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)

376 Prestressed concrete simple beams
Show that, by totally disregarding these four equations, it is possible to
draw up a simplified design procedure which does not necessitate the
separate checking of the stress conditions in service and at transfer.
Specifically, show that in the simplified procedure the following equations
give the minimum required Z values that will simultaneously satisfy both
the stress conditions in service and those at transfer:
z > M;max + (1 - a)Md
I - afamaxt - famin
Z
M;max + (1 - a)Mct
2 ;::: --'-'7"''----"----..,--.!--..0:
!amax - afamint
(Hint: Writef1 = aflt and[2 = a[2 1 in eqns 9.2-4 and 9.2-6; then eliminate
!It and [2 1 using eqns 9.3-2 and 9.3-4. If necessary, see pp. 7-9 of
Reference 2.)
9.2 A pretensioned concrete beam is of rectangular section 150 mm x
1100 mm. The tendon consists of 1130 mm 2 of standard strands, of
characteristic strengths 1700 N/mm 2 , stressed to an effective prestress
of 910 N/mm 2 , the tendon eccentricity being 250 mm below the centroid of
the section. The tendon stress/strain curve is as in Fig. 9.5-3. The concrete
characteristic strength feu is 60 N/mm 2 and its modulus of elasticity may be
taken as 36 kN/mm 2 for stresses up to 0.4fcu. Determine the ultimate
moment of resistance.
Ans.
(For method of solution, see Example 9.5-1. For complete
solution, see Reference 2: pp. 35-41.)
9.3 According to BS 8110:1985 and the CEB-FIP Model Code (1978),
the creep coefficient ifJ is defined, with reference to concrete under a
constant stress, by the equation
creep strain = ifJ x elastic strain
Show that eqn (9.8-6), namely
creep curvature = ifJ x elastic curvature
is compatible with the BS 8110/CEB-FIP definition of ifJ.
(Hint: If necessary, see the comments following Example 9.4-4. Satisfy
yourself that each fibre of the beam section creeps under a sustained
bending stress which does not change with time.)
9.4 In preliminary calculations for long-term deflections, the following
simplified formula is often used for estimating the curvature due to the
prestress:
.! = (1 + ifJ) Pes
r
~cl
Using this formula, calculate the long-term deflections of the beam in