Seismic Design of Beam-Column Joints in Concrete Frames

226
This paper i s t h £ r e s u l t of d e l i b e r a t i o n s o f t h e S o c i e t y ' s d i s c u s s i o n g r o u p o n ,
S E I S M I C D E S I G N OF D U C T I L E M O M E N T RESISTING REINFORCED CONCRETE F R A M E S
SECTION
J
D E S I G N OF B E A M - C O L U M N
JOINTS
R. W . G. B l a k e l e y *
JO.O
NOTATION
]Z
2
=
A
jh
gross area of section, m m
effective total area of horizontal
joint shear reinforcement, m m
2
effective total area of vertical
shear reinforcement, mm
A
s
A
=
area of bottom beam
forcement' at column
joint
2
horizontal design joint shear force
to b e r e s i s t e d by h o r i z o n t a l j o i n t
shear reinforcement, N
= capacity
lesser area of column flexural reinf o r c e m e n t in t e n s i l e o r c o m p r e s s i v e
face at joint, m m
force
nominal horizontal shear stress
effective joint area, MPa
reinforcement
2
A
shear
vertical design joint shear force
to b e resisted by v e r t i c a l joint
shear reinforcement, N
flexural reinface, m m
= area of top b e a m flexural
at column f a c e , m m
S
'sh
total horizontal joint
in z d i r e c t i o n , N
J1.0
reduction
factor
=
in
0.85
SCOPE
2
A *
SC
greater area of column flexural reinf o r c e m e n t in t e n s i l e or c o m p r e s s i v e
face at joint, mm
overall width
effective
of column,
joint width,
overall width
of beam,
mm
mm
mm
J1L
V
V.
f
+
V
= specified
concrete,
c
compressive
MPa
strength
of
specified yield strength of nonprestressed flexural reinforcement,
^yh
yv
MPa
= s p e c i f i e d y i e l d s t r e n g t h of h o r i z o n t a l
joint shear reinforcement, MPa
= specified yield strength of vertical
joint shear reinforcement, MPa
= overall
depth
= overall depth
of h o r i z o n t a l
of beam,
mm
of c o l u m n in the d i r e c t i o n
shear to b e c o n s i d e r e d , m m
= design axial compression column load,
including vertical prestressing force
where applicable, occurring simultaneously with V j ^ , N
=
*ch
force after all losses in p r e s t r e s s i n g
steel passing through a joint within
the central third of the beam d e p t h , N
horizontal joint shear force resisted
by concrete shear resisting mechanism
only, N
vertical joint shear force resisted
by concrete shear resisting mechanism
only, N
3V
-
| X
total horizontal shear force across
a j o i n t , N (= V .
or V. )
'
3X
jz'
total vertical shear force across a
joint, N
total horizontal joint shear force
in x d i r e c t i o n , N
Design Engineer, Ministry
Development, Wellington.
of Works
and
P r o v i s i o n s are made for the d e s i g n
of b e a m - c o l u m n joints s u b j e c t e d to the
forces imposed when a frame sustains
inelastic lateral displacements under
earthquake loading.
Both o n e - w a y and t w o way frames are considered.
D e s i g n for
h o r i z o n t a l a n d v e r t i c a l s h e a r f o r c e s is
required for b o t h p o s s i b l e c a s e s of p l a s t i c
hinges forming in the b e a m or the column.
Special concessions are m a d e for significant
c o l u m n a x i a l l o a d s , for i n c l u s i o n of
p r e s t r e s s i n g s t e e l , and for w h e r e m e m b e r s
are designed so that plastic h i n g e s w i l l
not form next to the joint.
The objective
o f t h e d e s i g n r e q u i r e m e n t s is t o m a k e t h e
joint stronger than the c o i n c i d e n t h i n g i n g
m e m b e r s , and therefore to avoid s i g n i f i c a n t
inelastic b e h a v i o u r w i t h i n the joint c o r e .
J2.0
DESIGN
FORCES
J2.1
The design shear forces acting on a
beam-column joint should be evaluated from
the m a x i m u m forces in all m e m b e r s c o i n c i d e n t
at the joint at flexural o v e r - s t r e n g t h of
the hinging member or m e m b e r s .
At columns
of t w o - w a y f r a m e s , w h e r e b e a m s f r a m e into
the joint from two directions", t h e s e forces
need only be c o n s i d e r e d in each d i r e c t i o n
independently.
J2.2
The m a g n i t u d e s of the d e s i g n horizontal
shear force,
jh* a n d t h e d e s i g n v e r t i c a l
s h e a r f o r c e , V j ^ , in t h e j o i n t s h o u l d b e
evaluated from a rational analysis taking
into a c c o u n t the effects of all forces
acting on the joint.
J3.0
GENERAL
REQUIREMENTS
J3.1
For shear design of the joint the
c a p a c i t y r e d u c t i o n f a c t o r , <j>, s h o u l d b e
0.85.
J3.2
The nominal horizontal shear stress
in the joint in e i t h e r p r i n c i p a l d i r e c t i o n ,
s h o u l d n o t e x c e e d 1.5/fr
j '
V
jh
where v
(J-D
jh
<j> b .
3
v
h
J3.3
The
effective
joint w i d t h , bj , should
B U L L E T I N O F T H E N E W Z E A L A N D N A T I O N A L S O C I E T Y F O R E A R T H Q U A K E E N G I N E E R I N G , V O L . 10, N O . 4, D E C E M B E R
1977
227
be
taken
as:
(a)
where b_ > b ,
c
w
either b. = b
3
c
or
b. = b
+ 0. 5 h
~j
w
c
whichever
, .
smaller.
J
is
the
or
(b)
where
< b
c
w
either b. = b
3
w
or
b
b. = b
3
+
0.5h
whichever
c smaller.
c
J4.0
REINFORCEMENT
J4.1
General
is
(c)
When frame design precludes the
formation of any beam plastic h i n g e s at
the j o i n t , or w h e n all b e a m s at the joint
are detailed so that the c r i t i c a l s e c t i o n
o f t h e p l a s t i c h i n g e is l o c a t e d a t a
d i s t a n c e of not less than the d e p t h of the
m e m b e r or 500mm, w h i c h e v e r is g r e a t e r ,
away from the c o l u m n f a c e , or for e x t e r n a l
joints w h e r e flexural s t e e l is a n c h o r e d
o u t s i d e the column core in a s t u b in
accordance with E4.4.4
c. N
V
(-J-5)
(i + 0.6JLA
rr)
2
ch
K
the
e x c e p t that, w h e r e the axial c o l u m n load
r e s u l t s in t e n s i l e s t r e s s e s o v e r t h e g r o s s
concrete area, the value of V h should be
linearly interpolated between the value
g i v e n b y E q . (J-5) w i t h N
taken as z e r o ,
and zero at an axial tensile stress of
0 . 2 f^.
