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S. Eleftheriadisa,c, C.F. Dunantb, M.P. Drewniokb, W. Rogers-Tizardc

aDepartment of Computer Science, University College London, UK

bDepartment of Engineering, University of Cambridge, UK

cPrice & Myers LLP

stathiseleftheriadis@gmail.com

Abstract. The study explores a practical engineering paradigm that aims to augment the cost and

carbon analysis of steel building structures. Cost and carbon functions were developed specifically

for this purpose including raw material, fabrication, design, fire protection, and erection

components. A customised computational model for the analysis of structural alternatives is

investigated. The proposed model is tested in an actual building case where several benchmark

designs are computed. The outputs from the model are compared with a small number of actual

design alternatives which were developed by engineering practitioners. The proposed method can

significantly increase the understanding of the design space’s boundaries whilst the computed

solutions have exhibited enhanced cost and carbon performance compared to actual designs.

1. Introduction

Although steel framed building structures are designed according to standards, which define

minimum safety limits, their material efficiency is rarely being systematically addressed in

practice. This inherently creates large inefficiencies in the way building structures are designed

and constructed. Moynihan and Allwood investigated 79 steel-framed buildings, and concluded

that unused mass of steel framed buildings could reach nearly 46% of the building’s total mass

due to over-specification of the steel sections (Moynihan & Allwood, 2014). Furthermore,

Dunant et al. in their study confirmed that 35-45% of the steel by mass of the steel frame is not

required in terms of structural efficiency (Dunant, et al., 2017).

Traditionally, the relationships between the cost of materials and the cost of fabrication in

construction is considered to have a significant impact on the final design selection. In the

literature, cost optimisation can be found in several instances: welded steel structures (Jarmai

& Farkas, 1999), steel frames with semi-rigid connections (Hayalioglu & Degertekin, 2005),

design, fabrication, and manufacturing (Sawada, et al., 2006; Heinisuo, et al., 2010; Haapio,

2012) and entire steel structures (BCSA & TATA, 2013). Cost as a single metric is easy to

comprehend and quantify, however, its relationship with other environmental impact metrics is

more complicated to determine. For example, even though material reductions are important in

CO2 optimisation this does not mean that material reduction will also yield cost optimum

solutions.

Although optimisation methods are available to engineering practitioners for more than three

decades, their implementation is limited by the different requirements addressed in every

project (Prager, 1970). Even though mathematical techniques are well established in structural

optimisation, which vary from construction scheduling (Zhou, et al., 2013), construction site

layout (Zhou, et al., 2009), construction management (Suliman, et al., 2011), size, shape and

topology optimisation (Frans & Arfiadi, 2014), and member optimisation in high rise buildings

(Kingman, et al., 2015; Stromberg, et al., 2012; Stromberg, et al., 2012), more practical

optimisation models are still needed. Despite the different optimisation studies of steel

buildings found in the literature, the relationship between cost and carbon performance in early

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design stages has not been effectively addressed in the past. Understanding these relationships

is a significant challenge and if appropriately addressed could offer structural engineers better

ways to evaluate optimised design configurations. The study investigates a practical

optimisation paradigm applied and validated in steel framed buildings developed to augment

both cost and carbon performance of the structure during the early phases of the design

development.

2. Research Approach

The objectives of the study are threefold: 1) To establish a cost and carbon model for the

assessment of steel structures, 2) To develop the computational model for the analysis of

structural alternatives, and 3) To verify the model in a real building case. In this study the results

obtained from the computational model are evaluated against actual design solutions in a

comparative study.

The study begins by defining the cost and carbon functions that are processed into a custom

cost and carbon analysis model of steel structures. The cost and carbon functions use data

factors from literature review and other empirical data sources. The analytical part of the study

comprises of two components. In both components, the objectives are cost and embodied

carbon minimisation of the steel structure. The functional unit of the study is defined as the

floor system of the structure. In the first component of the study, engineering-based alternatives

are developed using a manual trial-and-error design procedure. In this component, feasible

designs are articulated by engineers and indicated as “actual” solutions. These designs depend

on engineers’ perception of optimality and due to time constraints only a small part of the

solution space can be developed.

On the other hand, the second component includes theoretical design alternatives that are

computed in the parametric structural model. In this component, designs are specified as

“benchmark” solutions. Multiple configurations can be analysed rapidly and therefore the

design space can be fully explored. At this phase of the study, the outputs from both components

are used as inputs in the cost and carbon model in a separate process. However, an integrated

cost and carbon model within the parametric structural model is currently under development.

The cost and carbon model utilises the cost and carbon functions previously mentioned as well

as material quantities, construction properties, etc. from the structural analysis models. The cost

and carbon results for the actual and the benchmark solutions are evaluated and plotted in a 2D-

graph that assess discrepancies between the two solution sets.

