final year project report

Faculty of Technology and Built Environment DEPARTMENT OF CIVIL ENGINEERING ENGINEERING DEVELOPMENT PROJECT (ENGG MG7001) Design of Nail Connections: Various Methodologies and Their Influence on the Design of a Nailed Portal Joint Niloofar Arya 1423214 Supervisor: Wei Yuen Loo Disclaimer: This document is a report on “Design of Nail Connections: Various Methodologies and Their Influence on the Design of a Nailed Portal Joint” that was carried out as part of a student learning exercise. It has been marked and awarded a grade. However, regardless of the grade awarded, there is no guarantee that the contents of this document will be free from errors, inconsistencies, or discrepancies. While this document may contain findings and recommendations that could be of use to the client, or indeed anyone else reading this report, neither Unitec, the author of this report, nor any of the persons mentioned under the Acknowledgements section of this document, shall bear any responsibility or liability; should the client or anyone else, upon implementing the design or utilising any of the findings and recommendations contained within this document, incur any harm, damage, liability, injury, or any other kind of loss whatsoever. 2015 1 Permission Statement I hereby, give ------- OR don’t give -------- permission for my research/design project report entitled: __________________________________________________ to be held in the Unitec Library. Course: _____________________________________ Year of completion: ________ Department/School of _________________________________ I agree to this research being consulted for research or study purposes only provided that due acknowledgement of its use is made where appropriate and any copying is made in accordance with the Copyright Act 1994. I agree to this research being available for interlibrary loan. I have made all efforts to ensure that the information contained in the report is accurate. I will not be held responsible for any inaccuracies. Also, I agree to this work being copied for archive, external moderation, monitoring, promotional and future learning purposes. Name: __________________________ Signed: __________________________ Date: ___________ 2 Declaration for Ethical Approval of Research/Design Project I _________________________ declare that this research or design project: (Student’s full name) Either � Does not involve humans as participants? Or � Has ethical approval from UREC (as included in this project report)? Signed: ______________________ Date: _________________ (Signature) 3 Acknowledgements Foremost, I would like to express my sincere gratitude to my supervisor Wei Loo for his continuous support and motivation throughout my final year project. I could not have imagined having a better supervisor for my final year project. I thank him for taking his time and providing me with the required information regarding this project. With his constant supervision and immense knowledge I would not have completed this report to the standard that is required. 4 Executive Summary This project involves the investigation of timber nail connections and the ways in which they are designed using various methodologies. The New Zealand, Australian and European (Eurocode) structural standards are used in this project to determine the calculation procedure to design a nail connection. Some background theory on the history of the nails and general knowledge on timber nail connections are provided in this report. Also some information on the design of a nail plate joint are included. The calculations are done using spreadsheets and all the steps of creating a spreadsheets are included in the project, also the steps taken to do the calculations are provided. The results from the calculations based on these three codes are compared and discussed. Discussing the report includes stating the variations between the results and stating the conservative method. The report ends with provided recommendation on the discussed results. From this report it was found that the calculated Australian values were lower than both New Zealand and European standards. Whereas European values were higher compared to New Zealand and Australian standards. 5 Table of Contents Executive Summary ........................................................................................................... 5 1.0 Introduction .................................................................................................................. 9 1.1 General background ........................................................................................................... 9 1.2 Aims and objective............................................................................................................ 10 2.0 Methodology and Resources .................................................................................... 11 2.1 Methodology ...................................................................................................................... 11 2.2 Resources .......................................................................................................................... 12 3.0 Background Theory ................................................................................................... 13 3.1 History of Nail .................................................................................................................... 13 3.2 General Knowledge ........................................................................................................... 15 3.3 New Zealand Standard ...................................................................................................... 17 3.4 Australian Standard .......................................................................................................... 20 3.5 European Standard (Eurocode) ........................................................................................ 23 3.6 Nailed Plate Joints ............................................................................................................ 27 3.6.1 Nail Plate Moment Joints ........................................................................................... 27 3.6.2 Nail Strength ............................................................................................................... 28 4.0 Analysis ...................................................................................................................... 29 4.1 General............................................................................................................................... 29 4.2 Design of Spreadsheets ................................................................................................... 29 4.3 Nail Strength Calculations ................................................................................................ 38 4.4 Nail Plate Joint Calculations ............................................................................................ 39 5.0 Discussion .................................................................................................................. 44 5.1 General............................................................................................................................... 44 5.2 Assumptions ..................................................................................................................... 44 5.3 New Zealand Results ........................................................................................................ 45 5.4 Australian Results ............................................................................................................. 48 5.5 European Results .............................................................................................................. 49 5.6 Australia vs. New Zealand ................................................................................................ 50 5.7 New Zealand vs. Europe ................................................................................................... 53 5.8 Australia vs. Europe .......................................................................................................... 55 5.9 New Zealand vs. Europe vs. Australia ............................................................................. 57 5.10 Nail Plate Joint Results ................................................................................................... 61 6.0 Recommendation ....................................................................................................... 62 7.0 References ................................................................................................................. 63 6 Appendix A ....................................................................................................................... 64 Appendix B ....................................................................................................................... 68 Appendix C ....................................................................................................................... 73 Appendix D ....................................................................................................................... 77 Appendix E ....................................................................................................................... 80 List of Tables and Illustrations: Figure 3.1.1: Hand-Wrought Nail, before 1800….........................................................................13 Figure 3.1.2: Type A Cut Nail, late 1790s-1820s……………………………………………………..13 Figure 3.1.3: Type B Cut Nail, late 1810s-1900s……………………………………………………..14 Figure 3.1.4: Steel Wire Nail, 1890s to present………………………………………………………14 Figure 3.2.1: Typical Nail Types…………………………………………………………………….….15 Figure 3.2.2: Nail in Single and Double Shear……………………………………………………….16 Figure 3.3.1: Minimum Spacing of Nails (NZS3603)………………………………………………...18 Figure 3.3.2: Timber thickness and nail length (NZS3603)………………………………………..20 Figure 3.4.1: Two-member joint for nails and screws laterally loaded in shear (AS1720.1- 2010)…………………………………………………………………………………………………………21 Figure 3.4.2: Timber thickness and fastener length for nails, wood screws and coach screws (AS1720.1-2010)……………………………………………………………………………………………22 Figure 3.5.1: Different shear loading condition- Single Shear……………………………………24 Figure 3.5.2: Different shear loading, failure modes for timber-to-timber conditions-Double shear…………………………………………………………………………………………………………25 Table 3.5.3: Value of Kef (EN 1995-1-1:2004)…………………………………………………………26 Figure 4.2.1: Excel options window - Customize Ribbon………………………………………….30 Figure 4.2.2: New Zealand Spreadsheet -Coefficients allocated in cells……………………….30 Figure 4.2.3: Microsoft Visual Basic for Application Window…………………………………….31 Figure 4.2.4: Single Shear properties - Name tab…………...