Performance Aided Design - course report

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Kitazawa Kenchiku Factory – A structural analysis Piotr Zbierajewski Stud. MSc. 1 Ark, Department of Architecture & Design, Aalborg University, Denmark

ABSTRACT: This is the case study of the wooden structure of Kitazawa Kenchiku’s wood factory. This paper aims to explore use and possibilities of the Performance-Aided Design tools, such as RhinoCeros, Grasshopper plugin for Rhinoceros, Karamba plugin for Grasshopper and the FEM software Autodesk Robot.

1 COLLECTION OF THE MATERIAL The working process started with collection of the material. All of the data have been found on the internet, including presentations from the conferences and Japanese edition of the Detail Magazine. Photos have been taken from the internet as well (all sources are mentioned at the end of the report.

2 THEORETICAL READING OF THE CASE STUDY

2.1 Background Kitazawa Kenchiku Factory in Nagano, Japan, was designed by Funiko Misawa (designer from MOK-msd) and Masahiro Inayama (structural designer from University of Tokyo). Built in 2010 was quickly announced one of the most inspiring contemporary wooden structures in Japan. It all started from the earthquake in 2010 in Japan, where many people have died under the buildings and because of tsunami wave (which destroyed Fukushima’s nuclear plants). Soon after this disaster, in October 2010 Ministry of Agriculture and Forestry announced two main resolutions. First one was “Basic policy on promotion of the usability of wood in public buildings. The second one was interfering the first one in some aspects – all Japanese public buildings not higher than 3 floors shall use a wooden structure as the main one. This decision was made because wooden structures have good seismic resistance and they are also very energy efficient. This is where the idea of the Kitazawa Kenchiku Factory was born. It was build from local cedar. The workshop is used to utilize wood and produce wooden elements mainly for the structure and architecture purposes. Basically it is providing the materials for new buildings (authors did not only support new law with Kitazawa’s Kenchiku Factory but they also gave many public lectures on the topic how wooden structure costs generally speaking are much lower than steel one).

2.2 Dimensions In this step I decided to present basic technical data: Area: 500sqm Overall interior dimensions: 18x24m Span between the pillars: 18m Number of trusses: 5 Distance between the trusses: 6m 2.3 Static scheme The structure’s module consists of the following: four pillars, two trusses, beams on the top between the trusses and diagonal beams connecting lower lower chords of the trusses with the middle points of the top beams. For the basic static scheme, it had to be simplify to following 2D truss model:

Pic. 2.3.1 Static scheme

This simplification was crucial because Karamba is using very simplified inputs of the Karamba plugin. Further work included work on one whole 3D module of the structure. 2.4 Material Authors decided to use ordinary timber instead of glulam. Proper timbers have been chosen after moisture inspection and Young’s modulus examination. Wood type: cedar Wood used: 60m3

Pic. 2.4.1 Dimensions of the original structure members

2.5 Calculations 2.5.1 Snow load - short term

s = µi Ce Ct sk The roof slope is assessed to 17°, as it varies equally from 0°-20° − µi = Shape coefficient = 0.8 (EN 1991-1-3 5.6) − Ce = Exposure coefficient = 1 (EN 1991-1-3) − Ct = Thermal coefficient = 1 (EN 1991-1-3) − sk = Characteristic value of snow on the ground = 1,73 kN/m2 (EN 1991-1-3) Snow load information has been taken from Japanese codes, including data for coordinates of the project which are: 35°56'17.9"N 137°59'00.5"E. The snow load was found to be:

sk (z) = 1,384kN/m2

2.6 Wind load – short term The data for the wind loads were taken from the Danish euro codes. The fundamental basic wind velocity in Denmark is 24m/s and we will consider this as well for our project. The terrain category to which the project belongs is line number 3: isolated obstacle area. The maximum height of the building is about 7 meters, therefore the exposure factor is 1,5.

qp (z) = ce (z) * 0.613 * vb2 − Ce = Exposure coefficient = 1,5 − Vb2 = Wind velocity 24 m/s The peak velocity pressure was found to be: qp (z) = 0,265kN/m2

W = qp (z) cp (z) − Cp1 = -0,67 − Cp2 = -0,25 The chosen Cp values represent the worst case scenario for the roof load calculations

W1 = 0,265 *(-0,67)= -0,177 W2 = 0,265 *(-0,25)= -0,066

Considerations: The small values for the wind load are due to the very low roof. Moreover, since the width of the building is 18 meters and the height is 7 meters, h<b and the building doesn't face changes in shape of profile of velocity pressure along its height.

