Optimisation of hollow core slabs: Producing units of a smaller standard width

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ACKNOWLEDGMENTS

I would like to express my deepest appreciation to my supervisor in Strängbetong, Mr. Henrik Vinell, for his time, motivation, patience, continuous advising and support during those months. I strongly believe that his ideas and way of thinking, are of the most important things I gained from this experience. Without his guidance and persistent help this project would not have been possible. I would like to express my sincere gratitude to my thesis supervisor at KTH Royal Institute of Technology, Professor Johan Silfwerbrand, for bringing me in contact with Strängbetong and hence giving me the opportunity to work with this topic. Additionally, I am thankful for his help and comments on this report, but also for teaching me about the important field of theory and methodology on research.

I also wish to thank the employees in the office of Strängbetong in Stockholm for answering my questions, creating a nice working environment and making me feel comfortable from the first day. Many thanks to the employees of Strängbetong in the factory in Kungsör, for sharing with me their knowledge, providing me with useful material and being willing to answer all my questions.

This thesis was completed during a pandemic, under very special circumstances. I would like to thank my family and friends for their support during this difficult period.

Stockholm in September 2020, Konstantinos Apostolou

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Abstract [en]

The Swedish precast concrete company ‘Strängbetong’ produces a variety of Hollow Core slabs, with a standard width of 1200 mm. Quite often, the HC units are subjected to longitudinal cutting1, which takes place in the factory by a diamond blade, in order to achieve narrower elements. This results in a considerable material waste since the rest part of the HC unit cannot always be utilized. Regarding the cutting process, it requires a significant amount of time that slows down the production. Moreover, extra workhands are needed, while other factors such as the transfer and crash of unwanted pieces, contribute to a higher cost for the factory. Approximately 12% of the HC elements produced by Strängbetong are fillers. Aiming to achieve a more efficient and sustainable production, the reduction of the number of fillers is of vital importance.

This thesis project investigates if a line producing smaller width elements would be more profitable. The study starts by investigating the most common width that HCs are cut, with the aim to create a line according to this width2. Then, the most promising width is determined, taking into account the possible alternatives and fillers’ width trends that have been found. To estimate accurately the possible cost saving, the impact of the smaller width line on the production and the possible increase of thru put3_{, the production of the factory in Kungsör, is simulated on MATLAB. Firstly, the current}

situation is simulated (8 lines, 1200-mm-wide) in order to evaluate the current efficiency. Then, the studied scenario is simulated (7 lines 1200-mm-wide and one 813-mm-line), to evaluate the advantages of this alteration. Both simulations start by imposing the HC production load of 2019. This thesis is completed by a repetition of the simulations, where the input data are modified, in an effort to calculate accurately the possible cost saving as a function of designers’ adaption to the 813-mm-line. The results show that if an 813-mm-line were used instead of a 1200-mm-line during 2019, the possible cost saving would be at least 1.0 million SEK annually. The suggested line leads to a more sustainable production, as concrete and steel waste can be decreased by 51.6% and 50.3%, respectively. A significant amount of time due to less longitudinal cutting can be saved while there is a slight increase of thru put. Moreover, the results show that the factory will be able to handle the pressure on the production, despite the decrease by 1/8 of the physical production capacity of 1200 mm units. Finally, if the designers adapt fast to the new width alternative, the possible cost saving would rise significantly. If it is possible to design 1 out of 5 future fillers as a full-width element, cost saving can reach 1.4 million SEK annually.

1_{Elements produced at a width smaller than the full width (1200 mm), are mentioned as ‘fillers’ in the HC production. In} Sweden, usually those elements are mentioned as ‘passelement’.

2_{This that it is examined, is the modification of a full width line to a line with a smaller standard width. It should not be} confused with the creation of an extra casting bed.

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Sammanfattning [sv]

Den svenska betongelementtillverkaren Strängbetong producerar olika typer av håldäck med en standardbredd på 1200 mm. Ganska ofta blir håldäckselementen föremål för längdsågning som genomförs i fabriken med en diamantsåg med syftet att erhålla smalare element. Detta leder till ett inte försumbart materialsvinn eftersom den avsågade delen inte alltid kan användas. Beträffande sågningen kräver den en betydande tidsåtgång som fördröjer produktionen. Vidare krävs ytterligare arbetskraft medan andra faktorer som transport och krossning bidrar till högre kostnader för fabriken. Cirka 12 % av Strängbetongs håldäcksproduktion utgörs av så kallade passelement. För att nå en mer effektiv och hållbar produktion är det angeläget att minska antalet passelement.

I detta examensarbete studeras om en linje som produceras smalare element skulle vara lönsam. Studien inleds med att undersöka de vanligaste bredderna som håldäckselementen sågas i med syftet att skapa en linje för den bredden. Därefter bestäms den mest lovande bredden genom att beakta möjliga alternativ och identifierade trender kring passelementens bredder. För att noggrant kunna uppskatta de möjliga kostnadsbesparingarna, en smalare linjes inverkan på produktionen och en möjlig ökning av volymen (antalet produktionscyklar per dag) så har produktionen i Kungsörfabriken simulerats med hjälp av MATLAB. Först studerades den rådande situationen (8 st 1200 mm breda linjer) för att uppskatta dagens effektivitet. Därefter simulerades ett studerat scenario (7 st 1200 mm breda linjer och en med bredden 813 mm) för att utvärdera fördelarna med denna förändring. Båda simuleringarna utgår från 2019 års produktionsbelastning. Examensarbetet avslutas med en upprepning av simuleringarna, nu med modifierade ingångsdata, i ett försök att korrekt beräkna möjliga kostnadsbesparingar där hänsyn tas till konstruktörernas kännedom om den 813 mm breda linjens existens.

Resultaten visar att ifall en 813 mm bred linje hade använts i stället för en av 1200 mm-linjerna under 2019 så hade kostnadsbesparingarna uppgått till minst 1,0 miljon kronor årligen. Den föreslagna linjen leder till en mer hållbar produktion eftersom betong- och stålsvinn kan reduceras med 51,6 resp. 50,3 %. En betydande tidsbesparing kan göras på grund av mindre längdsågning samtidigt som volymen ökar något. Dessutom visar resultaten att fabriken förväntas kunna hantera det ökade trycket på produktionen trots att kapaciteten för 1200 mm breda element minskar med 1/8. Slutligen ifall konstruktörerna snabbt börjar tillvarata det nya alternativet så skulle de möjliga kostnadsbesparingarna kunna öka i hög grad. Om det vore möjligt att dimensionera 1 av 5 passelement som ett fullbreddselement så skulle kostnadsbesparingarna kunna uppgå till 1,4 Mkr per år.

