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)

Problem 377
Example 9.8-2 and compare your answers with those in Step 6 of the
solution to that example.
Ans. (a) When non-permanent load is acting, deflection = -94.3 mm
+ 68.4 mm + 12.8 mm = -13 mm (compared with +8 mm in
the solution).
(b) When non-permanent load is not acting, deflection = -94.3
mm + 68.4 mm = -26 mm (compared with -5 mm in the
solution).
Comments on Problem 9.4
The simplified equation neglects the effect of the prestress loss, as
represented by eqns (9.8-2) and (9.8-3). Indeed, in eqn (9.8-4), i.e. in
.! = Pes(a + 1 + alP)
r Eel 2
if the prestress loss ratio a is taken as unity, the simplfied equation results.
9.5 A pretensioned concrete beam is of uniform cross-section, the area of
which is A and the radius of gyration k. It has n layers of steel strands at
eccentricities e. 1, e52 ... esn respectively from the centroidal axis of the
section; these are tensioned to an initial stress of/51 ,/82 •.• fsn respectively.
The areas of then layers of strands are respectively Apst. Aps2 ••• Apsn·
The modulus of elasticity of the concrete is Ec and that of the steel Es.
Write down a system of n simultaneous equations, which can be solved for
the prestress losses ofst' ofs2 ... ofsn that occur in then layers of strands, as
a result of the elastic deformation of the concrete at transfer.
Ans.
0£1
= E!A :~ Usi - ofsi)Apsi( 1 + ~~est)
6 g" = E 1 A :f Usi - ofsi)Apsi(1 + ek~esn)
s c •=I
Hint: If n = 1, then equations reduce to that of Example 9.4-2, namely:
ofs = Us - of.)Aps(1 + e~)
Es EcA k
9.6 For the prestressed concrete beam of Problem 9.5, write down a
system of n simultaneous equations which can be solved for the prestress
losses due to a concrete shrinkage fcs·
Ans.