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7/28/2019 bond, anchor and shear
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3. Bond , Anchorage and Shear
This chapter will discuss the following topics:
Outline the theory of calculating the anchorage bond
length.,
length and compression lap length by using Table 8.4
and Table 8.5 of the code.
Outline the design formulae for the design of shear
reinforcement and the use of Table 6.3 of the Code.
RC Design and Construction HKC 2004 (2ndEdition)3-1
3. Bond, Anchorage and Shear
Minimum Distance Between Bars
The min. distance between bars are given in terms of
agg
.
( hagg + 5mm) or
.
RC Design and Construction HKC 2004 (2ndEdition)3-2
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3.1 Minimum and Maximum Percentages of
Reinforcement in Beams, Slabs and Columns
Minimum % : Table 9.1 of the code
Maximum %
(a) Beam (9.2.1.3)Neither the area of tension reinforcement nor the area of com ression
reinforcement should exceed 4% of the gross cross-sectional area of concrete.
(b) Column (9.5.1)
The longitudinal reinforcement should not exceed the followingamounts, calculated as percentages of the gross cross-sectional area of theconcrete :
~ vertically cast columns : 6%
~ horizontally cast columns : 8%
~ laps in the vertically or horizontally cast column : 10%
(c) Wall (9.6.2)
The area of vertical reinforcement should not exceed 4% of the concrete
RC Design and Construction HKC 2004 (2ndEdition)3-3
cross-sectional area of the wall.
3.2 Anchorage Bond
The steel bar subjected to tension shown in Fig.
anchorage length (embedded length) depends on
the bond between the bar and the concrete and the
contact area.
L
F
Fi . 3.1 Anchora e Bond
RC Design and Construction HKC 2004 (2ndEdition)3-4
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3.2 Anchorage Bond
L = Min. anchorage length to prevent pull out.
= .
fbu= Ultimate anchorage bond stress.fs = Direct tensile or compressive stress in the bar.
Consider the forces on the bar,
Tensile pull-out force = Area of bar * Stress of bar
=
4
fsRC Design and Construction HKC 2004 (2ndEdition)
3-5
3.2 Anchorage Bond
Anchorage force = Contact Area * Bond Stress
bu
= (L)fbu 2
4
0.87f=
bubu ffL
4=
4
The ultimate anchorage bond stress, .
Values of are iven in table 8.3.
f fbu cu
anchorage length L can be written as
RC Design and Construction HKC 2004 (2ndEdition)3-6
= A see a e . o e o e
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3.2 Anchorage Bond
Table 8.3 - Values of the bond coefficient ar ype
Bars in tension Bars in compression
Plain bars 0.28 0.35
Type 2 : deformed bars 0.50 0.63
Fabric 0.65 0.81
Normally deformed type 2 bars are used in
construction works.
Furthermore anchorage may be provided by hooks
. . . .
RC Design and Construction HKC 2004 (2ndEdition)3-7
Fig. 8.2 Anchorage of Links
Reproduce from HK Code
RC Design and Construction HKC 2004 (2ndEdition)3-8
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3.3 Lapping of Reinforcement
Lapping of reinf. may be required if the reinf. is of
insufficient len th or there is curtailment cuttin
off of reinf. when it is no longer required in order
to save mone of reinf.
u es or app ng are:-
The laps should be staggered and be away from sections
. . . .
with large bending moment as it induces large tensile stress
in reinforcement) Min. lap length should be not less than the greater of 15
or 300mm.
RC Design and Construction HKC 2004 (2ndEdition)3-9
3.3 Lapping of Reinforcement
The tension lap length should be at least equal to the design tension
anchorage length. Lap lengths for unequal size bars may be based
upon the diameter of the smaller bar. The following provisions also
apply:
minimum cover is less than twice the diameter of the lapped
reinforcement, the lap length should be increased by a factor
of 1.4
where a lap occurs at a corner of a section and the minimum
lapped reinforcement, the lap length should be increased by a
factor of 1.4
where both conditions above apply, the lap length should beincreased by a factor of 2.0
RC Design and Construction HKC 2004 (2ndEdition)3-10
Figure 8.5 and table 8.5 are referred.
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3.3 Lapping of Reinforcement
Rules for lapping are:-
Com ression la s should be at least 25% reater than the
compression anchorage length.
Lap lengths for unequal size bars may be based on thesmaller bar.
x 2.0x 1.4
If Cover < 2, multiple lap length by
1.4 or2.0
x .x 1.0
(Lap length = anchorage length x 1.0)
Fi . 3.3 La in of tension reinforcement
RC Design and Construction HKC 2004 (2ndEdition)3-11
3.4 Shear
Shear reinforcement can be in the form of shear
-
inclined bars are less frequently used in
construction toda .
ear n s rrups
Links can be broadly classified into shear link and
nominal link (minimum link) and the design
formulae for these types of links are as follows:
RC Design and Construction HKC 2004 (2ndEdition)3-12
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Design Formulae for Shear Reinforcementor cu a-
( )csv vvbA yvv fs 87.0
Minimum (nominal) Links:-
yvv
sv
f
b
s
A
87.0
4.0
RC Design and Construction HKC 2004 (2ndEdition)3-13
Design Formulae for Shear Reinforcement
Where:-
sv -
link.
= rea o eamfyv = Characteristic strength of the shear reinf. = fy
sv = ong u na spac ng o s ear n s
v = Design shear stress
= es gn s ear orce =
vc = The ultimate shear stress that can be resisted by the
concrete.