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1. Introduction

1.1 General information

Hollow Core slabs (HC slabs) are an alternative type of slab that offers many advantages and is gaining popularity, especially across Northern Europe and the United States. HC slabs are prestressed precast concrete elements manufactured using long line casting pallets. Longitudinal voids, or cores, run throughout a HC slab, resulting in a significant reduction of raw material consumption and weight of the slabs, while they provide ready-made ducts for services. With the prestress and low self-weight, longer spans can be achieved for the same loads or greater loads for the same depths. Moreover, higher erection speed of a building is achieved, as HC slabs are factory made. Site work is significantly reduced, and construction process is not vulnerable to weather conditions. HC slabs are cast in long beds, and then length-cutting with diamond blades takes place (IPHA 2020).

Picture 1-1. A hollow core slab (from Strängbetong)

Strängbetong is the major Hollow Core producer in Sweden. HC slabs are produced in three of the company’s factories: in Kungsör, Veddige and Långviksmon. The company produces a variety of types of HC slabs (with regard to thickness and number of cores), of a standard width 1200 mm. The factory in Kungsör leads the production of HC slabs, with 8 casting beds, 143 m long.

Even though the use of HC slabs is accompanied with certain benefits, their design, production and use are always a field under study. Innovative ideas have already been a subject under research with the intention of making the HC production more efficient. Additionally, as the use of HC slabs has been increased, recommendations and alterations of the design guidelines of HC slabs are often an issue under discussion.

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1.2 Description of the problem

As mentioned before, HC slabs can provide certain advantages against other types of slabs. However, as the width of the HC slabs is fixed at 1200 mm, one understands that the structural elements are often subjected to further cut, in order to fit projects’ specific needs. Apart from cutting for making specific angles on elements, or other cuts for details, length-cutting usually takes place (a HC unit is cut longitudinally in its long dimension). Elements subjected to length-cutting are mentioned as ‘fillers’4_{in the HC production.}

Length-cutting of HC units increases the material waste significantly, as it is not always possible to use the other side of the HC slab, when a 1200-mm-wide element has to be cut. Moreover, there is a slowdown of the production, due to the time needed to cut an element. Apart from the cost deriving from the material waste, there is an additional cost for the factory for transferring and destroying the unwanted pieces, while the removal of those elements from the beds requires time and workhands. The environmental impact is higher, due to the material waste and the additional CO2 emissions from

the produced unwanted pieces.

In this report, it is examined if a new casting bed of a standard width smaller than 1200 mm will result to more efficiency in the HC production. Firstly, the width that would lead to the highest possible efficiency is investigated. Then, the production is simulated and the possible cost saving is studied, as also the impact of a new width line on the production, based on the HCs produced during 2019 in the factory in Kungsör. Following this, more simulations are made, to predict the possible cost saving considering designers’ adaption to the new width line.

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2. Background Information

2.1 Types of HC slabs

There are in total six alternative depths of HC elements that are produced by Strängbetong today. Moreover, there are alternatives in the design patterns of cores for specific depths, which leads to nine types of HC slabs in total. The technical characteristics of each type are depicted below. A more detailed description of each type is given in the Appendix A1.

Table 2-1. Technical characteristics of the available HC types.

Type Thickness (depth) (mm) Width (mm) Number of cores Number of strands Cross-section area (m2₎ Weight (kg /m) HD/F 120/20 F155 200 1197 6 7 0.124 310 HD/F 120/20 F125 200 1197 6 7 0.160 399 HD/F 120/22 F155 220 1197 6 7 0.147 368 HD/F 120/22 F125 220 1197 6 7 0.172 430 HD/F 120/27 F184 265 1197 5 8 0.165 411 HD/F 120/27 F155 265 1197 5 8 0.211 527 HD/F 120/32 F236 320 1197 4 11 0.178 445 HD/F 120/38 F218 380 1197 4 14 0.214 534 HD/F 120/40 F172 400 1197 5 16 0.234 585

2.2 Regulations for longitudinal cutting of HC units

When a HC unit needs to be cut, it is important to cut at a point so that the strands (body) will not be affected. Affecting the body of the HC unit, will lead to lower capacity of the element and many other problems during the production stage. Hence, a distance from the strands is always required. There are two general regulations (Eriksson 2014) that are followed when a HC unit needs to be cut:

1. Cut of a HC unit according to allowable zones for cutting (SE-HDF00-525) (old regulation) According to that regulation, an engineer is allowed to cut a HC unit in a zone around the middle of the core, while he is recommended to cut in the smallest possible cross-section area. This regulation is used more often.

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Figure 2-1. Zones where it is allowed to cut a HC unit according to the old regulations. (Strängbetong handbook, SE-HDF00-525), (full document on the Appendix A2)

2. Cut of a HC unit at a recommended width (SE-HDF00-521) (new regulation)

This regulation defines the exact points that an engineer is allowed to cut, for each type of HC element. The regulation allows the designers to cut only in the middle of the cores. This regulation is used less often, but it is gaining popularity year by year, especially across the new designers.

Figure 2-2. Recommended cutting widths, leading to the lowest cross section area. (Strängbetong handbook, SE-HDF00-521), (Full document on the Appendix A3)

Cutting a HC unit in a cutting zone (SE-HDF00-525) is more time consuming, as most of the times, the element is not cut exactly in the middle of the core, leading to a higher cross-section area that needs to be cut by the diamond blade. Moreover, it is more difficult to combine fillers in the

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production, in order to reduce the waste. However, even when two fillers are placed beside each other to reduce waste, it is very common that the diamond blade may need to cut twice in order to create the required widths. Hence, cutting a HC unit according to that regulation slows down the production and makes the employees’ job more difficult. In addition, when an element is cut at a point far from the middle of the core, the blade during the cutting tends to turn towards the core center, something that increases difficulty and time, while it is quite common that the diamond blade will have to cut twice to succeed an acceptable result.

Cutting a HC unit in an exact point – which is the middle of the core (SE-HDF00-521), leads to cutting in the lowest cross-section areas and consequently to the lowest possible slowdown of the production. The blade is strained less and the cutting procedure is more efficient. In addition, it is easier for the production planners to place HC fillers beside each other in order to reduce waste. In that case, two HC fillers can be cut, by only one pass of the diamond blade.

