November,
November, 1968
U. S. Department of
of Agriculture
U.
Soil
S o i l Conservation Service
Engineering
Ehgineering Division
Design Branch
Design Note No. 5*
Subject:
l e x u r a l and Anchorage Bond S
tresses
Some Comments
Comments on F
Flexural
Stresses
National
Natf o n d Engineering Handbook, Section 6 eestablishes,
s t a b l i s h e s , ssUbject
u b j e c t tto
o ccertain
ertain
modifications,
modifications, tthe
h e American Concrete IInst
n s t i tute
t u t e Standard ""Building
~ u i l d i n gCode
Requirements for
Concrete" aass tthe
basic
reinf o r Reinforced concrete"
he b
a s i c design code ffor
o r reSnSee
NM-6,
4.2
forced concrete in
the
S~il
Conservation
Service.
NEH-6,
4.2
i n t h e Soil
he
o n c e r n b g tthe
Design Codes
Codes and Criteria.
C r i t e r i a . There has been some question cconcerning
f f e c t of tthe
h e ffirst
i r s t sentence contained
background,
background, interpretation{
i n t e r p r e t a t i o n and eeffect
ih
ih ACI Code section
s e c t i o n 1301(c).
l30l(cj.
The chapters on bond in
of tthe
ACI
(ACI 318-63)
318-63)
i n tthe
h e llatest
a t e s t rrevision
e v i s i o n of
he A
C I Code (ACT
s h i f t iin
n the
t h e philosophy of
o r bond.
contain an important shift
of providing ffor
bond. The
" f l e x u r a l bond" and "anchorage or
o r development bond" have been
terms "flexural
i s a function
f'unction of
h e rrate
a t e of
F l e x u r a l bond stress
s t r e s s is
introduced. Flexural
of tthe
of change ooff
moment with rrespect
Anchore s p e c t to
t o distance
d i s t a n c e along tthe
h e span, tthat
h a t iis,
s , shear. .An.chors t r e s s is the
t h e average bond stress
s t r e s s between a p
o i n t of
ar
age bond stress
point
of peak bbar
i s zero.
s t r e s s and the
t h e end of the
t h e bar
b a r where tthe
h e stress
s t r e s s is
stress
zero.
I n members in
i n which the
t h e longitUdinal
l o n g i t u d i n a l ttension
e n s i o n steel
s t e e l is p
a r a l l e l tto
o tthe
he
In
parallel
t h e nominal
nomind flexural
f l e x u r a l bond stress
s t r e s s ffor
o r tthe
h e ttension
e n s i o n ssteel
teel
compression face, the
a t any section
s e c t i o n is given by
at
u
= 2::0
v
jd"
C r i t i c a l sections
s e c t i o n s for
f o r flexural
f l e x u r a l bond stresses
s t r e s s e s for
f o r ttension
ension b
a r s occur
Critical
bars
t h e rate
r a t e of change of moment is
i s greatest
g r e a t e s t or
o r where tthe
h e steel
steel p
eriwhere the
periis least,
l e a s t , or
o r both. For simple spans, critical
c r i t i c a l sections
s e c t i o n s are
are a
he
meter is
att tthe
f a c e s of supports. For continuous spans: for
f o r negative steel,
s t e e l , critical
critical
faces
s e c t i o n s are
a r e located
l o c a t e d at faces
f a c e s of supports
supports and at
a t locations
l o c a t i o n s where b
ars
sections
bars
terminate;
f
o
r
p
o
s
i
t
i
v
e
s
t
e
e
l
,
c
r
i
t
i
c
a
l
s
e
c
t
i
o
n
s
a
r
e
at
p
o
i
n
t
s
of
terminate; for positive steel, critical sections are
points of infflection.
l e c t ion.
in its
its
fllthough the
t h e above
above relation
r e l a t i o n is
i s exact for
f o r the
t h e conditions assumed in
Although
i e
beam of constant depth and constant longitudinal
l o n g i t u d i n a l steel
steel
derivation, i.e.}
made
up
of
equal
b
a
r
s
i
z
e
s
all
i
n
one
l
a
y
e
r
,
t
h
e
r
e
l
a
t
i
o
n
i
s
more
f
d
ealmade up
equal. bar sizes all in
layer, the relation is
idealiistic
s t i c than realistic.
