Chapter 7 بسم الله الرحمن الرحيم Design of Concrete Structure I University of...
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Transcript of Chapter 7 بسم الله الرحمن الرحيم Design of Concrete Structure I University of...
Chapter 7
الرحمن الله بسمالرحيم
Design of Concrete Structure I
University of Palestine
Instructor:
Eng. Mazen Alshorafa
Page 1
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Concept of Bond Stress
Concrete
Reinforcing bar
C
T
T=Asfy
Bond stress
T2=fs2Ab
dbµ=Bond stress
T1=fs1Ab
l
M
fs2=fs1+∆fs
Bond stresses are existent whenever the stress or force in a reinforcing bar changes from point to point along the length of the bar in order to maintain equilibrium.
Page 2
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Concept of Bond Stress
C
T
T
Bond stress
M
L
forceBondTF 0.0
ldffd
bavgssb )(
4 12
2
avg
bss dffl
412
)(,' bdfkfck
T2=fs2Ab
dbµ=Bond stress
T1=fs1Ab
l
fs2=fs1+∆fs
Equilibrium Condition for Rebar
µavg= bond stress (coefficient of friction)
Page 3
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Mechanism of Bond Transfer
(a )Forces on bar
(b )Forces on concrete
Radial longitudinal
(c )Components of forces on concrete
(d )Splitting stresses
A smooth bar embedded in concrete develops bond by Adhesion
between concrete & reinforcement, and a small amount Friction.
Note: These bonds are quickly lost when the bar is loaded in tension
On the other hand, a deformed bar generates bond by friction and by
bearing on the deformations of the bar against the concrete
Page 4
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Mechanism of Bond Transfer
Splitting cracks result in loss of bond transfer.
Reinforcement can be used to restrain these cracks.
The load at which splitting failure develops is a function of :
1. The minimum distance from the bar to the surface of the concrete
or to the next bar. The smaller the distance, the smaller is the
splitting load.
2. The tensile strength of the concrete.
3. The average bond stress. The higher the average bond stress, the
higher is the splitting resistance.
Page 5
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Mechanism of Bond Transfer
If the concrete cover and bar spacing are large compared to the bar
diameter, a pullout failure can occur.
Page 6
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length
The development length ld is shortest length of bar in which the bar
stress can increase from zero to the yield strength, fy
The development Lengths are different in tension and compression,
because a bar loaded in tension is subject to in-and-out bond stresses
and hence requires a considerably longer development length
failurebondatvaluetheiswheredf
l avguavguavg
byd
,,
,4
Page 7
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Tension
5.2d
kcin which 30cm,d
d
kc
λγβα
fc'
f
7
2l
b
trb
b
tr
yd
'fc
According to ACI Code, the development length for deformed bars in tension is given by
to safeguard against pullout type failure
where,
ld = development length, cm
db = nominal diameter of bar, cm
fy = specified yield strength of reinforcement, kg/cm2
= square root of specified compressive strength of concrete, kg/cm2
C = spacing or cover dimension, cm
Ktr = transverse reinforcement index
Page 8
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Tension [contd.]
C is the smaller of
(a) the smallest distance measured from the center of the bar to the nearest concrete surface
(b) one-half the center-to-center spacing of bars being developed.
α is a bar location factor (a) Horizontal reinforcement so placed that more than 30 cm of fresh concrete is cast in the member below the development length or
splice……………………………………………………………………. 1.3
(b) Other
reinforcement………………………………………………………….. 1.0
β is a coating factor that reflects the adverse effects of epoxy coating
(a) Epoxy-coated bars or wires with cover less than 3db
or clear spacing less than 6db …………………………………………..
1.5 (b) All other epoxy-coated bars or wires………………………………...
1.2 (c) Uncoated
reinforcement……………………………………………………… 1.0
Page 9
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Tension [contd.]
