DEGREE OF BACHELOR OF SCIENCE IN ENGINEERING, FIRST CYCLE, 15 CREDITS
STOCKHOLM, SWEDEN 2021
Roof Structure of Bamboo for Solar Panels
KTH Bachelor Thesis Report
Alfons Hallgren and David Nordmark
Abstract
Sustainable urbanisation is a pressing challenge in some parts of the world and cost-efficient and environmentally friendly building materials could become a solution to achieve sustainability. Bamboo has shown promising properties in tensile- and bending strength to be able to substitute conventional building materials. If reinforced concrete gets implemented inside the anisotropic bamboo it further increases compressive strength, raw durability and makes the material more homogeneous.
This thesis report analyses and calculates the stress and deformation on these reinforced bamboo beams when used as a roof structure for a solar cell power charging station in Southeast Asia. The calculations were made in ANSYS Mechanical. Different structural designs were exposed to strong wind loads and the results were compared to optimize the usage of the materials.
The results show low values of stress and deformation after implementing reinforced concrete in the whole bamboo which indicates that excessively reinforced concrete might have been used. The results also show that using bamboo only in the structure gives considerably higher stress and deformation values even reaching critical levels at the edges of the roof and where the roof connects with the structural pillars.
By implementing reinforced concrete at only critical areas the amount of stress in the structure can be decreased to a manageable level. If this is done, no critical levels are reached and the arising stress levels in the bamboo fall below a safety factor of 3. With these results, one can argue to decrease the material usage by only using reinforced concrete at critical areas of the structure. By using the natural strength of bamboo and only complementing with concrete and steel where bamboo is weak, the overall environmental impact is kept low but also the costs for producing and transporting these materials.
Abstract
Med en konstant ökande urbanisering behövs nya miljövänliga och kostnads effektiva byggmaterial för att uppfylla den höga efterfrågan. Bambu har visat lovande egenskaper i drag och böjning för att kunna ersätta konventionella byggmaterial. Vidare bör den ihåliga anisotropiska bambun fyllas med armerad betong som bidrar med tryckmotstånd, styrka och ger materialet mer homogena egenskaper.
Detta kandidatexamensarbete analyserar och beräknar spänningar och deformationer på den armerade bambun vid användandet som en takstruktur för en laddningsstation i syd-östra Asien. Beräkningarna utfördes i programmet ANSYS Mechanical. Olika strukturella designer jämfördes vid starka vindtryck för att optimera användandet av resurser och material.
Vid implementeringen av armerad betong i hela bambun, visade resultaten otroligt låga spänningar och deformationer vilket indikerar på överanvändning av material. Vidare studerades tillämpningen av endast bambu där resultaten visade betydligt högre spänningar och deformationer som uppnår kritiska nivåer vid änderna av taket och kontakten mellan pelare och balkar.
Genom att införa armerad betong i endast de kritiska områdena gick det att minska spänningarna i strukturen tillräckligt för att göra den hanterbar. Då uppnås inga kritiska värden och de uppkommande spänningar i bambun visade en säkerhetsfaktor på 3.
Med det resultat som presenterades kan man argumentera för att minska användandet av material genom att utnyttja armerad betong på endast vid kritiska områden. Detta skulle leda till sparandet av resurser och transport som i sin tur gör strukturen mer miljövänlig och framtidsrelevant.
Acknowledgements
We want to express our gratitude to our helpful supervisor Artem Kulachenko who continuously supported us throughout the entire project. His patience, willingness to help, and immense knowledge significantly improved the quality of this study. We could not have wished for a better supervisor.
We also want to thank our client Ingemar Saevfors for continuously working together with us and being very clear with the intuitions of the project. Saevfors helped us to understand and grasp the core concept of his idea which gave an interesting insight into what the future might hold for bamboo as a building material and its possible areas of application.
Authors
Alfons Hallgren <alfonsha@kth.se> and David Nordmark <dnordm@kth.se>
KTH Royal Institute of Technology
Place for Project
Stockholm, Sweden
KTH Royal Institute of Technology
Examiner
Jonas Neumeister Place
KTH Royal Institute of Technology
Supervisor
Artem Kulachenko Place
KTH Royal Institute of Technology
Contents
1 Introduction ...1
2 Background ...3
3 Methodology ... 10
4 Results ... 14
5 Conclusion ... 20
References ... 23
1 Introduction
During the last couple of decades, an urgent strive for building and developing efficient and sustainable infrastructure has come to light. This is due to the fact that the world’s population is continuously growing and the demand for more advantageous solutions is increasing.
