2024-06-07

VE0215 | Lateral-Torsional Buckling with Normal Force – Connection of Trusses at Center of Gravity

Description

A structure consists of an I-section beam and two tube trusses. The structure contains several imperfections and it is loaded by the force F_z. The problem is described by the following set of parameters. The self-weight is neglected in this example. Determine the deflections u_y and u_z and axial rotation φ_x at the endpoint (Point 4). The verification example is based on the example introduced by Gensichen and Lumpe (see the reference).

Material	Steel S355	Modulus of Elasticity	E	210000.000	MPa
Material	Steel S355	Shear Modulus	G	81000.000	MPa
Geometry	Structure	Section 1 Length	L₁	4.000	m
		Section 2 Length	L₂	4.000	m
		Section 3 Length	L₃	2.500	m
		Truss Support Position	a	2.500	m
	Imperfections	Point 2	e_y2	-40.000	mm
	Imperfections	Point 4	e_y4	12.500	mm
	I-profile	Height	h	400.000	mm
		Width	b	180.000	mm
		Web Thickness	s	10.000	mm
		Flange Thickness	t₁	14.000	mm
	Tube	Outer Diameter	D	60.300	mm
	Tube	Wall Thickness	t₂	5.000	mm
Load		Force	F	14.000	kN
		Eccentricity	e_Fy	20.000	mm
		Eccentricity	e_Fz	-193.00	mm

Lateral Torsional Buckling with Normal Force - Connection of Trusses at Center of Gravity

Section and Connection Details

Analytical Solution

An analytical solution is not available. The results from the S3D software are taken as a reference.

RFEM and RSTAB Settings

Modeled in RFEM 6.14
The element size is l_FE= 0.020 m
Isotropic linear elastic material model is used
The number of increments is 10
Large Deformation Analysys is used
The problem is modeled both by members and a combination of members and surface elements

Results

Two modeling techniques are used in RFEM 6. First, the I-section is modeled as a beam with imperfections and tubes as trusses (only N). Second, the tubes are trusses while the I-section beam is modeled by means of plates, considering the given imperfections. A fixed support at Point 1 is created by rigid line supports. In case of a plate I-section beam the results are evaluated in the center point.

Results

Quantity	S3D	RFEM 6 - Members	Ratio	RFEM 6 - Members and Plates	Ratio
u_y [mm]	14.800	16.214	1.096	15.940	1.077
u_z [mm]	16.900	17.983	1.064	17.795	1.053
φ_x [mrad]	237.000	239.673	1.011	254.382	1.073

Verification Example 0215 | 1

References

Lumpe, G., & Gensichen, V. (2014). Evaluierung der linearen und nichtlinearen Stabstatik in Theorie und Software: Prüfbeispiele, Fehlerursachen, genaue Theorie. Berlin, Ernst & Sohn.
LUMPE, G. S3D (Vers. 09/25/2011). Biberach University of Applied Sciences, 2011.

Gensichen

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