2.1 Cost and Carbon Functions

A database of embodied carbon and cost inventories is established and associated with the

relevant material and structural type (beams, concrete, rebar). The review of the materials’ type

helps source the embodied carbon inventories: data input from Environmental Product

Declarations (EPD) related data or other Life Cycle Inventories (LCI) are utilised. In addition,

carbon data from GaBi and econinvent databases were utilised on several occasions. The cost

assessment model has been developed based on a feature based cost methodology. Cost factors

were used based on Spon’s Architect’s and Builder’s Price Book 2017. In feature-based models,

the manufacturing process of steel frames is divided into single processes. Each process is

executed at separate cost centres. The comprehensive cost components include raw material,

fabrication, design, fire protection, erection. The cost and carbon functions are developed using

Microsoft Excel making allowances for manual data input for bill of materials from the

structural analysis. The automatic query of cost and carbon functions is currently under

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development and it will be examined a later stage of the project. The cost functions are strongly

related to the structural analysis as beam-level information is used to derive total lengths, total

weights, number of elements and total surface area for painting and floor area. The function

utilises cost factors for rolled steel sections, precast units, connections, fire protection,

transportation, erection. The total cost of the structural system is adjusted in £/m2. The

embodied carbon component utilises concepts from the Life Cycle Assessment (LCA) theory

and particularly on environmental standards developed under the CEN/TC350 framework. The

scope of those standards follows a modular approach to buildings’ life cycle impacts based on

the corresponding life cycle stages starting from product and construction stages to use and end-

of-use stages. The carbon functions use material quantities from the structural analysis to

compute the embodied carbon of the structural steel, coating, precast concrete units, rebar and

screed. The output from the carbon model is given in kgCO2e/m2.

2.2 Computational Model

To help guide early stage structural steel designs, the computational model explored in this

study's principal role is to categorise technologies given the constraints which are often known.

For example, for a given load and combination of spans, what type of flooring is preferable? If

the ceiling height is restricted, is this different? In general, any number of restrictions in the

possible spans, loads, etc. can be applicable. At the same time, the design space is very large:

the number of commercially available options is considerable, and the grid, though it is

frequently fixed, generally allows for some flexibility. The difficulty is thus to explore as

completely as possible the complete solution space of possible floor solutions given a set of

constraints.

An exhaustive search is not possible, therefore, the proposed computational model functions as

a Monte-Carlo method, generating a large number of putative designs, rejecting those which do

not match the constraints and selecting the best so that they can be used as hints for the design

work of the structural engineers. The metric used to rank the solutions are predicted cost and

carbon footprint, both calculated on the basis of a detailed bill of materials generated by the

model. To generate putative designs, the model randomly generates bays from a user- provided

length probability distribution which was built in a custom C++ algorithm. Each bay, composed

of primary, secondary and tie beams is then calculated according to the prescribed loads. The

load on each beam is computed according to the area of the bay, the average area of its

neighbours, and its position as a corner, an edge or in the bulk of the floor. For each bay, all

possible combinations of technologies are investigated.

The design process envisaged would be this: the engineer uses the model according to the

specified spans and loads to choose the floor plate technology most appropriate for the project.

In a second step, the engineer would create a preliminary design and evaluate it. The engineer

would then use the design space described by the model to help them converge towards an

optimal solution: knowing the design space boundary should help deciding whether cheaper or

lighter designs are possible, particularly when the design of typical bays is suggested. The

definition of the bays (Figure 1) can take three form:

1. Free: a statistical distribution of the possible spans is given. This is appropriate for general

guidance where a general idea of the bay size is known, but is not fixed.

2. Semi-defined: the grid is defined in a single direction. This is typically the case for corridors

which follow the main grid but which length can be variable.

3. Fixed: the dimension of the bay is fixed along both direction

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Figure 1: Bay type definition

The computational model (Figure 2) can compute both composite and precast floor designs.

The study focuses on the analysis of precast systems only. A database of standard rolled sections

has been built in the algorithm but fabricated sections can also be identified. For the purposes

of this research the algorithm is searching for the optimum solution within the list of universal

sections available on the list. The method for selecting the beams in the precast design is the

following:

1. Universal sections are ranked according to their linear density

2. Each section, starting from the lightest is tested in turn for:

2.1 Frequency

2.2 Deflection

2.3 Bending moment

2.4 Shear strength

3. When a test is failed, the next section is tried

4. When no test fails, the section is selected.

5. Along the longest dimension of a bay, the opportunity to add secondary beams is

tried

5.1 The possible spans are selected

5.2 The primary and secondary beams are selected as above, taking into account the

additional stiffness.