Thereafter the entire horizontal
joint shear should be resisted by reinforcement .
c
u
J4.1.1
A rational system should be provided
to r e s i s t the h o r i z o n t a l and v e r t i c a l s h e a r
forces induced in the joint.
J4.1.2
The provisions of J4.2 and J4.3
apply to joints in w h i c h the shear r e i n f o r c e ment comprises horizontal and vertical stirrups
or b a r s .
T h e required horizontal and vertical
joint shear reinforcement should be placed
w i t h i n the effective- j o i n t w i d t h , d e f i n e d
in J 3 . 3 , r e l e v a n t to e a c h d i r e c t i o n o f
loading.
J4.1.3
Special joint reinforcement details,
such as d i a g o n a l b a r s b e n t across the j o i n t
in one or b o t h d i r e c t i o n s , or o t h e r s p e c i a l
d e v i c e s , m a y b e u s e d if it is s h o w n b y
analysis and/or tests that the shear forces
that may be induced during large inelastic
deformations of the coincident beams are
adequately transferred by an acceptable
m e c h a n i s m and that anchorage of the flexural
r e i n f o r c e m e n t a c r o s s t h e j o i n t is a s s u r e d .
J4.2
Horizontal
Joint
Shear
J4.2.1
The horizontal design shear force
to b e resisted by the h o r i z o n t a l joint shear
reinforcement should be
V.
V
V
(J-2)
sh
ch
u
where Vu
is t h e a l l o w a b l e h o r i z o n t a l s h e a r
carried by the concrete shear resisting
mechanism.
c
J4 .2.2
The value
to b e z e r o e x c e p t
of V ^
in the
should be
following
c
assumed
cases:
(a)
When the minimum average compressive
stress on the gross area of the column above
the joint, including prestress where
a p p l i c a b l e , e x c e e d s 0.1
f^/Cj
J4.2.3
The horizontal shear reinforcement
s h o u l d b e c a p a b l e of c a r r y i n g t h e d e s i g n
shear force to b e carried by the r e i n f o r c e ment,
, across a corner-to-corner
diagonal tension crack plane.
The effective
t o t a l area of h o r i z o n t a l r e i n f o r c e m e n t that
c r o s s e s the c r i t i c a l f a i l u r e p l a n e ,
determined according to the o r i e n t a t i o n
of the individual tie legs w i t h respect
to t h i s failure p l a n e , and t h a t is w i t h i n
the effective joint w i d t h , bj , should not
be less than
sh
V
L
A n y tie leg b e t w e e n b e n d s a r o u n d c o l u m n
bars that does not cross the p o t e n t i a l
f a i l u r e p l a n e , or is s h o r t e r t h a n o n e third of the d i m e n s i o n of the c o l u m n in
the appropriate plane of b e n d i n g , should
be neglected.
The required number of h o r i z o n t a l
sets of stirrup ties or b a r s should b e
placed between the outermost layers of
the top and b o t t o m b e a m r e i n f o r c e m e n t , and
s h o u l d b e d i s t r i b u t e d as u n i f o r m l y as is
practicable.
J4.3
Vertical
ch
=
°-
(b)
When
joint
*ch
+
2 5
0.7
beams
£c>
25
are
^ j u
C
N
A
g
__ c
f
1
(bj
c
through
the
and
J4.3.2
from
The value
sc
A'
sc
(J-4)
s
The values of V
E q . (J-4) m a y be
c
obtained
added when
n
force
shear
to
(J-7)
(J-3)
where P
is the force after all losses in
the p r e s t r e s s i n g s t e e l t h a t is l o c a t e d
within the central third of the beam depth.
c
shear
joint
v
A
P.
Shear
where V
is t h e a l l o w a b l e v e r t i c a l s h e a r
carried by the concrete shear r e s i s t i n g
mechanism.
h )
0
prestressed
Joint
J4.3.1
The vertical design
be resisted by the vertical
reinforcement should be
V.
V
- V
sv
c
V
(J-6)
yh
f r o m E q . (J-3)
applicable.
of V
c
should
v
be
determined
V.
j v
2
(1 +
j
0.6
(J-8)
C
A f'
g
except
(a)
Where the axial column load results
in t e n s i l e s t r e s s e s o v e r t h e g r o s s c o n c r e t e
a r e a , the value of V
should be linearly
c
v
228
interpolated between the value given by
E q . (J-8) w i t h N
taken as z e r o , and zero
a t a n a x i a l t e n s i l e s t r e s s o f 0.2 f £ .
Thereafter the entire vertical joint shear
should b e resisted by reinforcement.
C'
°
= c o m p r e s s i o n force in the concrete
in the flexural c o m p r e s s i o n zone
of a b e a m
C'
= c o m p r e s s i o n f o r c e in t h e
reinforcement of a b e a m
and
f*
u
s
= overstrength of longitudinal
f o r c e m e n t , g e n e r a l l y 1.25 f
Y
(b)
W h e r e plastic hinges are expected to
form in t h e c o l u m n a b o v e or b e l o w the j o i n t ,
as p a r t of the p r i m a r y seismic e n e r g y
dissipating mechanism, V
should be assumed
to b e zero for any axial load.
Grade
1 1
J4.3.3
The vertical joint shear reinforcement
should consist of intermediate column b a r s ,
p l a c e d in the plane of b e n d i n g b e t w e e n c o r n e r
bars, or vertical stirrup ties, or special
v e r t i c a l b a r s p l a c e d in t h e c o l u m n a n d
a d e q u a t e l y a n c h o r e d to t r a n s m i t the r e q u i r e d
tensile forces within the joint.