………………………………………32 Figure 4.2.5: Double Shear-Class Module Coding…………………………………………………..33 Figure 4.2.6: Command Button (ActiveX Control)…………………………………………………..33 Figure 4.2.7: Command button properties – Caption tab………………………………………….34 Figure 4.2.8: Command Button Code………………………………………………………………….35 Figure 4.2.9: New Zealand Standard Spreadsheet………………………………………………….35 Figure 4.2.10: European Standard Spreadsheet–Minimum Nail Capacity in Double Shear…36 Figure 4.2.11: Spreadsheet of Nail Plate Joint Design……………………………………………..37 7 Figure 4.2.12: Nail Plate Joint – Total Resultant Force Calculation……………………………..37 Figure 4.4.1: Nailed Plates - (Nail Groups)……………………………………………………………40 Figure 4.4.2: Quarter of nail group……………………………………………………………………..41 Table 4.4.3: Nail Group dimensions for a quarter of the nail group..........................................41 Figure 5.3.1: New Zealand, J4 timber (Double Shear vs. Single Shear)…………………………46 Figure 5.3.2: New Zealand - single shear (J4 vs. J5)………………………………………………..47 Figure 5.4.1: Australia, JD5 timber (side grain vs. end grain)…………………………………….48 Figure 5.4.2: Australia – Single Shear (JD4 vs. JD5)……………………………………………….49 Figure 5.5.1: European J4 vs. J5 (Single and Double shear)……………………………….……..50 Figure 5.6.1: Australian vs. New Zealand (J5/JD5)………………………………………………….51 Figure 5.6.2: Australian vs. New Zealand (J4/JD4)………………………………………………….52 Figure 5.7.1: New Zealand vs. European (Single Shear)…………………………………………...53 Figure 5.7.2: New Zealand vs. European (Double Shear)………………………………………….54 Figure 5.8.1: Australian vs. European (Single Shear)………………………………………………55 Figure 5.8.2: Australian vs. European (Double Shear)……………………………………………..56 Figure 5.9.1: Australia vs. New Zealand vs Europe (J5/JD5, Single Shear)…………………….57 Figure 5.9.2: Australia vs. New Zealand vs Europe (J5/JD5, Double Shear)…………………...58 Figure 5.9.3: Australia vs. New Zealand vs Europe (J4/JD4, Single Shear)…………………….59 Figure 5.9.4: Australia vs. New Zealand vs Europe (J4/JD4, Double Shear)…………………...59 8 1.0 Introduction 1.1 General background Nails are applied to fasten two materials together and to resist lateral loads. They are most commonly utilized for fastening woods. Generally all nails are composed of head, shank and point (round point, diamond point, or chisel point). Nails are accessible in different sorts of lengths, cross-sectional shapes and ranges. There are numerous sorts and types of nails, but the most commonly utilized nail is the bright smooth steel wire nail, mostly referred to as a smooth nail. Nails can be plain or enameled, carved, electroplated, galvanised or polymer coated to suit the finish that is needed and the environment that they are to be utilized. Nailed connections are easy to form and are suitable for structures with small loadings and where connections are framed from moderately thin members. They are usually utilized in wall framing, decks, floors, roofs and in about all construction that includes light loads and straightforward components. This project will start with the introduction and includes an explanation of the aim for this project. After the introduction, the methodology of how the report is going to be carried out and what resources are used to complete the project will be explained. Also this report will include a background theory about nail connection, explaining how the calculations must be done using New Zealand, Australian and European standard theories. Analysis and discussion will be provided in the report after the background theory. The analysis part will include how the excel spreadsheets were designed and some calculations will be provided. In the discussion part the result of the calculations will be discussed. Lastly recommendation will be provided for this project. This report is only considered with laterally loaded nails, in both single and double shear. Further on, in the report single and double shear conditions will be explained. 9 1.2 Aims and objective The aim of this research/design structural project is to: - Research some of the different ways in which nail connections are designed in New Zealand, Europe, and Australia referring to the structural timber standards of all three places. - Calculate the strength of a laterally loaded nail for various diameters using New Zealand, Australian and European standard methods. - Compare the outcomes obtained from the calculations carried out for a variety of loading and connection designs from the code requirements of New Zealand, Europe and Australian. - State and comment on the most conservative and least conservative countries between New Zealand, Europe and Australian codes in respect to the nail connections in different range of sizes and penetrations. - Design a nail plate joint using the three codes and commenting on the obtained result. 10 2.0 Methodology and Resources 2.1 Methodology The following steps were undertaken to complete this report: 1. Conduct a literature review of nail connections: - Research will be done on the background of nail connections and general information about the different types of connections and configurations. - Research on the different type of nails that are used in the New Zealand, Australian and European codes. 2. Review the design of nail connections using the European code: - Collect theory data of different nail connections and designs using European code. - Collect methods for calculating the lateral strength of variety of nails with different types of connections and configurations using the European Code. - Use computer programs such as excel to analyse the lateral strength calculations for various nail connections determined in the European code. 3. Review the design of nail connections using the New Zealand code: - Step 2 will be repeated, but in regards to the New Zealand standard. 4. Review the design of nail connections using the Australian code: - Step 2 will be repeated, but in regards to the Australian Standard. 5. Conduct a study comparing the design results using the three codes: - All of the results will be graphed using computer programs and will be compared. - Use the graphed results for all three codes to determine which codes produce the most conservative result and which codes produce the least. 11 6. Research how to design a portal frame nail plate joint 7. Design the nail plate joint using the procedure of the three codes separately: - Design the nail plate joint using computer using excel. 8. Comment on the results of the nail plate joint 9. Lastly, conclusions and recommendations will be provided for this report 2.2 Resources The following resources are used to complete this report: New Zealand, European and Australian standards: - Design codes NZS 3603, EN1995-1 and AS 1720.1. - Conduct a literature review on nail connections. - Using the structural and timber codes of nail connections to compare between the three countries and to calculate the lateral strength. Books, articles and Websites: - Find out background information about nail connections. - Receive general ideas about the different types and designs of nail connections. - Discover how to design a portal frame nail plate joint. Excel Spreadsheet: - To do the lateral strength calculations for the different types of timber and nail designs. - Graph the results to compare between New Zealand, Europe and Australian codes. 12 3.0 Background Theory 3.1 History of Nail The history of nails go back to a few thousand years ago, they were most commonly used for fastening and joining. Bronze nails were found 3400 BC in Egypt. In the 1790s and the mid-1800s, hand-wrought nails were made for fastening by Blacksmiths or Nailers, from a square iron rod. The rods were one by one heated, and every sides of it was hammered to shape a pointy end, then it was reheated and cut off. To create a nail head, the blacksmith would have to hammer the hot nail placed into an anvil. The hand-wrought nails were basically created to fasten the surrounding and roof covers on building frames. An example of hand-wrought nail, made in 1790s is shown in the figure below (Thomas D. Visser). Figure 3.1.1: Hand-Wrought Nail, before 1800 In the late 1790s and early 1800’s several nail cutting machines were invented in the United States to create nails from iron bars. In the beginning the nail heads were formed by hand as they used to be made before the nail cutting machine invention, but later on in the 1820s there was a different mechanical machine built to hammer the head of the nails, after the nails were made. Using these machines type A cut nails were produced (Type A cut nail shown in the figure 3.1.2)(Thomas D. Visser). Figure 3.1.2: Type A cut nail, late 1790s-1820s 13 However, by the 1810s, another nail cutting machine with a more adequate design was built, which could create a further developed design for nails and was also capable of carrying on with the mechanical operation to form a head for nails. Nails that were formed using this machine are known as type B nails (as shown in figure 3.3). In 1800s, type B cut nails were the most popular nails, and stayed popular for a long while. The differences between type A nails and type B nails can be known by the burrs along the edge of the material. In type A nails, burrs appear on the opposite edges, while type B nails have both burrs on the same side. Cut nails are still being used, however with the type B system and the reason for this is due to its great holding strength and hardness. They are used only for specific purposes such as flooring nails, boat nails and masonry nails(Thomas D. Visser). Figure 3.1.3: Type B cut nail, late 1810s-1900s In the 1850’s several nail companies were built up in New York, which produced steel wire nails (Shown in figure 3.4), and by 1886, only 10 percent of the nails were made from steel. But with the progress of producing nails, use of soft steel as a cheaper option, caused the iron popularity fade immediately, and even though many constructors preferred using nail cuts because of their large capability of joining. In the 1900s the percentage of steel wire nails increased to 90 percent. When the wire nails were first made, they were not used for construction purposes, but were used for creating products such as pocket book frames and cigar boxes (Thomas D. Visser). Figure 3.1.4: Steel wire nail, 1890s to present 14 3.2 General Knowledge Nails are most commonly utilised for light timber framing. Bearing in mind, nails offer less strength than the other connectors, they are utilised where limited forces are applied. Nails are generally used to attach two pieces of wood together directly or by method of using a metal plate that is joined to the two pieces. There needs to be a minimum of two nails in any nail connection (MetsaWood). There are different types of nails (for example, common nail, box nail, casing nail, finishing nail and brad nail), but there are mainly two types of nails that are commonly used (common nail and finishing nail). A common nail is the most wildly used nail and has a large flat head, so when it’s driven in to the wood material, it levels with the surface. However a finishing nail has smaller head, which is driven under the surface of the material using a particular nail gun. The finishing nails give result in a nicer surface, therefore there are largely used for interior paneling and cabinetwork. The strength in the joint of the common nail halves in two days after it has been driven into the material. Around a month later the strength will slowly increase as the wood fibers straighten out and catches the nail. Figure 3.2.1: Typical Nail Types Nails can be made out of different materials such as normal steel (Steel wire nail), stainless steel, silicon bronze and copper nails. Stainless steel nails are suitable for very destructive environment. Silicon Bronze fasteners give incredible corrosion resistance, however are soft and assist a correctly sized pilot hole to resist breakage. Steel wire nails are accessible "bright" or with an erosion 15 resistant coating. The most widely recognized manifestation of protection is zinc coating and can be