# Optimization of office building frame with semi-rigid joints in normal and fire conditions

##### Bzdawka, Karol (2012)

Bzdawka, Karol

Tampere University of Technology

2012

Rakennetun ympäristön tiedekunta - Faculty of Built Environment

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**Julkaisun pysyvä osoite on**

https://urn.fi/URN:ISBN:978-952-15-2812-5

##### Tiivistelmä

There are many framing systems for buildings. This thesis considers one particularly popular system for office buildings in the Nordic countries. The frame consists of welded steel box beams (WQ-beams) and composite square concrete-filled hollow section columns (CFHS). The frame is non-sway – in the horizontal direction it is supported by lift shafts, staircases or shear walls. In this thesis, only the vertical load bearing system is considered. The only imposed load is the live load for office buildings – 3.0 kN/m2. The live load is transferred to the beams via hollow core (HC) slabs. The optimization of a structure consisting of the three elements: slabs, beams and columns is the subject of this thesis.

Several different layouts of the structure are optimized using Particle Swarm Optimization (PSO). The objective function of the optimization is the structure cost. The cost is calculated based on data available in the literature.

The investigated structures differ in static layouts, dimensions and dimension proportions and complexity. The variables of the optimization are the cross-sections of the members. The semi-rigid joints are assumed in order to investigate the influence of joint rigidity on the optimum solution. The joint stiffness is either fixed or variable in the optimization. The joint design is not part of this thesis so the true rotational stiffness of the joint is not used but rather its proportion to the beam bending stiffness.

The feasibility of each solution is verified following Eurocodes (with Finnish national annexes) and Eurocode-based Finnish guidelines for structural design. The requirements of ULS are verified in both normal and fire-design situations. The beams and joints are insulated from fire conditions so that the beam resistance and stiffness do not change because of temperature increase.

The data obtained from the optimization is presented and analysed. It was found that due to their high cost, the HC slabs determine the building’s shape. The relatively low cost CFHS columns have considerable reserve of capacity in ambient conditions allowing the use of semi-rigid joints. A semi-rigid beam-column joint reduces the sagging moment in the beam and increases the moment in the column. However, the column cross-section does not get much bigger since the moment increase in a fire situation is low due to the low column stiffness. The use of semi-rigid joints reduces the structure cost by ~10 % and the frame cost by ~20 %. The use of semi-rigid joints is recommended.

The thesis proposes modifications to the current frame solution and indicates the direction for future studies.

The PSO algorithm is found to be suitable for these kinds of problems due to its ease of use and good convergence towards the minimum.

Several different layouts of the structure are optimized using Particle Swarm Optimization (PSO). The objective function of the optimization is the structure cost. The cost is calculated based on data available in the literature.

The investigated structures differ in static layouts, dimensions and dimension proportions and complexity. The variables of the optimization are the cross-sections of the members. The semi-rigid joints are assumed in order to investigate the influence of joint rigidity on the optimum solution. The joint stiffness is either fixed or variable in the optimization. The joint design is not part of this thesis so the true rotational stiffness of the joint is not used but rather its proportion to the beam bending stiffness.

The feasibility of each solution is verified following Eurocodes (with Finnish national annexes) and Eurocode-based Finnish guidelines for structural design. The requirements of ULS are verified in both normal and fire-design situations. The beams and joints are insulated from fire conditions so that the beam resistance and stiffness do not change because of temperature increase.

The data obtained from the optimization is presented and analysed. It was found that due to their high cost, the HC slabs determine the building’s shape. The relatively low cost CFHS columns have considerable reserve of capacity in ambient conditions allowing the use of semi-rigid joints. A semi-rigid beam-column joint reduces the sagging moment in the beam and increases the moment in the column. However, the column cross-section does not get much bigger since the moment increase in a fire situation is low due to the low column stiffness. The use of semi-rigid joints reduces the structure cost by ~10 % and the frame cost by ~20 %. The use of semi-rigid joints is recommended.

The thesis proposes modifications to the current frame solution and indicates the direction for future studies.

The PSO algorithm is found to be suitable for these kinds of problems due to its ease of use and good convergence towards the minimum.

##### Kokoelmat

- Väitöskirjat [4335]