1
'
n
1
c
T
Confinement
The horizontal transverse confinement
r e i n f o r c e m e n t in b e a m - c o l u m n joints should n o t
be less than that required by H 6 . 1 , except
for j o i n t s c o n n e c t i n g b e a m s a t all four c o l u m n
faces that are n o t expected to form plastic
h i n g e s or a r e d e s i g n e d a c c o r d i n g to J 4 . 2 . 2 ( b )
or ( c ) , in w h i c h case the t r a n s v e r s e joint
r e i n f o r c e m e n t may be reduced to one half
of t h a t r e q u i r e d in H 6 . 1 , b u t in no case
s h o u l d t h e s t i r r u p t i e s p a c i n g in t h e j o i n t
core exceed ten times t h e d i a m e t e r of the
c o l u m n b a r or 150mm, w h i c h e v e r is l e s s .
ECCENTRIC
BEAM-COLUMN
JOINTS
J5.1
The eccentricity of any beam relative
to the column into w h i c h it frames should not
exceed t h a t p e r m i t t e d in E 4 . 1 , e x c e p t as
allowed in J 5 . 2 ( b ) .
J5.2
All joint design provisions
section apply except that
of
this
(a)
In a d d i t i o n t o t h e e f f e c t i v e j o i n t
width limits of J 3 . 3 , the following should
apply;
b
^
b
w
+
b
c
+
0.25h
-
e
(b)
Where the eccentricity exceeds that
p e r m i t t e d in E 4 . 1 , all of the required
flexural steel in the column should be placed
within the effective joint area, b j h .
Additional longitudinal column reinforcement
should b e placed outside of the effective
joint area in accordance w i t h H 5 . 2 .
c
COMMENTARY
CJO.O
NOTATION
=
area
of
leg
of
tie
set
centre-to-centre
= length of clear span of b e a m ,
measured face-to-face of supports
= tension
,T
P
c
yv
J4 .3.5
T h e s p a c i n g of c o l u m n b a r s in e a c h
plane of any beams framing into a joint
should n o t exceed 200 m m , and in no case
should there b e less than one intermediate
bar in e a c h side of the c o l u m n in that p l a n e .
-
centre-to-centre
1
f
p
V
J
J5.0
n
steel
reinfor.
M* Mi = flexural over-capacity of beam
section at faces of a column
shear
joint
V -^
J4.4
2
275
span of b e a m between
of supports
, 1 ' = height of column,
°
of floors or roof
T
J4.3.4
T h e a r e a of v e r t i c a l j o i n t
reinforcement within the effective
w i d t h , bj , should not be less than
=
1
l
compression
o
1
CJ1.0
force
in t e n s i o n
reinforcement
= prestressing force at faces of
c o l u m n a t f l e x u r a l c a p a c i t y of
section
= horizontal
column
shear
force
across
a
a
SCOPE
Severe c o n d i t i o n s o f shear and of a n c h o r a g e of f l e x u r a l r e i n f o r c e m e n t c a n a r i s e in
joints.
Inelastic b e h a v i o u r in the form of
yield of shear r e i n f o r c e m e n t o r loss of bond
to f l e x u r a l r e i n f o r c e m e n t c a n lead to rapid
loss of strength under seismic conditions
and i s , t h e r e f o r e , to b e a v o i d e d .
CJ2.0
DESIGN
FORCES
C J 2 .1
In o r d e r t o p r o v i d e a d e q u a t e r e s e r v e
s t r e n g t h w i t h i n a j o i n t , t h e f o r c e s in t h e
coincident beams and columns m u s t be
evaluated at flexural o v e r s t r e n g t h of the
hinging members.
Generally the hinging
m e m b e r s w i l l be the b e a m s , e x c e p t in o n e
or two-storey frames or at the top of
c o l u m n s in m u l t i - s t o r e y f r a m e s w h e r e
columns may b e designed to h i n g e .
Where
b e a m flexural r e i n f o r c e m e n t is detailed
to force the p l a s t i c h i n g e to form away
from the c o l u m n f a c e , the f o r c e s in the
beam at the column face should b e
determined for flexural o v e r s t r e n g t h at
the critical section of the plastic h i n g e .
A l l o w a n c e for o v e r s t r e n g t h of flexural
r e i n f o r c e m e n t should b e as r e c o m m e n d e d in
E4 . 4.5.
P r o v i s i o n s for the c o n t r i b u t i o n
of the slab r e i n f o r c e m e n t , w h e r e a p p l i c a b l e ,
should be not less than those recommended
in E 4 . 4 . 2 . - B e c a u s e that c l a u s e r e p r e s e n t s
a lower b o u n d of e f f e c t i v e s l a b steel for
flexural design purposes, a greater
contribution from the slab should be
assumed appropriate to the u p p e r bound
required for joint shear d e s i g n .
The basis for d e s i g n of b e a m - c o l u m n
joints in two-way f r a m e s , by c o n s i d e r a t i o n
of forces acting in each principal direction
i n d e p e n d e n t l y , is r e c e n t (1977) t e s t i n g
at University of Canterbury.
A joint
designed on this b a s i s and e x t e n s i v e l y t e s t e d ,
including several major cycles of concurrent
h i n g i n g of b e a m s in b o t h p r i n c i p a l d i r e c t i o n s ,
performed satisfactorily.
W h i l e it m a y b e
undesirable to b a s e d e s i g n p r o v i s i o n s on
only one test, the complexity of such
tests means that there is unlikely to be
further t e s t i n f o r m a t i o n a v a i l a b l e in the
foreseeable future.
229
W h e n s t i f f s t r u c t u r a l s y s t e m s , such as
shear w a l l s , p r e v e n t yielding in beams or
columns in one or both principal directions
of the building, a rational analysis should
b e u s e d to d e t e r m i n e t h e f o r c e s in t h e
frame members at the maximum anticipated
seismic loading.
CJ2.2
The internal forces imposed on the
j o i n t by f l e x u r e of m e m b e r s in o n e v e r t i c a l
plane only at the connection are shown in
Fig. C J 1 , for b o t h internal and e x t e r n a l
beam-column joints.
The concentrated
t e n s i o n and c o m p r e s s i o n forces in b o t h
beam a n d column, minus the much smaller
v a l u e s of c o l u m n and b e a m s h e a r s , induce
r e s u l t a n t s h e a r s t r e s s e s in the p a n e l z o n e .
