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2024-03-08

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 uy and uz, moments My, Mz, Mω and MTpri and rotation φx. 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
Shear Modulus G 81000.000 MPa
Geometry Beam Length L 12.000 m
Span Ls 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 Fy, Fz 31.000 kN
Axial Force Fx 1550.000 kN
Spatial Bending with Axial Force and Warping
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 6.14, RSTAB 9.14
  • The element size is lFE= 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

RFEM 6 results:

Quantity S3D RFEM 6 - Second-Order Analysys Ratio RFEM 6 - Large Deformation Analysys Ratio
uy,max [mm] 12.600 13.361 1.060 13.241 1.051
uz,max [mm] 45.200 44.748 0.990 46.988 1.040
φx,max [mrad] 11.750 12.741 1.084 12.382 1.054
My,max [kNm] 163.000 162.337 0.996 165.736 1.017
Mz,max [kNm] 44.000 45.326 1.030 45.130 1.026
MTpri,max [kNcm] 47.000 49.241 1.048 47.987 1.021
MTsec(x=3) [kNcm] 172.000 202.451 1.177 142.141 0.826
Mω,max [kNm2] 1.440 1.535 1.066 1.499 1.041

RSTAB 9 results:

Quantity S3D RSTAB 9 - Second-Order Analysys Ratio RSTAB 9 - Large Deformation Analysys Ratio
uy,max [mm] 12.600 13.342 1.059 13.331 1.058
uz,max [mm] 45.200 44.659 0.988 47.787 1.057
φx,max [mrad] 11.750 12.898 1.098 13.335 1.135
My,max [kNm] 163.000 162.063 0.994 167.117 1.025
Mz,max [kNm] 44.000 45.261 1.029 45.434 1.033
MTpri,max [kNcm] 47.000 49.658 1.056 51.442 1.095
MTsec(x=3) [kNcm] 172.000 137.576 0.800 142.228 0.827
Mω,max [kNm2] 1.440 1.536 1.067 1.592 1.106
Model 004812 | Verification Example 0213 | 1
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Verification Example 0213 | 1
References
  1. Lumpe, G., & Gensichen, V. (2014). Evaluierung der linearen und nichtlinearen Stabstatik in Theorie und Software: Prüfbeispiele, Fehlerursachen, genaue Theorie. Berlin, Ernst & Sohn.
  2. LUMPE, G. S3D (Vers. 09/25/2011). Biberach University of Applied Sciences, 2011.
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