applied by tumbling barrels or hot dip galvanising (HDG)(Buchanan, A). Nails can be axially loaded, where they are loaded along their own axis or laterally loaded, in which the load is perpendicular to the axis of the nail. Also in some cases nail can be loaded laterally and axially combined. When the nail is perpendicular to the grain makes lateral loading in nail more effective (Soltis. A. L). There are a few conditions that affect the lateral strength of a nailed connection, such as the moisture content, nail diameter and the grain direction. Different nail diameters have different load carrying capacity. The proportion of a normal wire nails length to its diameter, mostly changes from 15 to 35 to avoid buckling (Buchanan, A). Deformed-shank nails are capable of carrying more lateral loads compared to the common wire nails. Variation in the moisture content of the wood creates difficulty in establishment of a lateral load for a nailed joint. Structural joints must be spaced at a certain distance and using additional nails to reinforce the joint if it has loosened while drying (Soltis. A. L). The nailed connections can be in single or double shear. A single shear nail connection has two timber members in a joint, and in a double shear nail connection there are three members or more fastened. An example of single shear and double shear is illustrated in figure 3.2.2. Figure 3.2.2: Nail in single and double shear Single Shear- Side Grain Single Shear – End Grain Double Shear 16 One of the advantages of a nail connection is the hole that the nail is driven into, is completely filled, therefore it won’t cause any slipping at the start. Also nail connections are suitable for jointing the site using untrained labour, but the jointing must be done carefully, because once the nail is in place the geometry is locked and it is very hard to remove (AU Guide). The capacity of a steel-to-timber connection relies upon the thickness of the steel plates. The steel plate is considered to be thin if the thickness of the plate is equal or less than 0.5d, and steel plates with thickness same or bigger than d are considered as thick plates. Nailed connections have restricted fire resistance, except if they are secured by sacrificial timber or covered with incombustible material. 3.3 New Zealand Standard New Zealand Standard 3603 sets out all the relative standard information and method of calculations for lateral loadings for timber nail connections in New Zealand. For the nail connection design, suitable timber species shall be appointed to a fitting group (Refer to NZS3603). For nails and screws in lateral loading, the timber species, Radiata Pine and Douglas fir larch are classified as group J5, and other timber species, Rimu, Silver beech, Red beech and Hard beech are classified as groups J4. Nails fasteners need to be positioned with a certain distance from the edge and from each other. The distance required for the position of nails depends on the hole being pre-bored or not pre-bored (refer to table 4.2-NZS). Minimum distance for holes not pre-bored in the standard are stated as following: • From end of member- 20da, may be reduced to 12da for Radiata pine • From edge of the member- 5da • Between nails along grain- 20da, may be reduced to 5da for Radiata pine • Between nails across grain- 10da, may be reduced to 5da for Radiata pine 17 Figure 3.3.1: Minimum spacing of nails (NZS3603) Based on the New Zealand Standard (Section 4.2-NZS3603) the laterally loaded nailed joint shall satisfy: S*≤ ɸQn The nominal strength for directly loaded joints shall be calculated using the following equation: Qn = nKQk Where (NZS3603-section 4.2.2.2): ɸ = Strength reduction factor Based on NZS 3603 the strength reduction factor for nails in lateral loading shall be taken as 0.8. Qn = Nominal strength of a joint appropriate to mode of loading S* = Design load effects on joint produced by strength limit state loads n = number of fasteners Qk = Characteristic strength- Refer to NZS3603-section 4.2.2.1 The characteristic strength values for one plain steel wire nail, single shear, side grain and in dry timber are provided in Appendix A, table A.1. K = Product of modification factors listed below 18 Green timber: 0.85 a) Duration of loading: Factor K1 as given by 2.7 b) Nails in end grain: 0.67 c) Nail in double shear: 2.0 d) Steel side plate < 3.0 mm thickness: 1.25 Steel side plate ≥ 3.0 mm thickness: 1.5 Plywood or particle board with flat head nails: 1.4 e) Nail length and timber thickness. i) Two-member joints (nails in single shear) Thickness of first member, • t1 (see figure 3.3.2(a)) > 10da in solid timber • t1 (see figure 3.3.2(a)) > 1.5da in plywood or particle board Depth of penetration of nail into second member, p (see figure 3.3.2(a)) > 10da ii) Three-member joints (nail in double shear) Thickness of central member t1 (see figure 3.3.2(b)) > 10da, Thickness of outer member t0 (see figure 3.3.2(b)) > 7.5da, Depth of penetration of nail into outer member, p (see figure 3.3.2(a)) > 7.5da, f) Number of nails: For connections that have 50 or more nails the design strength shall be increased by 1.3. For less nails, the factor will be gained using linear interpolation to value of 1.0 for four nails. As it’s shown in the figure 3.3.2(on the next page), t1 and t0 represent the thickness of the timber members, and p is the depth of penetration of the fastener into the last member. 19 Figure 3.3.2: Timber thickness and nail length (NZS3603) 3.4 Australian Standard Based on the Australian standard for joint design, timber species are categorized into six groups: J1, J2, J3, J4, J5 and J6 for unseasoned timber, and JD1, JD2, JD3, JD4, JD5 and JD6 for seasoned timber. Unseasoned timber means green timber and seasoned timber means dry timber. The characteristic capacities for laterally loaded nails in in single shear, whether hand driven or machine, for unseasoned and seasoned timber is given in AS1720.1-2010. The design capacity for the laterally loaded nails should be determined using the following equation (As1720.1-2010): Nd,j ≥ N* Nd,j = ɸ k1 k13 k14 k16 k17 nQk Where: N* = Design action effect on joint ɸ = Capacity factor K1 = Factor for duration of load joints (refer to AS1720-2010) K13 = 1.0 for nails in side grain (see figure 3.4.1(a)) = 0.6 for nails in end grain (see figure 3.4.1(b)) 20 K14 = 1.0 for nails in single shear (see figure 3.4.2(a)) = 2.0 for nails in double shear (See figure 3.4.2(b)) K16 = 1.2 for nails driven through close fitting holes into metal side plates = 1.1 for nails driven through plywood gussets = 1.0 otherwise K17 = Factor for multiple nailed joints (As1720.1-2010) The value of factor K17 is given in Appendix B, table B.1. n = Total number of nails in connection resisting design effect in shear Qk = Characteristic capacity (As1720.1-2010) The characteristic strength values from Australian standard for single plain shank steel nail laterally loaded in single shear, in side grain and using dry timber are provided in Appendix B, table B.2 Figure 3.4.1: Two-member joint for nails and screws laterally loaded in shear (AS1720.1-2010) 21 Figure 3.4.2: Timber thickness and fastener length for nails, wood screws and coach screws (AS1720.1-2010) From the figure 3.4.2 the following statements are made: a) For the nails in single shear, the thickness of first member shall satisfy, t1>10D and the depth of penetration of nail into second member shall satisfy, tp>10D. b) For nails in double shear, the thickness of central member shall satisfy, tm>10D, the thickness of outer member shall satisfy, to>7.5D, and the depth of penetration of nail into outer member shall satisfy, tp>7.5D. Minimum distance for holes not pre-bored in the standard are stated as following: • From edge of the member- 5da • Between nails along grain- 20da • Between nails across grain- 10da 22 3.5 European Standard (Eurocode) The characteristic load-carrying capacity, Fv,Rk, for fasteners in timber to timber connections using EN 1995-1-1:2004 (Eurocode 5), shall be calculated by taking into account six different failure modes, in single shear loading condition, a, b, c, d, e and f, shown in figure 3.5.1, and four different failure modes in double shear loading condition, g, h, j and k, shown in figure 3.5.2. Based on Eurocode there is a different equation for each condition in respect to the failure modes. In failure modes “a”, shown in figure 3.5.1 and “g”, shown in figure 3.5.2(Shown in next page), the fastener crushes the main timber member, and does not bend itself. Also in failure modes “b”, shown in figure 3.5.1 and “h”, shown in figure 3.5.2, the fastener does not bend but crashes the side timber member or in the case of double shear crashes the middle member. The fastener in failure mode “c” shown in figure 3.5.1, does not bend or yield but crashes both the side and main timber member. For the timber-to-timber connections in single shear, plastic hinge is formed in failure modes “d”, “e” and “f”, shown in figure 3.5.1. In failure mode “d” the plastic hinge is formed in the side timber member, but in case “e” the plastic hinge is formed in the main timber member, and in failure mode “f”, the plastic hinge is formed on both timber members. Also plastic hinge is formed in double shear failure modes “j” and “k”, shown in the figure 3.5.2. Where in failure mode “j”, the plastic hinge is formed in the middle timber member, but in failure mode “k”, the plastic hinge is formed in the all three timber members. 23 To calculate the characteristic load-carrying capacity of nails (FV,RK) in single shear the following 6 equations must be calculated for the conditions shown in figure 3.5.1. 𝐹𝐹𝑉𝑉,𝑅𝑅𝑅𝑅 = 𝑚𝑚𝑚𝑚𝑚𝑚 ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ 𝑎𝑎) 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 𝑏𝑏) 𝑓𝑓ℎ,2,𝑅𝑅𝑡𝑡2𝑑𝑑 𝑐𝑐) 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 1 + 𝛽𝛽 � �𝛽𝛽 + 2𝛽𝛽2 �1 + 𝑡𝑡2 𝑡𝑡1 + � 𝑡𝑡2 𝑡𝑡1 � 2 � + 𝛽𝛽3 � 𝑡𝑡2 𝑡𝑡1 � 2 − 𝛽𝛽 �1 + 𝑡𝑡2 𝑡𝑡1 �� + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 𝑑𝑑) 1.05 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 2 + 𝛽𝛽 � �2𝛽𝛽(1 + 𝛽𝛽) + 4𝛽𝛽(2 + 𝛽𝛽)𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 𝑡𝑡12 − 𝛽𝛽� + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 𝑒𝑒) 1.05 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡2𝑑𝑑 1 + 2𝛽𝛽 � �2𝛽𝛽2(1 + 𝛽𝛽) + 4𝛽𝛽(1 + 2𝛽𝛽)𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 𝑡𝑡22 − 𝛽𝛽� + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 𝑓𝑓) 1.15� 2𝛽𝛽 1 + 𝛽𝛽� 2𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅𝑓𝑓ℎ,1,𝑅𝑅𝑑𝑑 + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 Figure 3.5.1: Different shear loading condition- Single Shear To calculate the characteristic load-carrying capacity of nails (FV,RK) in double shear the following equations must be calculated for the conditions shown in figure 3.5.2. 