Different materials and structures are being researched and developed to aid against the current threat of climate change. A material that has not yet been used for industrial-scale construction is bamboo, even though it has promising strength properties. Bamboo is a fast-growing and renewable material with very interesting properties which could become a better alternative to many conventional materials when implemented with the correct technique.
Bamboo is primarily growing in locations where urbanization and demand for material are high. For instance in South-East Asia. Enabling the usage of bamboo here would lead to an easy-access stock of a high tensile strength material to use both in infrastructure, housing, and construction.
Bamboo consists of a long, circular hollow culm throughout the height of the tree. In addition, solid transverse diaphragms or ‘nodes’ are separating hollow regions with a circular cross-section containing unidirectional cellulosic fibres [2]. To make use of these inter-nodal regions, one is able to insert reinforced concrete into the bamboo shell which creates aesthetic beams with great constructional properties and strength.
However, the structural design is still imprecise for each given application since bamboo is anisotropic. Consequently, calculations and deep analysis is required to assure the safety of any design.
This report will analyze the structural design of a roof structure consisting of bamboo and reinforced concrete.
1.1 Project objective
This report aims to present the FEM results for the original roof structure, including total deformation and stress for the scenarios of interest. The most
critical areas of the structure will be discussed together with different improvements.
The goal is to be able to prefabricate natural material (such as bamboo) into building elements that effectively and safely can be used as a frame construction to bear specific loads.
2 Background
The innovative architect Ingemar Saevfors wants to push the boundaries of what can be built using natural materials and has therefore committed to researching the usage of bamboo as a beam substitution. This is the third year that Ingemar has cooperated with KTH bachelor strength theory students to research the use of bamboo as beams.
By compiling the conclusions from prior years, Ingemar sketched a beam structure that utilizes bamboo as the main body. This thesis starts by perfecting the model and analyzing its strength properties. The research on Double-Decker beam of bamboo done by Samuel Eriksson and Erik Rudquist was used to produce the model and estimating its bearing capacity. [3]
Strength values of bamboo were taken from Granta EduPack and will be used to simulate bamboo correctly in the FEM analysis and get accurate results. Parts of the structure are expected to get bent and stretched during strong winds, this report will highlight the bending resistance and stress of the structural bamboo beams.
Due to complex geometry and the high amount of calculations needed for this project, the software ANSYS Mechanical was used to evaluate the structure.
With valid inputs, ANSYS Mechanical could present an accurate analysis.
The student version for ANSYS Mechanical was used during the project. This version has limits on the maximum number of nodes.
2.1 Materials
The structure is made out of bamboo, concrete, structural steel for reinforcements, and solar panels as a roof.
2.1.1 Bamboo
Building with unconventional materials such as bamboo comes with a risk, but also great opportunities. Being able to use bamboo as a renewable and cost- efficient building material could prove valuable since it also absorbs carbon
dioxide during growth. Different institutions all around the world are conducting research to learn more about the properties of bamboo and how to preserve them.
However, bamboo comes with its drawbacks since it is a natural material.
Water- and termite damage are known risks that need to be taken into consideration when building with bamboo in more tropical areas of the world.
As mentioned in the introduction, bamboo has anisotropic properties, which is the case for many fibre-composite materials. However, only lengthwise properties for bamboo are being used in this analysis. This is due to the fact that the beam approximation was used for the slender members of the structure filled with reinforced concrete. In the beam approximation, the normal stresses dominate in bending. In addition, the beam is made of homogenous material and the stress level does not extend beyond the elastic limit where Young’s modulus is obeyed.
Properties Value Unit
E-modulus 15 GPa
Yield strength 35.9 MPa Tensile Strength 160 MPa Compressive Strength 60 MPa Shear modulus 1.21 GPA
Poisson's ratio 0.32 - Table 2.1: Table of bamboo properties.
2.1.2 Concrete
Since bamboo consists of a circular hollow, its compressive bearing capacity is relatively low and therefore limits its structural application. A study by Wen-Tao Li et al. evaluated 19 specimens under axial load regarding filling the hollow with concrete. This study concludes that the concrete increases the compressive strength significantly [4]. This project will also use concrete inside the bamboo to help with compressive strength and protecting the structural steel from corrosion.
