96x

2023-11-30

VE0049 | Twisted Beam Under Complex Loads with Warping

Description

A beam is fully fixed (warping is restricted) on the left end (x=0) and supported by the fork support (free warping) on the right end (x=4a). The beam is subjected to a torque M, longitudinal force F_x and transverse force F_z. Determine the behaviour of the primary torsional moment M_Tpri, secondary torsional moment M_Tsec and warping moment M_ω. 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	Shear Modulus	G	81000.000	MPa
Geometry	Beam	Section Length	a	2.000	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		Torque	M	6.000	kNm
		Longitudinal Force	F_x	800.000	kN
		Transverse Force	F_z	100.000	kN

Twisted Beam Under Complex Loads with Warping

Analytical Solution

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

RFEM and RSTAB Settings

Modeled in RFEM 5.05, RSTAB 8.05 and RFEM 6.01, RSTAB 9.01
The element size is l_FE= 0.025 m
Isotropic linear elastic material model is used
Second-Order Analysis is used
RF-FE-LTB and FE-LTB module is used in RFEM 5 and RSTAB 8
Torsional Warping and Steel Design add-on is used in RFEM 6 and

Total torsional moment

Primary torsional moment

Secondary torsional moment

Warping moment

Point A	S3D	ANSYS 15	RFEM 6	Ratio	RSTAB 9	Ratio
M_T [kNm]	3.92	-	3.90	0.995	3.92	1.000
M_Tpri [kNm]	0.00	-	0.00	-	0.01	-
M_Tsec [kNm]	3.92	-	3.90	0.995	3.91	0.997
M_ω [kNm]	-4.77	-4.74	-4.80	1.006	-4.80	1.006

Point B	S3D	ANSYS 15	RFEM 6	Ratio	RSTAB 9	Ratio
M_T [kNm]	3.86	-	3.88	1.005	3.86	1.000
M_Tpri [kNm]	1.44	-	1.40	0.972	1.42	0.986
M_Tsec [kNm]	2.42	-	2.48	1.025	2.44	1.008
M_ω [kNm]	-0.17	-0.17	-0.19	1.118	-0.17	1.000

Point C	S3D	ANSYS 15	RFEM 6	Ratio	RSTAB 9	Ratio
ΔM_T [kNm]	-6.00	-	-6.00	1.000	-6.00	1.000
M_Tpri [kNm]	0.34	-	0.34	1.000	0.33	1.000
ΔM_Tsec [kNm]	-6.00	-	-6.00	1.000	-5.99	0.998
M_ω [kNm]	3.88	3.89	3.95	1.018	3.94	1.015

Remark: ΔM_T and ΔM_Tsec are values of quantity change at point D. This change is caused by the loading moment M.

Point D	S3D	ANSYS 15	RFEM 6	Ratio	RSTAB 9	Ratio
M_T [kNm]	-2.21	-	-2.19	0.991	-2.20	0.995
M_Tpri [kNm]	-1.22	-	-1.19	0.975	-1.20	0.984
M_Tsec [kNm]	-0.99	-	-1.00	1.010	-1.00	1.010
M_ω [kNm]	1.39	1.40	1.42	1.022	1.42	1.022

Point E	S3D	ANSYS 15	RFEM 6	Ratio	RSTAB 9	Ratio
M_T [kNm]	-2.21	-	-2.19	0.991	-2.20	0.995
M_Tpri [kNm]	-1.65	-	-1.62	0.982	-1.63	0.988
M_Tsec [kNm]	-0.56	-	-0.57	1.018	-0.57	1.018
M_ω [kNm]	0.00	0.00	0.00	-	0.00	-

Remark: Values of the warping moment M_ω in all test points are furthermore calculated in ANSYS 15 using BEAM188 element. Note that element solution values are interpolated in desired test points. Numerical solution in ANSYS 15 was carried out by the company Designtec s.r.o.

Point A	S3D	ANSYS 15	RFEM 5 - RF-FE-LTB	Ratio	RSTAB 8 - FE/LTB	Ratio
M_T [kNm]	3.92	-	3.95	1.008	3.92	1.000
M_Tpri [kNm]	0.00	-	0.00	-	0.00	-
M_Tsec [kNm]	3.92	-	3.95	1.008	3.92	1.000
M_ω [kNm]	-4.77	-4.74	-4.73	0.992	-4.81	1.008

Point B	S3D	ANSYS 15	RFEM 5 - RF-FE-LTB	Ratio	RSTAB 8 - FE/LTB	Ratio
M_T [kNm]	3.86	-	3.89	1.008	3.87	1.003
M_Tpri [kNm]	1.44	-	1.41	0.979	1.42	0.986
M_Tsec [kNm]	2.42	-	2.48	1.025	2.45	1.012
M_ω [kNm]	-0.17	-0.17	-0.16	0.941	-0.17	1.000

Point C	S3D	ANSYS 15	RFEM 5 - RF-FE-LTB	Ratio	RSTAB 8 - FE/LTB	Ratio
ΔM_T [kNm]	-6.00	-	-6.00	1.000	-6.00	1.000
M_Tpri [kNm]	0.34	-	0.34	1.000	0.33	1.000
ΔM_Tsec [kNm]	-6.00	-	-6.00	1.000	-6.00	1.000
M_ω [kNm]	3.88	3.89	3.87	0.997	3.95	1.008

Point D	S3D	ANSYS 15	RFEM 5 - RF-FE-LTB	Ratio	RSTAB 8 - FE/LTB	Ratio
M_T [kNm]	-2.21	-	-2.19	0.991	-2.20	0.995
M_Tpri [kNm]	-1.22	-	-1.19	0.975	-1.20	0.984
M_Tsec [kNm]	-0.99	-	-1.00	1.010	-1.00	1.010
M_ω [kNm]	1.39	1.40	1.41	1.014	1.41	1.014

Point E	S3D	ANSYS 15	RFEM 5 - RF-FE-LTB	Ratio	RSTAB 8 - FE/LTB	Ratio
M_T [kNm]	-2.21	-	-2.19	0.991	-2.20	0.995
M_Tpri [kNm]	-1.65	-	-1.63	0.988	-1.63	0.988
M_Tsec [kNm]	-0.56	-	-0.57	1.018	-0.57	1.018
M_ω [kNm]	0.00	0.00	0.00	-	0.00	-

374x

18x

Verification Example 000049 | 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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