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)

338 Prestressed concrete simple beams
·I
Level of centroid
0 --·-r-·--1--
1
I
s ~
e ~o at
~0
~-~:~~-------------~~-~~~ __l__
o 1 10 (Level 1)
Mr
Z1
1~-~------------------- , ·I
Fig. 9.2-2 Stresses in a prestressed section
I
I
I
I
I
I
I
Figure 9.2-2 shows the stresses in a prestressed beam section. The line
0 1a 1b 1 represents Ievell, i.e. the beam-soffit; the line 0 2a2b2 represents
level 2, i.e. the beam top. Line CGD is the stress distribution due toPe;
therefore 0 10 is the prestress / 1 and 0 2C is fz. Line HGJ is the stress
distribution due toPe+ Mimin + Md and EGF that due toPe+ Mimax +
Md. The application of a sagging moment rotates the stress-distribution
line clockwise about G. 0 10 2 is the ordinate for zero stress; similarly a1a2
and b 1 b 2 are the ordinates for the stresses famin and famax respectively. The
reader should note that:
(a) Equation (9.2-4) represents the condition that point F must not pass
beyond the line a 1 a 2 •
(b) Equation (9.2-5) represents the condition that point J must not pass
(c)
beyond the line b 1b2 •
Similarly, eqns (9.2-6) and (9.2-7) represent the conditions that E
and H must not lie outside the region a2b2 •
(d) Under service condition, the maximum change of stress at the bottom
fibres is Mr/ Z 1 , where Mr is the range of imposed moments Mimax-
(e)
(f)
Mimin·
Similarly, the maximum change of service stress at the top fibres is
MriZz.
Therefore the minimum Z's to be provided must satisfy the
conditions: