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)

150 Reinforced concrete beams-the ultimate limit state
Comments on Step 3
The approximate moment (and shear) coefficients in Table 11.4-1 are
taken from BS 8110: Clause 3.4.3. More detailed calculations that take
advantage of moment redistribution, as illustrated in Example 4. 9-1,
usually lead to a more economical design. In practice Table 11.4-1 is used
for the less important structural members, particularly when they are not
to be constructed identically in large numbers.
Note that when Table 11.4-1 is used, moment redistribution is not
permitted.
Comments on Step4
At an interior support, the beam section resists a hogging bending
moment; hence the concrete compression zone is at the bottom. The beam
section is therefore designed as though it is rectangular. With reference to
Fig. 4.11-1(b), the effective depth d has been calculated as follows:
concrete cover = 30 mm
link diameter = 10 mm
main bar radius = 10 mm
50 mm
d = 375 - 50 = 325 mm, say
Admittedly, the diameter of the main bars, or even that of the links, is
not precisely known in advance. It turns out that the estimated effective
depth is slightly less than the actual value that corresponds to the bar sizes
finally adopted. Hence the design calculations have erred slightly on the
safe side, and may be left unamended; the designer should use his discretion
in deciding whether to revise the calculations.
Comments on Step 5
Within the sagging moment region, the concrete compression zone is at the
top of the beam section; hence the flanged beam equations are applicable.
The effective depth is
d = 375 - 30(cover) - lO(link) - lO(bar radius) = 325 mm
Also, the steel area As has been calculated from eqn ( 4.8-1) in which
the lever arm is taken as d - hr/2. In this particular example, the reader
should verify from Table 4.6-1 that 0.9x is less than hr, so that the
rectangular stress block is wholly within the flange thickness. Therefore,
strictly speaking, the tension steel area As should have been calculated
from eqn (4.8-3), leading to a saving of about 20%. Of course eqn
(4.8-1), used in Step 5 here, errs on the safe side.
Comments on Steps 6 and 7
The calculations for these steps are withheld until the reader has studied
Chapter 6.
Comments on Steps 8 and 9
Calculations are withheld until the reader has studied Chapter 5.
Comments on Step 10
In the design calculations that lead to the output listed in Step 10, the