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)

Stresses in service: elastic theory 337
The prestress values at a typical section must be such that the following
stress criteria are satisfied under service conditions:
,, Mimax
,, -
fz +
[2+
z 1 - amm (9.2-4)
+ Md > f .
z 1 - amax (9.2-5)
Mimin + Md <f
z 2 - amax (9.2-6)
Mimax + Md < f
z 2 - amm (9.2-7)
Mimin + Md > f .
where famax is the maximum allowable stress in the concrete and famin the
minimum allowable stress, the sign convention being, as usual, positive for
compression; BS 8110 gives the values in Tables 9.2-1 and 9.2-2, which
include allowances for the partial safety factor.
Comments on eqns (9.2-4) to (9.2-7)
With some loss in generality, it is possible to use only two of these four
equations. See the simplified design procedure in Problem 9.1 at the end of
this chapter.
Table 9.2-1 Compressive stresses in concrete for the serviceability limit states
(BS 8110: Clause 4.3.4.2)
Nature of loading Allowable compressive stresses Uamax)
Design load in bending 0.33fcu (in continuous beams this may be increased to
0.4fcu within the range of support moments)
Design load in direct
compression
0.25fcu
Table 9.2-2 Flexural tensile stresses for Class 2 members: serviceability limit state
of cracking (BS 8110: Clause 4.3.4.3)
Allowable tensile stress ( -famin)(N/mm 2 )
Characteristic strength feu (N/mm 2 )
30
40
50
60
Pre-tensioned members
Post-tensioned members
2.1
2.9
2.3
3.2
2.6
3.5
2.8
Note:
(a) For Class 1 members, famin = 0.
(b) Table 9.2-2 gives the allowable stresses in tension and hence a negative sign should be
used when assigning these stress values to fa min.
(c) Designers usually limit the tensile stresses under service conditions to less than the
limitin:f values in Table 9.2-2. For example, for a post-tensioned member of feu = 50
N/mm ,!amin may well be taken as, say, -2 N/mm 2 , instead of-2.6 N/mm 2 as permitted
by BS 8110.