However, the product αβ is not to be greater than 1.7
γ is a reinforcement size factor that reflects better performance of the smaller diameter reinforcement (a) Φ20mm and smaller bars.……………………………………………….. 0.8 (b) Φ22mm and larger bars.…………..…….………………………………. 1.0
λ is a lightweight aggregate concrete factor that reflects lower tensile
strength of lightweight concrete, & resulting reduction in splitting
resistance. (a) When lightweight aggregate concrete is used…….……..…….
0.8 (b) When normal weight concrete is used…………………..………….
1.0
Page 10
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Tension [contd.]
ns
fAk yttr
tr 100
Atr
Potential plane of splitting
Ktr is a transverse reinforcement index that represents the contribution of confining reinforcement
WhereAtr = total cross sectional area of all transverse reinforcement within
the spacing s, which crosses the potential plane of splitting along the reinforcement being developed with in the development length cm2
fyt = specified yield strength of transverse reinforcement, kg/cm2
s = maximum center-to-center spacing of transverse reinforcement within development length ld , cm.
n = number of bars being developed along the plane of splitting.
Note: It is permitted to use Ktr= 0.0 as
design simplification even if transverse reinforcement is present.
Page 11
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Tension [contd.]
Excessive ReinforcementAccording to ACI Code, reduction in development length is allowed
Where As provided > As required. the reduction is given by
-Except as required for seismic design
-Good practice to ignore this factor, since use of structure may
change over time.
providedA
requiredA factorReduction
s
s
Page 12
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 1
Determine the development length required for the uncoated bottom bars as shown in figure.Use fc’ = 250 kg/cm2 normal weight concrete and
fy = 420 kg/cm2
Solution:
α=1.0 for bottom bars, β=1.0 for uncoated bars
α β =1.0 <1.7 OK
γ=0.8 for Φ20mm,
λ=1.0 for normal weight concrete
C the smallest of 4.0+1.0+1.0=6 cm
[40-2(4.0)-2(1.0)-2.0]/(3)(2)=4.67 cm
i.e., C is taken as 4.67 cm
4Φ20
40 cm
60
cm
Φ10@20
Page 13
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 1 [contd.]
cml
OKd
KC
cml
d
KCuseei
d
KC
cmns
fAK
d
b
tr
d
b
tr
b
tr
yttrtr
1.520.233.2
)0.1)(8.0)(0.1)(0.1(
250
4200
7
2
5.233.220
07.46
0.0Kassuming
6.480.25.2
)0.1)(8.0)(0.1)(0.1(
250
4200
7
2
5.2.,.
5.275.20.2
83.067.4
83.0)4)(20(100
4200)79.0(2
100
tr
4Φ20
40 cm
60
cm
Φ10@20
Page 14
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Compression
Shorter development lengths are required for compression than for tension since flexural tension cracks are not present for bars in compression.
According to ACI Code, the development length ld , for deformed bars
in compression is computed as the product of the basic development
length ldc and applicable modification factors, but ld is not to be less
than 20 cm.
ld = ldc x applicable modification factors ≥ 20 cm.
The basic development length ldb for deformed bars in compression is
given as
by
c
bydc df
f
dfl 044.0
'
073.0
Page 15
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development Length of Deformed Bars in Compression [contd.]Applicable Modification Factors
1. Excessive reinforcement factor =As required / As provided
2. Spirals or Ties: the modification factor for reinforcement, enclosed
with spiral reinforcement ≥ 6mm in diameter and ≤ 10 cm pitch or
within Φ12mm ties spaced at ≤ 10 cm on center is given as 0.75
Development Lengths for Bundled Bars
Based on ACI Code, development length of individual bars within a
bundle, in tension or compression, is taken as that for individual bar,
increased 20% for three-bar bundle, and 33% for four-bar bundle.
For determining the appropriate modification factors, a unit of bundled bars is treated as a single bar of a diameter derived from the
equivalent total area of bars.
Page 16
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development of Standard Hooks in Tension
b
c
yhb d
f
fl
'
073.0
Hooks are used to provide additional anchorage
when there is insufficient length available
to develop a bar.