3 PARAMETRIC MODEL OF THE STRUCTURAL SYSTEM In this section I want to present the possibilities that come with parametric recreation of the original structure.

Original parameters: Ellipse width: 9,6m Ellipse height: 7,48m Number of bottom chord segments: 8 Trusses’ span: 18,24m Pillars’s top point position: 5,875m Trusses’ top points height: 8,35m Number of overhanged elements: 22 Width of the module: 6m Number of top beams: 76 Length of top chord overhangs: 2.1m Number of top diagonals and top beams removed from the center: 3 Number of start point for the extra diagonal in the truss: 5

Sample modifications:

Ellipse width: 13m

Trusses’ span: 7m

Number of overhanged elements: 7

Ellipse height: 5,5m

Pillars’ top point position: 8m

Width of the module: 10m

Number of bottom chord segments: 3

Trusses’ top points height: 13m

Number of top beams: 21

3.1 Further instructions The choice of the relevant parameters chosen should be clearly stated and illustrated, f.ex:

Length of top chord overhangs: 4m

Number of top diagonals and top beams removed from the center: 10

Number of start point for the extra diagonal in the truss: 10

4 PRELIMINARY STRUCTURAL ANALYSIS IN KARAMBA 4.1 Basic application of Karamba plugin I decided to focus on the full one module of the Kitazawa Kenchiku Factory because in my opinion it is impossible the be close to the original calculations when excluding the extra top beams between the trusses and the diagonals. I present the original structure with snow loads and wind loads (vectors are hidden for the clarity of the picture) from Karamba which is showing the modified geometries with assigned color like shown below:

Compression Tension

Pic. 4.1.1 Recreated structure of the Kitazawa Kenchiku Factory – Karamba view (tension, compression)

Note: The original geometry has hinges. But because of the simplified calculations I needed to use fixed joints. That is why above picture is showing only overall behavior of the structure instead of each element separately. The recreated structure had 36mm of displacement when both snow loads and wind loads from the worst case scenario have been applied. Below the simulation of much higher displacements:

Deformation scale: 10

Deformation scale: 25

Deformation scale: 50

After further Robot calculations I have found out that the original structure is already almost fully optimized. Because of that I decided to focus on one parameter which can give most interesting data to work with. I have chosen trusses’ top points height.

Because of that choice I had to take for consideration the different type of calculations from euro codes, depending on the angle of the slope, the same way I did in point 2.5. For snow load this time I have used Danish euro codes: Angle of pitch of a roof α µ1 µ2

0° ≤ α ≤ 30° 0,8 0,8 + 0,8 ∗ α / 30

30° ≤ α ≤ 60° 0,8 ∗ (60 - α) / 30 1,6

α ≥ 60° 0,0 –

Table. 4.1.2 Snow load shape coefficients

As I did in the first calculations, I did not took µ2 for consideration because the roof is symmetrical. I also knew what heights of trusses’ top points I want to choose for iterations: 10m, 15m and 22m. So again, because:

s = µi Ce Ct sk s10m = 1,384 kn/m2 s15m = 0,4 kn/m2 s22m = 0 kn/m2 As for peak velocity pressure Because of that choice I had to take for consideration the different type of calculations from euro codes, depending on the angle of the slope, the same way I did in point 2.5. Again, because:

qp (z) = ce (z) * 0.613 * vb2 and

W = qp (z) cp (z) qp 10m (z) = 0,6kn/m2 Wleft 1 = -0,12 Wright 1 = -0,24 Wleft 2 = 0,24 Wright 2 = 0 qp 15m (z) = 0,706kn/m2 Wleft 1 = 0 Wright 1 = -0,141 Wleft 2 = 0,424 Wright 2 = 0 qp 22m (z) = 0,812kn/m2 Wleft = 0,568 Wright = -0,162

Pic. 4.1.3 External pressure coefficients for duopitch roofs

Note: in case of combinations of both sides of the roof, the worst case scenarios loads were considered in further work.

I decided to use those values according to the angle of the slope, as shown on next page.