𝐹𝐹𝑉𝑉,𝑅𝑅𝑅𝑅 = 𝑚𝑚𝑚𝑚𝑚𝑚 ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ 𝑔𝑔) 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 ℎ) 0.5𝑓𝑓ℎ,2,𝑅𝑅𝑡𝑡2𝑑𝑑 𝑗𝑗) 1.05 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 2 + 𝛽𝛽 � �2𝛽𝛽(1 + 𝛽𝛽) + 4𝛽𝛽(2 + 𝛽𝛽)𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 𝑡𝑡12 − 𝛽𝛽� + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 𝑘𝑘) 1.15� 2𝛽𝛽 1 + 𝛽𝛽� 2𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅𝑓𝑓ℎ,1,𝑅𝑅𝑑𝑑 + 𝐹𝐹𝑎𝑎𝑎𝑎,𝑅𝑅𝑅𝑅 4 24 Figure 3.5.2: Different shear loading, failure modes for timber-to-timber conditions-Double shear Where: 𝛽𝛽 = 𝑓𝑓ℎ,2,𝑅𝑅 𝑓𝑓ℎ,1,𝑅𝑅 - Ratio between embedment strength of the members 𝐹𝐹ℎ,𝑅𝑅 = 0.082(1 − 0.01𝑑𝑑)𝜌𝜌𝑅𝑅𝑑𝑑−0.3𝑑𝑑 - Characteristic embedment strength in timber members Fax,Rk is the characteristic axial withdrawal capacity of the fastener - If Fax,Rk is not known, then the contribution from the rope effect should be taken as zero (EN 1995-1-1:2004). My,Rk = 0.3fud2.6 for round nails - Characteristic value for the yield moment (N.mm) d = fastener diameter ti = Timber or board thickness or penetration depth- with I = 1 or 2 n = number of fasteners 25 Pk = the characteristic timber density in kg/m3 fu = Tensile strength of the wire, (N/mm2) After calculating the characteristic load capacity for all the failure modes shown in figure 3.5.1 and 3.5.2, depending on the shear loading condition, the minimum value for single or double shear calculated, should be taken as the lateral characteristic load carrying capacity of the nail. However characteristic load-carrying capacity, FV,RK, calculated using the equations “a” to “k”, does not give very stable results. To get a more conservative result, the effective load-carrying capacity of fasteners must be calculated, using the following equation: FV,ef,RK = nef.FV,RK Where: FV,ef,RK = Effective characteristic load-carrying capacity of one row of fasteners parallel to the grain nef= nkef - The effective number of nails in a raw The value of Kef, depends on the spacing between fasteners, and it shall be taken from the table 5.3.3. Spacing (a1)* Kef (not predrilled holes) a1 ≥ 14d 1.0 a1 = 10d 0.85 a1 = 7d 0.7 *a1 = the spacing of nails within one raw parallel to grain Table 3.5.3: Value of Kef (EN 1995-1-1:2004) 26 3.6 Nailed Plate Joints 3.6.1 Nail Plate Moment Joints The nail plates are usually designed to prevent buckling from happening between rows of nails at the joint during bending. To check the nail plate being designed properly, the bending moment should be compared to the moment capacity. To calculate the moment capacity the following equation must be used: Mn = fb Zpi, and Zpi shall be taken as (t.d2.2)/6 Where: t = Plate thickness d = Full depth of the plate Mn = Moment capacity To figure out the compression bending stress (fb), the value of Le/ ry should be determined, where Le is the effective length between rows of nails and ry of the plate is the function of Ar2. If the space between the rows of nails is L then the area of plate either side in compression because of bending between the nails can be expected to have a buckling length of 70%L. Therefore: ry = t/12(1/2) and Le = 70%L Based on the value calculated by Le/ry, the value of reduction in the compression bending stress (fb) should be taken from the Appendix D, table D.1. To check the moment capacity calculated, the following check must be done: M*≤ ØMn 27 Where: Mn = Moment Capacity M* = the applied ultimate limit state moment Ø = Strength reduction factor 3.6.2 Nail Strength The overall resultant force acting on a plate determines the maximum capacity of load carried by any fastener. The different forces acting on a fastener can be due to axial load, shear force or the applied moment, and the total force, Ri, is the vertical sum of all of these forces. Force per fastener caused due to axial load, Fis, acts in the line of the axial load and can be calculated using the following equation: Fis = Pa / n Force per fastener caused due to shear force, Fis, mainly acts vertically, and can be calculated using the following equation: Fis = Ps / n Force per fastener caused due to applied moment, Fim, acts perpendicular to the line from the centroid of the nail group to the fastener, and can be calculated using the following equation: 𝐹𝐹𝑖𝑖𝑖𝑖 = 𝑀𝑀∗𝑟𝑟𝑖𝑖 ∑(𝑥𝑥2 + 𝑦𝑦2) Where: ri is the distance from the centroid to the fastener x and y are the distances from the centroid along the x and y axis to each fastener n is the number of fasteners Pa is the total axial force acting on the fastener Ps is the total shear force acting on the place 28 4.0 Analysis 4.1 General To calculate the lateral nail strength for various diameters and timber types using New Zealand, Australian and European codes, Visual Basic Application (VBA) using Microsoft Excel spreadsheet is designed. A different Excel spreadsheet is designed for each code, and in each spreadsheet at least two command buttons will be created to calculate the nail strength in single and double shear, but for European code there will be more than two command buttons designed. A command button runs the codes provided using VBA and calculates the nail strength. Also a different spreadsheet using VBA is made, for the design of a nail plate joint to calculate the moment capacity, and maximum load-carrying capacity of nail in joints. This report also provides detailed discussion of how the spreadsheets were constructed and the calculations contained within. Also this report includes the calculations for the design of a portal frame joint, according to the code requirements of New Zealand, Australia, and Europe 4.2 Design of Spreadsheets Starting off with designing VBA to calculate the nail strength. To design a VBA spreadsheet the first important step to do is to save the Excel file as “Macro Enabled Workbook”, otherwise the VBA spreadsheet will not work the next time it is opened. The next step is to add the Developer Ribbon, and to add the developer ribbon the following steps need to be taken: File → Option → Customised Ribbon Figure 4.2.1 on the next page shows the “customized ribbon” option on the “Excel option” window. To add the Developer tab tick “Developer” in the “customized ribbon” page. 29 Figure 4.2.1: Excel options window - Customize Ribbon Before coding starts, each coefficient of the equations that is going to be coded, such as modification factors, reductions factors and number of nails must be assigned to a cell. The figure 4.2.2 shows some coefficients allocated to cells in New Zealand spreadsheet. For example “Number of nails” is assigned to cell “C3”. Figure 4.2.2: New Zealand Spreadsheet - Coefficients allocated in cells 30 To start coding, first go to the developer ribbon, and then to Visual basic tab. A new window shown in figure 4.2.3 must be opened. Insert a “class module” from the insert tap on the new window. Developer → Visual Basics → Insert → Class Module Figure 4.2.3: Microsoft Visual Basic for Application Window Add two class modules and change the names to “Single shear” and “double shear” for the New Zealand or Australian spread sheet. For European Spreadsheet more class modules need to be added, 6 class modules for different single shear conditions and 4 class modules for different double shear conditions. The name of the class module can be changed, from the “name” bar under the properties on the left hand side of the window, as it’s showing in the figure 4.2.4, after the name is changed the coding can be started on the class module window. 31 Figure 4.2.4: SingleShear properties - Name tab To show how the coding in the class module is done, the New Zealand spreadsheet for coding of the equation for nail strength in double shear is used as an example. To calculate the nail strength in double shear using New Zealand method, the equation below is used: ɸQn = ɸnKQn Next step is to choose a symbol for each of the coefficients of the equation above. For example: Use “n” for number of nails Use “s” for strength reduction factor Use “Q” for characteristic strength Use “G” Modification factor for grain direction The modification shear factor for double shear is 2, and because the value is fixed, it will be directly added to the equation for coding instead of allocating a symbol to it. Also the duration factor, which is assumed to be 1, is directly added to the equation. And therefore the equation used for the coding is done as the following: DoubleShear = S * G * n * Q * 0.85 * 2 32 Having the symbols above set, the coding starts with adding the symbols under the “Option explicit”, then listing a “public function” and adding the equation underneath it. The equation must be assigned in a public function so it can be assessed by the command button code. Lastly, the coding finishes with closing it, by adding “End Function”, as it’s shown in the figure 4.2.5. Figure 4.2.5: DoubleShear-Class Module Coding After the coding for the class modulus is complete, a “Command Button” needs to be added, so that by pressing the command button the strength will be calculated. To add a “Command Button”, the following steps shall be taken on the excel spreadsheet: Developer → Insert → ActiveX Control → Command Button (ActiveX Control) as shown in figure 4.2.6 Figure 4.2.6: Command Button (ActiveX Control) 33 After inserting the “Command Button”, double click on it to start coding, but first make sure that “Design mode” on the developer ribbon, is on. By double clicking on the command button a new window will be opened, where the coding will be added, but before coding of the command button starts, change the “Caption” under Command button properties in the left hand side of the column window to “Double Shear”, as shown in figure 4.2.7. The new caption will appear on the command button on the spreadsheet. Figure 4.2.7: Command button properties – Caption tab The figure 4.2.8 shows the command button coding for the New Zealand Double shear equation. The coding starts with “Private sub” which means that the coding can only be used in this command button function. Then the class module is coded in to the command button so the command button knows the formula. To connect the class module to the command button, the coding must be done as the following: Dim shear As DoubleShear Set shear = New DoubleShear Where “DoubleShear” is the name of the class module that is to be connected to the command button Afterwards the cells that were assigned to the coefficients are coded. For example, number of nails (n) assigned to cell “C3” is coded as “shear.n = Range (“C3”). Value”. Likewise cells “C5”, “C7”, and “C11” are coded. 34 Lastly, the cell where the result of nail strength will be located, is coded as “Range (“C17”). Value = shear. DoubleShear”, where “C17” is the cell that the nail strength is assigned to, and for ending the command button coding the “End Sub” is stated. Figure 4.2.8: Command Button Code To work the VBA, the values of the coefficients must be entered in the assigned cells, and the “Design mode” must be turned off. By clicking on the “Command button” the nail strength value will appear on the assigned cell. All this procedures are carried out to create a command button for calculating the nail strength in single shear. Figure 4.2.9 shows the end result for the designed New Zealand spreadsheet. Figure 4.2.9: New Zealand Standard Spreadsheet 35 The Australian and European spreadsheets are done using the same procedure, but they use different equations and different coefficients. The New Zealand and Australian spreadsheet are very similar, they both need two command buttons and only the coefficients are different. The Australian spreadsheet can be seen in the Appendix B, Figure B.1. For the European spreadsheet, 6 command buttons are designed to calculate nail strength in single shear and 4 command buttons are designed to calculate the nail strength in double shear, the minimum of these cases must be chosen. To choose the minimum value for the nail strength in double shear, the code “= MIN (E33, E35, E37, E39)” is typed in to the cell as shown in the figure 4.2.10; where cells E33, E35, E37, E39 are the values of the European nail strength in double shear cases. The same procedure is used to calculate the minimum value of nail capacity in single shear. After calculating the minimum value for the nail capacity, 2 more command buttons are designed to calculate the effective nail capacity in single and double shear. The European spreadsheet can be seen in the Appendix C, Figure C.1. Figure 4.2.10: European Standard Spreadsheet – Minimum Nail Capacity in Double Shear For the design of the nail plate joint, a command button is created to calculate the moment capacity and another command button is created to calculate the value for Le/ry. These command buttons are also created using the same procedure that was undertaken to design the command button for nail strength in double shear using New Zealand standard. In the nail plate joint spreadsheet shown in figure 4.2.11, the values of ∑(x²+y²), number of nail, X1, Y1, shear force and moment are not to be calculated and must be entered manually. For figuring the value of X1 and Y1 refer to the Appendix D, figure D.2. 