r e a l i s t i c . Flexural
F l e x u r a l bond stress
s t r e s s distribution
d i s t r i b u t i o n is
i s actually
a c t u a l l y much
more complex
complex than
t h a n the
t h e above
above relation
r e l a t i o n suggests. The distribution
d i s t r i b u t i o n is
i s also
also
more
a
f
f
e
c
t
e
d
by
bond
concentrations
and
complications
a
r
i
s
i
n
g
from
such
affected
concentrations
complications arising
usual assumption that
t h a t concrete takes
t a k e s no tension, the flexflext h i n g s as
a s the
t h e usual
things
ural and diagonal tension
t e n s i o n cracking of concrete, the
t h e presence or
o r absence
ural
web reinforcement, and the
t h e cutting
c u t t i n g off
o f f or
o r bending of longitUdinal
longitudinal b
ars
of web
bars
l o n g been recognized that many
a c r o s s the
t h e web
web of the
t h e beam. Thus, it has long
across
. .,
&anch,
Edwin S. Alling
A l l i n g of the
t h e Design Unit, Design Branch,
*Prepared by Edwin
Hyatt s v i l l e , Maryland
HyattSVille,
bond s t r e s s c a l c u l a t i o n s with t h e f l e x u r a l bond s t r e s s formula a r e not
very f a c t u a l .
2
n e x m a l bond s t r e s s e s a l s o e x i s t between concrete and l o n g i t u d i n a l
compression s t e e l , However, such s t r e s s e s are not c r i t i c a l and need
bond
calculations
with F
the
are not
not bestress
considered
i n design.
l e xflexural
u r a l bondbond
s t r e sstress
s e s f oformula
r compression
very
factual.
s t e e l a r e low because t h e change i n t o t a l compression between any two
s e c t i o n s i s shared between t h e concrete and t h e s t e e l .
Flexural bond stresses also exist between concrete and longitudinal
compression
such
are not critical
and need
I f a r e i n f o r csteel.
i n g b a rHowever,
i n a beam
has stresses
enough embedment
i n concrete,
it
not
be
considered
in
design.
Flexural
bond
stresses
for
compression
cannot be p u l l e d out of t h e concrete. The minimum embedment l e n g t h
steel are low
because the
changea.-given
in total
bar compression
f o r c e , T = between
f s h , isany two
necessary
t o develop,
by bond,
sections is shared between / the
and the steel.
- fconcrete
sfis' f ,D
rL=-=
B
Ti'
If a reinforcing bar in a beam
has
"*"--% **a
0"enough embedment in concrete, it
cannot
concrete.
minimum
embedment
I f t h e be
a c t pulled
u a l l e nout
g t h of
o f the
a bar,
from &y The
point
of given
s t e e l length
stress t o
necessary
to
develop,
by
bond"~,~.,,,~~,~~en
.
..
J:?~
force,
T
=
fsAs,
is
length
i t s n e a r e r f r e e end, is equal t o o r l a r g e r than t h e above minimum
f sAs " f sD
( c a l l e d development l e n g t hr"""'-'
o r anchorage
l e n g t h ) , t h e b a r w i l l not f a i l
=s""""Ij:U.
by bond. For instance, i f(\, ..\Lt h =
e ~
given
t eUe l s t r e s s is equal t o t h e yield.
0
."~ """""''''">,,
y i ei"~=l d ,,~'i n~ g-~ • of t h e s t e e l , r a t h e r than by bond
s t r e s s , t h e b a r would f a i l by
a bar,
from l oany'
of given
fIf
a i lthe
u r e actual
. Thislength
i s t r u of
e even
though
c a lpoint
i z e d bond
s l i p ssteel
occurstress
i n t h eto
its
nearer
free
end,
is
equal
to
or
larger
than
the
above
minimum
length
immediate v i c i n i t y of f l e x u r a l o r diagonal t e n s i o n cracks. Permissible
(called
development
length
or
anchorage
length),
the
bar
will
not
fail
bond s t r e s s e s have been e s t a b l i s h e d , i n l a r g e p a r t , by beam t e s t s which
by
bond.