Number of bottom chord elements

Height of the trusses’ top points

10m

15m

22m

8

Angle between top chord edges: 131,32o Max. Displacement: 37,4mm Structure weight: 6 710kg Result. force (max/min): -45,81/26,47kN

Angle between top chord edges: 90o Max. Displacement: 62,5mm Structure weight: 9 507kg Result. force (max/min): -28,88/10,67kN

Angle between top chord edges: 59,15o Max. Displacement: 113,7mm Structure weight: 12 509kg Result. force (max/min): -31,28/13,47kN

Angle between top chord edges: 131,32o Max. Displacement: 37,55mm Structure weight: 7 672kg Result. force (max/min): -45,81/26,47kN

Angle between top chord edges: 90o Max. Displacement: 65,5mm Structure weight: 11 044kg Result. force (max/min): -33,51/10,66kN

Angle between top chord edges: 59,15o Max. Displacement: 114,1mm Structure weight: 14 636kg Result. force (max/min): -36,59/13,47kN

Angle between top chord edges: 131,32o Angle between top chord edges: 90o Max. Displacement: 38,29mm Max. Displacement: 66mm 4.2 The choice of the parameters Structure weight: 9 588kg Structure weight: 14 293kg Result. force (max/min): -45,81/23,86kN Result. force (max/min): -46,00/13,89kN

Angle between top chord edges: 59,15o Max. Displacement: 126,38mm Structure weight: 18 899kg Result. force (max/min): -47,26/19,49kN

16

32

Note: It is easy to see how the diagonal beams inside the front truss are more and more tensioned as their number is growing and the top points are going higher. 5 STRUCTURAL ANALYSIS IN ROBOT WITH LOAD CASES 5.1 Original geometry The reconstructed structure had some issues regarding not only the fixed joints mentioned before but also noticeable changes from the original Kitazawa Kenchiku Factory like overhangs on both sides of the roof, mirrored pillars (with the same parameters) and so on. That is why it also gave some imperfections with the original dimensions of the structure members. In the example below I tried to optimize resulted geometry to get rid of the elements which were too weak. Both examples used Ultimate Limit State (ULS) and Service Limit State (SLS) with dead load, snow load and wind load in the worst possible combination for the worst design conditions.

Max. Displacement: 11mm Weight: 4 463kg Result. force (max/min): -13,39/5,02kN

Max. Displacement: 10,7mm Weight: 6 163kg Result. force (max/min): -19,91/7,13kN

The optimization brought interesting results. For the need of changing the results in Robot I had to change the size of the members’ cross sections. Because of this the structure started to be more stable and solid (the maximum displacement went down a bit) however the weight has grown by 28%. Of course because of that the resulting forces have also increased (in both cases, tensions and compressions). New cross sections are shown on the next figure.

Pic. 5.1.1 Dimensions of the iterated structure members after optimilisation

5.2 Modified geometry At the beginning I wanted to do the iteration of the original structure with the height of the trusses’ top point at the level of 22m and 32 elements of bottom chord, shown on page 9. Unfortunately, because the Grasshopper2Robot plugin is still under development, it did not succeed with proper exporting the data to Autodesk Robot. It meant that I will need to optimize the file. So at the end I decided to go with the height of the trusses’ top point at the level of 22m and 24 elements of bottom chord, with the following results: Max. Displacement: 30,5mm Weight: 16 329kg Result. force (max/min): -40,83/19,08kN Note: It is easy to see that the height of the building connected with strong pressure and suction is making majority of external structure members easly destroyed with the given loads.

Pic. 5.2.1 Phase 1 – results of the iterarion

It clearly has shown that we can not apply at all the original parameters of the structure members to much different iteration. This is why I decided to change the geometry of the cross sections.

Max. Displacement: 10,31mm Weight: 55 308kg Result. force (max/min): -138,27/48,05kN

Pic. 5.2.2 Phase 2 – Optimization of the iteration

Note: Although there were no more elements which could be destroyed by the worst load combination, there were still many that were not using efficient amount of the material. However those are mainly dependent on the wind direction and pressure or suction. The results will clearly mirror when we will change the direction of the wind by 180 degrees. Of course the big disadvantage of this optimization was the dramatic rise of the weight.