The horizontal shear force V j ^ across a
g e n e r a l i n t e r n a l joint is
V..
jh
= T + C' + C
+ T
c
s
p
T
(CJ-1)
f
p
col
For conventionally reinforced
members without prestressing,
to:
concrete
this simplifies
internal
s v
f
s y
s •
j o i n t s V., = A ' f *
3h
s y
col
joints V .
external
K
= A'f* + A
-)h
J
col
(CJ-2a)
(CJ-2b)
The value of the column shear, V o l , will
depend on the column m o m e n t gradients above
and b e l o w the joint.
However, from Fig. CJ2
its v a l u e m a y b e estimated using a m e a n
moment gradient, thus
M*
V
(CJ-3)
^ M g ) / ( l
2
U
col
c
ln
2n
C
c
+
1
)
L
A l t e r n a t i v e l y , the maximum horizontal joint
shear m a y b e derived from the g r a d i e n t of
the column m o m e n t diagram through the joint.
W h e n necessary the value of the v e r t i c a l
joint shear force, V j , may be derived from
similar considerations to the above for
horizontal joint shear force.
Alternatively,
the vertical joint shear force may be
a p p r o x i m a t e d as follows:
s h e a r in j o i n t s o f o n e - w a y f r a m e s b i s e c t s
the joint along a diagonal from one beamcolumn edge to a n o t h e r ( 1 , 2 , 3 , 4 ) .
Under
cyclic loading, the diagonal tension cracks
o p e n and close in e a c h d i r e c t i o n as the
d i r e c t i o n of load a l t e r n a t e s .
If t h e
j o i n t r e i n f o r c e m e n t y i e l d s so t h a t the
cracks become w i d e , relative shear displacements along the crack can lead to u n e v e n
bearing followed by grinding o f the
c o n c r e t e and g e n e r a l d e t e r i o r a t i o n of the
joint.
G e n e r a l l y t h i s w i l l n o t o c c u r if
any y i e l d i n g is l i m i t e d to i s o l a t e d t i e
legs.
Shear transfer across the panel zone
m a y b e i d e a l i s e d as d u e , in v a r y i n g p r o p o r tions , to four m e c h a n i s m s :
diagonal strut
action, truss action, aggregate interlock
and d o w e l a c t i o n .
Concrete compression
forces tend to b e transferred d i r e c t l y by
diagonal strut action.
Although, theoretically,
diagonal strut action requires no shear
reinforcement, the diagonal compression
force creates a splitting force perpendicular
to it and r e i n f o r c i n g s t e e l is r e q u i r e d to
c o n t r o l the w i d t h of the c r a c k s .
Those
forces induced in the p a n e l zone t h r o u g h
bond to the reinforcing bars
tend to b e
transferred by a truss mechanism comprising
a number of diagonal compression struts
in the c o n c r e t e , p a r a l l e l to the p o t e n t i a l
failure p l a n e , and t e n s i o n ties in the
h o r i z o n t a l and v e r t i c a l s t e e l , as shown
in F i g . C J 1 .
Usually horizontal stirrup
ties are provided to resist the h o r i z o n t a l
forces but the vertical strut components
m u s t be resisted by intermediate column
bars, vertical stirrup ties or special
vertical bars.
Aggregate interlock may
only be relied on where the cracks are
n a r r o w and the b e a r i n g surfaces n o t w o r n .
Dowel action of the ties across the
diagonal tension cracks will only be
s i g n i f i c a n t w h e r e the cracks are w i d e and
t h e j o i n t is l i k e l y t o h a v e a l r e a d y
deteriorated.
v
K
V.
*
V.,
CJ3.0
~
(CJ-4)
GENERAL
REQUIREMENTS
CJ3.2
A n u p p e r limit for joint s h e a r s t r e s s
is s p e c i f i e d to safeguard the core c o n c r e t e
against excessive diagonal compressive stresses.
The horizontal nominal stress corresponding
to the c r i t i c a l h o r i z o n t a l shear f o r c e , V j ^ ,
is b a s e d o n t h e n o m i n a l g r o s s h o r i z o n t a l
area of the joint bj h
as d e f i n e d in J 3 . 3 .
c
CJ3.3
A l i m i t a t i o n is p l a c e d on the a r e a
of a joint core which may be considered to
b e e f f e c t i v e in r e s i s t i n g j o i n t s h e a r w h e n
the beam or beams framing into a connection
are considerably narrower than the column.
The e f f e c t i v e joint w i d t h , b j , w h e r e b j is
less than b
i s i l l u s t r a t e d in F i g . C J 3 .
W h e r e the b e a m is w i d e r than the c o l u m n , the
effective joint width is assumed to spread
b e y o n d the b o u n d s of the c o l u m n in a
similar manner•
c
CJ4.0
CJ4.1.1
REINFORCEMENT
The observed
failure
plane due
to
CJ4.1.3
Innovative details which encourage
a m o r e direct transfer of forces across
the panel zone, such as main b e a m or
column steel bent diagonally across the
joint or e n c o u r a g e m e n t of a r c h a c t i o n
by use of m e c h a n i c a l anchors o n flexural
steel at the extremities of the j o i n t ( 5 ) ,
appear attractive.
Any arrangement which
represents a major departure from previously
used details should be tested before
adoption.
CJ4.2
Horizontal
Joint
Shear
CJ4.2.1
The horizontal joint shear force
is assumed t o b e t r a n s f e r r e d b e t w e e n the
levels of the top and b o t t o m b e a m f l e x u r a l
r e i n f o r c e m e n t by s t r u t a c t i o n in the
concrete c o r e , V ^ , and by a truss mechanism,
V h.
The dependable shear capacity,
u s i n g <j> = 0 . 8 5 , i s t h e n e q u a t e d t o t h e
overstrength shear demand, Vjh.
s
CJ4.2.2
When plastic hinges form under
reversed load in r e i n f o r c e d c o n c r e t e b e a m s
immediately a d j a c e n t to the joint c o r e ,
wide cracks develop at the column face
and m o m e n t tends to b e t r a n s f e r r e d by a
steel couple.
The major part or all of
the internal c o m p r e s s i o n f o r c e in t h e
b e a m s is then t r a n s f e r r e d to the j o i n t by
the flexural reinforcement.
Consequently
it m u s t be assumed for this c o n d i t i o n , and
230
when column axial loads are low, that all
the beam forces are transmitted by a truss
m e c h a n i s m and
= 0.