For
instance,
if
the
given
steel
stress
is
equal
to
the
yield.
simulate actual. conditions, i n preference t o t h e formerly more prevalent
stress,
fail by yielding of the steel, rather than by bond
bond
p u l the
l o u t bar
t e swould
ts.
failure. This is true even though localized bond slips occur in the
inunediate bond
vicinity
Permissible
Anchorage
s t r e of
s s , flexural
c a l c u l a t eor
d diagonal
as thoughtension
it werecracks.
uniform over
the
bond
stresses
have
been
established,
in
large
part,
by
beam
tests
h and
embedded l e n g t h of a bar, i s a f u n c t i o n of b a r f o r c e and b a r l e n g t which
simulate
actual conditions,
more
i n f othe
r c i nformerly
g b a r may
be prevalent
developed,
i s not determined
d i r e c t l y byin s preference
h e w . A r e to
bond
pullout tests.
o r anchored,
i n a region of t e n s i o n o r a region of compression o r p a r t i a l l y i n both. For instance, negative s t e e l over t h e support of a conAnchorage
bond m
stress,
as though
were uniform
over moment
the
tinuous member
y be p calculated
a r t l y developed
i n t h it
e region
of negative
embedded
length
of
a
bar,
is
a
function
of
bar
force
and
bar
length
and p a r t l y developed i n t h e region of p o s i t i v e moment by extending t hand
e
determined
reinforcing
sist enot
e l beyond
t h e pdirectly
o i n t of i by
n f l eshear.
c t i o n , AThus,
f o r l o nbar
g i t umay
d i n abe
l s developed,
teel in
or
in a region
tension orf o ar region
f l e xanchored,
u r a l members,
a main of
requirement
s a f e t y of
a g acompression
i n s t bond f a or
i l uparre is
tially
in bboth.
For instance,
negative
over the
support
t h a t each
a r be provided
anchorage
l e n gsteel
t h adequate
on both
s i d of
e s aof continuous
developed
every s emember
c t i o n . may
I f be
t h epartly
embedment
l e n g t hini s the
i n sregion
u f f i c i e of
n t , negative
s p e c i a l moment
anchorand
region
of positive
age partly
must b edeveloped
provided tin
o the
ensure
adequate
bond s t rmoment
e n g t h . by extending the
steel beyond the point of inflection. Thus, for longitudinal steel in
flexural
main requirement
for f lsafety
Ln t h e p amembers,
s t , as a ageneral
rule, nominal
e x u r a lagainst
bond s t bond
r e s s efailure
s were is
that
each
bar
be
provided
anchorage
length
adequate
on
both
sides
of
l i m i t e d by design s o t h a t allowable values were not exceeded a t any
every
section.
If
the
embedment
length
is
insufficient,
special
anchorsection. Currently however, i n t h e l i g h t of questions regarding t h e
age
ensure
bond strength.
v a l i must
d i t y be
of provided
f l e x u r a l to
bond
s t r e s adequate
s computations
and an increased dependence
on anchorage bond s t r e s s , nominal f l e x u r a l bond s t r e s s e s t h a t a r e locaLly
In the past,
as a general
nominalbyflexural
bond According
stresses were
M I 318-63.
higher
t h a n allowable
a r e rule,
permissible
t o the
limited
that allowable
were not
exceeded
any
f f i c i e nso
t anchorage
l e n g t hvalues
i s provided
t o reduce
t h at
e anchorage
Code, i f bys udesign
section.
however,
in the
light
questions
the
times
t h eofusual
( s p e c iregarding
f i e d ) allowable
bond
s t r e s Currently
s t o not more
than 0.8
validity
value, f l eof
x uflexural
r a l bond bond
need stress
not be computations
considered. and
Thus,ant hincreaseCl
e n e c e s s i dependence
t y of checkon
bond stress,
stresses
are locally
i n ganchorage
f l e x u r a l bond
s t r e s s e snominal
may be flexural
avoided, bond
according
t o t hthat
e Code,
if
higher
thanl e nallowable
permissible
ACI 318-63.
