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)

182 Reinforced concrete beams-the serviceability limit states
Values of the concrete shrinkage Ecs are given in BS 8110: Part 2: Clause
7 .4. An approximate estimate may also be made using the method of
shrinkage prediction explained earlier in Section 2.5(c).
Loading for deflection calculations (BS 8110: Part 2: Clauses 3.3.2
and 3.3.3)
(a) If the purpose of the calculation is to check the serviceability limit
state of deflection, then the characteristic value should be used for
both the dead load and the live load (i.e. Yf = 1 for both).
(b) If the purpose of the calculation is to obtain a best estimate of the
deflection, then the characteristic value should be used for the dead
load, but the expected or most likely value should be used for the live
load.
Materials properties for deflection calculations
(BS 8110: Part 2: Clause 3.5)
(a) To check the serviceability limit state of deflection, the characteristic
strength of the concrete (Ym = 1) should be used to obtain the
modulus of elasticity in Table 2.5-6.
(b) To obtain a best estimate of the deflection, the expected concrete
strength should be used.
Short-term deflection
To calculate the short-term deflection, it is necessary only to apply the
curvature-area theorems, using the EI value appropriate to the partially
cracked section; creep and shrinkage effects do not come in.
Long-term deflection
In assessing the long-term deflection, the procedure of BS 8110 : Part
2: Clauses 3.6 and 3.7 may conveniently be summarized as follows.
Stepl
Calculate the instantaneous curvature 11 rit under the total load and the
instantaneous curvature 1/rip due to the permanent load; form the
difference (1/rit - 1/rip).
Step2
Calculate the long-term curvature l/r 1P due to the permanent load.
Step3
Add to the long-term curvature l/r1P the difference (1/rit - 1/rip).
Step4
Calculate the shrinkage curvature llrcs from eqn (5.5-6). The required
total curvature is then
~ = r~p + (,~t - r~J + r!s
StepS
From the total curvature so determined, deflections are readily
calculated from the curvature-area theorem.