Simplified prediction of deflections - Concrete Structures: Stresses and Deformations - page 343

Consider a column strip along AB; the curvature in the x direction at
the two ends is:

23.4 × 10 3
(25×10 9 )(694 × 10 −6 )

ψ 1 = − = − 1349 × 10 −6 m −1

47.3 × 10 3
(25×10 9 )(694 × 10 −6 )

2726 × 10 −6 m −1 .

ψ 3 = − = −

Curvature at middle of the strip (Equation 9.46) is

14.4)] 10 3
(25×10 9 ) (0.2) 3

12[28.1

− 0.2 ( −

ψ 2 = = 1859 × 10 −6 m −1 .

Basic de fl ection at mid-span of the strip relative to its ends (Equation

(9.43) ) is

(6.55) 2
96

2726)10 −6

δ ABbasic = ( − 1349 + 10 × 1859 − = 6.49 mm.

For a middle strip along EF, the basic curvatures at the ends and at the
middle are (Equation (9.46) ):

0.2(28.1)]10 3
(25×10 9 ) (0.2) 3

12[

− 14.4 −

ψ 1 = ψ 3 = = − 1201 × 10 −6 m −1

0.2(18.7)] 10 3
(25×10 9 ) (0.2) 3

12[10.1

−

ψ 2 = = 382 × 10 −6 m −1 .

Basic de fl ection at mid-span relative to ends (Equation (9.43) ) is

(7.00) 2
96

δ EFbasic = ( − 1201 + 10 × 382 − 1201) 10 −6 = 0.72 mm.

Basic de fl ection at centre of panel (point G, Equation (9.44) ) is

D basic = 6.49 + 0.72 = 7.21 mm (0.284 in).

A second pattern of strips may be used to calculate D basic as the
average

δ -value for column strips BC and AD plus δ -value for the