According to the
provided
t h a t a rby
e nowhere
l e s s than
anchorage
g t h s are are
Code, if sufficient anchorage length is provided to reduce the anchorage
bond stress to not more than 0.8 times the usual (spec ified) allowable
value, flexural bond need not be considered. Thus, the necessity of checking flexural bond stresses may be avoided, according to the Code, if
anchorage lengths are provided that are nowhere les s than
fsD
a
a
.
,+=
)*"
L
= 4(O.8ur
3
It should be noted tthat
h a t the
t h e necessary anchorage llength
e n g t h ffor
o r tension
bars
of' tthe
bar
b a r s is
i s proportional
proportional. to
t o the
t h e s'!uare
square of
he b
a r diameter ssince
i n c e tthe
he
a.llowable
diameter. This
o diameter.
allowable bond
bond. strens
s t r e s s is inversely proportional tto
indicates
bars, aass compared tto
i n d i c a t e s the
t h e superiority
s u p e r i o r i t y of
of small diameter bars,
o
large
viewpoint of
of bond,
bond. The use of
of small
l a r g e diameter bars, from the
t h e viewpoznt
bars reCluires
of bars
requires shorter
s h o r t e r anchorage
mchorage llengths
e n g t h s and a llarger
a r g e r number of
and thus minimizes difficulties
bond.
d i f f i c u l t i e s in
i n bond.
Experience has shown that
practice
of providing reinforcement
t h a t the
the p
r a c t i c e of
p e r h e t e r , LO,
Co, sufficient
s u f f i c i e n t to
t o satisfy
s a t i s f y fflexural
l e x u r a l bond sstress
t r e s s requirements
perimeter,
reCluirements
produces satisfactory
s a t i s f a c t o r y strUctures
s t r u c t u r e s under tthe
h e environmental conditions
i n Soil
S o i l Conservation Service hydraulic iinstallations.
n s t a l l a t i o n s . Pro
encountered in
ProCo,
t
o
c
o
n
t
r
o
l
f
l
e
x
u
r
a
l
bond.
s
t
r
e
s
s
sSten
vision
of
adequate
perimeter,
La,
to
control
flexural
stress
often
vision
perimeter,
r e s u l t s in
i n additional
a d d i t i o n a l steel
s t e e l over tthat
h a t required by area,
results
area, As.
As. This addiadditional
of tthe
t i o n a l steel
s t e e l Serves
serves to
t o distribute
d i s t r i b u t e and llimit
i m i t tthe
h e cracking of
h e concrete
t o increase the
t h e durability
d u r a b i l i t y of a structure.
structure. A
r t h e r , it shou.'ld
and hence to
Further,
shoQld
t h a t the
t h e ACI
A C I Code provides for
f o r minimum requirements
be recognized that
reCluirements and
i s oriented toward building frames
frames with ttheir
h e i r more con"iolled
is
controlled environenvironr a t h e r than toward hydraulic structures.
s t r u c t u r e s . Hence, it is conclud.ed
ment rather
concluded
t h a t the
t h e practice
p r a c t i c e of
o f holding flexural
f l e x u r a l bond stresses
s t r e s s e s within allowa,ble
that
allowable
s u b j e c t tto
o review
l i m i t s should be continued. This conclusion is SUbject
limits
revj.ew at
at
a s further
f u r t h e r satisfactory
s a t i s f a c t o r y experience iin
n neglecting fflexural
le2~~a.l
such time as
i s reported in
i n the
t h e literature
l i t e r a t u r e to
t o the
t h e profession.
bond is
profession.
-
-.
The above considerations explain why National Ehgineering
The
Engineering Handbook
was recently
r e c e n t l y issued. The notice
n o t i c e modifies NEH-6
o remove
Notice 6-2 was
NEH-6 tto
t h e option in
i n treatment of
of bond that
t h a t existed
e x i s t e d aass a
e s u l t of
h e 1963
the
a rresult
of tthe
1963
r e v i s i o n of the
t h e ACI Code.
revision
USDA-SCS·HYATTSVILLE,
MD.
1968