2.3 The difficulty of re-using scrap elements

For a filler to be produced, a full-width element is subjected to longitudinal cutting. The production planners try to utilize the rest of the casting bed (towards the transverse direction), by placing a filler there. In that way, material is saved, capacity is increased and with one pass of the diamond blade, two fillers are cut. This is easier when elements are cut according to the new regulations of cutting (SE-HDF00-521), because elements are cut in specific widths and as a result, it is easier to find an element that matches the dimensions. However, it is not always possible to place a filler on the other side of the element, resulting to a scrap element.

Generally, the scrap elements are utilized when this is possible. Elements that are possible to use again, are stored in the factory and their technical details and other characteristics are marked. When an order of a filler can be covered by an element of those on storage, then, instead of casting, the scrap element is utilized. However, for many reasons, it is very difficult to utilize scrap elements, and hence one understands the importance to reduce scrap elements produced by longitudinal cutting.

Firstly, it is quite difficult to match an order with a scrap element of those in storage, as the technical details have to match (dimensions, HC type, etc.). Secondly, storage of fillers is difficult for the production, as it requires extra workhands and a significant amount of space. Furthermore, elements most often include design details, something that increases the difficulty of finding a stored element which is compatible. More problems can derive in the re-use of scrap elements e.g. regarding the lifting of those elements on site. One way of lifting fillers is by using lifting wires locked on specific positions of the filler, which can be a problem when an element is re-used.

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The above shows that it is quite difficult to use a scrap element, and consequently, it is of vital importance to reduce the produced scrap elements, for a more efficient production.

2.4 Efficiency of a new width line

The efficiency of the width of a new line is generally depended on the following factors:

1. The biggest possible percentage of fillers that the new width line can cover. This can be done in two ways: directly and indirectly.

• Directly, if the element fits exactly to the actual need (less common).

• Indirectly, when a new element is used in combination with cast-in-situ concrete joints (more common).

2. By avoiding the highest possible length cutting. Usually, it implies that covering the biggest possible percentage of fillers leads to avoid the highest possible length cutting.

3. By reducing to the lowest possible, the material waste. This occurs in various ways:

3.a When the line covers the highest percentage of fillers, so there is no need for cutting of HC

units (factor 1).

3.b By reducing the material waste from the future fillers, after the new line is made. A new

line with standard width X < 1200 mm can lead to big reduction of material waste, when fillers with width smaller than the width of line X, are cast and cut on this line and not on a 1200-mm-line.

4. By increasing thru put. It implies that if a new line covers the highest possible percentage of fillers (factor 1), less time for longitudinal cutting is required and thru put is increasing. Moreover, by reducing units that need cutting on a 1200-mm-line, by casting and cutting them on the new line X (factor 3.b), thru put is increasing to the highest possible. In other words, if the cases of cutting on a 1200-mm-line are limited only to the fillers that have a width bigger than X, the thru put is increasing.

5. By decreasing the factory’s additional costs due to the production of scrap elements. When a scrap element is produced, the factory has to transfer and crash it or store it for future use, resulting to an extra cost.

6. By reducing in-situ casting to the highest possible.

7. By reducing the environmental impact. By reducing the material waste (factor 3) to the highest possible, a more environmentally friendly production is achieved, while CO2 emissions5 are

decreasing too.

5_{When a HC unit is cut in the long dimension and the one side of the HC unit is not utilized, more concrete is produced} than what is actually needed. From this aspect, there are additional CO2 emissions.

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3. Methodology

During the first part of this report (subchapters 3.1 – 3.5), the width of a new line that seems to be more beneficial was investigated. The main idea was to choose the width of a new line according to the width that fillers are usually longitudinally cut. Hence, the study aimed to discover the width that HC fillers are cut more often. As a first step, the geometrical characteristics of the fillers from the previous years’ production, were analysed. Then, a more extended study was made, by analysing those fillers by elements’ type. The results were grouped properly, in order to be able to make conclusions. Following this, the relationship between fillers’ width and the actual need on a project, was studied. Finally, the possible widths for a new line were discussed, based only on fillers’ characteristics. Other important aspects regarding fillers were also studied.

3.1 Data analysis of produced HC units

At this chapter, the data history of the produced HC units of the years 2010-2019 at the three factories, was analysed using the software MATLAB. Firstly, by company’s history, the number of HC units that are cut (fillers), was estimated.

Then, in order to investigate if there is any trend in the width that HC fillers are cut more often, the frequency of each width for the range of 1 – 1196 mm was calculated. Graphs were made, to show the widths that HC fillers tend to be cut more often.

The changes of the width frequencies’ graphs over the years were explained by the following two regulations regarding cutting (Eriksson 2014):

1. Cut of a HC unit according to allowable zones for cutting (SE-HDF00-525) (old regulation). 2. Cut of a HC unit at a recommended width (SE-HDF00-521) (new regulation).

Finally, a graph was made, that shows how many designers follow the new regulation year by year, based on the width that HC fillers are cut.

3.2 Data analysis of fillers by type of element

In this chapter, the width frequencies and additionally, the total cutting length for each width, are calculated. Due to the fact that the recommendations about cutting of HC fillers change depending on the type of the HC unit, but also because even when the old rules are used, the cutting point is strongly influenced by the position of the strands (which are different depending on the HC type), fillers are studied separately, regarding their HC type.

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The type of HC unit that produces most of the fillers was found. Then, based on the data of the production 2015-2019 and for all three factories, the width frequencies were plotted, per type of element, in order to show any trends.

It is important to notice that the way that designers choose to cut a HC unit, changes over the years. The later years, more and more designers adapt to the new regulations of cutting at specific points – the centres of the cores. Hence, the analysis counts only the production of the years 2015-2019 and not the previous years. Including, for example, the year 2012 in the analysis, would insert an error in the results, because the way that engineers design, has changed significantly since then. From the other side, even if the year 2019 is the most representative regarding the cutting rules at the moment, it is necessary to include the production of other years in the analysis in order to avoid errors due to specific project demands.

3.3 Grouping of width frequencies by cutting zones

The plotted width frequencies vary, due to the fact that many engineers cut an element according to the old rules. Hence, a width frequency diagram has peaks for widths that are very similar. For example, it can be seen in the results that there are peaks in a width of 592 mm and 600 mm. This difference is very small and it happens mainly due to the fact that engineers do not follow the same cutting rules. It is considered that those differences represent the same need.

In order to have a clearer and more representative image so as to make conclusions about the width trends, it was necessary to group the results of the widths that fillers are usually cut. This was made according to the cutting zones of the old rules (Appendix A2). The table below shows the allowable cutting zones for the first three cores of each type, according to which the frequencies were grouped.

