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)

170 Reinforced concrete beams-the serviceability limit states
(c) If it is necessary to limit the increase in deflection, and the
structural member is a cantilever, then the design must be justified
by deflection calculation (see Section 5.5).
Step 3 M odi.fication factor for tension reinforcement
The span/depth ratio is now multipled by the modification factor,
obtained from Table 5.3-2, to allow for the effect of the tension
reinforcement.
Step 4 M odijication factor for compression reinforcement
If the beam is doubly reinforced, the span/depth ratio may be further
multiplied by a modification factor, obtained from Table 5.3-3, to allow
for the effect of the compression reinforcement.
Comments on Step 1
Limiting the span/depth ratio is an effective and convenient method of
deflection control in practical design [7-10].
In Table 5.3-1, the span/depth ratios for flanged sections are smaller
than those for rectangular sections. This is because a flanged section has a
smaller area of concrete in the tension zone than that in a rectangular
section of the same width b. As we shall see in Section 5.5 on deflection
calculations, the concrete in the tension zone does contribute to the
stiffness of the member even after cracking.
Comments on Step 2
For spans exceeding 10 m, the use of the ratios in Table 5.3-1 may lead
to deflections exceeding span/500 or 20 mm after the construction of
partitions and finishes. Hence the modification factor of 10/span is
recommended. Long cantilevers are notorious as a source of troubles
associated with excessive deflections; hence BS 8110 requires their design
to be justified by deflection calculations.
Table5.3-2 Modification factor for tension reinforcement
(BS 8110: Clause 3.4.6.5)
Service stress M!bd 2 (N/mm 2 )
fs (N/mm 2 ) 0.50 0.75 1.00 1.50 2.00 3.00 4.00 5.00 6.00
(fy = 250) 156 2.00 2.00 1.96 1.66 1.47 1.24 1.10 1.00 0.94
(/y = 460) 288 1.68 1.50 1.38 1.21 1.09 0.95 0.87 0.82 0.78
Table5.3-3 Modification factor for compression reinforcement
(BS 8110: Clause 3.4.6.6)
100A~.prov
bd
0 0.15 0.25 0.35 0.50 0.75 1.00 1.50 2.00 2.50 ~3.00
Factor 1.00 1.05 1.08 1.10 1.14 1.20 1.25 1.33 1.40 1.45 1.50