**Structural Optimization**

Introduction

The structural optimization is a part of a closed competition proposal for a sport hall in a high-school campus. Parametric Support has been invited by the architect to collaborate and share its expertise in resolving complex structural problems. The aim of an exercise is to find the most optimal structure for a roof covering the sport hall.

Collaborations that start in a competition phase (or early design phase ) of a project are the most beneficial for a client and environment. Research in the field reveals that this scheme allows to save the biggest amount of resources in a building life-cycle [fig 1]¹. If one wants to design green architecture, the sustainable aspect should be included in the preliminary sketches, because only then we can fully benefit from the environment without destroying it for immediate gains. During the early design stage the structural optimization should support design decisions taken by an architect and all parties involved in the project. To do so, the high-level control of geometry and the ability to generate diverse solutions and strategies are desirable². Such method may identify alternative schemes, that a designer has not initially considered. In the early stage of design a close collaboration between a structural engineer and an architect would be of the greatest benefit to the project.

fig 1. Design Sketch

The study shows a comparison between the preliminary, traditional structural design and the nonlinear, optimized approach. A similar problem is widely presented in public buildings such as sport and concert arenas, theaters, museums and in the recent years in corporate architecture.

**Input data
**

Basing on the preliminary design and a discussion with the client we defined objectives and constraints for the optimization process.

The roof studied in this exercise is a rectangle, 35 meters wide and 65 meters long, and the preliminary distribution of steel, 25 meters height columns, is unequal due to constraints.

The simulation was performed under specific loads listed below.

Loads | Material | ||

Live load | 0.8 kN/mq * 1.5 | Cross section | rectangular hollow section RHS |

Dead load factor | 1.35 | Material | Steel S275 |

Wind load | 0.5 kN/mq * 1.5 |

Constraints

The building plot has a quite challenging condition, it is cut with a water pipeline, where excavation and foundation are impossible. Due to this conditions the locations of the columns have been restricted.

**Objectives**

We defined two objectives. The first was to minimize the amount of material used for the structure itself (beams and columns) and the second was to minimize displacement.

Each objective is closely related to the benefits which are both direct and indirect.

**Our approach and workflow**

Since it was a competition phase, no digital information was available, thus sketch plans, sections and views were the starting point for the parametric model of the building structure.

Firstly, we followed the classical approach. Eight columns supporting the roof with the cross bracing and spatial trusses were proposed. The constraint requires a non-standard approach to the structure design, so additional bracing for vertical and horizontal loads were added. A single simulation was run on a static model.

fig 2. Initial vs Optimal Design

Secondly, we built a dynamic model. Having that we were able to explore the solution space, searching through thousands of candidates to find the best solution. Using our software, based on Swarm Intelligence, we were looking for the solutions that minimize the mass and displacement.

Our tool represents a stochastic approach to optimization – an iterative process where an algorithms is learning and in each generation finds better solutions. As an initial design we proposed eight randomly placed columns and a system of primary and secondary beams. To discover the best solutions we ran the optimization process for 20 times³, each time for 30 generations. Pareto Front solutions were then compared and nine best solutions selected.

fig 3. Pareto Front and solution space

**Result and comparison**

The optimization algorithm generates a range of alternatives, then an architect and a structural engineer asses (20-50) options from Pareto Front with respect to external conditions that were not defined as constraints. The outcome of the optimization process is presented in a Catalogue of Digital Solutions, where each solution is an optimal compromise between two contradicting objectives and performs better than the others in one aspect: reducing the amount of material will always increase structural displacement.

fig 4. Catalogue of Optimized Design

There are clear direct and indirect benefits for the client and the environment.

Firstly, the selected options are reducing the amount of material. The initial amount of steel used for the primary, the secondary and the tertiary structure was estimated as 320 000 kg. The algorithm was looking for solutions that perform better than the initial design and it discovered the designs that, depending on the priority of objectives, reduced the total mass of the structure from 43 to 51 percent (solutions 1-9) or decreased the displacement by 54 percent (solutions 1-7). Secondly, less material means lower carbon footprint: less material to produce, transport and less working hours.

From the other point of view more work on the construction site is required. In traditional approach trusses are prefabricated and mounted, the nonlinear approach requires a crane to collocate.

**Why is this approach uncommon?**

**
**Most of structural engineers and architects work on static models. An architect sends 2-3 models /sets of drawings to an engineer for verification and calculation. Using traditional tools such as Robot or SAP a structural engineer has to model a problem for every option. The approach we are advocating for is based on dynamic model where thousands of models are considered. An engineer models a process, based on objectives and constraints, they define loads and a structural system. The calculation process is automatized. With this approach in a relatively short time we can evaluate many more options and approaches to find the most suitable and sustainable design. Most importantly, this method does not require that the structure is adjusted to the project but allows to work hand in hand with an architect to find the best solution.

Traditional approach is highly time consuming. Parametric approach allows to evaluate an option in significantly shorter time, less than 10 minutes, while to model and evaluate the same option in a traditional way could take a day, even when only changing the number of diagonals in a truss.

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The project was run by Adrian Krężlik (architect) and optimized by Marco Pellegrino (structural engineering).

1. Building life cycle optimization tools for early design phases; I.Kovacic, V.Zoller;Energy Volume 92, Part 3, 1 December 2015, Pages 409-419

2. Optimization and parametric modelling to support conceptual structural design;Kirk Martini; International Journal of Architectural Computing; Issue 02, Volume 09

3. Literature suggest that 20 tests should be run to find the optimal solution. Artificial Evolution: 12th International Conference, Evolution Artificielle, EA 2015, Lyon, France, October 26-28, 2015.