Figure 2: Representation of the computational model

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3. Optimisation Scope

The optimisation options were separated into global and local levels. Components at global

level refer to those elements that affect the project at high level, generally at the earlier stages

of the design/concept, and were more heavily influenced by Architecture. Typically these

factors could include: column grid, primary/secondary beam spacing, floor type depth,

loadings, structural zone, and fire strategy. Local optimisation methods were those that could

be decided upon at a later stage of design. These were factors that only really affected the beams

independently, with little impact on the surrounding members, and were generally governed by

the Engineer. Examples of these factors could be: member/section type, steel grade, connection

type, cell/opening type, fire protection. The optimisation model in this study has focused on

components from the global level analysis with aim to identify methods to augment early stage

efficient design solutions.

4. Case Study

An in-depth investigation into the optimisation of a simplified steel frame was carried out. The

frame selected was an actual design project. The building was part of a new 2 storey school

block, with a single line of seven uniform classrooms with corridor down one side and

circulation cores at either end (Figure 3).

Figure 3: Typical layout of beams at first floor (the roof used an identical layout)

5. Engineering-Based Designs

Due to time constraints, only limited variations were looked at, with the other potential variables

restricted. Fixed variables were:

Column grid – this was fixed in this instance. Partly as it vastly reduced the potential

number of options, but also because as a classroom block (room sizes fixed with non-

negotiable clear spans) there was limited potential to alter this anyway.

Imposed loads were fixed at the standard value for classrooms at 3.0 kPa + 1.0 kPa for

partitions on the classroom level (first floor) and 0.75 kPa for the roof.

Circulation cores – as the location of these was not altered, the general arrangement of

beams within them also remained unchanged. This meant that the vertical bracing that

provided the lateral stability system also remained unchanged. Wind loads were applied

using a modeller tool built into the software, and this was also unchanged between each

option.

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Cladding loads were ignored in all cases, as were the effect of any permanent partitions

(e.g. around lift cores and stairwells).

For all cases, the overall structural depth was left unrestricted. Whilst this may have

provided some interesting results, it would have resulted in too many variables, and

given that the primary load bearing members in all cases run along the perimeters of

rooms it also was unlikely to be a restrictive issue in practice.

Table 1: The areas that were varied in the study were

Floor Type

Floor Depths

Floor Finishes

Beam Spacing

Precast planks

For precast this involved

simply varying the depth of

the planks in standard 50 mm

increments (and allowing for

secondary beams were

necessary).

For the precast options,

typically a 75 mm topping

screed was added (as is

usually necessary to

provide an acceptable

finish), however this was

removed for comparison in

two of the options.

Several variations of floor

beam arrangement were

considered, representing

what were believed to be

the various realistic patterns

5.1 Design Assumptions

Design was carried out on Tekla Structural Designer software in full accordance with Eurocode

3 (Steel). In each option, members were selected with the aim of achieving the section with the

minimum possible weight to suit both ULS and SLS requirements – aiming for a utilisation

ratio as close to 1.0 as possible. In principle, due to the relatively small variance between

options only a small selection of member sizes were used across all options. Columns as well

as beams were altered where necessary. Bracing was maintained as the same sections

throughout.

5.2 Actual Solutions

In total, 11 precast options were identified. The layout and design options tested are shown in

Figure 4. The material outputs were used to calculate the equivalent embodied CO2 and cost for

each option using the cost and carbon models previously described. This figure was then used

for comparison between the options to determine which had the lowest value. Figure 5 shows

the cost and carbon results for the entire structure of the 11 actual solutions analysed. Designs

1-4 were sized based on the optimum beam size, and plates were added to achieve the minimum

175 mm thickness needed for the bearing distance of 2 precast planks. Designs 4-8 were

restricted, so that only beams with a minimum width of 175 mm were allowed, this meant that

additional plates were not needed. All of designs 1-8 were designed assuming a propped

construction. Designs 9-10 were designed as un-propped, and required torsion design for the

temporary case where planks would be present on one side of the beam only. The final two

cases are as per designs 1 and 2, but with no screed required. Designs 11 and 12 proved to be

the most cost and carbon efficient solutions. The reduced screed lowered the volume of concrete

and therefore the weight of the structure, subsequently reducing the steel weight. Designs 4 and

8 were both variations of beam layout 4, which required a larger number of steels with smaller

spanning planks. This layout was not cost effective, and produced the largest cost and carbon

solutions. There did seem to be a clear distinction between beams that had a limited minimum

width of 175 mm, and in each case, the addition of flat plates to a smaller beam appeared to

provide a most cost and carbon efficient solution. The results from Design 3 are interesting as

it appears to have 5% less carbon and 5% more cost compared to Design 1. This can be

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attributed due to the larger number of total steel members used in Design 3 which increases

erection, fabrication and fire protection costs. On the other hand, the total weight of steel is

approximately the same with Design 1 but the use of 150 mm planks significantly reduces the

carbon emissions in the floor construction. Design 9, which was equivalent to Design 1 with

additional design contingency for torsion applied to the beam was more carbon intensive and

costly than its counterpart (Design 1). However, this difference was smaller than many of the

other factors. It should be noted that Design 10 encountered difficulties during the design stage

and has been omitted from this results comparison.

