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2024-03-18

VE0213 | Spatial Bending with Axial Force and Warping

Description

Continuous beam with four spans is loaded by axial and bending forces (replacing imperfections). All supports are fork - warping is free. Determine displacements u_y and u_z, moments M_y, M_z, M_ω and M_Tpri and rotation φ_x. 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	Beam	Length	L	12.000	m
	Beam	Span	L_s	3.000	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 Forces	F_y, F_z	31.000	kN
Load		Axial Force	F_x	1550.000	kN

Spatial Bending with Axial Force and Warping

Analytical Solution

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

RFEM and RSTAB Settings

Modeled in RFEM 6.05, RSTAB 9.05
The element size is l_FE= 0.300 m
Isotropic linear elastic material model is used
Second-Order Analysis and Large deformation Analysys is used
Torsional Warping is used in RFEM 6 and RSTAB 9

Results

Quantity	S3D	RFEM 6 - Second-Order Analysys	Ratio	RFEM 6 - Large Deformation Analysys	Ratio
u_y,max [mm]	12.600	13.334	1.058	13.242	1.051
u_z,max [mm]	45.200	44.675	0.988	46.989	1.040
φ_x,max [mrad]	11.750	12.701	1.081	12.389	1.054
M_y,max [kNm]	163.000	162.084	0.994	165.738	1.017
M_z,max [kNm]	44.000	46.077	1.047	45.131	1.026
M_Tpri,max [kNm]	47.000	49.000	1.043	47.930	1.020
M_Tsec,max [kNm]	172.000	224.071	1.303	118.061	0.686
M_ω,max [kNm²]	1.440	1.530	1.063	1.500	1.042

Remark: This verification example is not available in Large Deformation Analysis in RSTAB 9 now.

Quantity	S3D	RSTAB 9 - Second-Order Analysys	Ratio	RSTAB 9 - Large Deformation Analysys	Ratio
u_y,max [mm]	12.600	13.339	1.059	-	-
u_z,max [mm]	45.200	44.660	0.988	-	-
φ_x,max [mrad]	11.750	12.845	1.093	-	-
M_y,max [kNm]	163.000	162.064	0.994	-	-
M_z,max [kNm]	44.000	45.251	1.028	-	-
M_Tpri,max [kNm]	47.000	49.435	1.052	-	-
M_Tsec,max [kNm]	172.000	137.759	0.801	-	-
M_ω,max [kNm²]	1.440	1.536	1.067	-	-

40x

Verification Example 0213 | 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.

Gensichen

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