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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 Fx and transverse force Fz. Determine the behaviour of the primary torsional moment MTpri, secondary torsional moment MTsec and warping moment Mω. 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
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 Fx 800.000 kN
Transverse Force Fz 100.000 kN
Twisted Beam Under Complex Loads with Warping
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 lFE= 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
Total Torsional Moment
Primary Torsional Moment
Primary Torsional Moment
Secondary Torsional Moment
Secondary Torsional Moment
Warping Moment
Warping Moment
Point A S3D ANSYS 15 RFEM 6 Ratio RSTAB 9 Ratio
MT [kNm] 3.92 - 3.90 0.995 3.92 1.000
MTpri [kNm] 0.00 - 0.00 - 0.01 -
MTsec [kNm] 3.92 - 3.90 0.995 3.91 0.997
Mω [kNm] -4.77 -4.74 -4.80 1.006 -4.80 1.006
Point B S3D ANSYS 15 RFEM 6 Ratio RSTAB 9 Ratio
MT [kNm] 3.86 - 3.88 1.005 3.86 1.000
MTpri [kNm] 1.44 - 1.40 0.972 1.42 0.986
MTsec [kNm] 2.42 - 2.48 1.025 2.44 1.008
Mω [kNm] -0.17 -0.17 -0.19 1.118 -0.17 1.000
Point C S3D ANSYS 15 RFEM 6 Ratio RSTAB 9 Ratio
ΔMT [kNm] -6.00 - -6.00 1.000 -6.00 1.000
MTpri [kNm] 0.34 - 0.34 1.000 0.33 1.000
ΔMTsec [kNm] -6.00 - -6.00 1.000 -5.99 0.998
Mω [kNm] 3.88 3.89 3.95 1.018 3.94 1.015

Remark: ΔMT and ΔMTsec 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
MT [kNm] -2.21 - -2.19 0.991 -2.20 0.995
MTpri [kNm] -1.22 - -1.19 0.975 -1.20 0.984
MTsec [kNm] -0.99 - -1.00 1.010 -1.00 1.010
Mω [kNm] 1.39 1.40 1.42 1.022 1.42 1.022
Point E S3D ANSYS 15 RFEM 6 Ratio RSTAB 9 Ratio
MT [kNm] -2.21 - -2.19 0.991 -2.20 0.995
MTpri [kNm] -1.65 - -1.62 0.982 -1.63 0.988
MTsec [kNm] -0.56 - -0.57 1.018 -0.57 1.018
Mω [kNm] 0.00 0.00 0.00 - 0.00 -

Remark: Values of the warping moment Mω 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
MT [kNm] 3.92 - 3.95 1.008 3.92 1.000
MTpri [kNm] 0.00 - 0.00 - 0.00 -
MTsec [kNm] 3.92 - 3.95 1.008 3.92 1.000
Mω [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
MT [kNm] 3.86 - 3.89 1.008 3.87 1.003
MTpri [kNm] 1.44 - 1.41 0.979 1.42 0.986
MTsec [kNm] 2.42 - 2.48 1.025 2.45 1.012
Mω [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
ΔMT [kNm] -6.00 - -6.00 1.000 -6.00 1.000
MTpri [kNm] 0.34 - 0.34 1.000 0.33 1.000
ΔMTsec [kNm] -6.00 - -6.00 1.000 -6.00 1.000
Mω [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
MT [kNm] -2.21 - -2.19 0.991 -2.20 0.995
MTpri [kNm] -1.22 - -1.19 0.975 -1.20 0.984
MTsec [kNm] -0.99 - -1.00 1.010 -1.00 1.010
Mω [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
MT [kNm] -2.21 - -2.19 0.991 -2.20 0.995
MTpri [kNm] -1.65 - -1.63 0.988 -1.63 0.988
MTsec [kNm] -0.56 - -0.57 1.018 -0.57 1.018
Mω [kNm] 0.00 0.00 0.00 - 0.00 -
Verification Example 000049 | 1
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Verification Example 000049 | 1
References
  1. LUMPE, G. and GENSITEN, V. Evaluation of Linear and Nonlinear Member Analysis in Theory and Software: Test examples, causes of failure, detailed theory. Ernest.
  2. LUMPE, G. S3D (Vers. 09/25/2011). Biberach University of Applied Sciences, 2011.
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