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Effective length calculation of concrete columns in Eurocode2 1

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Pretty Girl

Structural
Joined
Nov 22, 2022
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155
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AU
The following equation is the effective length calculation in Eurocode 2 (page 66) for concrete columns.

Screenshot_2023-07-08_at_5.45.39_pm_pe5ug5.png



In that equation, the "k" is defined as follows,

Screenshot_2023-07-08_at_5.41.59_pm_onwkk8.png


However, in almost all the calculations (in the books, videos etc) have eliminated "θ/M" and "E" from the above and only considered "I/l". (As shown below). Removal of "E" is most probably due to the reason that column and beam both having same stiffness.

Screenshot_2023-07-08_at_5.48.58_pm_cpmgi6.png



My question is,
1. Why they have removed "θ/M" (the rotation for the bending moment)? the rotation (θ) could be different for both column than the beam, so isn't it unsafe to remove it from the equation?. What is the reason for removal of "θ/M" from the equation?
 
This simplification is described in PD 6687.

In short, it is a substitution and simplification of 'θ/M' for the beam member cracked section properties.
 
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