Flexural buckling capacity calculation in centered compression according to CTE DB SE-A (6.3.2) and EAE (35.1.1).

• Buckling is an insability phenomenon which occurs in axial compressed members, producing a reduction of their resistance capacity.
  
  
• The compression resistance of a member is its mechanical capacity reduced by a factor depending of the member characteristics (slenderness, nerce, constraints...)
  
  

Parameters:
Section class:	1234
Area =		cm2	It is not required to consider the holes at the ends of the element (EAE 35.1.1)
Inertia I =		cm4
Length =		cm
fy =	.235275355450.	N/mm2	YM1 =		(*1) EAE 15.3
Young modulous E =		N/mm2
Buckling curve:	.a0abcd.			Intraslational
Constraints at ends:	.Double-pinnedDouble-fixedPinned-fixedCantilever.			Traslational
(*1)Usually: 1.05. For steel bridges: 1.10. For buildings with tight tolerances, guaranteed steel and intense control: 1.00.
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Results:
Buckling length factor β=	1	(*2)		CTE DB SE-A 6.3.2.1, table 6.1, y EAE annex 5
Buckling length Lk =	550	cm		CTE DB SE-A 6.3.2.1
Critical compression Ncr =	1331.27	kN		CTE DB SE-A 6.3.2.1
Reduced slenderness λ =	0.7673			CTE DB SE-A 6.3.2.1
Imperfection factor α =	0.21			CTE DB SE-A 6.3.2.1 table 6.3
Factor Ø =	Value visible only to users with active subscription. (+info)
Reduction factor χ =	0.8139			CTE DB SE-A 6.3.2.1
Maximum axial Nb,Rd =	607.49	kN		CTE DB SE-A 6.3.2
Minimum axial Ned =	53.25	kN (*3)		EAE 35.1.2
(*2) The value of the β factor for cantilevers at traslational structures was not found, so a value of β=10 has been considered for being double than the double-pinned bars, as in intraslational structures.
(*3) With lower calculation axial streses "the buckling check could be ommitted, being only required to check the transversal section resistance."

• The program calculates the buckling in one plane only. In members with the same length and constraints at both ends, the calculation with the innerce of the weak plane will be enough. For elements with different length or constraints at each plane (as the top member of a truss, or a column in a plane portico with several spans) will be neccessary to make a calculation for each plane of the member.
  
  
• The CTE and the EAE include the buckling curves relating the slenderness with the buckling reduction factor. Although for practical purposes they are not too helpful (as the complete evaluaion does not avoid the use of calculators or spreadsheets, and the formulation is quite simple), in author's opinion they can be interesting to show how both values are related.
  
  
• In this program the same value is assigned to the different notations of the reduced slenderness showed at CTE: λ, λ_k , etc.
  
  

Version 12/07/2012