ratio,
, i n t r o d u c e d in d e s i g n Step 1 6 .
The m i n i m u m v a l u e u s e d in the e x a m p l e
s t r u c t u r e w i t h two 3 m w a l l s w a s 0 . 4 4 .
The q u e s t i o n a r i s e s as to the m i n i m u m v a l u e
of the w a l l shear r a t i o ,
, r e l e v a n t to a
h y b r i d s t r u c t u r e , for the d e s i g n of w h i c h
the p r o p o s e d p r o c e d u r e in Section 3 is still
applicable.
A s the v a l u e of
diminishes,
i n d i c a t i n g that l a t e r a l load r e s i s t a n c e
m u s t b e a s s i g n e d p r i m a r i l y to f r a m e s , p a r a m e t e r s of the d e s i g n p r o c e d u r e m u s t a p p r o a c h
v a l u e s a p p l i c a b l e t o framed b u i l d i n g s .
At
a s u f f i c i e n t l y low v a l u e of t h i s r a t i o , say
$ < 0.1, a d e s i g n e r may decide to ignore
the c o n t r i b u t i o n o f w a l l s .
W a l l s could t h e n
b e t r e a t e d as s e c o n d a r y e l e m e n t s w h i c h w o u l d
n e e d to f o l l o w , w i t h o u t d i s t r e s s , d i s p l a c e m e n t s d i c t a t e d by the b e h a v i o u r of d u c t i l e
frames.
1
The m i n i m u m v a l u e o f
for w h i c h the p r o c e d u r e in S e c t i o n 3 is a p p l i c a b l e h a s n o t
5.
SUMMARY
(1)
The m e t h o d o l o g y e m b o d i e d in c u r r e n t
capacity d e s i g n p r o c e d u r e s used in
N e w Z e a l a n d , r e l e v a n t to b o t h
d u c t i l e framed
b u i l d i n g s and those in w h i c h s e i s m i c r e s i s t ance is p r o v i d e d e n t i r e l y by s t r u c t u r a l
w a l l s , h a s been e x t e n d e d to e n c o m p a s s
hybrid structures.
Appropriate values were
s u g g e s t e d for g o v e r n i n g d e s i g n p a r a m e t e r s .
(2)
Regular 6 and 12 s t o r e y b u i l d i n g s
w i t h varying w a l l c o n t e n t s w e r e
d e s i g n e d using this a p p r o a c h , and s u b s e q u e n t l y subjected in a n a l y t i c a l s t u d i e s to
the El Centro and P a c o i m a Dam a c c e l e r o g r a m s .
The generally good p e r f o r m a n c e of these
b u i l d i n g s during the El C e n t r o e x c i t a t i o n
s u g g e s t e d that p r o t o t y p e s t r u c t u r e s should
e x h i b i t good s e i s m i c p e r f o r m a n c e .
(3)
As intended, energy dissipation was
found to o c c u r p r i m a r i l y in b e a m and
w a l l base p l a s t i c hinge z o n e s .
(4)
C o l u m n s w e r e found to e n j o y p r o t e c t ion against f l e x u r a l y i e l d i n g e x c e p t
at the b a s e and top floor l e v e l s , w h e r e
h i n g e formation w a s e x p e c t e d .
A dynamic
m a g n i f i c a t i o n factor for c o l u m n m o m e n t s of
(a ~ 1.2 proved s a t i s f a c t o r y .
(5)
Column d e s i g n shear f o r c e s w e r e
adequately p r e d i c t e d by the d e s i g n
p r o c e d u r e and g e n e r a l l y found to be n o n critical .
(6)
The p r o v i s i o n s of the linear d e s i g n
w a l l moment e n v e l o p e s r e s t r i c t e d
s i g n i f i c a n t inelastic w a l l d e f o r m a t i o n s ,
e v e n d u r i n g the e x t r e m e P a c o i m a Dam e v e n t ,
to the b a s e .
(7)
P e a k w a l l base s h e a r f o r c e s e n c o u n t e r e d during a n a l y s e s w e r e s o m e w h a t
u n d e r e s t i m a t e d by the p r o p o s e d d e s i g n p r o c e d u r e . In the c o n t e x t o f u n c e r t a i n t i e s in
the a n a l y s i s a v a i l a b l e r e s e r v e shear
s t r e n g t h , and in p a r t i c u l a r the p r e d i c t e d
very short duration of these s h e a r f o r c e s ,
it w a s felt that this a n a l y t i c a l l y p r e d i c t e d
p h e n o m e n o n should not be v i e w e d w i t h c o n c e r n .
c
(8)
The p r o p o s e d e n v e l o p e s for d e s i g n
w a l l shear forces a d e q u a t e l y e s t i m a t e d
u p p e r level shear d e m a n d s .
(9)
It is b e l i e v e d t h a t the m e t h o d o l o g y
p r o p o s e d is l o g i c a l and s t r a i g h t forward.
It should p r o v i d e b u i l d i n g s so
d e s i g n e d , and carefully d e t a i l e d , w i t h
e x c e l l e n t seismic p e r f o r m a n c e c a p a b i l i t y .