Table 3-1. Grouping of data – zones of cutting for each type of HC unit

Type of slab HD/F 120/20 HD/F 120/22 HD/F 120/27 HD/F 120/32 HD/F 120/38 HD/F 120/40

1st core (mm) 1013-1116 1013-1116 995-1107 937-1112 963-1112 1010-1087 2nd core (mm) 824-940 824-940 772-872 659-821 680-800 786-859

3rd core (mm) 635-751 635-751 548-649 376-538 397-517 562-635

After grouping the data, the amount of fillers that are cut at each core for all HC types, was presented. The total cutting length in meters and the percentage to the total cutting length, were calculated.

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3.4 Relation between fillers’ width and actual need

At this part, a discussion was made about the relationship between the final width that fillers are cut and the actual need for a project. The width that an element is longitudinally cut, is not the same with the actual need on a project, due to the fact that engineers are not allowed to cut a HC element at every point. Moreover, cast-in-situ concrete joints are necessary beside fillers, especially when two fillers are placed beside each other in a project. Hence, the position that an engineer decides to cut an element, is influenced by more factors.

In general, the first part of this chapter investigates the most common widths that HC units are cut, with the purpose to create a line with this width. Producing elements that depict, to the nearest possible, the actual need on a project and as a result, do not require big cast-in-situ concrete joints, will reduce the construction costs and make designers’ jobs easier. Thus, a discussion was made, in order to find the link between the filler’s width and the actual need. When the width of the new line is to be decided, this relationship is counted for finding the most cost-effective solution.

3.5 Possible widths of a new line based only on fillers’ characteristics

At this part, the possible widths of the new line, that seem to be more beneficial, were presented. Conclusions at this point, were based only on aspects such as the width frequencies that fillers are usually cut and the corresponding cutting length at each width. Moreover, the relationship between the cutting width and the actual need, was counted in the decision.

Other aspects, that are of interest for the efficiency of the new width line, are not possible to be estimated accurately at this point. For example, the possible reduction of the material waste (and consequently the possible environmental benefits), the possible increase in thru put, the time saved due to less longitudinal cutting and the reduction of other additional costs due to fillers’ production, are some of the factors that cannot be estimated accurately at the moment.

This happens because various practices are followed during the HC production, in order to reduce material waste and speed up the production. In order for someone to calculate accurately the above-mentioned factors, one has to simulate the production firstly. For example, in order to calculate accurately the material that is wasted, it is important to take into account the fillers that are placed beside other fillers, and how much material is wasted in that case.

The same implies for other aspects such as the possible increase in thru put. In order for someone to have a more representative and accurate picture, a simulation of the production should take place, where one can understand better the impact of a different line on the production.

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Even factor 2 (from chapter 2.4), which refers to the cutting length, cannot be answered accurately, by only considering the geometrical characteristics of the fillers. This is because the final cutting length is not exactly equal to the sum of the length of the fillers. For example, when two fillers are placed beside each other on the casting bed, to reduce waste, the cutting length is equal to the length of the longer filler.

3.6 The choice of the new line’s width

The width of the new line was determined in this chapter. Any decisions were made by taking account the width frequencies, the corresponding cutting length for each width and the possible alterations that can be made in a 1200-mm-line.

It is noted that the decision regards only the factory in Kungsör, the one with the highest HC production. The factory hall has eight casting beds which are 1200 mm wide and 143 meters long, and there is no space in the hall for the creation of an extra casting bed. Hence, the decision of the new width, is for modifying one of the eight existing casting beds.

In the first part of this subchapter, the basic principles regarding splitting of a 1200-mm-line to smaller standard widths, were explained. Then the basic principles regarding the chamfer were presented and a decision was made for which one is of preference. A table showing the possible alterations of a full width line by the provider company for machinery and equipment was described. The percentages of fillers for each HC type were compared with the available alternatives. Alternatives that are not available for the HC type that produces the highest percentage of fillers, were rejected. Then, an extended comparison of the alternatives that are compatible with the most common HC type were made, based on the following criteria:

• Amount of fillers cut at each width. The results about width frequencies and trends on these, as they had derived from the previous chapters, were used.

• Possible direct reduction of longitudinal cutting.

• Possible reduction of the material waste and additional costs for the factory.

• Speed up of the production and the general impact of any alternative on the production.

A more qualitive comparison was made between criteria that include production aspects. This is because during the production, various practices are followed for reducing waste or speeding up the production, for which, an accurate calculation was done later by simulating the production.

Additionally, one extra criterion that was included in the choice of the width of the new line, was the increase of the possibility to avoid cutting elements in the future, when a new width line will be

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available. This is an aspect from the designers’ point of view, regarding the span combinations that a new width element can offer when the HC elements are placed on a project. More specifically, a comparison was made, about the possible combinations that new width elements together with 1200 mm wide elements can offer, to cover a span6.

Finally, since some of the used HC types are not available for the chosen width alternative, it was necessary to change the core pattern in some of these cross-sections, in order to make the 800-mm-line available for all the depths. Moreover, one extra HC type was introduced.

3.7 Required time for longitudinal cutting of HC units

The delay of the production due to longitudinal cutting at the current situation, but also the possible increase of thru put in the case of an 800-mm-line, and other aspects that involve time, are calculated when the production is simulated. For those calculations, the required time for longitudinal cutting of a HC element is needed. This time varies for every HC type and is strongly depended on the cross-section area that is cut.

At this subpart, a mean value was calculated for every type of HC unit. This time, in other words, is the speed that the diamond blade longitudinally cuts a HC element. It does not involve the time needed for starting the blade or the time needed for positioning of the blade before each element. The data of the time needed for every longitudinal cut, as also the corresponding cutting length, are kept on blade’s database. The data from the factory in Kungsör for the year 2016 are used, to estimate the average time in minutes/meter of HC type.

It should be mentioned that those data have a very high variation. This is because many factors influence the time needed to cut an element. A main reason for this variation is the difference in the cross-section that is cut each time. However, the point of cutting, in order to find the time needed as a function of the cross-section, is not kept. The only data kept are the time needed in seconds, the corresponding longitudinal cutting in meters and the depth of the element that is cut. This means, that there is no information either for the core pattern – data of different HC types with the same depth are mixed. This inserts a type of error which is inevitable.

A filter was used to reject the extreme values and consequently obtain more representative results. According to this, all the values smaller than 0.4 minutes/meter or higher than 4.5 minutes/meter, were rejected.

