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)

396 Prestressed concrete continuous beams
moment diagram. Let the tendon eccentricity e 5 at the interior support
B be
es = ~(-174.3- 159.1) = -167 mm
where - 174.3 mm and -159.1 mm are the limiting values of the
eccentricity eP (not es) at B. Then
Mi atE
es atE= Mat B X (-167) mm etc.
I
The tendon profile is as shown in Fig. 10.5-1.
StepS
Since the tendon profile in Step 4 is concordant (Rule 4) and since it lies
within the permissible zone, it is acceptable.
Step6
From eqn (9.3-7), the prestressing force at transfer is
P = Pcla = 1000/0.85 = 1175kN
Consider Section B (Fig. 10.5-1)
From eqn (10.4-1), bottom fibre stress is
P Pep Mimax + Md
A+ Z 1 - Z 1
1175 X 103 1175 X 10 3 ( -167) 0 - 36.8 X 106
= 160 X 103 + 22 X 106 - 22 X 106
= 0.097 N/mm 2 > famint of - 1 N/mm 2
Therefore this is acceptable.
From eqn (10.4-3), top fibre stress is
p Pep Mimax + Md
A- Zz + Zz
1175 X 103 1175 X 10 3 X ( -167) 0 - 36.8 X 106
= 160 X 103 - 23 X 106 + 23 X 106
= 14.3 N/mm 2 < famaxt of 16 N/mm 2
Therefore this is acceptable.
Equations (10.4-2) and (10.4-4) are not critical. Similarly, it can be
shown that stresses are everywhere within the allowable values at
transfer. (Note: If the 'kink' of the tendon at B is considered too sharp,
this can be reduced by linear transformation. After such linear
transformation, the tendon may be outside the shaded zone in Fig.
10.5-1, but this does not matter, because (Rule 2) the line of pressure
remains within the zone.)
Example 10.5-2
Explain whether the following statements are true or false:
(a) The line of pressure (line of thrust) in a prestressed concrete continuous
beam is a linear transformation of the tendon profile.