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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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