6_{A span can be used in two cases: The parallel dimension with the strands of HC units, when those are placed to cover an} area, and the transverse dimension, by adding the width of the HC units. Here, the 2nd_{is implied.}

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3.8 Simulation of the production

During the production of HC slabs, units are placed in such a way in the casting bed, so as that the cost for the factory will be the smallest possible. This cost includes the material waste (concrete and steel), the time and workhands needed for longitudinal cutting, the handling, transfer and crash of the scrap elements, but also the slowdown of the production and the reduction of thru put.

Hence, the concrete waste for example, cannot be accurately calculated by looking only on the fillers’ dimensions; one has to take into account the way that each element is placed on the casting bed. Other examples that are also influenced by the way that elements are placed on the bed, are the total casting length of a casting program, or the total longitudinal cutting. In order for someone to study those aspects with high accuracy, one has to take into account the position of elements on the bed.

Figure 3-1. The placement of the HC fillers on the bed influences the cost calculations and the efficiency of the production. For example, the longitudinal cutting in the case shown above is equal to the length of the longer filler.

Figure 3-1 shows a common case of fillers placed on the casting bed. Fillers are placed beside each other, to reduce the material that is wasted and increase the capacity of the casting bed. Moreover, by placing fillers beside each other, there is less use of the diamond saw, because for one pass of the blade, two elements are cut. Apart from fillers, HC units with diagonal cuts are placed in such a way to reduce waste.

The data of the produced HC elements, apart from the technical details (length, width, HC type, thickness, etc.), also contain the casting date, the casting bed, the casting program and the order of the unit on the casting bed. In addition, each filler which is positioned beside another element is marked

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with a note ‘SPLIT’7. By that information, it is easy to understand the placement of elements and estimate the above-mentioned aspects.

However, it is quite common to not follow a strict numbering of the elements on the bed for many reasons. Quite often, when a casting bed contains fillers, the numbering starts with the full-width elements and thereafter the fillers follow (which is not the actual positioning on the bed, fillers are positioned in a way to reduce waste). In that case, the only possible way for someone to understand the actual position of fillers on the bed, and hence estimate the exact waste, is by studying each casting program’s report8_.

Another practice that it is followed during the casting, for reducing concrete waste, is that when an element fails to be cast correctly (or any other problem), the workers directly pause the casting machine, instead of letting it cast the whole length of the element. The system pushes another element, the casting of which, directly starts. The scrap element is noted in the system as ‘DISCARDED’; however, the initial length is still shown in the data (not the actual cast length). The same notation is used even if the element has been fully cast, but some problems occur.

As mentioned before, when two fillers are placed beside each other, the shorter element is noted in the system as ‘split’. However, sometimes, when two fillers are cast beside each other, and there is an error in the longer one, there are cases where this filler is not mentioned as a scrap element. The shorter filler is still noted as ‘split’. In that case, if someone does not study in detail the casting program report, it is likely to underestimate the concrete waste, thinking that the other side of the shorter filler was utilized. In fact, the other side gives a scrap element that should be counted in the waste calculations. In other words, a filler that is noted as ‘SPLIT’, does not imply that the other side of the filler has been necessarily utilized.

The above-mentioned shows that in order to calculate accurately aspects such as the concrete waste, one has to look at each casting program’s report. As the total production is of interest, the production is simulated9. With a simulation, split fillers can be matched and a higher accuracy in calculations is succeeded. Moreover, other aspects such as the estimation of pressure (load) on the system, or the possible increase of thru out, make the simulation of the production of vital importance.

Consequently, in this chapter, the HC production in Kungsör is simulated with the use of MATLAB in order to study the efficiency of the production. Then, the simulation is modified, to study the

7_{Usually, the shorter of the two elements is noted as split. If they have the same length, then the narrower of them.} 8_{It is possible though to understand the way that fillers are placed on a bed by only looking at the elements’ dimensions, in} simple cases.

9_{By a simulation, in other words, elements are reordered in a casting program in a way that the efficiency will be the} highest possible, as the production planners do on the factory.

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efficiency of the case of an 800-mm-line instead of a 1200-mm-line. Hence, two basic systems were created:

• Simulation of the production when there are eight lines, 1200 mm wide (current situation) • Simulation of the production in the case of seven lines of 1200 mm and one line of 813 mm

(the studied scenario).

For the simulation, production’s data of the year 2019 from the factory in Kungsör were used. This year’s production was one of the highest, while it is considered the most representative for the following years, due to the high adaption to the new cutting regulations (SE-HDF00-521).

3.8.1 Simulation of the current situation (8x1200 mm system)

For every working day of the factory in Kungsör in 2019, all the produced HC units from the database are sorted by the casting program they belong to. Then for each casting program, HC units were sorted by their casting program order10. Due to the fact that a strict numbering is not followed and in order to understand how many fillers were possible to be placed beside others to make the production more efficient, for each filler it is checked if it is possible to be placed beside another element (of the same casting program). This was done by implementing an algorithm with the following rules, in priority:

• If two fillers have the same length and their width is 1200 mm in total, then they are placed beside each other.

• If two fillers do not have the same length, but their total width is 1200 mm in total, the shorter filler is marked as a split element. Then an irritative procedure takes place, to see if it is possible to place one more filler from the same casting program, beside the longer one (following the shorter filler).

• If two fillers are of the same length, but their width in total is smaller than 1200 mm, then the fillers are placed beside each other. However, in that case, different rules apply. The cutting length is equal to the length of the two fillers, and there is a concrete waste between them. The time needed for longitudinal cutting is higher in that case.

• If two fillers X and Y have a width of 1200 mm in total, but there is the possibility to place the e.g. Y beside another filler Z of the same casting program, even if the total width of the new match YZ, is less than 1200 mm, but the saving in material is much higher (because of a significant length difference between X and Y), then Y and Z are matched together.

• For each match of fillers, it is checked if any other combination of fillers on the bed can lead to a more efficient production (e.g. less waste).

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• HC elements with diagonal cuts, were placed in a way so as to reduce waste (angles of both full width elements and fillers are matched).

The above steps are parts of an irritative procedure between the elements of the same casting program, where in the end they converge to the most efficient placement. Elements with status ‘DISCARDED’ are then excluded of the analysis, as many of them are not cast in their full length and another element is pushed by the system. Including those elements while e.g. in reality only 1 meter can be cast in a 10-meter-long element, can insert high errors in the simulation. As only the efficiency regarding the impact of fillers is of interest, excluding those elements is on the safe side and gives more accurate results. However, aspects such as the general material waste of the factory cannot be calculated; any results about material waste, concern only the waste due to production of fillers.

By comparing each simulated casting program to the corresponding casting program report, it is estimated that only 1.24% of the simulated casting programs deviates from the actual situation.