According to ACI Code development length ldh , for deformed bars in
tension terminating in a standard hook is computed as the product of
the basic development length lhb and applicable modification factors,
but ldh is not to be less than 8db, nor less than 15 cm.
ldh = lhb x applicable modification factors ≥ 15 cm or 8db.
The basic development length lhb for hooked bars is given as
Page 17
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development of Standard Hooks in Tension [contd.]
Applicable Modification Factors
1. Concrete cover: for db ≤ Φ36mm, side cover (normal to plane of
hook) ≥ 6.35 cm, and for 90 degree hook, cover on bar extension
beyond hook ≥ 5.0 cm, the modification factor is taken as 0.7.
2. Excessive reinforcement factor =As required / As provided
3. Spirals or Ties: for db ≤ Φ36mm, hooks enclosed vertically or
horizontally within ties or stirrups spaced along the full development
length ldh not greater than 3 db , where db is diameter of hooked bar, is
taken as 0.8.
4. Lightweight aggregate concrete: the modification factor is 1.3.
5. Epoxy-coated reinforcement: the modification factor for hooked
bars with epoxy coating is taken as 1.2.
Page 18
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Development of Standard Hooks in Tension [contd.]
Part (a)
Part (b)
Φ10 through Φ25
Φ28 through Φ36
Φ44 through Φ56
4db or 64mm
ldh
ldh
Development length ldh is measured
from the critical section of the bar
to the out-side end or edge of the
hooks. Either a 90 or a 180-degree
hook, shown in Figure, may be used
Development of reinforcement- General* ACI code notes that hooks are not considered effective in compression and may not be used as anchorage.* The values of used in this Lecture Shall not exceed 26.5 kg/cm2.
'fc
Page 19
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Splices of Reinforcement
Forces on bar at splice
Splicing of reinforcement bars is necessary, either because the available bars are not long enough, or to ease construction, in order to guarantee continuity of the reinforcement according to design requirements.
Types of Splices
(a) Welding (b) Mechanical connectors
(c) Lap splices (simplest and most economical method)
In a lapped splice, the force in one bar is transferred to the concrete,
which transfers it to the adjacent bar.
Splice length is the distance the two bars are overlapped.
Page 20
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Splices of Reinforcement
Important note: Lap splices have a number of disadvantages, including congestion
of reinforcement at the lap splice and development of transverse cracks due to stress concentrations. It is recommended to locate splices at sections where stresses are low.
Types of lap Splices
1. Direct Contact Splice as figure a
2. Non-Contact Splice (spaced) the distance between two bars cannot be greater than 1/5 of the splice length nor 15 cm
Bars are spaced
ls
ls
s
Direct contact
T
T
T
T
Page 21
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Splices of Deformed Bars in Tension
ACI code divides tension lap splices into two classes, A and B. the class of splice used is dependent on the level of stress in the reinforcing and on the percentage of steel that is spliced at particular location.
The splice lengths for each class of splice are as follow
Class A splice: 1.0 ld
Class B splice: 1.3 ld
Tension Lap Splices
Maximum Percent of As
spliced within required lap length
As providedAs required
50 100
Equal to or greater than 2
Less than 2
Class A Class B
Class B Class B
Page 22
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Splices of Deformed Bars in Compression
Bond behavior of compression bars is not complicated by the problem of transverse tension cracking and thus compression splices do not require provisions as strict as those specified for tension
Based on the ACI code the Compression lap splice length shall be
0.007 fy db ≥ 30.0 cm for fy ≤ 4200 kg/cm2
(0.013 fy-24) db ≥ 30.0 cm for fy > 4200 kg/cm2
The computed splice length should be increase by 33% if fc’<210kg/cm2
According to ACI code when bars of different size are lap spliced in
compression, splice length shall be the larger of either development
length of larger bar, or splice length of smaller bar.
