Development Length - Dr. Bart Quimby

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Development Length

CE A433


RC Design

T. Bart Quimby, P.E., Ph.D.

Revised Spring 2009

Consider a bar embedded in a
mass of concrete

P =
t
*[L
b
*
p
*d
b
]

P =
s

* [
p
*d
b
2
/4]

t

= P / [L
b
*
p
*d
b
]
<

t
max

P
<

t
max

* [L
b
*
p
*d
b
]

s

= P/ [
p
*d
b
2
/4]
<

s
max

P
<

s
max

* [
p
*d
b
2
/4]

To force the bar to be the weak link:
t
max

* [L
b
*
p
*d
b
]
>

s
max

* [
p
*d
b
2
/4]


L
b

>

(
s
max

/
t
max
)* [d
b
/4]

L
b

d
b

Development Length


L
d

= development length


the shortest distance over which a bar can achieve it’s
full capacity


The length that it takes a bar to develop its full
contribution to the moment capacity, M
n

C
c

T
s

M
n

= (C or T)*(dist)

M
n

0

L
d

Steel Limit,
s
max


Using the bilinear assumption of ACI 318:

s
max

=
+

f
y



L
b

>

(f
y

/
t
max
)* [d
b
/4]


L
b

>

f
y

* d
b

/ (4*
t
max
)


Concrete Bond Limit,
t
max


There are lots of things that affect
t
max


The strength of the concrete, f’
c


Type of concrete (normal weight or light weight)


The amount of concrete below the bar


The surface condition of the rebar


The concrete cover on the bar


The proximity of other bars transferring stress to the
concrete


The presence of transverse steel

Concrete Strength, f’
c


Bond strength,
t
max
, tends to increase with
concrete strength.


Experiments have shown this relationship
to be proportional to the square root of
f’
c
.


Type of Concrete


Light weight concrete tends to have less
bond strength than does normal weight
concrete.


ACI 318
-
08 introduces a lightweight
concrete reduction factor,
l
, on
sqrt
(
f’
c
) in
some equations.


See ACI 318
-
08, 8.6.1 for details

Amount of Concrete Below Bars


The code refers to “top
bars” as being any bar
which has 12 inches or
more of fresh concrete
below the bar when the
member is poured.


If concrete > 12” then
consolidation settlement
results in lower bond
strength on the bottom side
of the bar


See ACI 318
-
08, 12.2.4(a)

Surface Condition of Rebar


All rebar must meet ASTM requirements
for deformations that increase pullout
strength.


Bars are often surface coated is inhibit
corrosion.


Epoxy Coating


The major concern!


Galvanizing


Epoxy coating significantly reduces bond
strength


See ACI 318
-
08, 12.2.4(b)

Proximity to Surface or Other Bars


The size of the concrete “cylinder” tributary to
each bar is used to account for proximity of
surfaces or other bars.

2D


3D

Presence of Transverse Steel


The bond transfer tends to cause a splitting plane


Transverse steel will increase the strength of the
splitting plane.


See text for other possible splitting locations

The ACI 318
-
08 Development
Length Equation (ACI 318
-
08 12.2)

b
b
tr
b
s
e
t
c
y
d
d
d
K
c
f
f
L

































5
.
2
,
min
)
7
.
1
,
min(
40
3



l
sn
A
K
tr
tr
40

The Modifiers



t
, Modifier for reinforcement location


1.3 for top bars, 1.0 for other bars



e
, modifier for epoxy coated bars


1.5 when cover < 3d
b

or clear spacing < 6d
b


1.2 for other epoxy coated reinforcing


1.0 for non
-
epoxy coated reinforcing


The product,

t

e
, need not exceed 1.7

More Modifiers…



s
, Modifier for bar size


0.8 for #6 and smaller


1.0 for #7 and larger


l
, Modifier for lightweight concrete


ACI 318
-
08, 8.6.1


l
= 1.0 for normal weight concrete


l

as low as 0.75 for the lightest weight
concrete

The Transverse Reinforcement
Index,
K
tr

(ACI 318
-
08 Eq. 12
-
2)


A
tr

= total cross sectional area of
all transverse reinforcement which
is within the spacing, s, and which
crosses the potential plane of
splitting through the
reinforcement being developed.


s = maximum C
-
C spacing of
transverse reinforcement within
the development length


n = number of longitudinal bars
being developed along the plane
of splitting.

sn
A
K
tr
tr
40

The outer bars are #10, the center one is #6, the others are #8

Other Development Lengths


Development in Compression: ACI 318
-
08
12.3


Development of standard hooks in
tension: ACI 318
-
08 12.5


There are some very specific cover and/or
confinement requirements


Mechanical connectors (such as bearing
plates at the beam ends) may also be
used.

Effect on Moment Capacity


Moment Capacity,
f
M
n
, is a function of “x”


If different bars develop differently then
you need to look at the “contribution” that
each bar makes to the moment capacity

Moment Capacity Diagram

Moment Capacity
0
100
200
300
400
500
600
0
50
100
150
200
250
300
350
400
X (in)
phiPm (ft-k)
Cutting Bars


The
f
M
n

diagram can be made to more closely
fit the M
u

diagram by terminating or cutting bars
when they are no longer needed. (ACI 318
-
08
12.10.3)

Moment Capacity
0
100
200
300
400
500
600
0
50
100
150
200
250
300
350
400
X (in)
phiPm (ft-k)
End of #6 bar

End of #8 bars

End of #10 bars

>

max(d, 12d
b
)

>

max(d, 12d
b
)

Beam Profile Showing Bar Cutoff
Locations