3.8.2 Simulation of the studied scenario (7x1200 mm and an 800-mm-line)

In the previous chapters, the optimal width, if a full-width line is to be modified, was investigated. The results, based on the most common widths that HC fillers are usually cut and the available alternatives, showed that an 813-mm-line is the most promising option. However, certain aspects, such as the material saving or the possible increase in thru put due to less cutting, were not possible to be estimated.

In order to study the cost benefits of an 813-mm-line for the factory, and also the impact in the production, the simulation of the system of 8x1200 mm lines was modified to a 7x1200 and 1x813 mm lines system. For the simulation, MATLAB was used with the data of the HC production of 2019 in Kungsör, so as to be able to compare with the current situation and draw conclusions.

The following modifications of the created simulation (8x1200 mm system), in combination with certain assumptions, took place:

• One of the existing casting beds in Kungsör is modified from 1200 mm to 813 mm. As a result, in the new situation, only seven lines can be used for casting 1200-mm wide elements. • The modified casting bed is the 8th_{in position, the one in the end of the hall. In this line, 813}

mm wide elements will be produced in combination with fillers of a width smaller than 813 mm. One understands that the most of longitudinal cutting in the new situation will take place in the new line, hence it is chosen to modify the last -in position- bed in the hall, with the aim to not influence the production in the other seven lines. Moreover, from this bed smaller

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elements will be produced; the impact of transferring these elements is lower. Hence, choosing to produce elements in the 8th line – the one which is the most remote in the factory11 – is advantageous for the production.

• The total HC production for the year 2019 in Kungsör is imposed to the new system. However, elements with a status ‘DISCARDED’ are not included. When an element fails to be cast correctly, it is cast again some days after. Hence, including ‘DISCARDED’ elements will lead to more load on the new system, as elements appear twice, which is not the case. However, it should be mentioned that not including casting failures on the new system, gives an advantage for the efficiency of the new system12_.

• It is initially assumed in the simulation, that the number of working days in the new system, is the same with that in the current situation. Moreover, it is assumed that the maximum number of casting beds each day in the new situation cannot exceed the number of casting beds of each day, in the current situation.

• It is assumed that the 8th_{line (the 813-mm-wide line) can be cast at a maximum of once per}

working day. This is conservative, in fact, under certain circumstances, this line can be cast twice per day.

• It is assumed that elements of a width in a range of 800-822 mm, would be designed at 813 mm if the new line is available. Hence, for those elements, no longitudinal cutting will take place. The designer, in other words, will take advantage of the 813 mm option.13

The load (the total production of HC elements) is imposed to the new system on the following steps: • Initially, the daily production according to the casting date of the current situation, cast at all

beds apart from that on the 8th_{line, is imposed to the 7x1200 mm lines of the new system.}

However, only full-width elements and fillers wider than 822 mm are put in those lines. Fillers narrower than 822 mm will be placed in the 8th_{line of the new system.}

• Up to this point, the daily production that was cast on the 8th_{line of the current situation, is not}

imposed in the new simulation, as there is no space for this. The physical capacity for 1200-mm-wide elements has decreased by 1/8, as the 8th line will be used for narrower elements.

11_{Units from each line, are transferred to the end of the hall, in a space between the 4}th_{and the 5}th_{line. Hence, the 1}st_and the 8th_{line, are the most remote in the production hall.}

12_{The results will show a higher efficiency than the expected.}

13_{This is very conservative. In fact, most of the elements that now are cut at a width range of 772-872 mm, are believed to} be designed as 813 mm wide elements, if the designers had that option. Apart from this, if a new width line is available, designers will utilize this new dimension in the possible combinations to avoid cutting elements. Hence, there will be an increasing number of elements designed at 813 mm and a decrease of fillers at other widths. This assumption does not take this into account.

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• Due to the fact that fillers are moved from the full-width casting programs to the 813-mm-wide line, a significant amount of space is available in the former one. This is utilized by placing full-width elements of the 8th casting bed of the current situation to those lines14. The above will result in a reorder of the elements on the lines. Until this point, the elements that have been reordered on the 7x1200 mm wide lines of the new simulation, are only full-width elements and fillers wider than 822 mm. Moreover, until this point, all the elements that have been imposed, have the same casting date as in the current situation.

The simulation is based on placing the HC elements on the lines, according to the date that they have been cast in the current situation. Since the capacity of 1200-mm-wide elements is decreased by 1/8, and also, the casting of the 8th line requires that there will have been collected enough elements to cast an 143-meters-long casting bed, one understands that many elements in the new situation will be reordered in a way so that they will be cast in a different day than the one in the current situation. It would be preferable to make this simulation according to the date that orders arrive in the company or, better, the day that elements have to be delivered. However, those dates are not available, and as a result, the casting date of the element in the current situation is used.

It would be against the external validity of the whole study to impose the load on the system without taking a dating system into account. In other words, placing the whole HC production of the year 2019 without any limitation regarding the casting date of elements, would result in a more efficient production than the actual.

The simulation continues by imposing the load of the rest of elements, that have not been imposed until this point, in the new lines’ system. This occurs according to the following:

• As mentioned before, all elements with a width equal or smaller than 822 mm, are moved from the casting program they belonged to, on the 8th_{line. This load is imposed to the 8}th_{line, when}

there are enough fillers of a specific HC type, so as to cast a 143-meters-long line. One understands that there will be a waiting time for those elements to be cast. The simulation takes into account a limitation on this waiting time. It is set that there will not be a time difference of the elements being cast on the same day of the new 8th line in the new system, higher than 15 working days (according to the casting date of elements on the current situation). This is a reasonable assumption for the way that elements in the 8th line will be cast when the 813-mm-line will be available. The production planner will have to wait before

14_{If elements are moved from the casting program they belong to in the current situation, they are always moved to a new} casting program which is of the same HC type.

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casting a bed, for enough elements of a specific HC type to be collected. It is considered that a waiting time of 15 working days before the delivery date reflects the reality; however, as the delivery date is not available, the current casting date is used.

• It is highlighted that the 8th_{line is assumed to be cast once per day. This means if e.g. there}

have been collected enough elements to cast two beds, the 2nd one will be cast the next working day.

• If there are not enough elements to complete a 143-meters-long line in 15 working days waiting period, and the collected elements result to a casting length of e.g. 110 meters, the load is imposed on the line.

• An irritative procedure takes place in order to fill all the space of the seven lines that has derived by taking away all elements with width ≤ 822 mm. Firstly, elements of the 8th casting program of the current situation are distributed among the seven lines system of the new situation. Secondly, a reorder of the production takes place, to reduce the casting programs – of the new system – to the highest possible.

