VE0047 | Snap-Through with Spring Support

Description

A structure made of I-profile trusses is supported on the both ends by the spring sliding supports and loaded by the transversal forces according to the following sketch. The problem is described by the following set of parameters. The verification example is based on the example introduced by Gensichen and Lumpe (see the reference).

Material	Steel	Modulus of Elasticity	E	210000.000	MPa
Material	Steel	Poisson's Ratio	ν	0.300	-
Geometry	Structure	Section Length 1	L₁	2.000	m
		Section Length 2	L₂	4.000	m
		Section Length 3	L₃	4.000	m
		Section Height 1	h₁	0.130	m
		Section Height 2	h₂	0.520	m
	Cross-section	Height	h	400.000	mm
		Width	b	180.000	mm
		Web Thickness	s	10.000	mm
		Flange Thickness	t	14.000	mm
Load		Transversal Force	F₁	10.000	kN
Load		Spring Stiffness	c_u,X	84000.000	kN/m

The self-weight is neglected in this example. Determine the deflection of the structure at point 1 (u_z1), the bending moment at point 2 (M_y2) , the normal force in the truss N and horizontal deflection of the spring support at point 3 (u_x3).

Snap-Through with Spring Support

Analytical Solution

Analytical solution is not available. Results from software S3D are taken as reference.

RFEM and RSTAB Settings

Modeled in RFEM 5.26, RSTAB 8.26 and RFEM 6.01, RSTAB 9.01
The element size is l_FE = 0.200 m
The number of increments is 5
Isotropic linear elastic material model is used
The structure is modeled using members (Trusses)
Shear stiffness of the members is neglected
Large deformation analysis is used

Results

Quantity	S3D	RFEM 6	Ratio	RSTAB 9	Ratio
u_z1 [mm]	53.8	53.6	0.996	53.7	0.998
M_y2 [kNm]	41.0	41.0	1.000	41.0	1.000
N [N]	-209.0	-208.4	0.997	-208.6	0.998
u_x3 [mm]	2.47	2.47	1.000	2.47	1.000

Quantity	S3D	RFEM 5	Ratio	RSTAB 8	Ratio
u_z1 [mm]	53.8	53.7	0.998	53.8	1.000
M_y2 [kNm]	41.0	41.0	1.000	41.0	1.000
N [N]	-209.0	-208.4	0.997	-208.6	0.998
u_x3 [mm]	2.47	2.47	1.000	2.47	1.000

391x

26x

Verification Example 000047 | 1

References

LUMPE, G. and GENSITEN, V. Evaluation of Linear and Nonlinear Member Analysis in Theory and Software: Test examples, causes of failure, detailed theory. Ernest.
LUMPE, G. S3D (Vers. 09/25/2011). Biberach University of Applied Sciences, 2011.

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