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)

Applying the concept of the line of pressure 391
(c)
superimpose 0.5 times Fig. 10.3-3(d) to the profile in Fig. 10.3-3(c),
i.e.
Fig. 10.3-3(e) = Fig. 10.3-3(c) + 0.5 x Fig. 10.3-3(d)
Specifically, the tendon must be lowered by 0.125 m at the interior
support C. Within each ofthe spans AC and CB, the tendon is moved
as a rigid body without changing its shape.
In its new position, the tendon does not fulfil its original purpose,
because the new line of pressure is no longer that shown in Fig.
10.3-3(c) but is as shown by the full line in Fig. 10.3-3(e).
10.4 Applying the concept of the line of pressure
Equations (9.2-2) to (9.2-7) become applicable to continuous beams if
the eccentricity eP of the line of pressure is substituted for the tendon
eccentricity e 5 • Thus, for a continuous. beam, the prestressing force Pe and
the profile of the line of pressure must satisfy the conditions:
Pe Peep Mimax + Md
-+-- f
A zl zl ;;::::: amin
(10.4-1)
Pe Peep Mimin
-+-- + Md <f
A zl zl - amax
(10.4-2)
Pe Peep Mimax + Md < f
(10.4-3)
----+
A Zz z2 - amax
Pe Peep Mimin + Md f
(10.4-4)
---+ z2 ;;::::: amin
A Z 2
where ep is the eccentricity of the line of pressure at the section considered,
and the meanings of the other symbols are as in eqns (9.2-1)
to (9.2-7). Rearrangement of these equations gives the limits of the
permissible pressure zone, i.e. the permissible zone for the line of pressure:
Mimin + Md Zz Zz/amin
(10.4-5)
(10.4-6)
(10.4-7)
eP ::;:; p + A - p (10.4-8)
e
e
If a concordant profile is used then the line of pressure is coincident with
the tendon profile and e 5 and eP are synonymous; the above equations then
become identical to eqns (9.2-18) to (9.2-21).
Equation (9.2-8) is applicable to continuous beams, irrespective of
whether the tendon is concordant or not:
Zt (bottom)} ;;::::: Mimax - Mimin
Zz (top) fa max - fa min
(10.4-9)