Recent recommendations
(°' a l l o w i n g t h e c o n c r e t e t o c a r r y s o m e s h e a r
are n o t c o n s i d e r e d j u s t i f i e d in t h a t c a s e .
V h is a s s u m e d to b e e f f e c t i v e
following circumstances:
c
in
the
beams w h e r e w i d e cracking at the column
face is a v o i d e d .
Case studies of the
c o n t r i b u t i o n of the c o n c r e t e s t r u t to
shear transfer have been made based on a
m o d e l s h e w n in F i g . C J 4 .
The shear forces
from the b e a m s and columns may be assumed
as b e i n g t r a n s f e r r e d in the c o r r e s p o n d i n g
compression zones only.
V
and V
are
the h o r i z o n t a l and vertical components of
the d i a g o n a l thrust D that w i l l pass
through the centre of the joint c o r e .
The
case studies have shown that approximately
one half of the horizontal joint shear, Vjh,
can b e t r a n s f e r r e d by t h e d i a g o n a l c o n c r e t e
s t r u t w h e n t h e r e is zero a x i a l c o m p r e s s i o n
on the c o l u m n and w h e r e there is e q u a l top
and b o t t o m b e a m s t e e l .
The proportion of
joint shear resisted by the diagonal strut
i n c r e a s e s w i t h i n c r e a s i n g axial load and
d e c r e a s e s as t h e r a t i o of a r e a s of top and
bottom beam steel increases.
These trends
a r e r e p r e s e n t e d i n E q . (J-5) a n d i l l u s t r a t e d
in F i g . C J 5 .
T h e i n t e n t i o n of E q . (J-5)
is t h a t A
is e q u a l to or g r e a t e r than
A , which normally will mean that A
is the
area of top b e a m s t e e l and A
the area of
bottom beam steel.
When columns are
s u b j e c t e d to a x i a l t e n s i o n it is a s s u m e d
that the shear resistance from diagonal strut
action diminishes.
When the axial tensile
stress on the gross column section exceeds
0.2fc f u l l j o i n t s h e a r r e i n f o r c e m e n t is
required.
In e x t e r n a l b e a m - c o l u m n j o i n t s
f a v o u r a b l e d i a g o n a l s t r u t a c t i o n is
developed provided anchorage of flexural
b a r s is a s s u r e d , p a r t i c u l a r l y w i t h u s e o f
external stubs.
Testing of such joints
i n d i c a t e s t h a t E q . (J-5) r e p r e s e n t s s a t i s factorily the contribution of the concrete
strut.
c
(a)
With increasing axial loads on columns
the internal column concrete c o m p r e s s i v e
forces tend to increase, w i t h c o n s e q u e n t
i n c r e a s e in the w i d t h of the d i a g o n a l
compression strut.
When axial compression
e x c e e d s 0.1 f^ , s u f f i c i e n t b o n d t r a n s f e r
from t h e f l e x u r a l r e i n f o r c e m e n t is a s s u m e d to
occur within the strut region, even considering y i e l d p e n e t r a t i o n i n t o the j o i n t , to
allow some of the beam bar forces to be
transferred by this strut.
E q . (J-3) i s s i m i l a r t o E q . (F.l) f o r
members subject to flexure and axial load.
On the basis of analyses and limited test
d a t a ( 7 ) , t h i s e q u a t i o n is c o n s i d e r e d to
underestimate the advantages of column axial
load on joint shear s t r e n g t h and w i l l be
reviewed w h e n further e v i d e n c e is a v a i l a b l e .
T h e f a c t o r C j is i n t r o d u c e d t o a l l o c a t e
the e f f e c t of axial c o m p r e s s i o n to the two
p r i n c i p a l directions x and z of the e a r t h quake loading when joint shears V j
and
Vj
are concurrently developed.
The e f f e c t of
t h i s p r o v i s i o n is t o p r e v e n t t h e a d v a n t a g e s
of full a x i a l load b e i n g u t i l i s e d in each
p r i n c i p a l d i r e c t i o n for the i n d e p e n d e n t
shear design provisions of J 2 . 1 .
For a
s y m m e t r i c a l t w o - w a y frame Cj = 0.5; for a
one-way frame Cj = 1.0.
x
z
n
c
v
s
s
s
s
(b)
Prestressing within the central area
of the b e a m h a s the e f f e c t of e n c o u r a g i n g
joint concrete strut action and of restraining
diagonal tension c r a c k i n g ( 2 , 3 )
However,
prestressing steel near the extreme fibres
of the section sustains p e r m a n e n t sets and
loss of p r e s t r e s s after i n e l a s t i c b e a m h i n g e
rotations .
Thus, only the prestressing
steel at the central third of the beam depth
may b e c o n s i d e r e d for shear r e s i s t a n c e in
the joint.
It should b e r e c o g n i s e d t h a t
where prestressed concrete beams support
cast insitu floor slabs, the effective
p r e s t r e s s is likely to b e d i s t r i b u t e d into
the slab.
The full p r o v i s i o n s should n o t
be applied unless the p r e s t r e s s can be
relied o n , for example w h e r e the floor
s y s t e m is n o t r e s t r a i n e d to the b e a m .
Where
t h e f l o o r s l a b is m o n o l i t h i c w i t h t h e b e a m
and t h e p r e s t r e s s is i n d e t e r m i n a t e , b o n d e d
cables w i l l still serve a function of
restraining diagonal tension joint cracks
a n d h a l f t h e a l l o w a n c e o f E q . (J-4) m a y b e
assumed.
CJ4.2.3
Research on planar beam-column
assemblies has shown that the c o r n e r - t o corner crack across the joint represents
the critical failure p l a n e .
Strain gauge
r e a d i n g s o n t i e s in j o i n t c o r e s ( 1 , 2 , 3 , 4 )
have shown considerable scatter of strains
w i t h i n any tie set and m o d e r a t e v a r i a t i o n
of e f f e c t i v e n e s s o f d i f f e r e n t tie s e t s .
In p a r t i c u l a r , t i e s e t s i n t h e c e n t r a l
region of t h e core tend to be m o r e e f f e c t i v e
than those near the top and bottom of the
core.
