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)

BS 8110 design charts-their construction and use 99
reinforcement As and compression reinforcement A~, the trial and error
procedure in Section 4.2 may be used. A trial neutral axis depth is first
assumed and the steel strains £ 5 and e~, in the tension and compression
reinforcement respectively, are then worked out from the compatibility
condition (eqns (4.2-1) and (4.2-2)):
£ 5 = d ~ X (0.0035) (4.5-5)
£~ = X - d' (0.0035)
X
(4.5-6)
where d is the effective depth and d' the depth to the centroid of the
compression reinforcement (see Fig. 4.2-1). The steel stressesfs andf~ are
next obtained from the appropriate stress/strain curve in Fig. 4.5-1. The
equilibrium condition (eqn 4.2-3) is then checked:
i.e.
kdeubx = Asfs -
A~f~
(4.5-7)
where e = A 5/bd, e' = A~lbd, and k 1 is as read off from Fig. 4.4-4. If eqn
(4.5-7) is not satisfied, the trial value of x is increased or decreased by
inspection and the process repeated until it is reasonably well satisfied. The
ultimate moment of resistance of the doubly reinforced beam is then given
by eqn (4.2-5):
i.e.
Mu = Asfs(d - kzx) + Alf~(kzx - d')
(4.5-8)
Thus, for a specified value of e' and a given combination of ifeu,/y, d' /d)
values, the curves of Mulbd 2 egainst e may be constructed (see Example
4.5-1). Fi§ure 4.5-2 shows a set of such curves for feu= 40 N/mm 2 ,fy =
460 N/mm and d'/d = 0.15.
BS 8110 gives a comprehensive set of design charts covering different
combinations of feu, fy and d' I d values.
Design for the ultimate limit state (BS 8110)
The design use of the BS 8110 design charts will be illustrated by the
worked examples below. The first two examples deal with the construction
of the BS 8110 charts and serve as an introduction to the later ones.
Example 4.5-1
With reference to the BS 8110 design chart in Fig. 4.5-2, verify the M!bd 2
value for a beam withe(= Aslbd) = 3% and e' ( = A~lbd) = 1% for feu =
40 N/mm 2 ,fy = 460 N/mm 2 • Work from first principles and conform to BS
8110.