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)

194 Reinforced concrete beams-the serviceability limit states
(b) The corner distance ac is well defined at the midspan section. At the
support section, Fig. 5.7-3 shows that ac is defined only for the
right-hand side corner, but not for the left-hand side. Allen (22] has
drawn attention to this ambiguity and asked the following question
with reference to monolithic beam-and-slab construction: 'Where is
the corner of the beam when considering the tension bars over a
support?' It is reasonable to say that the 'corner' should not be
literally interpreted as the point of intersection of the vertical face of
the beam rib with the top face of the slab. Allen (22] has suggested
that, in such circumstances, what needs checking is not ac, but the
clear distance between an outside tension bar and the adjacent slab
bar near the top face of the slab.
5.8 Computer programs
(in collaboration with Dr H. H. A. Wong, University of Newcastle upon
Tyne)
The FORTRAN programs for this chapter are listed in Section 12.5. See
also Section 12.1 for 'Notes on the computer programs'.
Problems
S.l Table 3.11 of BS 8110 (see Table 5.3-2 here) gives the modification
factors for the tension reinforcement, for use in determining the allowable
span/effective depth ratio. In the table, the quantity Mlbd 2 is used as a
measure of the amount of tension reinforcement. Comment on whether
the modification factor depends on: (a) the tension steel area required for
Mlbd 2 ; or (b) the tension steel area actually provided.
Ans.
Strictly speaking, the modification factor depends on the amount of
tension reinforcement actually provided. The values in Table
5.3-2, being based on M/bd 2 (and hence on the As required), are
approximate and err on the safe side. For further information, see
eqns (5.3-1(a) (b)) and the associated 'Comments on Step 3'.
S.l Table 3.12 of BS 8110 (see Table 5.3-3 here) relates the modification
factor to the amount of compression reinforcement. How does the
compression steel affect the deflection?
Ans. See 'Comments on Step 4' on p. 172.
5.3 In university courses, deflections are frequently calculated using
Macaulay's method, which is based on the differential equation
d 2 w M
dx2 = -El
where w here denotes the deflection and x the distance along the beam
axis. Readers who use American textbooks will be familiar with the