It has been shown(3) that yield of
isolated tie legs need n o t lead to joint
d i s i n t e g r a t i o n , and it is felt t h a t t h e
n o r m a l c a p a c i t y r e d u c t i o n f a c t o r o f 0.85
allows s u f f i c i e n t account to b e taken of
the variation of effectiveness of d i f f e r e n t
tie sets.
Because the contributions to shear
s t r e n g t h of the joint f r o m c o l u m n a x i a l load
and from b e a m prestress involve d i f f e r e n t
mechanisms, the contributions toward V
may be added.
Stirrup ties should be placed adjacent
to t h e t o p a n d b o t t o m b e a m f l e x u r a l r e i n forcement as in this position they are
e f f e c t i v e in bond transfer from the flexural
bars.
U n i f o r m spacing of tie sets is
consistent w i t h the desired uniform diagonal
crack spacing.
m
c
n
(c)
The advantages for shear d e s i g n w h e r e
b e a m s a r e d e t a i l e d so t h a t p l a s t i c h i n g e s
are forced to form away from the column
face include the prevention of beam bar
yield penetration with consequent loss of
bond in the joint region, the increased
c o n t r i b u t i o n of the c o n c r e t e strut to shear
transfer, and the confinement effects of the
In t h e c a s e of s t i r r u p t i e s o f d i a g o n a l
shape in p l a n , the appropriate component
of each tie leg c r o s s i n g the f a i l u r e p l a n e
in the d i r e c t i o n of the joint s h e a r f o r c e
should be considered.
CJ4.3
Vertical
Joint
Shear
CJ4.3.1
Vertical joint shear reinforcement
is r e q u i r e d t o c o m p l e t e a t r u s s m e c h a n i s m
capable of resisting diagonal compressive
forces.
The d e s i g n of such r e i n f o r c e m e n t
may b e made u s i n g the same a p p r o a c h as that
for t h e h o r i z o n t a l j o i n t s h e a r r e i n f o r c e m e n t .
The vertical joint shear force may be
approximated as suggested in Eq. (CJ-4}.
CJ4.3.2
Generally columns will not yield
when the flexural overstrength of the b e a m s ,
adjacent to the joint, is d e v e l o p e d .
Therefore , the concentrated compression forces
in t h e c o l u m n s m a y b e e x p e c t e d t o b e t r a n s ferred by direct concrete strut action.
These forces also provide partial vertical
restraint to the joint truss mechanism,
thereby reducing the vertical joint steel
requirements.
Case studies indicate that
V
increases sharply with increasing
axial load.
c
v
Where V
may be determined according
t o E q . (J-5) a n d V
may be determined
a c c o r d i n g t o E q . { J - 8 ) , t h e n in c o m p u t i n g
vertical steel
c
h
c
V
V
( C J
"
ECCENTRIC
BEAM-COLUMN
JOINTS
231
When the axes of beams and columns
are eccentric at a connection, secondary
actions such as torsion w i l l b e generated.
The behaviour of joints under the combined
shear and torsion is m o r e c o m p l e x than
t h o s e u n d e r s h e a r a l o n e and is a s y e t
unresearched.
Evidence from earthquakes
shows that such joints are to b e avoided.
Torsion introduced through such details
caused heavy d a m a g e in b u i l d i n g s d u r i n g
the Tokachioki e a r t h q u a k e .
C J 5 . 2 ia) T h e e f f e c t o f t h i s e x t r a l i m i t
on effective joint w i d t h , b j , is to follow
the same assumption m a d e for e c c e n t r i c
joints as shown in Fig. C J 3 , b u t to cover
t h e c a s e of an e c c e n t r i c j o i n t w h e r e t h e
face of the c o l u m n is c l o s e r t h a n 0 . 2 5 h
to the side of the beam for b o t h poss ibilities
of the beam b e i n g narrower or w i d e r than
the column.
c
v
c v = ch ITc
CJ5.0
5 )
W h e r e f r a m e d e s i g n is o n the b a s i s of c o l u m n
p l a s t i c h i n g i n g , for e x a m p l e in the c o l u m n s
o f o n e of two-storey frames or in the top
storey of a multi-storey b u i l d i n g , these
provisions require that the vertical joint
shear r e i n f o r c e m e n t be d e s i g n e d on the
same b a s i s as t h e h o r i z o n t a l j o i n t shear
r e i n f o r c e m e n t for h i n g i n g b e a m s .
(b)
In c i r c u m s t a n c e s w h e r e e c c e n t r i c i t i e s
exceeding the limit of E 4 . 1 c a n n o t be
a v o i d e d , all of the required c o l u m n flexural
s t e e l as w e l l as all of t h e r e q u i r e d joint
s h e a r s t e e l is to b e i n c l u d e d w i t h i n the '
effective joint area, b j h .
Outside of
this area additional column longitudinal
reinforcement and transverse reinforcement
for c o n f i n e m e n t w i l l b e r e q u i r e d .
c
REFERENCES
CJ4.3.3
The simplest solution to p r o v i s i o n
o f v e r t i c a l s h e a r r e i n f o r c e m e n t i s to u s e
the existing column bars w i t h i n the joint
core.
The intermediate bars are not
expected to be fully stressed by column
flexure alone.
If e x t r a b a r s a r e p l a c e d
they need not extend over the full height
of the column, but they need to be adequately
a n c h o r e d in the c o l u m n above and b e l o w the
joint.
-
CJ4.3.4
W h e n only four corner b a r s are
required for the column flexural reinforcement, at least one intermediate vertical
b a r m u s t b e p l a c e d in e a c h f a c e in e a c h
plane of bending.
For larger columns two
or more intermediate vertical column bars,
situated between corner bars, should pass
through the joint with spacing not exceeding
200 m m .
T h i s r e q u i r e m e n t is to allow t r u s s
action consistent with uniformly spaced
diagonal tension cracks.
CJ4.4
1.
2.
3.
4.
Confinement
The diagonal compression stresses
induced within the joint core may be very
l a r g e and h e n c e e f f e c t i v e c o n f i n e m e n t is
necessary.
When plastic hinges could form
in the b e a m s a d j a c e n t to the c o l u m n f a c e s ,
the m i n i m u m transverse reinforcement
r e q u i r e d in t h e j o i n t is the same as the
c o n f i n e m e n t r e i n f o r c e m e n t r e c o m m e n d e d for
the c o l u m n ends immediately above or below
the joint.