Properties Value Unit
E-modulus 30 GPa
Tensile Ultimate Strength 5 MPa Compressive Ultimate Strength 41 MPa Shear modulus 1.27 GPA
Poisson's ratio 0.18 - Table 2.2: Table of concrete properties.
2.1.3 Structural steel
Structural steel is widely used as reinforcement in concrete since it makes a perfect combination of compressive and tensile strength. The implementation of a structural steel rod contributes to the bamboo beams being much more ductile, which was also discovered in Wen-Tao Li et al. study.
Properties Value Unit
E-modulus 211 GPa
Tensile Strength 250 MPa Compressive Strength 250 MPa Shear modulus 76.9 GPA
Poisson's ratio 0.3 -
Table 2.3: Table of structural steel properties.
2.1.4 Solar panel
The solar panels are 2x1[m] aluminum framed with 30mm thick laminate consisting of glass, ethyl-vinyl acetate (EVA), and silicon [5]. Each solar panel weighs 22kg and brings stability to the structure and acts as the roof.
Material E-modulus (GPA) Poisson's ratio
Glass 66G 0.23
Silicon 112.4 0.28
EVA 0.0677 0.33
Aluminum 69 0.33
Table 2.4: Table of material properties for solar panels.
2.2 Structure & Sketch
This thesis is based on the detailed design shown in Figure 2.1 and Figure 2.2.
The structure is grounded with ten 5m reinforced concrete pillars.
Figure 2.1 shows there are ten bent trusses (labeled ”02-11”) horizontally attached near the top of the pillars. On top of the trusses are purlins (labeled
”A-J”) going along the entire structure of 20 meters which are attached to each truss. The solar panels are attached to the purlins which stabilize the structure and act as a roof. Struts are implemented between the bent trusses to distribute the loads, see Figure 2.1. All of these beams consist of bamboo, concrete and structural steel except for the struts which are made of bamboo only.
Figure 2.1: The sketch of the model.
Figure 2.2: Detailed geometry of the pillars.
2.2.1 Cross-section
Each beam consists of the three materials listed above (bamboo, concrete, and structural steel). The structural steel can be found at the center of the beam’s cross-section with a diameter of 12mm, as shown in Figure 2.3. Concrete is applied between the structural steel and the bamboo shell and has a diameter of 90mm. Bamboo makes up the outer edge of the beam with a diameter of 120mm.
Figure 2.3: Cross-sections of a reinforced bamboo beam.
2.2.2 Contacts
The contacts between the structural steel, concrete, and bamboo within each beam, as stated in Paragraph 2.2.1, have to be taken into consideration. This thesis assumes that concrete and bamboo are bonded, permitting adequate force transfer between the materials [1].
Furthermore, the structure contains plenty of crossing beams in contact with each other and with the reinforced pillars. Since the hollow bamboo is 15mm thick it is arguably easy to connect them with screws and bolts. However, the contact area that the bamboo walls share with the screw is minimal and some might fracture or loosen over time. This is where the reinforced concrete can help to absorb and distribute the occurring forces.
2.2.3 Loads
Since the structure is mainly purposed to be used in areas surrounding the Indian ocean, it must be able to withstand the violent storms that can occur there. During these storms, the wind can reach speeds of up to 30 m/s. Wind speeds of this magnitude would, according to calculations done in eurocodeapplied.com, correspond to an upward pressure of 2170Pa in the
critical areas, see appendix. To bear in mind, this value is in relation to the F-zones, see Figure 2.1.
3 Methodology
A model in ANSYS was made by studying the geometries of the sketch shown in Figure 2.1. This was an iterative process and the model was regularly updated or entirely remade from scratch. The first model was made using only solids which lead to an immense amount of nodes and contacts which made the analysis impossible with the student license of ANSYS. As a consequence, the model was remade with beam elements decreasing the number of nodes almost a thousandfold.
3.1 Finite elements
As a result of the structure’s scale, there were plenty of connections between the faces and edges that had to be defined manually. To simplify the issue, all the connection was defined as bonded which means there is no separation or gliding allowed.