• For the elements on the seven lines, it is set as a time limitation, that all elements are cast in a maximum period of ten working days from the casting date of the current situation.

3.8.3 Estimation of the daily required time for longitudinal cut of fillers

The time needed to longitudinally cut HC elements was found according to the method described in section 3.7. This is, in other words, the speed that the diamond blade can achieve for each HC type. The total required time for length-cutting of each casting program, is calculated based on that speed. According to the production employees, before each filler, the blade needs about 2 minutes for positioning. Moreover, at the beginning of each casting program containing fillers, the saw requires about 10 minutes as a starting time.

Generally, it is difficult to estimate accurately the daily required time, as it is depended on many different factors (similarly to the speed for cutting). Even if the cutting speed for each HC type is found, the total time for cutting a filler, can be considerably different between fillers of the same HC type, depending on the point of cutting and the difficulties that can occur. Cutting of fillers according to SE-HDF00-521 (the new cutting regulations, according to which, a filler is cut only in the middle of cores), is generally easier and difficulties or delays are less common. The difficulty and consequently the probability of delay in the cutting process increases when the cutting point deviates from the middle of the core. When the deviation is significant, apart from the extra time needed due to the higher cross-section, more problems can occur due to the fact that the blade tends to turn towards the center of the core. Sometimes, a second pass of the blade is taking place, to achieve the desirable

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result. This extra time is taken into account by increasing the calculated time by 40% (Eriksson 2014).15

The time needed for each casting program is obtained according to the following:

𝐶𝑢𝑡. 𝑡𝑖𝑚𝑒 = 2 𝑚𝑖𝑛 + 𝑐𝑢𝑡𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑏𝑙𝑎𝑑𝑒 𝑠𝑝𝑒𝑒𝑑 [if cutting point < 70 mm from center] 𝐶𝑢𝑡. 𝑡𝑖𝑚𝑒 = 2 𝑚𝑖𝑛 + 1.4 × 𝑐𝑢𝑡𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑏𝑙𝑎𝑑𝑒 𝑠𝑝𝑒𝑒𝑑 [if cutting point ≥ 70 mm from center] 𝑇𝑜𝑡𝑎𝑙 𝑐𝑢𝑡𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑎 𝑐𝑎𝑠𝑡𝑖𝑛𝑔 𝑏𝑒𝑑 = 10 𝑚𝑖𝑛 + ∑(𝑐𝑢𝑡𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑓𝑖𝑙𝑙𝑒𝑟)

Consequently, the daily cutting time is equal to the total cutting time of all the casting beds that contain fillers, that particular day.

3.8.4 Parameters concerning waste and cost calculations

This subchapter focuses on the procedure followed in order to calculate all the factors that contribute to the final cost of the production. A cost estimation of the production took place for both simulations, and the cost saving by modifying one full-width line derived from the difference of the former one. The cost calculations concern only aspects due to the production of fillers. For example, the estimated concrete waste, regards only the scrap elements that were not used when full-width elements were longitudinally cut; it should not be confused with the total waste produced by the factory. In order to find the total production waste, more information is needed which is not available (e.g. the actual casting length of an element, whose production was stopped due to a problem16). From the other side, since the aim is to discover if a smaller-width line is more profitable, taking into account the waste and additional costs made only by the production of fillers leads to a more objective comparison. Below (Figure 3-2), the procedure followed in order to estimate the cost, is presented. From each simulation, the amount of scrap elements and their corresponding volume of concrete and steel for both cases have been derived. It should be noted though that certain assumptions took place in the new simulation (7x1200-mm,1x813-mm), aiming to approach to the highest possible, the situation when an 813-mm-line will be available:

• For all fillers with width < 800 mm, it is assumed that 25% of them will be possible to be placed beside other fillers to save material. For all fillers with width >822 mm (hence cast at

15_{On the referring report, every calculation of cutting time that it is not made according to SE-HDF00-521, is increased by} 40%. After contact with the production planners, since this thesis report calculates the speed of the blade by data of cuts at various points (not only in the middle), it is chosen to increase by 40%, only the time for cuttings that take place at a point more than ± 70 mm from the center of the core.

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the 7x1200 mm lines), it was assumed that it will not be possible to place other fillers beside them. However, it should be mentioned that this is a conservative assumption.

• Since the simulation is based on data of 2019, it is assumed that all fillers that were cut at a width in the range of 800-82217, would be produced as 813-mm-wide elements. Hence, for those fillers, it is considered that there will not be any longitudinal cutting or waste.

The final cost is calculated by using the values presented in Figure 3-2. It should be mentioned that a casting team consists of four persons, while the removal of each filler from the casting bed is estimated at 10 minutes.

Figure 3-2. The followed procedure for the estimation of cost.

17_{A very conservative assumption. It is believed that more fillers would be designed as 813-mm-elements. But it is of} preference to make a conservative study of the possible cost saving, and hence eliminate the possibility to overestimate the advantages of a smaller-width line. During the last part of this thesis, the case where more elements are designed according to the 813-mm-line, is also presented.

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3.8.5 Evaluating thru put

The possible increase in thru put is one of the main factors for determining if the modification of a 1200-mm-line to an 800-mm-line is profitable. By an increase of thru put, it is implied that for the same production time, more beds will be cast. Hence, thru put contributes to the possible cost-saving of a smaller-width line.

However, estimating accurately thru put is difficult. Even if the time saved with the introduction of the smaller-width line can be estimated, thru put is depended on many other factors that are difficult to strictly determine. Some of those factors are mentioned below:

• During a production cycle, problems can occur that will lead to delays, which are impossible to predict or simulate. Those delays decrease thru put.

• Production planners can always do a reorder of the production, to maximize thru put. This reorder can also be made for cases when a problem has been occurred. One understands that it is impossible to simulate that factor.

• The maximum number of casting beds that can be achieved daily, is strongly dependent on the order of casting programs, the work that elements require (e.g. cutting of details) and the possibility to take advantage of the night hours for curing. Those aspects are difficult to include in the estimation of thru put; they are either unknown (e.g. required work) or including them is not on the conservative side.

• Curing time is one of the basic parts of a production cycle. Even if elements’ thicknesses are known, more factors that influence this, cannot be predicted (e.g. variation in temperature). From the above, one understands that thru put cannot be strictly estimated, like the other factors which contribute to the possible cost saving. Below, the two approaches that were made, are described. However, it should be mentioned that in terms of the methodology of science, the robustness of the simulation regarding thru put is low; a small change in the assumptions implies a considerable change in the results. For this reason, it is chosen to refer to thru put separately from the possible cost-saving resulting from the other factors, whose accuracy is significantly higher.

