RF-CONCRETE Members Version 5

RF-CONCRETE Members Version 5

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9.1.5 Determination of Deflection

Determination of Deflection

As described in chapter 2.2.5, it is possible to determine the probable value of the deformation according to equation (7.18) of EN 1992-1-1.

Distribution coefficient

The distribution coefficient ζ between state I (uncracked sections) and state II (cracked sections) is determined as follows:

ζ = 1 - β1 · β2 · σs,crσs2 = 1 - 1.0 · 0.5 · 232.87269.262 = 0.63 

where

    • β1 = 1.0 : ribbed steel
    • β2 = 0.5 : permanent load

The first cracking moment Mcr is:

Mcr = fctm · W1 = 2.2 · 0.007270 · 103 = 16.0 kNm 

The stress σs,cr immediately after cracking is determined with Mcr as follows:

σs,cr = McrAs · d - x3 = 16.0 · 10-34.45 · 10-4 ·0.17 - 0.04683 = 232.87 N/mm2 

Mean curvature

With the distribution coefficient ζ, the mean curvature is determined as follows:

1rm = ζ · 1rII + 1 - ζ · 1r1 = 0.63 · 0.01417 + 1 - 0.63 · 0.00304 = 0.01005 m-1 

Deformation

Thus, the deflection f in the beam center can be determined as follows:

f =k · leff2 · 1rm = 548 · 4.212 m2 · 0.01005 m-1 = 18.6 mm

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