The occurring contacts are defined with CONTA177 which is a 3-D beam-to- beam contact element used to represent the 3-D beam-to-beam contacts in ANSYS. The element is aligned with the beam and can represent both internal and crossing contacts, see Figures 3.1 and 3.2. A contact is defined when element CONTA177 penetrates a target element, in this case, TARGE170.
TARGE170 represents a target surface that shares interaction points with a contact element. When a contact is detected, the element is set to specify the properties of that interaction. This leads to each contact in the structure having properties according to the materials present. Further on, a shape function for the stiffness is used for each contact according to Equation 1 [6].
𝑊𝑊 = 𝐶𝐶1+ 𝐶𝐶2𝑥𝑥 + 𝐶𝐶1𝑥𝑥2 (1)
Figure 3.1: Beam sliding inside a Figure 3.2: Crossing beams in
hollow beam. contact.
We used element BEAM189, which is a quadratic 3-D element with three-nodes.
Each node has six degrees of freedom, which include translation and rotation in x-,y- and z-direction, see shape functions Equations 2-7 [7]. BEAM189 is based on Timoshenko beam theory which includes shear deformation effects. The cross-section is assigned an effective shear area As. The deflection is a sum of the bending 𝑤𝑤𝑏𝑏and shear 𝑤𝑤𝑠𝑠 in regards to differential equations, see equations 8-10 [8].
𝑢𝑢 =12 �𝑢𝑢𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝑢𝑢𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝑢𝑢𝑗𝑗 (1 − 𝑠𝑠2) (2) 𝑣𝑣 =12 �𝑣𝑣𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝑣𝑣𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝑣𝑣𝑗𝑗 (1 − 𝑠𝑠2) (3) 𝑤𝑤 =12 �𝑤𝑤𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝑤𝑤𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝑤𝑤𝑗𝑗 (1 − 𝑠𝑠2) (4) 𝜃𝜃𝑥𝑥 =12 �𝜃𝜃𝑥𝑥𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝜃𝜃𝑥𝑥𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝜃𝜃𝑥𝑥𝑥𝑥 (1 − 𝑠𝑠2) (5) 𝜃𝜃𝑦𝑦 = 12 �𝜃𝜃𝑦𝑦𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝜃𝜃𝑦𝑦𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝜃𝜃𝑦𝑦𝑥𝑥 (1 − 𝑠𝑠2) (6)
𝜃𝜃𝑧𝑧 =12 �𝜃𝜃𝑧𝑧𝐻𝐻 (−𝑠𝑠 + 𝑠𝑠2) + 𝜃𝜃𝑧𝑧𝐼𝐼 (𝑠𝑠 + 𝑠𝑠2)� + 𝜃𝜃𝑧𝑧𝑥𝑥 (1 − 𝑠𝑠2) (7)
𝑤𝑤 = 𝑤𝑤𝑏𝑏+ 𝑤𝑤𝑠𝑠 (8)
𝑤𝑤𝑠𝑠′= 𝛾𝛾 =𝐺𝐺𝐴𝐴𝑇𝑇
𝑠𝑠 (9)
𝑇𝑇 = −𝐸𝐸𝐸𝐸𝑤𝑤𝑏𝑏′′ (10)
The element REINF264 was used to simulate the structural steel reinforcements inside the pillars. Each fiber segment is separately modeled as a spar which has only uniaxial stiffness. The degrees of freedom and nodal location for REINF264 are the same as the element of which it resides which insures proper load transfer along with the embedded spar element. We used REINF264 inside the pillars to simulate its ∅12mm and ∅25mm structural steel reinforcements.
As previously mentioned, solar panels consist of different materials which should be taken into consideration. To decrease calculations the solar panels were defined as one material and meshed as a shell element. It is a four-node element with six degrees of freedom at each node. The Young’s modulus was defined as 66GPa and a density of 383kg/m2 which correspond to each solar panel weighing exactly 22kg.
3.2 Safety Margin
Finding the most critical areas of the model is crucial for building a durable structure. It will also help to understand the strengths and weaknesses of using bamboo in this way. The parts where most stresses are expected are within the F-zones but also the contacts between the beams and pillars.
The model got analyzed under more extreme conditions than required to ensure the safety of the design. It was defined that the wind created a pressure equal to 2170Pa under the entire roof. According to the calculations (see Paragraph 2.2.3) this pressure could only occur within the F-zones but for the benefit of safety, this pressure was defined under the entire roof. In addition, the weakest properties, presented by EduPack were selected for the materials. This report aims to have a 2x stress safety margin.
