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Is a first-order analysis enough? (alpha_cr)

Elastic critical load factor of a storey from its horizontal deflection, and the limit for first-order analysis. Reference: EN 1993-1-1 5.2.1(4).

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Is a first-order analysis enough? (alpha_cr): worked example sheet in Equation Pad with typeset equations and results.

Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of Eurocode 3 and its national annex before you use it, and have the result checked by a competent person. See the disclaimer.

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# Storey
H_Ed := 50 kN
V_Ed := 2000 kN
h_st := 6.0 m
delta_H := 8 mm

# Check
alpha_cr := (H_Ed/V_Ed)*(h_st/delta_H) =
alpha_cr >= 10 =
# TRUE: second-order effects may be ignored. Between 3 and 10 the sway effects can be amplified by 1/(1 - 1/alpha_cr).

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