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)

Analysis of prestressed continuous beams: elastic theory 385
0·082
A 0 0·18 C E B
l--12-!!m -l-12·5m -4-1om --!-1sm ---1
fa) Tendon profile (angles in radians)
410kN JSkN/m 790kN 400kN
5~!1 It II t I I I Ill f
A D C E
f bJ Loading due to prestressing
100kN
8 j;)~kN
500kNm
36kN/m 400kN
tt tt t tt I It I f )500kNm
A 1 £
(c) Transverse loading for moment distribution
F.E.M. +1875 ·1875 +1440 -960 -500
Distr. -1875 -- _n 37 ---+1460
c.o. ..
Distr. +32
Tot81 (M,I 0 -2492 +2490 +500 -500
Fig. 10.2-4
(d) Moment distribution
~-·___J_l0·1m
e 0·5m '0·22m !,'
Af D C E B
• I
60kN 120kN 60kN
(e) Line of pressure
(Resulting moment diagram: 1m=5000kNm)
but where there are five or more spans a solution using a standard computer
program may be quicker. The final moments in Fig. 10.2-4(d) are
the resultant moments due to the effect of the prestressing on the
continuous beam. Hence the eccentricity eP of the line of pressure at
C must be -M 3/Pc = -2491 kNm/5000 kN = -0.5 m, as shown in
Fig. 10.2-4(e). The complete line of pressure is then obtained by a process
called linear transformation, which is described in Section 10.3.
The support reactions induced by the prestressing may be determined
from the secondary moments M 2. Equation (10.1-1) states that the
secondary moment diagram is the difference between the resulting
moment diagram (which is Fig. 10.2-4(e)) and the primary moment
diagram (which is Fig. 10.2-4(a) ); that is the secondary moment diagram
is a triangle (Rule 3 in Section 10.3 will make this point clear) in which
M 2 at A = (M 3 at A) - (M 1 at A) = 0
Mz at C = (M:. at C) - (M1 at C)