36 Figure 4.2.11: Spreadsheet of Nail Plate Joint Design For calculating the total resultant force on a fastener in joint, different coding is produced within the cells of the spreadsheet as shown in figure 4.2.12. The equations to calculate the force due to applied moment, force per fastener, distance to the most remote nail from center, vertical resultant force and overall resultant force must be coded into the cells. So when the values of ∑(x²+y²), X1, Y1, total number of nails, shear force, moment and the resultant angle are entered, the value of total resultant force is automatically calculated. For example to calculate the overall resultant force enter the code “=((D38+D31)^2+(D38^2))^0.5”; where cell “D38” is the vertical resultant force and the cell “D31” is Shear force per fastener. Figure 4.2.12: Nail Plate Joint – Total Resultant Force Calculation Also in the nail plate joint spreadsheet, the calculation for reversing the overall resultant force (maximum nail strength) to characteristic strength “QK” is coded. Nail plate joint spreadsheet can be seen in the Appendix D, Figure D.1. 37 4.3 Nail Strength Calculations The calculation of the nail strength for various nail diameters and timber types using the spreadsheet created for all three codes, are done using the values of coefficients taken from each of the standards. The following is an example of nail strength calculation for the Australian method. Calculate the nail capacity for a 3.15 mm diameter nail in single shear, in end grain using JD4 timber. Nd,j ≥N* Nd,j = ɸ k1 k13 k14 k16 k17 nQk Qk = 1377 N n = 1 ɸ = 0.85 Modification factors: Duration loading factor, k1 = 1 End grain, K13 = 0.6 Single shear, K14 = 1.0 K16, K17 = 1.0 Nd,j = 1377 x 1 x 0.85 x 1 x 0.6 x 1 x 1 = 702.27 N To check if the design is correctly done, make sure the Nd,j= 702.27 N is bigger or equal to N*. Similar to this example for New Zealand method is given in Appendix A, and for European method is given in the Appendix C. All the results of nail strength for various diameters and timber groups which are calculated using the spreadsheets, are provided in Appendices A, B and C. 38 4.4 Nail Plate Joint Calculations For the design of a nail plate joint the values for plate length, depth, thickness and the moment must be given. In this report one example is used to check the plate design and to calculate the moment capacity, in accordance to code requirements of New Zealand, Australia and Europe. Example: Part 1: Analyse two 3 mm plate connection for moment capacity in a lamibeam knee joint with clear distance between rows of nails of 30 mm and full width of plate at the joint interface 190 mm, with a moment of M* = 1.2 KNm. M* ≤ ØMn Ø = 0.8 for the design of nail plate Mn = fb Zpi Zpi = (t.d2.2)/6 Zpi = (3 x 1902 x 2) / 6 Le = 0.7L = 0.7 x 30 = 21 ry = t/12(1/2) = 3/(12)0.5 = 0.866 Le/ ey =  21/ 0.866 = 24.25 Choose value of fb from Appendix D, table D.1 fb = 245 MPa ØMn = 0.8 x 245 x (3 x 1902 x 2) / 6 = 8.845 KNm Check the moment capacity: M*= 1.2 KN.m ≤ ØMn = 7.0756 KN.m (OK) 39 Part 2: Analyse the nail group shown in figure 4.4.1 and design a suitable sized nail fastener to transfer a moment of 1.2 KNm and shear force of 3 KN. Use Dry timber J4/JD4 timber of 30 mm thickness. The connection is in single shear and in side grain. Assume: - European steel plate modification factor is 1.2 - When using European method assume the nail strength calculated for a nail, is equal to the effective strength of a nail in a joint with more than one nail. Figure 4.4.1: Nailed Plates - (Nail Groups) To make the calculations easier, nail group dimension calculations can be done for a quarter of the nail group, as shown in figure 4.4.2. The calculations of (x²+y²) is provided in table 4.4.3(shown in the next page). 40 Figure 4.4.2: Quarter of nail group Table 4.4.3: Nail Group dimensions for a quarter of the nail group ∑(x²+y²) total = 187200 Total number of nails = 64 Shear force (N) = 3000 Moment (KN.m) = 1.2 Load per Nail, Fis = 3000/64 = 46.875 Y1 = 75mm X1 = 75mm Distance to the most remote nail from centroid, ri = √ ((y1) ² +(x1) ²) = √ ((75) ²+ (75) ²) = 106.066 mm X No nails Y No nails x²+y² 75 3 75 3 33750 45 3 45 3 12150 15 2 15 2 900 46800 41 𝐹𝐹𝑖𝑖𝑖𝑖 = 𝑀𝑀∗𝑟𝑟𝑖𝑖 ∑(𝑎𝑎2+𝑦𝑦2) Force due to applied moment (Fim) = (M* x √ ((y1) ²+(x1) ²))/ ∑ (x²+y²) = (1400000 x 106.066)/ 187200 = 679.9104 N Angle = 45 Deg Moment Vertical force = (Cos 45 / Fim) = (cos 45)/679.9104 = 480.769 N Overall Resultant Force (N) = ((480.769+46.875) ^2+ (480.769^2)) ^0.5 = 714 N The overall resultant force is the maximum load that any fastener in the connection can carry. New Zealand Method: Provided in the New Zealand standard, the modification factor for steel side plate ≥ 3.0 mm thickness is taken as 1.5. Nail Capacity in single shear: 714/1.5 = 476N Use New Zealand results calculated for lateral nail capacity in side grain and in single shear connection for dry J4 timber. From Appendix A, Table A.2, choose a nail diameter for the Nail plate joint. From Appendix A, Table A.2, adopt 2.8 mm diameter nail Nail Strength = 562 N Check the geometry: Minimum spacing between nail along grain =10da = 28 mm (OK) Minimum spacing from edge = 5 da = 14 mm (OK) 42 Australian Method: In Australian standard the modification factor for steel side plate is 1.2 Nail Capacity in single shear: 714/1.2 = 595 N Use Australian results calculated for lateral nail capacity in side grain and in single shear connection for dry JD4 timber. From Appendix B, Table B.2, choose a nail diameter for the Nail plate joint. From Appendix B, Table B.2, adopt 3.15 mm diameter nail Nail Strength = 689 N Check the geometry: Minimum spacing between nail along grain =10da = 32 mm Minimum spacing from edge = 5 da = 16 mm Geometry needs to be rearranged European Method: European method does not have factor for side grain, therefore use European results calculated for lateral nail capacity in single shear connection for dry J4 timber. From Appendix C, Table C.2, choose a nail diameter for the Nail plate joint. Steel plate modification factor = 1.2 Nail Capacity in single shear: 714/1.2 = 595 N From Appendix C, Table C.2, adopt 2.5 mm diameter nail Nail Strength = 694 N Check the geometry: Minimum spacing between nail along grain =10da = 25 mm (OK) Minimum spacing from edge = 5 da = 13 mm (OK) 43 5.0 Discussion 5.1 General After the excel spreadsheet for New Zealand, European and Australian Standards were created. The lateral nail capacity in J4/JD4, J5/JD5 for various diameters were calculated, and for these calculations a few assumptions were made. All the results obtained from the spreadsheets are tabled in Appendices A, B and C. Also the nail plate joint design calculations were done according to the three codes, using the created spreadsheet for nailed plate joint design. All the calculated results for the three codes were graphed, showing the nail strength calculated using the three methods for different nail diameters. Therefore the different shear connection and joint group results can be compared between the three codes easily. Based on the results, the following will be discussed in this part of report: - How the lateral strengths vary for NZ, Australia, and Europe. - Whether the current design practice is conservative or non-conservative. - Discuss the differences in the design of your portal frame joint, and the influence of the various codes on those differences. 5.2 Assumptions The following assumptions were made in order to calculate the lateral nail capacity based on the three codes using the spreadsheets: • Number of nails used to calculate the strength in all methods is assumed to be 1. The calculations are done for the strength in a single nail. • J4 and J5 joint groups are used for calculating the nail capacity for New Zealand and European method, and for Australian method JD4 and JD5 timber joint groups are used. • The duration factor, K1, is taken as 1, because it is assumed that the design of the joint is for a brief moment. 44 • The density of wood is assumed to be 400 kg/m3 for J5 joint group and 600 kg/m3 for J4 joint group, when calculating the nail strength using European method. Also in a single or double shear the density for the timber members are assume to be the same. • The minimum value of tensile strength (fu), 600 N/mm2, should be taken, when calculating with European Method. • The thickness of the outer timber member used for calculating the European method is assumed to be 7.5 times the diameter of the fastener and the thickness of the inner timber member is assumed to be 10 times the diameter of the fastener. Note: these assumptions may cause variations to the actual value of nail strength 5.3 New Zealand Results The results for the nail strength based on New Zealand standard are calculated using a minimum of 2.0 mm to the maximum of 6.0 mm diameter nail. The graph in figure 5.3.1 shows the results of J4 group nail capacity for different nail diameters using New Zealand method, for a joint in both single and double shear connections and for nails in both side grain and end grain. The graph shows that whether the nails are in side grain or end grain, in single or double shear, the capacity increases as the diameter of nail increases. Therefore nails with smaller diameters contain lower capacity and nails with larger diameters have higher strength. Also shown in the graph in figure 5.3.1 (graph in next page) the results for the nail strength in double shear have greater values than single shear. The reason is that the modification factor for double shear is 2 and in single shear is 1, therefore the results in double shear is twice the results in single shear. 45 Figure 5.3.1: New Zealand, J4 timber (Double Shear vs. Single Shear) Comparing nails in side grain to end grain shown in figure 5.3.1; the results show that the values for nails in side grain for both single and double shear is higher than the values for nails in end grain. The reason for the differences between them is because side grain has greater strength than end grain, therefore the value of modification factor in side grain is higher than the value of modification factor for end grain. The graph of single shear vs. double shear for J5 timber groups shown in the Appendix A, Figure A.1, has a similar shape to the graph of single shear vs. double shear for J4 timber groups. The graph in figure 3.5.2 demonstrates the nail strength results in single shear for both J4 and J5 timber groups. The graph shows that the values of J4 in respect to the diameter have higher values than the J5 joint groups. The reason of J4 joint groups having higher values than J5 is because of the timber density. Radiata pine timber is specified under J4 joint group and Douglas fir timber is specified under J5 joint group. The density of Radiata pine timber is higher than Douglas fir. