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2024-06-10

VE0215 | Lateral Torsional Buckling with Normal Force – Connection of Trusses at Center of Gravity

Description

A structure is consisted of an I-section beam and two tube trusses. The structure contains several imperfections and it is loaded by the force Fz. The problem is described by the following set of parameters. The self-weight is neglected in this example. Determine the deflections uy and uz and axial rotation φx at the endpoint (Point 4). 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 Structure Section 1 Length L1 4.000 m
Section 2 Length L2 4.000 m
Section 3 Length L3 2.500 m
Truss Support Position a 2.500 m
Imperfections Point 2 ey2 -40.000 mm
Point 4 ey4 12.500 mm
I-profile Height h 400.000 mm
Width b 180.000 mm
Web Thickness s 10.000 mm
Flange Thickness t1 14.000 mm
Tube Outer Diameter D 60.300 mm
Wall Thickness t2 5.000 mm
Load Force F 14.000 kN
Eccentricity eFy 20.000 mm
eFz -193.00 mm
Lateral Torsional Buckling with Normal Force - Connection of Trusses at Center of Gravity
Lateral Torsional Buckling with Normal Force - Connection of Trusses at Center of Gravity
Section and Connection Details
Section and Connection Details

Analytical Solution

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

RFEM and RSTAB Settings

  • Modeled in RFEM 6.06
  • The element size is lFE= 0.020 m
  • Isotropic linear elastic material model is used
  • The number of increments is 10
  • Large Deformation Analysys is used
  • The problem is modeled both by members and a combination of members and surface elements

Results

Two modeling techniques are used in RFEM 6. First, the I-section is modeled as a beam with imperfections and tubes as trusses (only N). Second, the tubes are trusses while the I-section beam is modeled by means of plates, considering the given imperfections. A fixed support at Point 1 is created by rigid line supports.

Results

Quantity S3D RFEM 6 - Members Ratio RFEM 6 - Members and Plates Ratio
uy [mm] 14.800 16.300 1.101 15.900 1.074
uz [mm] 16.900 18.000 1.065 17.800 1.053
φx [mrad] 237.000 242.200 1.022 254.400 1.073
Model 005052 | Verification Example 0217 | 1
114x
25x
Verification Example 0215 | 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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