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)

102 Reinforced concrete beams-the ultimate limit state
depth 700 mm is 300 kNm. If feu = 40 N/mm2 and [y = 460 N/mm2, design
the reinforcement.
SOLUTION
M _ (300)(106) _ 2
bd2 - (250)(7002) - 2.45 N/mm
From design chart (Fig. 4.5-2), (! = 0.68%,
As = (~gg)(250)(700)
= 1190 mm2
Provide four 20 mm bars (As = 12~7 mm2 from Table A2-1)
Example 4.5-4
Repeat Example 4.5-3 if the design ultimate moment is 900 kNm. What
then is the x/ d ratio of the beam section so designed?
SOLUTION
M _ (900)(10 6 ) _ 2
bd2 - (250)(7002) - 7.35 N/mm
If no compression steel is used, then the design chart (Fig. 4.5-2) shows
that (! = 2.9%. Moreover, xld will be well over 0.5, which is not good
practice (see comments below). Therefore use compression steel; let e' =
0.5% say. Using the curve fore' = 0.5% in Fig. 4.5-2, we have
X
(! = 2.26%; (! 1 = 0.5%; d = 0.45
A~ = (?o~)(250)(700) = 875 mm 2
Provide two 25 mm bars (982 mm2)
A~ = (;~g)(250)(700) = 3955 mm 2
Provide five 32 mm bars ( 4021 mm2)
The tension reinforcement would be arranged in two layers, such that 700
mm is the average effective depth.
Comments
The above solution shows that a singly reinforced section with(! = 2.9%
would have satisfied the M/bd 2 requirement. However, such a beam
section would have an xl d ratio well in excess of 0.5 and would fail in a
brittle manner with inadequate warning before collapse. Section 4.9 gives
further information on ductility and the significance of the xld ratio.
Example 4.5-5
The effective depth d of a beam section is to be 2-! times its width b. The
design ultimate moment is 1600 kNm. If the tension steel ratio is not to
exceed 3% and the compression steel ratio is not to exceed 1.5%,