CFS Building talks to Cold Formed Steel expert and Structural Engineer, Simon Bechara about his self developed Torsion Theory and modifications to the S.Vlasov Warping Theory.
Cold Formed Steel technologies are found in numerous market segments across residential and commercial applications, mainly composed of open C channel sections using small gauges.
Structural analysis and design tools, as offered in the market by machine fabricators and software developers, are still following the classical 2D and/or 3D analysis using the 6 degrees of freedom beam element. However, this does not represent the warping effect and evaluate the actual and additional induced stresses to perform design checks accordingly.
Knowing that the Finite Elements Method is considered as an alternative to evaluating the stresses due to the warping (non-linear torsion), it is not practical to model a complete structure for every job. Even when applied, the stress checking is limited to classical methods to determine the allowable stresses, where the buckling effect and the stability of a beam element are not considered.
The result of a research done by Simon Bechara titled ‘Simon Torsion Theory ‘and ‘Modified Vlasov’ to further study the warping effect of thin members, lead to a modification of S.Vlasov warping theory, finding the missing point in S.Vlasov initial equation, by adding the bi-shear slide due to the bi-moment effect.
Applying the ‘Simon Torsion Theory’ or ‘Modified Vlasov’, the twist rotation of a circular hollow section with an open wall, subject to torsion, was greater by 20% from the application of the original S. Vlasov.
C Sections in LGSF typically having a thickness range from 0.55 mm (23ga) to 1.6 mm (16ga) and are a perfect example to apply the ‘Modified Vlasov’ that leads to a substantial change in 3D analysis and design results of a 3D CFS Structure when torsion moment can not be ignored.
Establishing the theoretical formulation, we developed a practical application into software. We developed an analysis and design tool where the warping and the Modified Vlasov theory is built into the code, and it was successful in performing the warping analysis and design for H shapes.
Titled GMatrix-7, the software can deal with a large number of nodes and members with a fast stiffness matrix solver.
As a user interface, GMatrix-7 is empowered and equipped by different API’s to interface with the designer, or any other user interfaces upon the company’s requirements listed as follows:
-Text File (Language) that can easily link with other menus upon the user’s requirement.
-PEB module, where the user needs only to define the building’s parameters and GMatrix-7, will automatically generate the necessary file, perform the automatic design, and generate approval drawings and the bill of materials.
With the above specifications that GMatrix-7 supports, it is now successfully implemented in the field of Porta-Cabins, Cold-Formed 3D Steel Structures, and Pre-Engineered Buildings.
GMatrix-7 was also used to analyze and design check the Hull Beams of the first planned floating island in the world located at Jounieh Bay, Lebanon. This ambitious project by the Daou family was under construction in the seaside resort town, but in recent times, the project has unfortunately ground to a halt. The base structure consisted of a main deck, 1 to 2 meters above sea level, and built to house a 5-star luxury resort of 64 rooms, restaurant, nightclub, and fitness facility spread over 3,300 square meters. The man-made floating island was designed to be a self-sustaining, independent structure. The Hull Beams that were carrying the building and connecting it to the specialized Floating System were under a very heavy loading induced by the building weight and waves lateral kicks. As such, the Hull Beams required additional special analysis to check for warping.
Effect (Non- Linear Torsion) could be analyzed using GMatrix-7 Analysis software that can perform the 9 DOF Beam Element. The design checking becomes more accurate and aligned with the design code requirements instead of other methods to check the stress when the Finite Elements method was applied.
GMatrix-7 has never been supported or sponsored by any third party. The theoretical research and software application is the fruit of a lifetime work completed by Simon Bechara. Simon is a structural engineer who graduated from University Saint Joseph Lebanon (USJ, ESIB) with a Masters degree in structural analysis and finite elements. Simon has always believed in personal development and knowledge to help build a better world.