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)

394 Prestressed concrete continuous beams
saved by trying concordant profiles; in this respect, Rule 4 is helpful.
Rule 5 will be found useful if the trial profile has to be modified while
maintaining its concordancy (see Example 10.3-1(b) ).
StepS
If the profile selected in Step 4 is such that the tendon is too near the
beam top or the beam soffit at a section, increased concrete cover may
be achieved by linear transformation-which renders the tendon nonconcordant
but which does not affect the position of the line of pressure.
Similarly, if the 'kink' or change of slope of the tendon is too sharp
over a support (consequence: too much loss of prestress due to friction),
this may be eased by linear transformation; for example, in Fig. 10.3-2,
the 'kink' over the interior support is less in the profile (b) than in the
profile (a).
Step6
Check stresses at transfer and calculate loss of prestress; revise design as
necessary.
Step7
Check ultimate flexural strength and ultimate shear resistance at critical
sections. See Sections 9.5 and 9.6.
StepS
Design end blocks if necessary [1, 2].
Example 10.5-1
A post-tensioned beam of uniform cross-section is continuous over three
equal spans of 10 m, and carries imposed loads of 100 kN acting
simultaneously at each of the third-span points. The allowable stresses in
service are /a max = 14 N I mm 2 , /amin = 0 and those at transfer are /amaxt =
16 N/mm 2 and /amint = -1 N/mm2• The prestress loss ratio (ratio of the
prestressing force in service to that at transfer) is a = 0.85. Design:
(a)
(b)
(c)
SOLUTION
the concrete section;
the prestressing force; and
the tendon profile.
Step I
The reader should verify that the imposed-load moments Mi and the
dead-load moments Md are as shown in Fig. 10.5-1.
By inspection, section B is critical. From eqn (10.4-9),
Z(min) = Mimax - Mimin = 0 - ( -266) = 19 .0 x 106 mm3
famax - famin 14 - 0
To obtain a reasonable depth of the permissible zone for the line of
pressure, choose a section with, say, the following properties:
Z 1 (bottom) = 22 x 10 6 mm3 Z2(top) = 23 x 10 6 mm3
area A = 160,000 mm 2
overall depth h = 770 mm