RC Design and Construction HKC 2004 (2ndEdition)3-14
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Design Formulae for Shear Reinforcement
The values of vc is given in table 6.3 of the Code.
It shall be noted that the values given in table 6.3 is forgrade 25 conc. For other grades of conc., adjustment shall
be made by multiplying fcu
1
3 The values of v increases for shallow members and those
25
with larger percentages of tensile reinforcement.
RC Design and Construction HKC 2004 (2ndEdition)3-15
3.5 Enhanced Shear Resistance
Within a distance of 2d from a support or a
vc may be increased to
c v
The distance av is measured from the support or
concentrated load to the section being designed.
Avera e shear stress should never exceed the
lesser of or 7 N/mm2.0 8. fcu
RC Design and Construction HKC 2004 (2ndEdition)3-16
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Figure 6.3 Shear failure near supports
RC Design and Construction HKC 2004 (2ndEdition)3-17
epro uce rom o e
Table 6.3 - Values of vc Design Concrete Shear Stress
RC Design and Construction HKC 2004 (2ndEdition)3-18
epro uce rom o e
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Table 9.1 - Minimum Percentage of Reinforcement
RC Design and Construction HKC 2004 (2ndEdition)3-19
epro uce rom o e
Table 8.4 Ultimate Anchorage Bond Lengths (lb)
Reproduce from HK Code
RC Design and Construction HKC 2004 (2ndEdition)3-20
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Table 8.5 Ultimate Lap Lengths
Reproduce from HK Code
RC Design and Construction HKC 2004 (2ndEdition)3-21
Figure 8.5 - Factors for lapping bars
Reproduce from HK Code
RC Design and Construction HKC 2004 (2ndEdition)3-22
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Self-Assessment Questions
Q1. Determine the anchorage bond length from the first
principle for a T32 bar in tension (deformed type 2)
and fcu = 35 N/mm2. the bars as listed below:
Choices:
(a) 1000 mm
(b) 1082 mm
(c) 1360 mm
RC Design and Construction HKC 2004 (2ndEdition)3-23
Self-Assessment Questions
Q2. Determine the anchorage bond length by using table 8.4
of HKC 2004 for a R16 bar in compression and fcu = 30
N/mm2 .
Choices:(a) 464 mm
(b) 528 mm
(c) 540 mm
RC Design and Construction HKC 2004 (2ndEdition)3-24
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Self-Assessment Questions
Q3. Determine the ultimate shear resistance of concrete vcfor the singly reinforced concrete section shown in Fig.
Q3, without shear enhancement. Given that fcu = 35
N/mm2 and fy = 460 N/mm2.
050
403
2T32
Choices:
(a) 0.70 N/mm2
Fig. Q3
(b) 0.90 N/mm2
(c) 1.10 N/mm2
RC Design and Construction HKC 2004 (2ndEdition)3-25
Assignment No. 3
AQ1 Fig. AQ1 shows the lapping of steel reinforcement of a beam.
Determine the lap length for the bar groups 1, 2, 3 and 4. Given
and fcu = 35 N/mm2. The spacing between group 1 and 2 bars is
greater than s and the spacing between group 3 & 4 bars is less
t ans.
(a) The lapping of steel reinforcement is at tension zone.
(b) The lapping of steel reinforcement is at compression zone
3T16
(1) (2)
3T323T32
(3) (4)
RC Design and Construction HKC 2004 (2ndEdition)3-26
Fi . A 1
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Assignment No. 3
AQ2 Determine the nominal cover and breadth of the web for the
simply supported beams whose sections are shown in Fig.
AQ2a, AQ2b & AQ2c. The maximum size of the aggregate
in each case is 20 mm, f cu = 40 N/mm2
and the link size is3. -
cement ratio = 0.55).
a xposure con on: severe
Fire resistance: 2 hours
(b) Exposure condition: moderate
Fire resistance: 1 hours
(c) Exposure condition: severe
RC Design and Construction HKC 2004 (2ndEdition)3-27
re res s ance: ours
Assignment No. 3
Fi . A 1a
3T40
Fi . A 1b
4T20
. .
2T32
RC Design and Construction HKC 2004 (2ndEdition)3-28
Fig. AQ1cFig. AQ2c
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Assignment No. 3
AQ3. Determine the average shear stress for the section
shown in Fig. AQ3a, AQ3b & AQ3c, and state whether
shear reinforcement is required. Given that fcu = 30
N/mm2 and fy = 460 N/mm2.
225 300 200
350
300
2T20450
400
260
300
2T16
Ultimate Shear = 150 kN
Fi . A 2a
3T25 Ultimate Shear = 250 kN
Fig. AQ2c
Fig. AQ3c Ultimate Shear = 60 kNFig. A 2b
.
Fig. AQ3b
RC Design and Construction HKC 2004 (2ndEdition)3-29
Assignment No. 3
AQ4 The sections in Fig. AQ4a & AQ4b are subject to shear
forces at the ultimate limit state as shown. Determine
the spacing of R10 links. Given that fcu = 35 N/mm2, fy
= 460 N/mm2 and fyv = 250 N/mm2.
225 300
350
310
2T204
50
400
Ultimate Shear = 40 kN
Fi . A 3a
3T25
Ultimate Shear = 160 kN
Fi . A 3b
g. a
Fig. AQ4b
RC Design and Construction HKC 2004 (2ndEdition)3-30