1
(10)
U s i n g e n g i n e e r i n g j u d g e m e n t , the
approach is capable of b e i n g e x t e n d e d
to o t h e r structural c o n f i g u r a t i o n s
not
c o v e r e d in this p a p e r , b u t o n l y b y c o n s i s t e n t a p p l i c a t i o n of c a p a c i t y d e s i g n p r i n c i p l e s .
16
The e x c e l l e n t s e i s m i c b e h a v i o u r of
well balanced interacting ductile
f r a m e - w a l l s t r u c t u r e s , p a r t i c u l a r l y in t e r m s
of d r i f t c o n t r o l and d i s p e r s a l of e n e r g y
d i s s i p a t i n g m e c h a n i s m s t h r o u g h o u t the
structural system, should encourage their
e x t e n s i v e use in r e i n f o r c e d c o n c r e t e b u i l d i n g s
F r a m e s " , B u l l e t i n of the N e w Zealand
N a t i o n a l Society for E a r t h q u a k e
E n g i n e e r i n g , V o l . 9, N o l . 4, D e c .
1976, pp.205-212.
(11)
6.
7.
REFERENCES
1.
N Z S 3 1 0 1 : 1 9 8 2 , P a r t s 1 and 2 , "Code
of P r a c t i c e for the D e s i g n of C o n c r e t e
S t r u c t u r e s " , S t a n d a r d s A s s o c i a t i o n of
N e w Z e a l a n d , W e l l i n g t o n , 2 8 3pp.
3.
B l a k e l e y , R . W . G . , C o o n e y , R . C . and
M e g g e t , L.M., "Seismic Shear L o a d i n g
a t F l e x u r a l C a p a c i t y in C a n t i l e v e r
W a l l s " , B u l l e t i n o f the New Zealand
N a t i o n a l Society for E a r t h q u a k e
E n g i n e e r i n g , V o l . 8, N o . 4 , D e c .
1975, pp.278-290.
10.
P a u l a y , T. and G o o d s i r , W . J . , "The
Ductility of S t r u c t u r a l W a l l s " ,
B u l l e t i n of the N e w Zealand N a t i o n a l
Society for E a r t h q u a k e E n g i n e e r i n g ,
V o l . 1 8 , N o . 3, S e p t . 1 9 8 5 , p p . 2 5 0 269.
11.
G o o d s i r , W . J . , "The Design on C o u p l e d
F r a m e - W a l l S t r u c t u r e s for S e i s m i c
A c t i o n s " , R e s e a r c h R e p o r t N o . 85-8 ,
D e p a r t m e n t of C i v i l E n g i n e e r i n g ,
U n i v e r s i t y of C a n t e r b u r y , C h r i s t c h u r c h ,
N e w Zealand, 1 9 8 5 , 38 3pp.
• ACKNOWLEDGEMENTS
This study, b e i n g p a r t of a p r o j e c t w h i c h
i n v o l v e d also c o n s i d e r a b l e e x p e r i m e n t a l
work, would not have been possible without
g e n e r o u s g r a n t s from the N e w Zealand
M i n i s t r y of W o r k s and D e v e l o p m e n t a n d the
University Grants Committee.
Thanks are
due to M r s . V. Grey for p r e p a r a t i o n of
i l l u s t r a t i o n s , M r . L. G a r d n e r for p h o t o g r a p h i c w o r k and M r s . J.Y. J o h n s for t y p i n g
the t e x t .
The authors w i s h
to a c k n o w l e d g e
s p e c i a l l y the i n v a l u a b l e a s s i s t a n c e and
a d v i c e r e c e i v e d from D r . A . J . Carr w i t h
r e s p e c t to c o m p u t a t i o n a l w o r k .
2.
9.
P a u l a y T. and W i l l i a m s , R . L . , "The
A n a l y s i s and D e s i g n o f and the
E v a l u a t i o n of D e s i g n A c t i o n s for
Reinforced Concrete Ductile Shear
W a l l s " , B u l l e t i n of the N e w Zealand
N a t i o n a l Society for E a r t h q u a k e
Engineering, V o l . 1 3 , N o . 2, June
1980, pp.108-143.
r
G o o d s i r , W . J . , P a u l a y , T. and C a r r ,
A . J . , "A Study of the I n e l a s t i c
S e i s m i c R e s p o n s e of R e i n f o r c e d
C o n c r e t e C o u p l e d F r a m e - Shear W a l l
S t r u c t u r e s " , B u l l e t i n of the N e w
Zealand N a t i o n a l Society for E a r t h q u a k e E n g i n e e r i n g , V o l . 16 , N o . 3,
Sept. 1983, pp.185-200.
8.
LIST OF
A
c^
c
D
E
f^
=
=
=
=
=
=
hb
I ,Ik
a
=
=
I
c
=
c
I
=
w
G o o d s i r , W . J . , "The R e s p o n s e o f
C o u p l e d Shear W a l l s and F r a m e s " ,
Research Report No. 82-10, Department
of C i v i l E n g i n e e r i n g , U n i v e r s i t y of
Canterbury, Christchurch, New Zealand,
1982, 155pp.
5.
