F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

The ultimate limit state: shear (BS 81 10) 365
centroidal axis. Therefore, for a general section, eqn (9.6-1) should
take the modified form
bvf ( 2 )
Vco = A)!~ ft + 0.8/cp/t
where, for practical I sections, the quantity bviiAY usually works out
to be about 0.8bvh so that eqn (9.6-1) errs on the safe side.
However, for such sections, the maximum principal tensile stress
does not necessarily occur at the centroidal axis (though the
maximum shear stress exists there) but frequently at the junction of
the web and the tensile flange; eqn (9.6-1) refers only to the
condition at the centroidal axis and in this respect errs on the unsafe
side. The two effects tend to cancel out [8], so that in practice eqn
(9.6-1) is applied to both rectangular and !-sections. For similar
reasons, eqn (9.6-1) is judged suitable for use with L- and T-beams
also.
Design procedure for shear (BS 8110)
Step I
Calculate the shear force V L and the bending moment M due to the
design ultimate loads. The shear force V L• which is due to the external
loading, is then adjusted as explained below.
Case 1 (section uncracked in flexure):
V = VL - Pesinf3 (9.6-3)
where the term Pc sinf3 (see Fig. 9.2-S(a) and eqn 9.2-22) allows for the
effect of the tendon force.
Case 2 (section cracked in flexure):
V = V L - P c sin f3 or V L (9.6-4)
whichever is greater.
Step2
Calculate Vco from eqn (9.6-1).
Step3
Calculate Vcr from eqn (9.6-2).
Step4
The design ultimate shear resistance Vc is taken as follows:
(a) uncracked sections: where M from Step 1 is less than M 0 as defined
for eqn (9.6-2), the section is considered uncracked in flexure, in
which case Vc = V c0 of Step 2
(b) cracked sections: where M from Step 1 is not less than M 0 as
defined for eqn (9.6-2), the section is considered cracked in
flexure, in which case
Vc = Vco of Step 2 or Vcr of Step 3
whichever is the lesser.