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)

Flanged beams 129
(4.8-2)
When using this quick method, designers do not check whether 0.9x
exceeds hr. Instead, the design moment M is compared with Mu of eqn
(4.8-2). If M s Mu, then the steel area As is calculated from eqn (4.8-1).
In the unlikely event that M > Mu of eqn (4.8-2), it is usually simplest to
increase the web dimensions. Otherwise, use the I.Struct.E. Manual's
procedure [14] below.
I.Struct.E. Manual's design procedure (Case 1: Moment redistribution not
explicitly considered)
The procedure given below is that of the I.Struct.E. Manual [14].
Comments have been added to explain the derivation of the formulae and
the technical background. Though moment redistribution is not explicitly
considered, this 'Case I procedure' is in fact valid for up to 10% moment
redistribution.
Stepl
Check xld ratio. Calculate
M
K = fcubd 2
where M is the design moment and b the effective flange width. Obtain
zld and xld from Table 4.6-1.
Comments
See comments on Table 4.6-1.
Step2
Check whether 0.9x s hr. If 0.9x s hr the BS 8110 rectangular stress
block lies wholly within the flange thickness. The tension steel area As is
determined as for a rectangular beam, using eqn (4.6-12):
A - M (4.8-3)
s - 0.87/yz
where z is obtained from Table 4.6-1 (see Step 1 above).
Comments
See eqn ( 4.6-12) and Table 4.6-1 and the comments that follow it.
Step3
Check whether 0.9x > hr. If 0.9x > hr, the BS 8110 rectangular stress
block lies partly outside the flange. Calculate the ultimate resistance
moment of the flange Mur:
Muf = 0.45fcu(b - bw)hr(d - 0.5hr) (4.8-4)
Comments
The flanged section in Fig. 4.8-3(a) is considered to be made up of two
components as shown in Fig. 4.8-3(b): the flange component and the web
component. Equation (4.8-4) is obtained by considering the forces in Fig.
4.8-3(c) and taking moments about the tension steel As.