The weight had much higher values mainly because of the much larger profiles. Actually they turned out to be even much larger than I thought at the beginning. However not all profiles were scaled a lot as it is connected with their part in taking the loads and working with other structure’s members. Again, iteration was optimized as far as was it possible and even almost not used beams are showing clearly that they will start to work depending on the side and amount of both pressure and suction. Pic. 5.2.3 Thickness of the elements from Robot

Pic. 5.2.3 Dimensions of the optimized structure members of chosen iteration.

6 VERIFICATION OF A SINGLE MEMBER ELEMENT Selected beam member: 588 (top_beam_section) Cross section dimensions: 150mm (height) x 140mm (width) Normal (kN) F 0,66

Moment (kNm) My -4,19

Moment (kNm) Mz 3,73

Table. 6.0.1 Internal forces from Robot

Following statement should be true to verify the member: !",$ %",$,&

+

đ?œŽđ?‘?, đ?‘œ =

!(,) %(,),&

+ đ?‘˜đ?‘š ∗

!(,%(,-,&

≤ 1, đ?‘˜đ?‘š = 0,7 (đ?‘“ đ?‘“đ?‘œđ?‘&#x; đ?‘&#x;đ?‘’đ?‘?đ?‘Ąđ?‘Žđ?‘›đ?‘”đ?‘˘đ?‘™đ?‘Žđ?‘&#x; đ?‘?đ?‘&#x;đ?‘œđ?‘ đ?‘ đ?‘ đ?‘’đ?‘?đ?‘Ąđ?‘–đ?‘œđ?‘›)

đ??š 0,66đ?‘˜đ?‘ đ?‘š = = 0,031 đ?‘€đ?‘ƒđ?‘Ž đ??´ 0,15đ?‘š ∗ 0,14đ?‘š

đ?œŽđ?‘š, đ?‘Ś =

đ?‘€đ?‘Ś −4,19đ?‘˜đ?‘ đ?‘š = = −7,981 đ?‘€đ?‘ƒđ?‘Ž 1 đ?‘Šđ?‘Ś ∗ (0,15đ?‘š)Q ∗ 0,14đ?‘š 6

đ?œŽđ?‘š, đ?‘§ =

đ?‘€đ?‘§ 3,73đ?‘˜đ?‘ đ?‘š = = 7,104 đ?‘€đ?‘ƒđ?‘Ž 1 đ?‘Šđ?‘§ ∗ (0,15đ?‘š)Q ∗ 0,14đ?‘š 6

Partial factor

Service class

Îłm 1,3

kmod 0,9

Characteristic strength (tension) đ?‘“ c,o,k 14MPa

Table. 6.0.2 Design values from euro codes

đ?‘“đ?‘?, đ?‘œ, đ?‘‘ =

đ?‘“đ?‘?, đ?‘œ, đ?‘˜ ∗ đ?‘˜đ?‘šđ?‘œđ?‘‘ 14đ?‘€đ?‘ƒđ?‘Ž ∗ 0,9 = = 9,69 đ?‘€đ?‘ƒđ?‘Ž đ?‘Śđ?‘š 1,3

đ?‘“đ?‘š, đ?‘Ś, đ?‘‘ =

đ?‘“đ?‘š, đ?‘˜ ∗ đ?‘˜đ?‘šđ?‘œđ?‘‘ 16đ?‘€đ?‘ƒđ?‘Ž ∗ 0,9 = = 16,6 đ?‘€đ?‘ƒđ?‘Ž đ?‘Śđ?‘š 1,3

��, �, � =

đ?‘“đ?‘š, đ?‘˜ ∗ đ?‘˜đ?‘šđ?‘œđ?‘‘ 16đ?‘€đ?‘ƒđ?‘Ž ∗ 0,9 = = 16,6 đ?‘€đ?‘ƒđ?‘Ž đ?‘Śđ?‘š 1,3

0,031đ?‘€đ?‘ƒđ?‘Ž −7,981đ?‘€đ?‘?đ?‘Ž 7,104đ?‘€đ?‘?đ?‘Ž + + 0,7 ∗ = 0,783 9,69đ?‘€đ?‘?đ?‘Ž 16,6đ?‘€đ?‘ƒđ?‘Ž 16,6đ?‘€đ?‘ƒđ?‘Ž Because đ?œŽđ?‘š, đ?‘Ś turned out to have negative value I removed the negative from the equation because it does not matter in case of momentum.