N Z S 4 2 0 3 : 1 9 8 4 , "Code o f P r a c t i c e for
G e n e r a l S t r u c t u r a l Design and D e s i g n
L o a d i n g s for B u i l d i n g s " , S t a n d a r d s
A s s o c i a t i o n of N e w Z e a l a n d ,
Wellington, 80pp.
6.
K h a n , F.R. and S b a r o u n i s , J.A.,
"Interaction o f Shear W a l l s w i t h
F r a m e s in C o n c r e t e S t r u c t u r e s u n d e r
L a t e r a l L o a d s , J o u r n a l of t h e
Structural Division, ASCE, V o l . 9 0 ,
No. S T 3 , June 1 9 6 4 , p p . 2 8 5 - 3 3 5 .
g r o s s c o n c r e t e area of section
t h e o r e t i c a l n e u t r a l axis depth
c r i t i c a l n e u t r a l axis depth
dead load
e a r t h q u a k e load
s p e c i f i e d c o m p r e s s i o n s t r e n g t h of
c o n c r e t e (MPa)
depth of b e a m
second m o m e n t of a r e a of b e a m
sections
second m o m e n t of area of a c o l u m n
section
second m o m e n t of area of a w a l l
section
= span lengths
- clear h e i g h t of c o l u m n
= l e n g t h of w a l l , o v e r a l l depth of
w a l l section
Lr
~ r e d u c e d live load
Mg
= flexural o v e r s t r e n g t h of b e a m
m e a s u r e d at c o l u m n centre line
code
= m o m e n t due to code s p e c i f i e d
lateral load
c o d e top
°l
m o m e n t at the top of a
'
column d e r i v e d f r o m lateral code
loading
^col
~ design m o m e n t for a column at ideal
strength
col
~ f l
o v e r s t r e n g t h at a c o l u m n
section
M°
= m o m e n t d e v e l o p e d at f l e x u r a l o v e r strength
M
= m o m e n t due to f a c t o r e d loads
n
= n u m b e r of s t o r e y s above a g i v e n
level
P
= a x i a l load on c o l u m n due to dead
load
P
,P
^
= d e s i g n a x i a l load on c o l u m n
including earthquake effects
P q
= e a r t h q u a k e i n d u c e d a x i a l load in a
c o l u m n a t the d e v e l o p m e n t o f b e a m
overstrengths
P
= axial load on c o l u m n due to r e d u c e d
live load
P
= axial load due to factored loads
Rjn
- column d e s i g n m o m e n t r e d u c t i o n
factor
I
i
1^
n
e
4.
a
m
M
M
=
M
D
e f
e
7.
R o s m a n , R., "Laterally L o a d e d S y s t e m s
C o n s i s t i n g o f W a l l s and F r a m e s " , Tall
B u i l d i n g s , U n i v e r s i t y of s o u t h h a m p t o n ,
1966, pp.273-289.
L R
u
8.
P a u l a y , T., "Moment R e d i s t r i b u t i o n in
Continuous Beams of Earthquake Resistant M u l t i s t o r e y R e i n f o r c e d C o n c r e t e
c
e
u
M
SYMBOLS
m
a
x
e
m
x
u
u
m
n
r
a
l
v
code
v
code
v
col
V
o
e
~ shear force for c o l u m n s d e r i v e d
f r o m code s p e c i f i e d l a t e r a l s t a t i c
load
total
t o t a l b a s e s h e a r for t h e
e n t i r e s t r u c t u r e d e r i v e d f r o m code
s p e c i f i e d l a t e r a l load
d e s i g n shear force for a c o l u m n a t
ideal strength
- d i s p l a c e m e n t i n d u c e d shear f o r c e in
b e a m at the d e v e l o p m e n t o f its
flexural overstrength
=
=
w a l l base
ig
shear f o r c e for a w a l l
'
a t its b a s e
w a l l , c o d e ~ shear force for a w a l l d e r i v e d
from code s p e c i f i e d l a t e r a l load
U
= u l t i m a t e f a c t o r e d load
u
= displacement ductility factor
$>
= strength reduction factor
<f>
= o v e r s t r e n g t h factor
<t>
= flexural overstrength factor for a
wall
<j>3
- global overstrength factor
<j>
= ultimate curvature
= w a l l shear r a t i o
co
= d y n a m i c m a g n i f i c a t i o n f a c t o r in
general
u)
= d y n a m i c shear m a g n i f i c a t i o n f a c t o r
for a c o l u m n
oj
= d y n a m i c shear m a g n i f i c a t i o n f a c t o r
co*
= d y n a m i c shear m a g n i f i c a t i o n for
w a l l s in h y b r i d s t r u c t u r e s
- a x i a l load r e d u c t i o n factor
S
= s t r u c t u r a l type factor
code
=^dependable strength required by
code s p e c i f i e d l a t e r a l load only
= ideal strength
S
= m a x i m u m or o v e r s t r e n g t h t h a t m a y b e
developed
v
= i d e a l shear s t r e s s p r o v i d e d b y
c o n c r e t e (MPa)
X
= superscript indicating direction
o f e a r t h q u a k e attack
v
=
v
A
0
0 w
u
c
s
Q
c
d
e
s
n