However, in two-way frames when
the b e a m p l a s t i c h i n g e s are forced to form
away from the column faces, or where the
column will hinge rather than the beams at
a joint, the beam region adjacent to the
c o l u m n is a s s u m e d to p r o v i d e a d e q u a t e
transverse confinement.
Consequently the
c o n f i n i n g steel may b e reduced to one h a l f
of that otherwise required.
To safeguard
column bars against buckling, particularly
those at the corners of rectangular column
sections which may be outside the joint
c o r e , t h e tie spacing is l i m i t e d .
5.
P a r k , R. a n d P a u l a y , T . , " B e h a v i o u r o f
R e i n f o r c e d C o n c r e t e E x t e r n a l Beam--Column
J o i n t s u n d e r C y c l i c L o a d i n g " , V o l . 1,
Paper 88, Proceedings 5th W o r l d Conference
on Earthquake Engineering, R o m e , 1973,
pp 772-781.
P a r k , R. a n d T h o m p s o n , K . J.,
"Progress
Report on Cyclic Load Tests on Prestressed,
Partially Prestressed and Reinforced
Concrete Interior Beam-Column Assemblies",
Bulletin of the N . Z . National Society
f o r 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 . 1, M a r c h , 1 9 7 5 , p p 1 2 - 3 7 .
B l a k e l e y , R . W . G . , E d m o n d s , F. D . , M e g g e t ,
L. M . , a n d P r i e s t l e y , M . J. N . , " P e r f o r m ance of Large Reinforced Concrete BeamColumn Joint Units Under Cyclic Loading",
Proceedings 6th World Conference on
Earthquake Engineering, New Delhi,
January 1977, 6 pp.
B l a k e l e y , R. W . G . , M e g g e t , L . M . a n d
Priestley, M. J « N . , "Seismic Performance
of Two Full Size R e i n f o r c e d C o n c r e t e
Beam-Column Joint U n i t s " , Bulletin of
the N . Z . National Society for Earthquake
E n g i n e e r i n g , V o l . 8, N o . 1 , M a r c h , 1 9 7 5 ,
pp 38-69.
F e n w i c k , R. C .
and I r v i n e , H. M. ,
"Reinforced Concrete Beam-Column Joints
for Seismic L o a d i n g " , B u l l e t i n of the
N J . N a t i o n a l Society for E a r t h q u a k e
Engineering, Vol. 10, No. 4, December
1977.
6.
7.
ACI-ASCE Committee 352, "Recommendations
for Design of B e a m - C o l u m n J o i n t s in
Monolithic Reinforced Concrete Structures",
A C I J o u r n a l , P r o c e e d i n g s V 6 9 , N o . 7,
July 1976, pp 375-393.
H a n s o n , N. W . , "Seismic R e s i s t a n c e of
C o n c r e t e F r a m e s w i t h G r a d e 60 R e i n f o r c e m e n t , Journal of the Structural Division,
A S C E , V o l . 97, S T 6, J u n e 1 9 7 1 , p p
1685-1700.
Paper
received
25 N o v e m b e r ,
1977.
232
I
I
T"
c
c
V"
C's
7 7 7 "
T
\
V
fv
/ - / f t
V
*
r,
V'"
fc?
cm
T
»'
V'"
T
i
t
FORCES ON INTERNAL JOINT
FORCES ON EXTERNAL JOINT
Transfer of concrete
compression forces
STRUT
ACTION
Transfer of steel
bond f o r c e s
TRUSS
F I G U R E C J 1 : B E A M - C O L U M N J O I N T FORCES A N D I D E A L I Z E D
M E C H A N I S M S OF RESISTANCE.
ACTION
whichever
is smaller
C J 3 : EFFECTIVE JOINT A R E A FIGURE
FIGURE C J 2 : F R A M E D I M E N S I O N S AT INTERNAL BEAM-COLUMN
JOINT FIGURE
1 -0
reinforcement
A
0-75
' •. ' ,
" I
s(o
•.
CO I
|-.
.
2 ('Cj
Shear
+0-25
CD
V
jh
|v]
Mi
fa
•.' ..X|.'-.
0-5CL
Vjh (v)
0-50
• • • . • ' • • • • • • • • • • • • ^
0-2E
*S1 <
f
f
V
c
n
= D
C O S oc
V
r
v
- D
sin
oc
S2 <
s 3
f
Y
f
Y
«f
0-75
X\X^^
Concrete
strut
NN^v
^^^^^^^^^^^^
Y
Vch-tfco!*'
v
cv
=D'sin«'
C J 4 : M E C H A N I S M OF S H E A R T R A N S F E R BY A DIAGONAL S T R U T IN
" E L A S T I C " BEAM-COLUMN J O I N T S
"0-2
-0-1
Tension
0-1
0-2
0-3
CK
Compression
0-5
0-6
,1-00-7
C
A
t
N
g
fc
u
FIGURE C J 5 : NOMINATED CONTRIBUTION OF DIAGONAL S T R U T ACTION
TO V E R T I C A L AND HORIZONTAL J O I N T SHEAR R E S I S T A N C E
£
go
234
ADDENDUM:WORKED
EXAMPLES
The following worked examples illustrate
application of the provisons of this section
to d e s i g n of b e a m - c o l u m n j o i n t s .
The
examples chosen are a conventional beamcolumn joint, designed to form plastic
h i n g e s in t h e b e a m s a d j a c e n t to t h e j o i n t ,
w i t h a n d w i t h o u t c o l u m n a x i a l l o a d , a n d an
"elastic" joint with beam plastic hinges
designed to form the required distance away
from the column face.
D e t a i l s of all c o n c e n t r a t e d forces in
the m e m b e r s h a v e b e e n s h o w n for i l l u s t r a t i o n .
Only the c o n c e n t r a t e d b e a m forces and column
shear need be calculated during routine design.
In d e r i v a t i o n o f t h e d i a g o n a l s t r u t f o r c e ,
D, t h e a s s u m p t i o n h a s b e e n m a d e i n E x a m p l e s
1 and 2 t h a t t h e r e is a l i n e a r r a t e of
c h a n g e o f s t r e s s in t h e f l e x u r a l r e i n f o r c e m e n t
b e t w e e n the m a x i m u m tension and compression
values at opposite column faces.
