REINFORCED CONCRETE DESIGN
102
SHEAR, BON D AND TORSION
103
A n, hor o gQ
I"
XI I
I Qng th
'i
"'2 '--==-.J
XI Sb ' /d - d'}! co l ll +col
I
(a)
Slng l~
OJ I
Syst Qm
2
- T25
A.
: 982sq.mm
DoublQ SystQm T25 bQ n t up bar s A,o . 49 1sq.mm (ZOch
SQc ti o n
Figu re 5.4 Beam with Itirrups and bent·up barr
Thus, for the stirrups, Arv/sv = 2 x 113/ 100 = 2.26. The shear resistance of the stirrupsrplus the concrete is given by equat ion 5.3 as V, '" Arv X 0.87 fyvd + bvcd
"
= 2.26 (b)
Mu ltlp ll2 Sys t am
=(319+114)x 103 N=433 x 10 3 N
Figure 5.3 Bent-up hoff
For a multiple system of bent-up bars, as in part (b) of the figure , the shear resistance is increased propor tionately to the spacing, Sb_ Hence
.
V==. OB7!yv A sbsma:
(d - d'}(C010'+ cot(1)
(S.S)
'b
The angles a: and (j should both be greater than or equa1 to 45 ° and the code requires that the spacing Sb has a maximum value of l. Sd. With 0: = (j "" 45° and Sb = (d - d '), equation 5.5 becomes
v: 1.23fY'.Asb
(S.6)
an d this arrangement is commonly referred to as a double system. Example 5. J Shear Resistance at a Section Determine the shear resistance of the beam shown in figure 5.4 , which carries a uniformly distributed load. The characteristic st rengths are: fyv = 250 N/mm'l for 2 the stirrups, fyv '" 460 N/mm'l for the bent-up bars and feu = 30 N/mm for the concrete. lOOA . '" IOO x982 =0.43 bd 350 x 650 Thus, from table 5, I, lie 2 size 12 bar - 11 3 mm ,
,.
x 0.87 x 250 x 650 + 350 x 0.5 x 650
0.5 N/mm2 by Interpolutlon , CrOIS·secUonallireli of a
The bent-up bars are arranged in a double system. Hence the shear resistance of the bent-up bars is Vb = 1.23fyvA$b
= 1.23 x 460 x 49 1
=278x 1QlN Total shear resistance o f the stirrups, concrete and bent-up bars is therefore V= VI + Vb ::(433 +278)10 3
:: 711 x IIY N 1\ should be noted that the shear resistance of 3 19 kN provided by the stirrups is grealer than the shear resistance of the bent·up bars, 278 kN, as require d by BS 81 10. It should also be checked that at the face ofsthe support V!bd does not exceed the lesser of 0.8 vfcl.l or 5 N/nlln 2.
5.2 Anchorage Bond T he reinforcing bur subject to direct lon. lolI.hown In n"ure 5,5 mu st be firmly anchored if it is nOI to be pu lled 0'11 of the ,"ounclo Oara . ubjected to forces Induced by nexurc must Sim ilarly be IlndlUlid lu dev.lull their design st resses. The