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 2.00 3.00 4.00 5.00 6.00 N ai l S tre ng th Nail Diameter New Zealand, J4 (Single Vs. Double Shear) Single Shear, Side Grain Double Shear, Side Grain Single Shear, End Grain Double Shear, End Grain 46 The graph for J4 and J5 timber groups in double shear has a similar shape to the graph in figure 5.3.2, only the values are double, therefore can be compared in a similar way. The graph for J4 and J5 in double shear is shown in the Appendix A, figure A.2. Figure 5.3.2: New Zealand - single shear (J4 vs. J5) The graphs 5.3.1 and 5.3.2 both show that with smaller diameters the result values vary less, than in larger diameters. The variation between the results for J5 and J4 groups for a single shear joint in side grain is 99 N for a 2.0 mm diameter nail, and 424 N for a 6.0 mm diameter. Also comparing the variation, between the side grain and end grain in single shear for J4 timber, from the graph in figure 5.3.1 shows that the result value of end grain and side grain for a 2.0 mm nail varies by 103 N and for a 6.0 mm nail varies by 702 N. The values for graphs in figure 5.3.1 and 5.3.2, shows the results of nail strength calculated for various diameters, which are taken from the Appendix A, Tables A.2, A.3, A.4 and A.5. 0 500 1000 1500 2000 2500 2.00 3.00 4.00 5.00 6.00 N ai l S tre ng th Nail Diameter New Zealand, Single Shear (J4 vs. J5) J5, Side Grain J4, Side Grain J5, End Grain J4, End Grain 47 5.4 Australian Results The Australian standard has less nail diameters compared to the New Zealand Standard. The strength is calculated for nails with a minimum diameter of 2.5 mm and a maximum diameter of 5.6 mm. The graph in figure 5.4.1, illustrates the nail strength results for JD5 timber in side grain and end grain. The graph also includes the results for both single and double shear. Figure 5.4.1: Australia, JD5 timber (side grain vs. end grain) Comparing side grain to end grain of the graph in figure 5.4.1; similarly to the New Zealand code results, shows that the nails in side grain have higher strength than end grain. Also a nail in double shear connections have twice the strength of a nail in single shear. Same as New Zealand results the graph shows that the nails with smaller diameters have less strength than nails with larger diameters. The graph for JD5 timber, comparing side grain to end grain has a similar shape to the graph in figure 5.4.1. A graph in Appendix B, Figure B.2 is added for comparing the nail strength results for JD4 timber in side grain and end grain. 0 500 1000 1500 2000 2500 3000 3500 2.50 3.50 4.50 5.50 6.50 N ai l S tre ng th Nail Diameter Australian JD5 (Side vs End Grain) Single Shear, Side Grain Double Shear, Side Grain Single Shear, End Grain Double Shear, End Grain 48 The graph shown in figure 5.4.2 is comparing JD5 to JD4 timber groups, in single shear. The graph shows that the strength in JD4 timber is higher than JD5. Similar to New Zealand standard, JD4 timber groups have higher density than JD5 timber groups. Figure 5.4.2: Australia – Single Shear (JD4 vs. JD5) The graph of JD4 vs. JD5, for nail in double shear connection is shown in Appendix B, Figure B.3, as it has a similar configuration to the graph in figure 5.4.2. 5.5 European Results To calculate the nail strength using European standard, the nails diameters from the New Zealand standard are used. European method of calculating the nail strength varies a lot from New Zealand and Australian methods. The European method calculates the strength using the failure modes, and does include the grain direction. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2.50 3.50 4.50 5.50 6.50 N ai l S tre ng th (N ) Nail Diameter (mm) Australian, Single Shear (JD4 vs. JD5) JD5, Side Grain JD4, Side Grain JD5, End Grain JD4, End Grain 49 Figure 5.5.1: European J4 vs. J5 (Single and Double shear) The graph in figure 5.5.1 shows the nail strength results for J4 and J5 groups including both single and double shear. Same with Australia and New Zealand results, the graph shows that nails with smaller diameters have lower strength and J4 timber groups have higher strength than J5 timber groups. Also the values of double shear are higher than single shear, but they are not exactly twice as much as single shear values. 5.6 Australia vs. New Zealand Based on New Zealand and Australian Standards the method of calculating the capacity of laterally loaded nails are quite similar, but there still are some differences between the two methods. One of the differences between Australian and New Zealand method is the value of modification factors, for example nails in side/end grain and the shear factors. Another difference between the two methods is the characteristic strength values for different nail diameters. According to New Zealand standard, the value of characteristic strength for a laterally loaded nail shall be decided based on the timber species, using the joint groups J4 and J5. Whereas, according to Australian Standard for designing a 0 1000 2000 3000 4000 5000 6000 7000 2.00 4.00 6.00 N ai l S te ng th (N ) Nail Diameter (mm) European (J4 vs.J5) J5, Single Shear J4, Signle Shear j5, Double Shear J4, Double Shear 50 laterally loaded nailed joint, timber species have been classified into six joint groups, J1-J6 for unseasoned timber and JD1-JD6 for seasoned timber, and in this report only Dry JD4 and JD5 timber are used. Figure 5.6.1: Australian vs. New Zealand (J5/JD5) This graph in figure 5.6 shows the result of nail strength for various diameters using New Zealand and Australian codes. The graph includes the results of nail strength in J5/JD5 timber groups, side/end grain, single and double shear. The graph shows that in both New Zealand and Australian standards, the value of nail strength in side grain is higher than end grain, whether the joint is in single shear or double shear. The graph 5.6.1 also shows, that for J5/JD5 nail connections in end grain and in single shear, the nail strength value for the Australian calculations in smaller diameters is higher than New Zealand. The value of a 2.5mm diameter nail strength calculated for New Zealand is 218 N and for Australia it is 227 N, but as the diameter increases the line of “JD5, Single Shear, End Grain” and “J5, Single Shear, End Grain” shown in the graph cross each other. In larger nail diameters, 0 500 1000 1500 2000 2500 3000 3500 4000 2.00 3.00 4.00 5.00 6.00 7.00 N ai l S tr en gt h Nail Diameter New Zealand vs Australian (J5/JD5) J5, Single Shear, Side Grain J5, Double Shear, Side Grain J5, Single Shear, End Grain J5, Double Shear, End Grain JD5 Single Shear, Side Grain JD5, Double Shear, Side Grain JD5, Single Shear, End Grain JD5, Double Shear, End Grain 51 New Zealand nail strength results ends up higher with the value of 809 N for a 5.0 mm diameter nail, and Australia having the value of 768 N for a 5.0 mm diameter nail. Same shape is appearing on the graph 5.6.1 for the calculated result in double shear, between the graphed lines “JD5, Double Shear, End Grain” and “J5, Double Shear, End Grain”, shows the calculated values for New Zealand are lower than Australian values. For smaller diameters and for larger nail diameter the nail strength values calculated by New Zealand method are higher than Australian method. In the graph shown in figure 5.6.1, J5/JD5 joint groups with side grained nail in both double and single shear, shows a higher values for the calculated New Zealand method compared to the calculated Australian method. Therefore, for nails in end grain, calculated New Zealand method has more conservative results for smaller diameters and for larger nail diameters calculated Australian method has more conservative results. For nails in side grain calculated Australian method gives more conservative results. Figure 5.6.2: Australian vs. New Zealand (J4/JD4) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 2.00 3.00 4.00 5.00 6.00 7.00 N ai l S tr en gt h (N ) Nail Diameter (mm) Australian vs. New Zealand (J4/JD4) J4, Single Shear, Side Grain J4, Double Shear, Side Grain J4, Single Shear, End Grain J4, Double Shear, End Grain JD4, Double Shear, Side Grain Jd4, Single Shear, End Grain JD4, Double Shear, End Grain JD4, Single Shear, Side Grain 52 The graph in figure 5.6.2 (graph in the previous page) shows the nail strength in single/Double shear, end/side grain using J4 and JD4 timber groups. Calculated results for side grain in double shear, using JD4 and J4 have very similar values, and also the values for side grain in single shear between J4 and JD4 are close. The graph shows that for J4 and JD4 joint groups, calculated Australian method has lower values compared to New Zealand, therefore Australian method has the most conservative results between the two standards. 5.7 New Zealand vs. Europe There are many differences in calculating the lateral nail strength between European and New Zealand methods. In New Zealand Standard, the nail capacity is calculated by taking the product of modification factors, reduction factor, characteristic strength value and the number of the nails used. But in European method the exact density of the timber must be taken to calculate the nail strength. Also instead of taking the modification factors, for European method, a different equation for each possible design failure mode is used to calculate the strength of nails. For a joint design in single shear, the European standard takes 6 different failure modes and for double shear, 4 different failure modes into account. Figure 5.7.1: New Zealand vs. European (Single Shear) 0 500 1000 1500 2000 2500 3000 3500 2.00 3.00 4.00 5.00 6.00 N ai l S tre ng th Nail Diameter New Zealand vs European (Single Shear) J5, Side Grain (NZ) J4, Side Grain (NZ) J5, End Grain (NZ) J4, End Grain (NZ) J5 (European) J4 (European) 53 The graph in figure 5.7.1 (graph in the previous page) shows the calculated nail strength in single shear. In single shear, “J4” calculated by European method has the highest value and “J5, end grain” calculated by New Zealand method has the lowest value. The largest variation is 1801N, for the calculated nail strength in single shear, between 2943 N (European, J4) and 1142 N (NZ, J5, end grain) for a 6.0 mm diameter nail, and the lowest variation is 39N, between 352 N (European) and 313 N (NZ, J4, side grain) for a 2.0 mm diameter nail. The graph in figure 5.7.2 shows the calculated nail strength in double shear. In double shear as well as single shear the European calculation for J4 has the highest value of 6286 N and the New Zealand calculations for J5, end grain has the lowest value of 2283 N for a diameter of 6.0 mm. The largest variation for the calculated nail strength in double shear is 4003 N; between 6286 N (European, J4) and 2283 N (NZ, J5, end grain) for a 6.0 mm diameter nail, and the lowest variation is 77N; between 703 N (European, J5) and 626 N (NZ, J4, side grain) for a 2.0 mm diameter nail. Figure 5.7.2: New Zealand vs. European (Double Shear) 0 1000 2000 3000 4000 5000 6000 7000 2.00 3.00 4.00 5.00 6.00 N ai l S tr en gt h Nail Diameter New Zealand Vs European (Double Shear) J5, Sied Grain (NZ) J4, Side Grain (NZ) J5, End Grain (NZ) J4, End Grain (NZ) J5 (European) J4 (European) 54 Between New Zealand and Europe, the calculated nail strength has higher values for European, and low values for New Zealand, therefore the calculated nail strength using New Zealand method is more conservative. However in this report the calculations are done only for one nail and the European method gives more conservative results if there are more nails in a joint. 