Experimental
e v i d e n c e s u p p o r t s this assumption at the
stage of c y c l i c loading i l l u s t r a t e d in the
example, before wide full-depth cracks have
formed in the beams and there has b e e n yield
penetration along the flexural reinforcement
into the joint.
The bond forces from the
flexural reinforcement within the assumed
bounds of the principal diagonal compression
strut have b e e n taken as contributing to the
p r i n c i p a l d i a g o n a l s t r u t f o r c e , D.
In
Example 3 the simplifying assumption has
b e e n m a d e that the f l e x u r a l steel c o m p r e s s i v e
f o r c e o n l y is a n c h o r e d w i t h i n t h e b o u n d s
of the d i a g o n a l strut and contributes to
that force.
In all c a s e s it h a s b e e n
assumed that beam and column shear forces
are t r a n s f e r r e d in the r e s p e c t i v e m e m b e r
compression zones only.
T h e p r o c e d u r e i l l u s t r a t e d in E x a m p l e s
1 and 2 for t h e c a l c u l a t i o n of t h e m e a n
e f f e c t i v e area of the tie sets w a s as f o l l o w s .
L i n e s c o r r e s p o n d i n g to the i n t e r s e c t i o n of
the plane of the corner-to-corner diagonal
crack and the planes of each tie set w e r e
projected on to the plan view of the column.
T h e sum of the components of area of the
tie l e g s , A ^ , c r o s s i n g the c r a c k in the
d i r e c t i o n of the joint shear force has b e e n
shown for each tie set.
A mean effective
area of all tie sets has then been calculated.
A simpler but more conservative procedure
would h a v e b e e n to n e g l e c t the legs of the
rectangular tie not extending full depth
in each s e t , and d i r e c t l y d e r i v e the m e a n
e f f e c t i v e a r e a a s (4 + /2) A £ = 5.4 A £ .
This
p r o c e d u r e w a s f o l l o w e d i n E x a m p l e 3.
235
M :995kNm
<^ CT°825kN
4 9 2 6 mm
C
2
0.013
275,
f*
30,
3 4 0 MPa
f <*
4 5 MPa
(^=1370
C<~ 3 8 0
8-D28
3
| F
O
1256
M*=898kNn
M* =1232kNm
cr
V =331kN
b
T=1256
Cs=^00
6-D28
o a
-450mm
BEAM
o
'
<
CM
t o
CD
%mK
jjjh16-HD32
mi5
+
^
^
+
t;
+
^
+
S2
!£
<S
i£j
4-
It
C
o
e
(a) H o r i z o n t a l J o i n t Shear
V.. = 1 2 5 6 + 1 6 7 4
825
2105 kN
Jh
450 + 350 = 800 }> 700 mm
J
2105/(0.85 x 700 x 700) = 5.05 MPa
< 1.5/30 = 8.2 MPa
V
= 2105/0.85 - V
s h
Try 5 tie sets, A
J h
c h
= 2476 kN ( V = 0 )
ch
h _
2476kN
=-V
^H
= |476kN
s
=
275MPa
9
0
Q
^
4
"
9004.
lt
Jl
5 7 ^ 6
'
Use 5 sets R20 ( A = 3 1 4 m m )
h
A
=
=
2
7
y
m
m
2
2
£
(b)
Vertical
v
jv
J o i n t Shear
2105x900/700 = 2706 kN
Vjh
b/ c
s c J v (1
x
A
h
h
Cf
0.6A f< )
V
u
+
g
V
12868 mm !
2
Pt
0.026
380 MPa
30 MPa
= 1 x 2706/2 (1 + 0 ) = 1353 kN
= 2706/0.85 - 1353 = 1830 kN
AjV
-700mm
COLUMN
THROUGH
V /fy
s v
V
1830/380 = 4 8 1 6 m m
6 ^ HD32 (4825 m m ) O.K.
2
JOINT
E X A M P L E 1: C O L U M N W I T H O U T
AXIAL
LOAD
2
236
M = 9 9 5 k N m ^j^'l
Nu=U10kN (0-3fc Ag)
A'
s
V |=825kN
4926 mnr
=
C 0
340 MPa
275, f*
30, f'^
c
=
45 MPa
Cc=137i
C = 380
T = 494
s
Mi=898kNm
V = 331kN
b
T=1256
= 0.25
(1 +^)v'(0.3~0. 1 )30 (700x700)
(J-3)
= 660 kM
u
2
5
1816 kN
1816 kN = 6604 m m
Vj ^V
v
J h
x h /h
b
c
= 2105x900/700 = 2706 kN
:
2029 kN
2029 = 1155 kN
Ajv = V
COLUMN THROUGH JOINT
\
s v
6^HD
/f
y v
=• 11.55/380 = 3039 m m
32 (4825 m m ) O.K.
E X A M P L E 2 : C O L U M N W I T H A X I A L LOAD
2
2
2
237
Cj N
C
c
=390
u
=0
2510 m m
s
M=249kNm
2
0.0167
500
275 MPa
f
30 MPa
f
c
Cc = 4 7 6
C =2U
-D20
S
500mm
8 ~D20
r>
f =275MPa
s
when
350mm-
at
plastic
d
hinge
BEAM
f =340MPa
s
Horizontal
J o i n t Shear
476 + 214 + 690 - 178 = 1202 kN
1202/(0.85x400x600) = 5.9 MPa
'jh
< 1 .5 / f = 8.2 MPa
c
f\
A'
ch
c
V..
2
C.N
0.6 A f
M
s
gc
1202
1 x - ^ r - (1 + 0) = 601 kN
= 1202/0.85 - 6 0 1 = 813 kN
sh
sh |13kN
4 tie sets, Ajh
275MPa
. yh
2956
185 m m
4x4
.-. Use 4 sets R16 ( A = 2 0 1 m m )
w
=
=
2
9
5
6
m
m
2
f
2
2
£
Vertical
J o i n t Shear
V. = 390+110+500-89 = 911 kN (V..x b=1002)
jv
jh —
. . .
C.N
c
V = s c liv (1 + - L "
)
A
e
sc
911
1 x
V
V= 8 9 k N
s v
A
= 911/0.85 - 455 = 617 kN
., sv'V
V
s v
(1 + 0) = 455 kN
617/380
1623 m m
Use 6 * HD 20 (1884 m m )
2
H = 178kN
6400
EXAMPLE
3: " E L A S T I C "
BEAM-COLUMN
JOINT
2