3.3 Improvements
This thesis will consider decreasing the usage of reinforced concrete within the bamboo beam to further reduce cost and climate impact. First, the possibility of removing all reinforced concrete will be analyzed, see Figure. 3.3. Another case that will be analyzed is when only the nodal regions of bamboo which are in contact with a body are filled with reinforced concrete, see Figure 3.4. Hence,
regions that are not in direct contact with another beam remain naturally hollow. This will reduce the weight of the structure and the material usage.
Figure 3.3: Bambo skeleton.
Figure 3.4: Concrete and structural steel locations within the trusses and purlins.
4 Results
This chapter will include figures which display resulted stress and deformation following the work explained in chapter 3.
4.1 Original structure
The sketch of the original structure consists of bamboo beams filled with reinforced concrete. The results are in regards to the load presented in Paragraph 2.2.3.
The calculations resulted in a deformation of approximately 6mm located in the F-zone, see Figure 4.1. The deformation is mainly concentrated in those areas while other regions show very small deformations.
Figure 4.1: Total deformation with the pressure of 2170Pa acting under the entire roof.
As shown in Figure 4.2, the occurring stress within the bamboo stays at a maximum of approximately 4MPa. The maximum occurring stress will be located in the structural steel at roughly 19MPa, see Figure 4.3. Highly concentrated stress is predominantly acting at contacts between the solar panels and purlins, and at the same time, the contacts between the pillars and trusses.
Figure 4.2: Normal stress in the bamboo with 2170Pa acting under the entire roof.
Figure 4.3: Normal stress in the structural steel at the contacts between the trusses and pillars.
In Figure 4.4, the pressure was increased to 10850Pa and show that the bamboo skeleton only extends between the light blue regions (-49MPa) and green regions (26MPa).
Figure 4.4: Normal stress in the bamboo with 10850Pa pressure acting under the entire roof.
4.2 Removing all reinforced concrete
This case will be based on removing all reinforced concrete and analyzing how the bamboo performs by itself.
The deformation is mainly located in the F-zone with a value of 20mm. The rest of the structure falls below this value, see Figure 4.5.
Figure 4.5: Occurring deformation while no reinforced concrete is present.
Some regions have combined stress under compression of up to -27MPa while other regions are affected by a tensile stress of approximately 31MPa as shown in Figure 4.6.
Figure 4.6: Normal stress in the bamboo skeleton.
4.3 Concentrating reinforced concrete at contact areas
The following case is based on implementing reinforced concrete at only contact areas.
The deformation is primarily located within the F-zone with a maximum of 13mm, see Figure 4.7.
Figure 4.7: Deformation with reinforced concrete at contact areas.
As shown in Figure 4.8 the stress in the beams is mainly located around the contact between the trusses and the pillars where it reaches values of 18MPa. At the same time, compression can be observed at the top of the trusses at around 20MPa.
Figure 4.8: Normal stress in the bamboo with reinforced concrete at contact areas.
5 Conclusion
5.0.1 Original structure
When filled with reinforced concrete, the bamboo beams are strong enough to resist the forces of nature presented in Paragraph 2.2.3. For these beams, the critical values of the stress are only reached after increasing the load fifth fold, see Paragraph 4.1. The maximum stress occurs at the very center of the cross- section, in the structural steel. Hence, bamboo works as a decoration rather than an actual load supporter.
It is easy to argue that the original structure is using more material and resources than needed. This leads to the question of how bamboo would be performing without the support of reinforced concrete.
5.0.2 Removing all reinforced concrete
By removing all reinforced concrete, the entire load will be supported by the bamboo beams. Using bamboo only will however not be enough, shown in Paragraph 4.2. The result shows values near and above bamboo’s yield strength which would result in plastic deformation. This would rather lead to crack initiation or a total breakdown of the structure. Furthermore, bamboo has weak compression capacity, which the FEM analysis showed could reach up to 23Mpa. This would also weaken the structure and probably cause it to crack.
Although, the results give an interesting insight into how the bamboo would hold up by itself. With this result, the report could argue for the following study, concentrating reinforced concrete at contact areas.
