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Shear-Friction
For providing shear transfer mechanism in such
cases as
1) At interface between concretes cast at
different times
2) At junction of a corbel (bracket) with column
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3) At junction of precast concrete
4) At interface between steel and concrete
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Shear-Friction Concept
Shear resistance Friction force
Vn Avf fy m
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Inclined Reinforcement
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Coefficient of Friction ( m )
1) ??????????????????????????? m 1.4 l
2) ??????????????????????????????????????????
1/4 m 1.0 l
3) ????????????????????????????????????????? m
0.6 l
4) ????????????????????? Headed stud
?????????????? m 0.7 l
l 1.0 for normal weight concrete
0.85 for sand-lightweight concrete 0.75 for
all lightweight concrete
Maximum Nominal Shear Strength
max Vn vn Ac 0.2 fc Ac ? 56.3 Ac
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??????????? 5.8 ????????????????????????????????
??????????????????????????????? 35 ??. ??? 70
??. ?????????????????????? 10 ??. ??????????????
Vn ??????? 48 ??? ??????????? ????????????????????
????????????????????????????? ????????????????????
???????? 0.3 ??? ?????????????? ????????????? fy
4,000 ??./??.2
?????? (a) ??????????????????????????????????????
????????????????????????? ????????????? ??????????
??????????? 15o ??????????????????????????????????
??????????????????????? ???????? 10 ??.
??????????????????????????????????????????????????
????
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(b) ???????????????????????????????????? Avf
?????????????????????? Nu ??? Vu
???????? ???????????????????????????????????
(c) ?????????????????????????? An
???????????????????????????????????
???????????????????????? ????????????????????? Vu
??? Nuc ???????????????????????????????????????
???????? Nuc ?????? ????????????????
Nuc ?????????????????? 0.3 ??? Vu
??????????????????????????, ACI ??????????? f
0.85
(d) ?????????????????????????????????????????
As Avf An 10.1 4.24 14.3 ??2
??? 5DB20(As 15.7 ??2) ??????????????????
???????? 15o ????????? ???????????????????? ??????
??????????????????????????????????????????????????
?
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??????? 4DB20(Ash 4(3.14) 12.56 ??2)
(f) ?????????????????????????????????????????????
??????????????????????????????????????? ??????????
25 ???????????????????????????
???????????????????????????????????????????
?????????? Ach ???????? ??? Acv ????????? ???????
??? 2DB12 ??? 2DB10 ??????????????????????????????
??????????????
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?????????????????????? 5.8
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Brackets and Corbels
Vu
a
As rbd
Nuc
h
d
Ah
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Cracking in Corbel
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Equilibrium of Forces on Bracket
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Introduce f Vn Vu /f , Nnc Nuc /f
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Minimum Horizontal Stirrups
To prevent premature diagonal tension failure
Reduce required As due to stirrup
required As Avf An - Ah
ACI Code Provisions
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Brackets and Corbels Design Requirements
1) Shear span to depth ratio a /d ? 1.0
2) Tensile force Nuc ? Shear force Vu
3) Tensile force Nuc ? 0.2Vu
4) Critical section is at face of support where
d is measured
5) Strength reduction factor f 0.85 for all
calculation
6) Maximum strength Vn using normal weight
concrete is
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7) Minimum reinforcement ratio r for main tension
steel As is
8) Main tension steel at front face must be
anchored by
(a) Welded to transverse bars to develop force As
fy
(b) Bend As back to form horizontal loop
(c) Some means of positive anchorage
9) Bearing area must not project beyond As bar
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Effective Depth of Corbel
Outer edge of bearing area
Vu
a
Nuc
As
d1
d ? d1
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??????????? 5.9 ????????????????????????????????
35 ??. ???????????? 14 ??? ???????????? 23 ???
??????????????????????????????????
?????????????????????????????????? 2.5 ??.
??? fc 350 ??./??.2 ??? fy 4,000 ??./??.2
?????? (a) ????????????? Vn 1.4 VD 1.7VL
1.4 (14) 1.7(23) 58.7 ???
???????????????????????? 10 ??.
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(c) ????????????????????????????????????? Vn
????????? ACI
????????? 0.2fc 70 ??./??.2 ??????? max vn
56.3 ??./??.2
????????????????? h 40 ??. d 36 ??. (????????
4 ??.)
(d) ???????????????????????????????????? Avf
??? m 1.4 ??????????????????????????????????
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(e) ????????????????????????? As ?????????????
Af ??????????????????????
Mu Vu a Nuc (h - d ) Vu a 58.7(10)/100
5.87 ???-????
f 0.85 ??? ACI ??????????????????
???????????????? r 0.0039
???????????????? Af 0.0039(35)(36) 4.9 ??2
????????? As ?????????????????????????????????????
????????
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(f) ??????????????????
???????????????? Ah 0.5(As - An) 0.5(9.42)
4.71 ??2
???????????????????????? a/d 0.28 ????? Af
?????????????????????? 3DB10 ??????? Ah
2(3)(0.79) 4.7 ??2 ???????????????????????????
??????????????????????????????
(g) ????????????????? ???????????????????????????
??
h 36 2.5 (????????) 0.8 (??????????????)
39.3 ?? ??? 40 ??.
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???????????????????????
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