5.8 Australia vs. Europe For calculating the laterally loaded nail strength the differences between Australian and European method is similar to the differences between New Zealand and European method, as the method of calculating nail strength using Australian and New Zealand standards are very similar. The graph in figure 5.8.1 shows the calculated nail strength in single shear. In single shear the European method calculations for J4 has the highest value of 2626 N and the Australian method calculations for J5, end grain has the lowest value of 933 N for a diameter of 6.0 mm. The largest variation for the calculated nail strength in single shear is 1693 N; between 2626 N (European, J4) and 933 N (Australian, JD5, end grain) for a 5.6 mm diameter nail, and the lowest variation is 49 N; between 512 N (European, J5) and 463 N (Australian, JD4, side grain) for a 2.5 mm diameter nail. Figure 5.8.1: Australian vs. European (Single Shear) 0 500 1000 1500 2000 2500 3000 2.50 3.50 4.50 5.50 N ai l S tr en gt h Nail Diameter Australian vs European (Single Shear) J5 (Euro) J4 (Euro) JD5, Side Grain (Aus) JD4, Side Grain (Aus) JD5, End Grain (Aus) JD4, End Grain (Aus) 55 The graph in figure 5.8.2 shows the calculated nail strength in double shear. The European method calculations for J4 has the highest value of 5594 N and the Australian method calculations for J5, end grain has the lowest value of 1867 N for a diameter of 6.0 mm. The largest variation for the calculated nail strength in double shear is 3727 N; between 5594 N (European, J4) and 1867 N (Australian, JD5, end grain) for a 5.6 mm diameter nail, and the lowest variation is 96 N; between 1023 N (European, J5) and 927 N (Australian, JD4, side grain) for a 2.5 mm diameter nail. Figure 5.8.2: Australian vs. European (Double Shear) Comparing between Australian and Europe method, the calculated nail strength has higher values using European method, and lower values for Australian method. Therefore the calculated nail strength using Australian method is more conservative. 0 1000 2000 3000 4000 5000 6000 2.50 3.50 4.50 5.50 N ai l S tre ng th Nail Diameter Australian vs European (Double Shear) J5 (Euro) J4 (Euro) JD5, Side Grain (Aus) JD4, Side Grain (Aus) JD5, End Grain (Aus) JD4, End Grain (Aus) 56 5.9 New Zealand vs. Europe vs. Australia The following graphs contain all the results of nail capacity obtained for various nail diameters using New Zealand, Australian and European methods. Figure 5.9.1: Australia vs. New Zealand vs Europe (J5/JD5, Single Shear) The graph in figure 5.9.1 shows that the results of J5 and JD5 groups in single shear obtained using New Zealand method, compared to the results from the European method, are very close to the results of Australian method. Also shown in the graph, the capacity of nails in end grain, calculated using New Zealand method have lower values for smaller nail diameters (up to around 3mm diameter) than the Australian method. But for the nails with larger diameter, it has higher values than the Australian method. The highest variation of nail strength calculated using the three methods shown in the graph is 873N, between European method and the Australian method for nail in end grain. The European method results in the highest value of 1641 N and the Australian (end grain) results in the lowest value of 768N for a 5.0 mm diameter nail. The lowest variation is 9N; between 218N (NZ, end grain) and 227N (Australian, end grain) for a 2.5 mm diameter nail. 0 500 1000 1500 2000 2500 2.00 4.00 6.00 N ai l S tre ng th (N ) Nail Diameter (mm) Aus vs. NZ vs. Euro (J5/JD5, Single Shear) J5, Single Shear (European) J5, Single Shear, Side Grain (NZ) J5, Single Shear, End Grain (NZ) JD5, Single Shear, Side Grain (Aus) JD5, Single Shear, End Grain (Aus) 57 Figure 5.9.2: Australia vs. New Zealand vs Europe (J5/JD5, Double Shear) The figure 5.9.2 is a graph of the calculated nail strength for J5 and JD5 groups in double shear for all three codes. The graph shows that the calculated Australian (end grain) results have lowest values, and the European results have the highest values. The highest variation is 1746N; between 1535 N (Australia, JD5, end grain) and 3281N (European) using a 5.0 mm diameter nail, and the lowest variation is 18N; between 2416N (New Zealand, end grain) and 2599N (Australian, Side grain) using 2.5 mm diameter nail. Between all three codes for both single and double shear, using J5/JD5 joint groups, Australian (end grain) calculated method has the most conservative results for nail diameters larger than 3.0 mm. New Zealand (end grain) calculated method has the most conservative results for nail diameters less than 3.0 mm. The European method has the highest calculated value for J5/JD5, in both single and double shear, for all nail diameters. Therefore the European method is the least conservative between the three codes when using J5/JD5 joint groups. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 2.00 3.00 4.00 5.00 6.00 N ai l S tre ng th Nail Diameter (mm) Aus vs. NZ vs. Euro (J5/JD5, Double Shear) J5, Double Shear (European) J5, Double Shear,Side Grain(NZ) J5, Double Shear, End Grain (NZ) JD5, Double Shear,Side Grain(Aus) JD5, Double Shear, End Grain (Aus) 58 The graph of J4 and JD4 groups in single shear for all three codes are shown in figure 5.9.3 for side grains. New Zealand and Australian results are very close and they partially overlap. The highest variation is 1245N; between 2178N (European), and 933N (Australian, End Grain) using a 5.0 mm diameter nail, and the lowest variation is 1N; between 463N (Australian, side grain) and 462N (New Zealand, side grain), using a 2.5 mm diameter nail. Figure 5.9.3: Australia vs. New Zealand vs Europe (J4/JD4, Single Shear) Figure 5.9.4: Australia vs. New Zealand vs Europe (J4/JD4, Double Shear) 0 500 1000 1500 2000 2500 3000 3500 2.00 4.00 6.00 N ai l S tre ng th (N ) Nail Diameter (mm) Aus vs. NZ vs. Euro (J4/JD4, Single Shear) J4, Single Shear (European) J4, Single Shear, Side Grain (NZ) J4, Single Shear, End Grain (NZ) JD4, Single Shear, Side Grain (Aus) JD4, Single Shear, End Grain (Aus) 0 1000 2000 3000 4000 5000 6000 7000 2.00 3.00 4.00 5.00 6.00 N ai l S tre ng th Nail Diameter (mm) Aus vs. NZ vs. Euro (J4/JD4, Double Shear) J4 Doublea Shear (European) J4, Double Shear, Side Grain (NZ) J4, Double Shear, End Grain (NZ) JD4, Double Shear, Side Grain (Aus) JD4, Double Shear, End Grain (Aus) 59 The graph in figure 5.9.4 shows the nail strength of J4/JD4 groups in double shear. Both single (Figure 5.9.3) and double shear (Figure 5.9.4) graphs have similar shape for J4/JD4 timber groups. In figure 5.9.4 the value of the largest variation is 2754N; between 4621N (European) and 1867N (Australian, end grain) using a 5.0 mm diameter nail, and the value of minimum variation is 4N between 927N (Australian, side grain) and 923 (New Zealand, side grain), using a 2.5 mm diameter nail. From the graphs shown in figure 5.9.3 and 5.9.4, calculated Australian method for J4/JD4 timber joint group, has the lowest values for both single and double shear. The European method has the highest values in both graphs, therefore using J4/JD4 timber group, Australian method has the most conservative and European method has the least conservative results. The values of variations are taken from Table E.1 and E.2 provided in the Appendix E. The tables provide minimum and maximum values of variations for all the calculated methods in single and double shear. The graph of J4/JD4 vs. J5/JD5 for single shear is shown in the Appendix E, Figure E.1 and the graph of J4/JD4 vs. J5/JD5 for double shear is also shown in the Appendix E, Figure E.2. Overall, between the three codes, calculated Australian values are the most conservative results, and calculated European values are the least conservative. As mentioned before in this report, one reason for European method having the least conservative result is because the calculations are done for one nail. The European method will have more conservative results if there are more nails in the joint. Aside from calculating the laterally loaded nail strength for only one nail, assumptions made for the calculations might have also caused the European method having less conservative results. 60 5.10 Nail Plate Joint Results Based on the results obtained from the nail plate joint calculations, using a metal plate increases the joint strength; therefore by adding a nail plate in a joint, smaller diameter or less nails will be needed. The analysis of the nail plate gave an overall resultant force of 714 N on a fastener embedded in the nail plates joint of overall 64 nails, using J4/JD4 timber, with a moment of M* = 1.2 KNm and a shear force of V*=3 KN. Based on the calculated overall resultant force, a suitable nail diameter was adopted to the design using each of the New Zealand, European and Australian standards. The nail diameter adopted to the design based on calculated nail strength using New Zealand standard was 2.8 mm. The nail diameter adopted to the design based on calculated nail strength using Australian standard was 3.15mm and using European standard was 2.5mm. The results prove that the Australian method has the most conservative result. However by using the nail diameter of 3.15mm, for a correct geometry the distance between the nails and from the edge should increase. Therefore either the number of nails used in the joint need to be decreased, which results in design failure since the joint will carrying less load than 714N per nail or the dimensions of the plate need to be increased. The assumptions made for the European method causes, the nail diameter adopted to the design to be less conservative. The results would have been more conservative if the effective load carrying capacity of a nail for a joint with 64 nails was used to calculate, according to the European standard. Since the adopted nail using calculated European standard is the least conservative and the Australian method fails the geometry design, for this case the calculated New Zealand method with a diameter of 2.8 mm is the best option to adopt. 61 6.0 Recommendation From the analysis and the discussion provided in this report, it is recommended, not to make any changes to the New Zealand standard. But for connections using many nails, if the calculated strength values for New Zealand are higher than European method, the values should be at least decreased to the values calculated by the European standard. It is recommended to use Australian Standard, to assure more stable joints but the values of nail strength for the Australian standard can be increased to the values calculated by the Eurocode. Due to the limited time for the report completion, many assumptions were made for the strength calculations using European Standard, therefore it is recommended to carry out further research on the European standard nail connection design. 62 7.0 References 1995-1-1, B.