DLL 04: Slender beam simply supported subjected to axial load – eigen modes – global buckling

Description

Material		Modulus of elasticity	$E=200 000 N/mm^2$
		Density	$\rho=7800 kg/m^3$
		Poisson’s ratio	$\nu= 0.3$
Geometry	Cross-section	Dimensions	$b=h=50mm$
	Boundary conditions	In point A	Simple support
		In point B	Roller support
		Along line AB	$R_z, M_x$ and $M_y$ fixed to impose 2D behaviour
Loads		In point B	$F=10kN$
Mesh		No. of divisions	20

Results

Eigen modes

Eigen mode	Shape	Independent reference	Diamonds	Difference
1		28,702Hz	28,702Hz	0,00%
2		114,807Hz	114,807Hz	0,00%

Note: only the mass of vertical loads contributes to the eigenmodes. So these eigen modes are calculated with the mass of the self-weight. The horizontal force of 10kN does not contribute.

Global buckling factor

When you do a second order calculation, Diamonds calculates the global buckling factor. This global buckling factor is the factor with which the loads on the structure must be multiplied to obtain buckling. Resulting in the critial buckling force.

Equilibrium check in Diamonds

Which result	Independent reference	Diamonds	Difference
Critical load	257,02kN	$25,702 \cdot 10kN=257,02kN$	0,00%

References

Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 05: poutre élancée sur 2 appuis, soumise à un chargement axial

Tested in Diamonds 2023r01.

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