Verification: 0,783 ≤ 1 Autodesk Robot verification: 0,8 ≤ 1

Characteristic strength (bending) đ?‘“ m,k 16MPa

ULTIMATE LIMIT STATE (ULS): ∑γG Gk + γQ Qk,1 + ∑γQ ψ0 Qk,i γG = partial factor for permanent loading = 1,35 Gk = is the permanent action = 0,536 kN/m2 γQ = is the partial factor for variable loading = 1,5 ψ0 = is the factor that converts its variable action into its combination value = 0,5 for sites with an altitude of no more than 1000 meters above sea level Qk,1 = is the leading variable action Qk,i = is an accompanying variable action Loads combinations with snow as a leading action were found to be: LC1: ULS = 2,749kN/m2 LC2: ULS = 2,932kN/m2 Loads combinations with wind as a leading action were found to be: LC3: ULS = 1,662kN/m2 LC4: ULS = 1,496kN/m2

SERVICEABILITY LIMIT STATE (SLS): ∑Gk + Qk,1 + ∑ψ0Qk,i Snow is the leading action. Loads combinations with snow as a leading action were found to be: LC1: SLS = 1,886kN/m2 LC2: SLS = 1,831kN/m2 Loads combinations with wind as a leading action were found to be: LC3: SLS = 1,161kN/m2 LC4: SLS = 1,051kN/m2 7 CONCLUSIONS In modern day of an architect it is crucial to have actual knowledge about the new tools which are being developed and which can help understand better the core elements which (joint) are used to make the architecture. Performance Aided Design is one of the approaches to better understanding not only the structure but also overall forms, materials and acoustics. Karamba plugin for RhinoCeros turned out to be a wonderful tool in understanding the basics of how the structure may behave when specific loads will be added. At this very point it can give us a lot of information which can be crucial for some design decisions and it does not need a lot of afford to make the changes and get new results from the Karamba (for example what will be the deformation of the structure, what will be the maximum displacement in the structure, how heavy will it be, how big forces will occur in the structure members and will it make tensions or compressions in specific member areas. Robot (with RhinoCeros to Robot export components) is supporting Grasshopper and Karamba with very detailed data about the ULS and SLS as well as loads combinations and detailed information about each structure elements including the tension or compression limit for each of them.

Note: Thanks to Grasshopper and Karamba we have already created great interface for structural work without the need of learning whole Autodesk Robot software. This is speeding up our own work and also may help to discuss with the civil engineers on the detailed level instead of overall information’s. Although this paper is using a lot of simplifications when compared to the original design, mentioned software have proven to be very useful and handy during the design process. The most importantly it is easy to check needed data in real time simulation which is also very crucial for not only architects’ but also other branches’ professional work. From author: Big thanks to my structure research group: Gianmarco Lucarini Aleksi Rastas 8 REFERENCES Japanese codes for the snow loads: http://www.aij.or.jp/jpn/symposium/2006/loads/Chapter5_com.pdf"_com.pdf Information about the building (in Japanese): http://www.ms-a.com/2013/10/ http://www.kenchikushikai.or.jp/data/rengokai-sho/2013/04.pdf http://special.nikkeibp.co.jp/ts/article/aa0c/108540/p4.html http://rinken.exblog.jp/13476092/ http://ieinoue.exblog.jp/14917370/ http://obing.exblog.jp/tags/講習会/ http://length.jugem.jp/?eid=217 http://landship.sub.jp/stocktaking/archives/003012.html http://megumi-design.cocolog-nifty.com/blog/cat20987234/index.html http://www.inayama.net/works_detail/北沢建築-本社工場棟 http://irimasa.hamazo.tv/e2331100.html http://funakou.exblog.jp/13494749/ http://mokuyoren.jp/act/1841 http://nejiblog.seesaa.net/article/295650283.html http://unohideoblog2011.seesaa.net/article/191503337.html http://newssk.exblog.jp/20875647/ https://jsfmf.net/kokunai/kitazawamisawa/kitazawamisawa.html http://tsekkei.exblog.jp/14885785/ Technical drawings and specifications: Detail Magazine, Japanese Edition, nr. 198, October 2013 Shinkenchiku Magazine, nr. 3/2011 Pictures used: page 1, 2, “Kitazawa architecture Misawa Fumiko forest forestry Kyoto convention” presentation by MOK page 3: http://sumikura.jugem.jp/?eid=851

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