-E. (2004). Eurocode 5, Design of Timber Structures. European Standards. Aghayere, A., & Vigil, J. (2007). Structural Wood Design. JOHN WILEY & SONS, INC. AS1720.1. (2010). Timber Design Standard . Sydney: Stnadards Australia. Buchanan, A. (n.d.). The Timber Design Guide. In Nails and Screws (p. Chapter 27). Engineering, D. o. (2008). AU Guide on Connections in Timber. In Timber Engineering (p. Section 4). University of Auckland. Joints. (2011). Retrieved from archexamhandbook: http://www.archexamhandbook.com/lessons/structural-systems/study-notes/1-0- general-structures-and-lateral-forces/1-14-joints/ MetsaWood. (2013, April). Nailed Connections. Retrieved from MetsaWood: http://www.metsawood.com/global/Tools/MaterialArchive/MaterialArchive/Kerto- manual-nailed-connections.pdf Nail. (n.d.). Retrieved from HobbitHouse: http://www.hobbithouseinc.com/personal/woodpics/_g_NO.htm NZS3603. (1993). Timber Structures Standard. Wellington, New Zealand: Standards New Zealand. Soltis, A. L. (n.d.). Fastenings. Retrieved from woodweb.com: http://www.woodweb.com/Resources/wood_eng_handbook/Ch07.pdf Timber Connections. (2012). Retrieved from Roymech: http://www.roymech.co.uk/Related/Construction/Timber_connections.html Timber Joint Design-2 (Nails, Staples and Screws). (2001). Retrieved from The Australian Timber Database: http://www.timber.net.au/images/downloads/joinery/joint_design2.pdf Visser, T. D. (n.d.). Nails: Clues to a Building's History. Retrieved from The University of Vermont: http://www.uvm.edu/~histpres/203/nails.html 63 Appendix A New Zealand 64 Table A.1- Characteristic strengths (N) for one plain steel wire nail in single shear in side grain in dry timber (NZS3603) Characteristic strength QK (N) for one plain steel wire nail in single shear in side grain in dry timber Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 268 331 407 504 526 631 695 790 868 990 1240 1510 1690 2130 J4 391 476 577 703 733 863 951 1060 1165 1310 1610 1930 2140 2660 Table A.2- Nominal strength of laterally loaded nail ØQn (Single shear, Side grain) Table A.3- Nominal strength of laterally loaded nail ØQn (Double shear, Side grain) Strength limit for laterally loaded nails ØQn (Double shear for side grain) Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 429 530 651 806 842 1010 1112 1264 1389 15884 1984 2416 2704 3408 J4 626 762 923 1125 1173 1381 1522 1696 1864 2096 2576 3088 3424 4256 Table A.4- Nominal strength of laterally loaded nail ØQn (Single shear, End grain) Strength limit for laterally loaded nails ØQn (single shear for End grain) Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 144 177 218 270 282 338 373 423 465 531 665 809 906 1142 J4 210 255 309 277 393 463 510 568 624 702 863 1034 1147 1426 The nominal strength of laterally loaded nail ØQn (single shear, side grain) Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 214 265 326 403 421 505 556 632 694 792 992 1208 1352 1704 J4 313 381 462 562 586 690 761 848 932 1048 1288 1544 1712 2128 65 Table A.5- Nominal strength of laterally loaded nail ØQn (Double shear, End grain) New Zealand Calculation Example: Calculate the nail capacity for a 2.87 mm diameter nail in single shear, in end grain using J4 timber. ɸ Qn = ɸ nKQk Qk = 733 N n = 1 ɸ = 0.8 Modification factors: Duration loading factor, k1 = 1 End grain = 0.67 Single shear = 1.0 ɸ Qn = 733 x 1 x 1 x 0.8 x 0.67 =393 N To check if the design is correctly done, make sure the ɸ Qn = 393 N ≥ N* Strength limit for laterally loaded nails ØQn (Double shear for End grain) Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 287 355 436 540 564 676 745 847 930 1061 1329 1619 1812 2283 J4 419 510 619 754 786 925 1019 1136 1249 1404 1726 2069 2294 2852 66 Figure A.1- New Zealand, J5 (Double Shear vs. Single Shear) Figure A.2- New Zealand, Double Shear (J4 vs. J5) 0 500 1000 1500 2000 2500 3000 3500 4000 2.00 3.00 4.00 5.00 6.00 N ai l S tr en gt h (N ) Nail Diameter (mm) New Zealand, J5 (Double Shear Vs. Single Shear) J5, Single Shear, Side Grain J5, Double Shear, Side Grain J5, Single Shear, End Grain J5, Double Shear, End Grain 0 500 1000 1500 2000 2500 3000 3500 4000 4500 2.00 3.00 4.00 5.00 6.00 N ai l S tr en gt h (N ) Nail Diameter(mm) New Zealand, Double Shear (J4 vs. J5) J5, Side Grain J4, Side Grain J5, End Grain J4, End Grain 67 Appendix B Australia 68 Table B.1- Values of factor K17 for use in the design of the multiple nail and screw joints – To resist direct loads Condition of timber Values of K17 Number of rows of fasteners (ns) ns ≤ 4 ns = 5 ns = 10 ns ≥ 20 Unseasoned 1.0 0.9 0.8 0.85 Seasoned 1.0 0.94 0.9 0.85 Table B.2-The characteristic strength QK for single plain shank steel nail laterally loaded in single shear in side grain (Dry timber) Characteristic strength QK (N) for one plain steel wire nail, laterally loaded, in single shear in side grain in dry timber Timber Group Nail shank Diameter (mm) 2.50 2.80 3.15 3.75 4.50 5.00 5.60 JD5 445 545 680 915 1255 1505 1830 JD4 545 665 810 1110 1520 1830 2225 Table B.3-The Lateral Design Capacity (Nd,j) for single steel nail in Single Shear in Side Grain The Lateral Design Capacity (Nd,j) for single steel nail in single shear in side grain Timber Group Nail shank Diameter (mm) 2.50 2.80 3.15 3.75 4.50 5.00 5.60 JD5 378 463 578 778 1067 1279 1556 JD4 463 565 689 994 1292 1556 1891 69 Table B.4-The Lateral Design Capacity (Nd,j) for single steel nail in Double Shear in Side Grain The Lateral Design Capacity (Nd,j) for single steel nail in Double shear in side grain Timber Group Nail shank Diameter (mm) 2.50 2.80 3.15 3.75 4.50 5.00 5.60 JD5 757 927 1156 1556 2134 2559 3111 JD4 927 1131 1377 1887 2584 3111 3783 Table B.5-The Lateral Design Capacity (Nd,j) for single steel nail in Single Shear in End Grain Table B.5-The Lateral Design Capacity (Nd,j) for single steel nail in Single Shear in End Grain Timber Group Nail shank Diameter (mm) 2.50 2.80 3.15 3.75 4.50 5.00 5.60 JD5 227 278 347 467 640 768 933 JD4 278 339 413 566 775 933 1135 Table B.6-The Lateral Design Capacity (Nd,j) for single steel nail in Double Shear in End Grain The Lateral Design Capacity (Nd,j) for single steel nail in Double Shear in End Grain Timber Group Nail shank Diameter (mm) 2.50 2.80 3.15 3.75 4.50 5.00 5.60 JD5 454 556 694 933 1280 1535 1867 JD4 556 678 826 1132 1550 1867 2270 70 Figure B.1- Australian Standard Spreadsheet Figure B.2- Australia - JD4 timber (side grain vs. end grain) 0 500 1000 1500 2000 2500 3000 3500 4000 2.50 3.50 4.50 5.50 6.50 N ai l S tr en gt h Nail Diameter Australian JD4 (Side vs End Grain) Single Shear, Side Grain Double Shear, Side Grain Single Shear, End Grain Double Shear, End Grain 71 Figure B.3- Australia – Double Shear (JD4 vs. JD5) 0 500 1000 1500 2000 2500 3000 3500 4000 2.50 3.50 4.50 5.50 6.50 N ai l S tr en gt h (N ) Nail Diameter (mm) Australian, Double Shear, (JD4 vs. JD5) JD5, Side Grain JD4, Side Grain JD5, End Grain JD4, End Grain 72 Appendix C European 73 Table C.1- Effective load-carrying capacity (FV,ef,RK) of one fasteners in Single Shear Effective load-carrying capacity (FV,ef,RK) of one fasteners in single shear Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 352 425 512 619 645 754 828 927 1011 1127 1374 1641 1810 2230 J4 480 579 694 837 872 1016 1114 1244 1355 1507 1831 2178 2398 2943 Table C.2- Effective load-carrying capacity (FV,ef,RK) of one fasteners in Double Shear Effective load-carrying capacity (FV,ef,RK) of one fasteners in Double Shear Timber Group Nail shank Diameter (mm) 2.00 2.24 2.50 2.80 2.87 3.15 3.33 3.56 3.75 4.00 4.50 5.00 5.30 6.00 J5 703 851 1023 1238 1290 1509 1657 1853 2023 2255 2749 3281 3619 4459 J4 986 1193 1436 1738 1812 2120 2328 2606 2845 3172 3869 4621 5098 6286 Eurocode Calculation Example: Calculate the effective load carrying capacity (FV,ef,RK) for a nal with diameter of 2.87 mm in single shear. Assume: • Timber density in both members = 400 kg/m3 • Tensile Strength (fu) = 600 Nmm • Thickness of timber, t1 = 7.5.d and t2 =10.d (Taken from the New Zealand Standard) 𝛽𝛽 = 𝑓𝑓ℎ,2,𝑅𝑅 𝑓𝑓ℎ,1,𝑅𝑅 β = 1 (The density of the members are the same) fh.1.k = fh.2.k = 0.0082(1-0.01d)Pk d-0.3 d fh.1.k = fh.2.k =0.0082 x (1-(0.01 x 2.87)) x 400 x 2.87-0.3 x 2.87 fh.1.k = fh.2.k = 23.906 N/mm2 74 t1 = 2.87 x 7.5 = 21.525 mm t2 = 2.87 x 10 = 28.70 mm My,Rk = 0.3fud2.6 = 2791.063 Case a: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 𝑓𝑓ℎ,1,𝑅𝑅𝑡𝑡1𝑑𝑑 FV,RK = 23.906 x 21.525 x 2.87 = 1476.843 N Case b: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 𝑓𝑓ℎ,2,𝑅𝑅𝑡𝑡2𝑑𝑑 FV,RK = 23.906 x 28.7 x 2.87 = 1969.124 N Case C: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 𝑓𝑓ℎ,1,𝑘𝑘𝑡𝑡1𝑑𝑑 1 + 𝛽𝛽 ��𝛽𝛽 + 2𝛽𝛽2 �1 + 𝑡𝑡2 𝑡𝑡1 + � 𝑡𝑡2 𝑡𝑡1 � 2 � + 𝛽𝛽3 � 𝑡𝑡2 𝑡𝑡1 � 2 − 𝛽𝛽 �1 + 𝑡𝑡2 𝑡𝑡1 �� FV,RK = (1476.843/2) x (2 x (1+(28.7/21.5250) +(28.7/21.5250)2) +(28.7/21.5250)2)0.5 = 726.084 N Case d: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 1.05 𝑓𝑓ℎ,1,𝑘𝑘𝑡𝑡1𝑑𝑑 2 + 𝛽𝛽 ��2𝛽𝛽(1 + 𝛽𝛽) + 4𝛽𝛽(2 + 𝛽𝛽)𝑀𝑀𝑦𝑦,𝑅𝑅𝑘𝑘 𝑓𝑓ℎ,1,𝑘𝑘𝑑𝑑 𝑡𝑡1 2 − 𝛽𝛽� FV,RK =1.05 x (1476.843/3) x (2 x 1 x (1 +1) + ((4x1 x(2+1) x 2791.063)/ (23.906x 2.87 x 21.5252))0.5 – 1 = 645.094 N Case e: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 1.05 𝑓𝑓ℎ,1,𝑘𝑘𝑡𝑡2𝑑𝑑 1 + 2𝛽𝛽 ��2𝛽𝛽2(1 + 𝛽𝛽) + 4𝛽𝛽(1 + 2𝛽𝛽)𝑀𝑀𝑦𝑦,𝑅𝑅𝑘𝑘 𝑓𝑓ℎ,1,𝑘𝑘𝑑𝑑 𝑡𝑡2 2 − 𝛽𝛽� FV,RK =1.05 x (1969.124/3) x (2 x 12 x (1 +1) + ((4x1 x(1+ 2) x 2791.063)/ (23.906 x 2.87 x 28.72))0.5 – 1 = 787.779 N 75 Case f: F 𝑉𝑉,𝑅𝑅𝑅𝑅 = 1.15� 2𝛽𝛽 1 + 𝛽𝛽� 2𝑀𝑀𝑦𝑦,𝑅𝑅𝑘𝑘𝑓𝑓ℎ,1,𝑘𝑘𝑑𝑑 FV,RK =1.15 x ((2 x 1)/ (1 + 1))0.5 x (2 x 2791.063 x 23.906 x 2.87)0.5 = 711.690 N Take the minimum value from the calculated cases : Min FV,RK = 645.094 N Fv,ef,Rk =nef.Fv,Rk nef= n^kef = 1 0.85 =1 Fv,ef,Rk = nef.Fv,Rk = 645.094 N Figure C.1- European Standard Spreadsheet 76 Appendix D Nail Plate Joint 77 Table D.1- Reduction value of the compression bending stress, fb (MPa) Figure D.1: Nail Plate Joint Design Spreadsheet Le/ry fb (MPa) 0 250 10 249 20 247 30 243 40 236 50 226 60 213 70 195 80 174 90 152 78 Figure D.2: Distance of nails from center of the plate along Y and X axis 79 Appendix E Comparisons 80 Table E.1-Maximum and Minimum Variations for Single Shear connections Table E.2-Maximum and Minimum Variations for Double Shear connections Max/Min variation table in Double shear European Australian New Zealand Side Grain End Grain Side Grain End Grain max Variation Min Variation Unit J5/JD5 N 5mm Dia 3281 2559 1535 2416 1619 1746 84 N 2.5mm Dia 1023 757 454 651 436 587 18 N J4/JD4 N 5mm Dia 4621 3111 1867 3088 4138 2754 23 N 2.5mm Dia 1436 927 556 923 1237 880 4 N Max/Min variation table in single shear European Australian New Zealand Side Grain End Grain Side Grain End Grain Max Variation Min Variation Unit J5/JD5 5mm Dia 1641 1279 768 1208 809 873 41 N 2.5mm Dia 512 378 227 326 218 294 9 N J4/JD4 N 5mm Dia 2178 1556 933 1544 2069 1245 12 N 2.5mm Dia 694 463 278 462 619 694 1 N 81 Executive Summary 1.0 Introduction 1.1 General background 1.2 Aims and objective 2.0 Methodology and Resources 2.1 Methodology 2.2 Resources 3.0 Background Theory 3.1 History of Nail 3.2 General Knowledge 3.3 New Zealand Standard 3.4 Australian Standard 3.5 European Standard (Eurocode) 3.6 Nailed Plate Joints 3.6.1 Nail Plate Moment Joints 3.6.2 Nail Strength 4.0 Analysis 4.1 General 4.2 Design of Spreadsheets 4.3 Nail Strength Calculations 4.4 Nail Plate Joint Calculations 5.0 Discussion 5.1 General 5.2 Assumptions 5.3 New Zealand Results 5.4 Australian Results 5.5 European Results 5.6 Australia vs. New Zealand 5.7 New Zealand vs. Europe 5.8 Australia vs. Europe 5.9 New Zealand vs. Europe vs. Australia 5.10 Nail Plate Joint Results 6.0 Recommendation 7.0 References Appendix A Appendix B Appendix C Appendix D Appendix E