1. The Application of Topology Optimisation to the Design of Steel I-Section Beam Web Openings
James Kingman, MEng Graduate1
Konstantinos Tsavdaridis, Lecturer1
Vassili Toropov1,2 ,
Professor of Aerospace and Structural Engineering
1School of Civil Engineering
2School of Mechanical Engineering

2. A beam with Web Openings
Perforated Beams
Benefits:
Perforations in the web of steel I-section beams increase the mass to stiffness ratio of the section
Longer spans or increased load capacities can be achieved without increasing material usage
A beam with Web Openings

3. Services Passing Through Web Openings
Perforated Beams
Benefits:
Services can also be passed through openings reducing overall storey height
Some perforation shapes are considered aesthetically pleasing
Services Passing Through Web Openings

4. Fabrication of Perforated Beams
Castellation/Profile Cutting:
A “parent” I-section is cut and welded to form a deeper section with web openings
Classic fabrication method first suggested 100 years ago
Considered the most cost effective
Geometry and layout of perforations significantly constrained

5. Fabrication of Perforated Beams
Plate Assembly:
Three flat plates are welded together to form the I-section
Openings are cut into the web prior to assembly
Only recently commercially implemented
Almost any conceivable web opening geometry or configuration can be fabricated

6. Hexagonal Web Openings
Perforation Shapes
Development:
Initially only hexagonal openings were considered
Circular openings first investigated in the 1980s
Circular openings are currently the most popular
Hexagonal Web Openings

7. Sinusoidal and Elliptical Opening Types
Perforation Shapes
Current Research:
Sinusoidal openings
Elliptical openings
Sinusoidal and Elliptical Opening Types

8. Perforation Shapes
Limitations of Current Research:
All of the currently considered opening types are restricted by the requirement that they can be fabricated using the castellation process
New opening shapes are developed through engineering intuition and experience
Can an Improved Web Perforation Concept be Developed using Structural Optimisation Tools?

9. Topology Optimisation
Background:
The most general structural optimisation tool
Most effective when used at a conceptual design level
Yields information on the optimum number, location and shape of openings within a structural continua
Structural Optimisation Problem Types a) Sizing b) Shape c) Topology

10. Topology Optimisation
Solution Techniqiues:
Topology optimisation is the most challenging class of structural optimisation problems
The Solid Isotropic Material with Penalisation (SIMP) technique is currently considered to be the most effective

11. Topology Optimisation
The SIMP Techniqiue:
Based on finite element modeling
Density of finite elements are design variables
Penalisation employed to attain a clear solid-void design

12. Studies on a Steel I-Beam
Approach:
Model a five meter long simply supported 305x165x40 UB with a uniformly distributed load applied to the top flange
Define the web the area to be topology optimised
Optimise for maximum stiffness subject to a constraint on the available material

13. Studies on a Steel I-Beam
Result:
Very irregular truss-like design
Iterative Optimisation Process

14. Studies on a Steel I-Beam
Manufacturing Constraints:
Design generated using topology optimisation was highly irregular
Manufacturing constraints can be applied to improve the rationality of topology optimised designs
Topology optimisation rerun with symmetry constraints
Lines of Enforced Symmetry

15. Studies on a Steel I-Beam
Result:
Regular truss like design with some interesting features
Iterative Optimisation Process

16. Performance of Optimised Beam
Aim:
Compare the structural performance of a beam with circular web openings and a beam with a topology optimised web
Beam Web Designs for Comparison

17. Performance of Optimised Beam
Determination of Structural Performance:
Beams with web openings often exhibit complex behavior
Full scale testing was outside of the scope of the project
Extensive evidence in the literature that geometric and materially nonlinear Finite Element Analysis can accurately simulate the behavior of beams with web openings
Nonlinear Finite Element Analysis Employed

18. Performance of Optimised Beam
Finite Element Analysis Approach:
Multistep approach:
Nominal properties for S355 steel used
Modeling approach previously calibrated against experimental samples
Linear Static Analysis
Eigenvalue Buckling Analysis
Imperfections Applied to Mesh
Geometric and Materially Nonlinear Analysis

19. Plots of von Mises’ Stress at yield load level
Results
Comparison of Circular and Topology Optimised Beam:
Total weight of both beams is identical
Topology optimised beam found to have improved structural characteristics
Plots of von Mises’ Stress at yield load level

20. Results

21. Studies on a Steel I-Beam
Conclusion:
Topology optimisation led to a design with improved structural characteristics
Significant effort required to develop the design
Lengthy analysis procedure required to verify the capacity of the section
Approach would not be suitable for every day design of beams

22. Parametric Study
Aim:
Conduct a parametric study to determine the topologically optimum web opening type for the wide range of beam cross sections found in practice

23. Local modelling approach employed in parametric study
A local modeling approach on a short length of beam was employed
Internal forces applied directly to the short length of beam
Same topology optimisation approach as previously detailed
Local modelling approach employed in parametric study

24. Parametric Study Results:
Depth of Section found to be critical parameter
Different opening types suggested for shallow and deep beams
Optimal opening topology for beams below 700mm deep
Optimal opening topology for beams deeper than 700mm

25. Conclusions
Increasing popularity of plate assembly fabrication technique enables new web opening designs to be considered
Topology optimisation can lead to web designs that have beneficial properties when compared to currently used opening types
A topologically optimum web opening concept has been suggested for both deep and shallow beams

26. Recommendations
Investigate the performance and failure modes of the suggested opening concept
Investigate the manufacture of the suggested opening concept
Develop design equations that can be used for the routine design of the topologically optimum web opening concept

27. Questions?