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)

172 Reinforced concrete beams-the serviceability limit states
Comments on Step 4
Figure 5.2-3 shows that the neutral axis depth x decreases with the
compression steel ratio A~lbd. Therefore, for a given value of the service
stress fs in the tension steel, an increase in the compression steel ratio will
increase the quantity (d - x) in eqn (5.3-2) and consequently will reduce
the curvature, and hence the deflection of the beam. Therefore, if the
compression steel ratio is increased, the allowable span/depth ratio may
also be increased.
Note also that the final span/depth ratios as determined from Steps 1 to 4
above will take account of normal creep and shrinkage deflections.
Example 5.3-1
The design ultimate moment for a rectangular beam of 11 m simple span is
900 kNm. If feu = 40 N/mm 2 and [y = 460 N/mm 2 , design the cross-section
for the ultimate limit state and check that the span/effective depth ratio is
within the allowable limit in BS 8110: Clause 3.4.6.
SOLUTION
Example 4.5-4 shows that a beam section having the following properties
are appropriate for the ultimate limit state:
b = 250 mm; d = 700 mm; As = 4021 mm 2 ;
As - 2 300/.
bd - . to,
A~ 0 56°1
bd = . /O
Hence the allowable span/depth ratio may be determined by the step-tostep
procedure described on pp. 169-170.
Stepl
From Table 5.3-1, the basic span/depth ratio is 20.
Step2
We shall assume that it is necessary to restrict the increase in deflection,
after construction of the partitions and finishes, to the BS 8110 limits.
Hence the modified factor for long span is
_lQ_ = 10 = 0.91
span 11
Step3
M _ (900)(10 6 ) _ 2
bdz - (250)(7002) - 7.35 N/mm
From Table 5.3-2, the modification factor for tension reinforcement is
0.78. (More accurately, eqn 5.3-1(a) gives 0.75.)
Step4
1001~prov = 0.56
From Table 5.3-3, the modification factor for compression reinforcement
is 1.15. Therefore the allowable span/depth ratio is
(20)(0.91 )(0.78)(1.15) = 16.33