Page 23
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 2
Determine the development or embedment length required for the epoxy-coated top bars of the beam as shown in figure.(a)If the bars are straight(b)If a 180 hook is used(c)If a 90 hook is used
Use fc’ = 280 kg/cm2 and fy = 4200 kg/cm2
Solution: (a) Straight Bars
α=1.3 for top bars, β=1.5 for coated bars
α β =1.3x1.5 = 1.95 > 1.7 use 1.7
γ=1.0 for Φ32mm, λ=1.0 for normal weight concrete
C the smallest of 4.0+1.2+1.6=6.8 cm
[40-2(4.0)-2(1.2)-3.2]/(3)(2)=4.4 cmi.e., C is taken as 4.4 cm
4Φ32
40 cm
50
cm
Φ12@15
4Φ32
Page 24
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 2 [contd.]
(b) Using 180 hook
ldh = lhb x applicable modification factors ≥ 150 mm or 8db.
applicable modification factors =1.2 for epoxy-coated hooks
cml
OKd
KC
cmns
fAK
d
b
tr
yttrtr
1672.387.1
)0.1)(8.0)(7.1(
280
4200
7
2
5.287.12.3
58.14.4
58.1)4)(15(100
4200)13.1(2
100
cmdf
fl b
c
yhb 3.582.3
280
4200073.0
'
073.0
20815702.13.58 bdh dandcml
4Φ32
40 cm
50
cm
Φ12@15
Page 25
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 2 [contd.]
(c) Using 90 hook
ldh=70 cm
5db =16 4db =12.8
Critical section
180o hook
Ldh=70 cm
Critical section
12
db=
38
.4
90o hook
Page 26
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 3
To facilitate construction of a cantilever retaining wall, the vertical reinforcement shown in Figure, is to be spliced to dowels extending from the foundation. Determine the required splice length when all reinforcement bars are spliced at the same location.
Use fc’ = 300 kg/cm2 and fy = 4200 kg/cm2
Solution: Class B splice is required where ls = 1.3 ldα=1.0, β=1.0 → α β =1.0 < 1.7 OK
γ=0.8, λ=1.0 for normal weight concrete
C the smallest of 7.5+0.8=8.3 cm
25/2=12.5 cm
i.e., C is taken as 8.3 cm
Ktr =0.0, since no stirrups are used
ls
Φ16 @ 250
Φ16 @ 250
Page 27
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 3 [contd.]
OKcm
cml
d
KCei
d
KC
d
b
tr
b
tr
3001.46)3.1(5.35llengthspliceRequired
5.356.15.2
)0.1)(8.0)(0.1(
300
4200
7
2
5.2.,.5.219.56.1
03.8
s
Ls=50 cm
Φ16 @ 25
Φ16 @ 25
Page 28
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 4
Design a compression lap splice for a tied column whose cross section is shown in Figure when:
(a) Φ16 mm bars are used on both sides of the splice.(b) Φ 16 mm bars are lap spliced with φ 18 mm bars.
Use fc’ = 300 kg/cm2 and fy = 4200 kg/cm2
Solution: (a) For bars of similar diameter
splice length in compression and for fy =4200 kg/cm2
is equal to 0.07 fy db
= 0.07 (4200)(1.6) = 47 cm >30 cm
taken as 47 cm
Page 29
Design of Concrete Structure I
University of Palestine
Bond, Development Lengths, and Splices
Instructor:
Eng. Mazen Alshorafa
Example # 4 [contd.]
(b) For bars of different diameters
splice length in compression shall be the larger of either development
length of larger bar, or splice length of smaller bar.
The development length of larger bar
ld = ldb x applicable modification factors
applicable modification factors =1.0
Splice length of smaller diameter bar is evaluated in part (a) as 470mm. Thus, the splice length is taken as 470 mm.
cm33.31.0ll
cm33.30)1.80.0044(420fd0.0044thanlessnotbut
cm31.8300
1.842000.073
'f
d0.073fl
dcd
yb
c
bydc