Figure 4: Grid layout and design options for engineering-based designs

Type Design

No.

Beam

Layout

Beam

Restrain

Beam

Type Comments

Precast

Type

Plank

Depth

(mm)

Screed

Depth

(mm)

Floor

Areas (m2)

Precast 1 Option 1 Pinned Universal N/A Hollowcore 200 75 1259

Precast 2 Option 2 Pinned Universal N/A Hollowcore 250 75 1259

Precast 3 Option 3 Pinned Universal N/A Hollowcore 150 75 1259

Precast 4 Option 4 Pinned Universal N/A Hollowcore 150 75 1259

Precast 5 Option 1 Pinned Universal

No steel

plate

Hollowcore 200 75 1259

Precast 6 Option 2 Pinned Universal

No steel

plate

Hollowcore 250 75 1259

Precast 7 Option 3 Pinned Universal

No steel

plate

Hollowcore 150 75 1259

Precast 8 Option 4 Pinned Universal

No steel

plate

Hollowcore 150 75 1259

Precast 9 Option 1 Pinned Universal Torsion Hollowcore 200 75 1259

Precast 10 Option 4 Pinned Universal Torsion Hollowcore 150 75 1259

Precast 11 Option 1 Pinned Universal No screed Hollowcore 200 -1259

Precast 12 Option 2 Pinned Universal No screed Hollowcore 250 -1259

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Figure 5: Results for Engineering-Based Designs for the whole structure

6. Computational-Based Designs

The design conditions and constraints used to populate the actual solutions were also

implemented as input data in the computational-based designs. Based on the defined data input

possible design configurations were computed to satisfy Eurocode 3 and the structural

requirements set by the engineering practitioners. The resulting 20,000 designs were computed

in less than 5 min. The material listings for these solutions were then compiled, using direct

output from the structural analysis. In total the data collected included:

Total steel weight by member type

Total steel surface area – this is to calculate the area of paint needed.

Total volume of precast planks

Total volume of in-situ concrete. This included the infill concrete around and between

planks for the precast options

Total weight of reinforcing steel. For precast options it allowed a basic weight for the

pre-stress tendons, as well as allowance for tying bars around the perimeter and between

planks.

Total weight of additional steel. This is to allow for plates and/or angles required where

beams are selected that don’t meet the required minimum bearing areas. No allowance

has been made for connections for any of the options.

Figure 6 shows the representation of the design space as populated by the model for the steel

beams of the structure. The swarm with the black nodes includes all the computational-based

solutions and is combined with engineering-based designs which are represented by the red

nodes. The comparative analysis with the actual designs only includes the first nine designs

excluding the ones without screed (designs 11 and 12) in order to understand the impacts of the

steel members on the cost and carbon results. It is evident that all the design solutions populated

from the computational model are more economical than the cheapest actual solution by 12-

18%. The carbon performance of the computational-based solutions lies on the lower boundary

of the actual designs. Almost 50% of the swarm has similar carbon performance compared to

the most carbon efficient actual solution. Furthermore, the design space showed that additional

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6-8% carbon reductions could be achieved from the design of steel beams by optimising mainly

the spans’ distribution and the classification of more efficient beam sizes.

Figure 6: Design space and cost and carbon relationships

7. Conclusions

The study has focused on the development of a practical computational model for the

optimisation of steel structures based on their cost and carbon performance. The research offers

a new paradigm to structural engineers for the analysis of design alternatives during the early

design stages where time restrictions often limit the exploration of the entire design space. The

proposed computational model provides rapid analysis of the solution space which can increase

the understanding of available designs and overall could enhance decision-making.

Comprehensive cost and carbon functions were established using relevant material,

manufacturing, fabrication, and construction factors which were then computed using the bill

of materials generated by the computational model. An actual building was used to verify the

proposed methodology. The engineering efficiency of the solutions was validated utilising an

engineering-based approach. The results obtained from the completed computations on the

tested building has showed that both cost and carbon performance could be enhanced when

compared to the actual designs solutions by 12-18% and 6-8% respectively. The reasons for the

enhanced efficiencies were mainly due to more appropriate use of spans and beam sections.

This is part of a larger study and therefore additional investigations in multiple building

scenarios are required in order to fully verify the efficiency of the computational model.

Nevertheless, the initial findings are encouraging and could be used in the refinement of a new

engineering paradigm for cost and carbon optimisation in steel building structures.

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Acknowledgements

This work has been made possible through funding provided by Innovate UK, project

‘Innovative engineering approach for material, carbon and cost efficiency of steel buildings’

ref. 102477 and this is gratefully acknowledged here.

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