5.0.3 Concentrating reinforced concrete at contact areas
By concentrating reinforcement at areas where contacts are present, natural hollow bamboo could support areas where reinforcement is not needed. As explained in Paragraph 3.3, the insertion of reinforced concrete at specific areas could reduce the usage of materials but still result in a safe structure. The results in Paragraph 4.3 indicate that neither the deformation nor stress will
approach critical values. In this case, the maximum stress occurs within the bamboo, just outside the contact with the reinforced pillars, see Figure 4.8. This still leads to the desired stress safety margin of 2x. At the same time, the higher compression levels occur at contacts which in this case have reinforcement concrete. This result showed to be very promising and tolerates being further researched.
5.1 Discussion
From this conclusion, it is interesting to discuss the possibility of minimizing the amount of material used in the structure while preserving its strength.
Using bamboo only will according to the results not be enough to withstand the load put on the structure. Disregarding the concrete filling will also decrease the compression strength of the beams. Furthermore, the simplification made about the contacts between different bodies cannot be forgotten. It is believed that if only bamboo is used in the structure there can arise practical difficulties in the contacts.
To avoid this problem, consider the possibility of using reinforced concrete at only some parts of the structure, such as where the beams connect with the pillars and with each other. The concrete helps the bamboo by absorbing the local forces created by the contacts. Using a structural steel rod where the bamboo connects with the pillars greatly decreased the maximum stress put on the bamboo in this critical area.
By concentrating the reinforced concrete at the contact areas, the amount of concrete and steel used in the structure can be halved while still supporting bamboo in its weaker areas. This would lead to savings in both material usage but also in transportation and maybe even making the structure easier to assemble.
The results show that the trusses are subjected to both tensile stress and compression stress. By analyzing this further one can understand where concrete or steel should be used. In this thesis, reinforced concrete was present at all contacts, see Figure 3.4. This might not be needed and there should exist
an optimal way to place it regarding structure strength, costs, etc. which might be worth researching.
References
[1] Hector Archila, et al. “Bamboo reinforced concrete: a critical review”. In:
Materials and Structures 51:102 (2018). DOI: https://doi.org/
10.1617/ s11527-018-1228-6.
[2] Qingfeng Xu Jennifer Gottron, Kent A. Harries. “Creep behaviour of bamboo”. In: Construction of Building Materials (2014), pp. 79–88. DOI:
https://doi.org/10.1016/j.conbuildmat.2014.05.024.
[3] Samuel Eriksson, Erik Rudqvist. “Double-decker beam of bamboo [An alternative to I-section beams in construction of multistory housing]”. In:
(2020). URL: http://www.diva-portal.org/smash/get/ diva2:
1456866/FULLTEXT01.pdf.
[4] Wen-Tao Li, et al. “Axial load behavior of structural bamboo filled with concrete and cement mortar”. In: ConstructionofBuildingMaterials (2017), pp. 273–287. DOI: https://doi.org/10.1016/j.conbuild mat.2017.05. 061.
[5] Yixian Lee, Andrew A.O. Tay. “Stress Analysis of Silicon Wafer-Based Photovoltaic Modules Under IEC 61215 Mechanical Load Test”. In:
ConstructionofBuildingMaterials (2013), pp. 265–271. DOI:
https://doi. org/10.1016/j.egypro.2013.05.067.
[6] Ansys® Academic Research Mechanical, Release 18.2, Help System, CONTA177, ANSYS, Inc. URL: https://www.mm.bme.hu/~gyebro/files /ans_help_v182/ans_elem/Hlp_E_CONTA177.html
[7] Ansys® Academic Research Mechanical, Release 18.2, Help System, BEAM189, ANSYS, Inc. URL: https://www.mm.bme.hu/~gyebro/files/
ans_help_v182/ans_elem/Hlp_E_BEAM189.html
[8] Alfredsson, B. 2014. Handbok och formelsaming I hållfastighetslära.
Stockholm: Institute of mechanics, Royal Institute of Technology.
[9] Ansys® Academic Research Mechanical, Release 18.2, Help System, REINF264, ANSYS, Inc. URL: https://www.mm.bme.hu/
~gyebro/files/ans_help_v182/ans_elem/Hlp_E_REINF264.html
Appendex
Figure .1 and Figure .2 show how the pressure was calculated from wind speed and geometries using eurocodeapplied.com.
Figure .1: Wind load calculations
Figure .2: Resulting loads from calculations
