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)

152 Reinforced concrete beams-the ultimate limit state
parabola
Problem 4.1
(a l (b)
4.3 Briefly describe the modes of failure of (a) an under-reinforced beam
and (b) an over-reinforced beam.
Ans. See paragraphs following: (a) eqn (4.3-1); and (b) eqn (4.3-4).
4.4 Figure 4.4-5 shows that, in BS 8110's simplified rectangular stress
block, the stress intensity is 0.45/cu· Does this value of 0.45fcu already
include the allowance for the partial safety factor Ym?
Ans. Yes (see Section 4.4(d)).
4.5 Figure 4.5-2 shows a beam design chart reproduced from BS 8110.
Explain how you can construct such a design chart from first principles.
Ans. See Section 4.5, particularly Examples 4.5-1 and 4.5-2.
4.6 BS 8110: Clause 3.4.4.1. states that, for a beam section subjected to
combined bending and axial force, the effect of the axial force may be
ignored if it does not exceed 0.1fcu times the cross-sectional area.
Comment.
Ans. See Example 4.5-6.
4. 7 Moment redistribution is not explicitly considered in Section 4.6.
Nevertheless, all the design formulae and procedures in that Section are
valid for up to 10% moment redistribution. Explain.
Ans. This is because eqn (4.7-3) is implicitly satisfied.
4.8 Clause 3.4.4.4 of BS 8110 and Clause 4.4.5.1 of the I.Struct.E.
Manual [14] give the following formula (reproduced here as eqn 4.6-12
and 4.7-9) for the tension steel area A,:
M
A,= 0.87/yz