Description of the two methods followed to estimate thru put:

• Initially, the total amount of time saved is calculated. By considering that curing can be made during night hours, and that a production cycle without curing lasts 5 hours, thru put is calculated by dividing the time saved by 5 hours. This is a very rough approach, followed mainly in production. The confounding factors resulting to an overestimation are that it is not always possible to take advantage of the night hours. Moreover, by this method, if e.g. a small

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amount of time is saved in a particular day, this amount of time is counted, while in fact no increase of thru put is made. A confounding factor resulting to an underestimation, is that production planners can order the production in such a way that they could cast more beds. This method does not count this aspect.

• In an effort to calculate thru put more accurately, simulation searches for days where the saved time is higher than 2.5 hours (placement of wires and casting). For such days, it is assumed that curing can take place overnight and it is checked if the following day, there is enough time to continue with the cutting process and remove the elements from the casting bed. If the above conditions are fulfilled, thru put is increased by 1 bed. However, if the day, due to the reorder of the production, has a negative time difference, thru put is decreased by 1 bed. This method is more conservative and it is considered more reliable. Still some confounding factors exist, such as the way that the production has been reordered.

3.8.6 Evaluating production’s pressure when a full-width line is modified

If a 1200-mm-line is modified to an 813-mm-line, the physical production capacity of 1200-mm elements is reduced by 1/8 (there are eight casting beds, 1200 mm wide, in the current situation). From the one hand, the longitudinal cutting on the 7x1200 mm lines of the studied scenario is decreased significantly, hence faster production cycles will be achieved. From the other hand, there are days that the production of 1200-mm elements is high; the fact that there will be seven available lines for casting those elements (instead of eight), could be a problem for the production (regarding the additional pressure on those lines).

Thus, the additional pressure on the seven lines producing 1200-mm-elements is examined, to conclude if the factory will actually be able to handle such a situation. For that purpose, an indicator (a factor) is defined for each working day, as the daily number of casting programs divided by the number of casting beds.

𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 =𝑑𝑎𝑖𝑙𝑦 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 1200 𝑚𝑚 𝑐𝑎𝑠𝑡𝑖𝑛𝑔 𝑝𝑟𝑜𝑔𝑟𝑎𝑚𝑠 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑐𝑎𝑠𝑡𝑖𝑛𝑔 𝑙𝑖𝑛𝑒𝑠

This is considered a reliable method to evaluate the pressure on the system, however, due to the fact that pressure is influenced by the day that it is decided to cast a program, the results should also be seen as a total. Moreover, the whole simulation analysis is based on the casting date of elements in the current situation which is considered a big advantage for the reliability of this evaluation.

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3.9 Estimation of cost saving, considering designers’ adaption to the

813-mm-line

The method that was used to estimate the possible cost saving due to the introduction of the 813-mm-line leads to conservative results. This happens because the simulation was based on the production data of 2019, where designers did not have the option of the 813-mm line and consequently, they designed based only on 1200 mm wide elements. Regarding the simulation, only the elements that during 2019 were cut at a range of 800-822 mm, were assumed to fit exactly in an 813-mm line and hence do not need longitudinal cutting. One understands that this is very conservative; fillers cut at e.g. 780 mm during 2019, most probably would be designed as 813-mm wide full width elements if this were possible. Moreover, if two width choices are available (1200 mm, 813 mm), it will be easier for the designers to make more combinations when they decide how to place the HCs, and hence avoid to some extent, the longitudinal cutting of further elements (cast-in-situ concrete joints can also be utilised for this purpose).

Hence, more simulations took place, where the input data of 2019 were slightly modified, depending to the percentage of fillers that will be designed as 1200-mm or 813-mm wide elements. This was made by creating a vector of the total number of fillers produced in 201918 on MATLAB. Then a random choice was made, modifying some of the fillers with width < 800 mm or > 822 mm to full width elements, depending on the degree of adaption considered at each simulation. The percentage of the adaption to the new situation, was implemented by setting a corresponding step in an irritative loop of that vector, for each simulation.

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4. Results

4.1 Data analysis of produced HC units

By analysing the data history of the HC production, important outcomes are made. For example, by company’s history one can estimate the number of units that are longitudinally cut (fillers), and by further investigation, one can discover the most common widths that HC units are cut and if there is any trend in those widths. This is made by plotting the frequency of fillers being cut at each width (width frequencies).

Firstly, an analysis of the HC production for the years 2010-2019 is made, and the results are illustrated below. In total, 532614 HC units were tested, from which, 65740 were longitudinally cut (fillers). Thus, fillers are 12.34% of the total HC production of 2010-2019. With the use of MATLAB, graphs were made, to see at which width the fillers are usually cut (width frequencies). The results are depicted below.

Figure 4-1. Number of HC units that are longitudinally cut (fillers) and their corresponding widths. (production 2010-2019, all factories)

The figure above depicts the most common widths that the HC units are cut. For example, the highest peak means that 2202 units were cut at 816 mm.

As it is seen, there are general trends on the widths of fillers. The results show that most of the HC units are cut at specific widths: the majority of them seems to be cut around 800 mm wide, followed by a trend of units cut at almost 600 mm wide.

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It is interesting to notice the differences over the years. During the years 2010-2017, the width of the fillers varies more, comparing to the later years (2018-2019). For example, Figure 4-2 shows that there are a lot of units cut at 790 mm and 800 mm, while Figure 4-3 shows that the HC units are usually cut at specific widths (e.g. 816 mm).

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The reduction in the width variation during 2018 – 2019, is explained due to the new regulation about cutting of HC units, that is followed by engineers mainly after 2017, which defines the exact width that a HC unit should be longitudinally cut (Figure 2-2). Cutting at those specific widths leads to the smallest cross-section area and consequently to less work for the diamond saw.

As it is seen from the graph below, during the last years more and more engineers follow the new rules of cutting at a specific width, instead of cutting in a zone (old rules). In 2019, almost 50% of HC units were cut according to the new rules.

Figure 4-4. Percentage of fillers cut according to the new rules per year. (production 2015-2019, all factories)

49.99 23.1 10.7 9.4 8.3 50.01 76.9 89.3 90.6 91.7 0 10 20 30 40 50 60 70 80 90 100 2015 2016 2017 2018 2019 PE R CE N TA G E (% ) O F F IL LE R S YEAR