Technologies for designing structural wood diaphragms and applying the same to manufacture

Abstract

Technologies for designing structural wood diaphragms and applying the same to manufacture include a system comprising circuitry configured to obtain structural design data indicative of a structure of a building with at least one wood diaphragm. The circuitry may also be configured to construct, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm as semi-rigid. Further, the circuitry may be configured to analyze the mesh as the equivalent truss to determine deflections and forces associated with the wood diaphragm, thereby providing computationally efficient and accurate semi-rigid analysis of the wood diaphragm to improve reliability of the structure of the building. Other embodiments are also described and claimed.

Description

MITEK-00019TECHNOLOGIES FOR DESIGNING STRUCTURAL WOOD DIAPHRAGMS AND APPLYING THE SAME TO MANUFACTURECROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the benefit of U.S. Provisional Patent Application No. 63 / 690,621, filed September 4, 2024, the disclosure of which is incorporated herein by reference.BACKGROUND

[0002] The demand for multi-family and mixed-use light-framed wood buildings with complex designs continues to grow nationally, as an economical means of addressing the housing crisis. While there have been significant advancements in the design of wood shear walls and other lateral systems, there has been a lack of guidance and regulation for lateral analysis of semi-rigid diaphragms in these complex buildings. The diaphragms have been commonly assumed to be either fully flexible or fully rigid. However, as shown in recent full-scale shake table tests, wood diaphragms, particularly in multi-family buildings, do not behave as fully flexible or fully rigid structures. As such, conventional systems may inaccurately model the behavior of such buildings during events that cause changes in lateral loads, such as earthquakes or winds.BRIEF DESCRIPTION OF THE DRAWINGS

[0003] The concepts described herein are illustrated by way of example and not by way of limitation in the accompanying figures. For simplicity and clarity of illustration, elements illustrated in the figures are not necessarily drawn to scale. Where considered appropriate, reference labels have been repeated among the figures to indicate corresponding or analogous elements. The detailed description particularly refers to the accompanying figures in which:

[0004] FIG. 1 is a simplified block diagram of at least one embodiment of a system for analyzing, with enhanced efficiency and accuracy, structural wood diaphragms based on an equivalent truss model;

[0005] FIG. 2 is a diagram of at least one embodiment of a compute device of the system of FIG. 1;- 1 -175350189v4MITEK-00019

[0006] FIGS. 3-4 are flowcharts of at least one embodiment of a method for analyzing structural wood diaphragms with enhanced efficiency and accuracy based on an equivalent truss model that may be performed by the system of FIG. 1;

[0007] FIGS. 5-6 are example meshes that may be produced by the system of FIG. 1 to efficiently and accurately analyze one or more structural wood diaphragms based on an equivalent truss model;

[0008] FIG. 7 is a diagram of elements of an equivalent truss model that may be produced by the system of FIG. 1;

[0009] FIG. 8 is a diagram of a simply supported diaphragm and a corresponding equivalent truss model of the diaphragm;

[0010] FIG. 9 illustrates three variations of an equivalent truss model;

[0011] FIG. 10 illustrates diagrams of diaphragms used in a set of method validation operations;

[0012] FIG. 11 illustrates a set of equivalent truss models of corresponding diaphragms;

[0013] FIG. 12 is a chart of test results pertaining to equivalent truss model validation operations;

[0014] FIG. 13 illustrates a set of diaphragms associated with equivalent truss models in an example embodiment of the method of FIGS. 3-4;

[0015] FIG. 14 illustrates a chart of deflections in structural wood diaphragms;

[0016] FIG. 15 illustrates a diaphragm with an opening;

[0017] FIG. 16 illustrates shear forces and chord / collector axial forces associated with a diaphragm;

[0018] FIG. 17 illustrates a floor plan and a corresponding equivalent truss model of a building;

[0019] FIG. 18 illustrates varying models of a building with semi-rigid, flexible, and rigid properties;

[0020] FIG. 19 illustrates a set of charts indicative of shear force distributions associated with the models of FIG. 18;

[0021] FIG. 20 illustrates a floor plan and equivalent truss model of a complex building; and175350189v4MITEK-00019

[0022] FIGS. 21 and 22 illustrate rigid and semi-rigid models of the complex building of FIG. 20.DETAILED DESCRIPTION OF THE DRAWINGS

[0023] While the concepts of the present disclosure are susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and will be described herein in detail. It should be understood, however, that there is no intent to limit the concepts of the present disclosure to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives consistent with the present disclosure and the appended claims.

[0024] References in the specification to “one embodiment,” “an embodiment,” “an illustrative embodiment,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may or may not necessarily include that particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. Additionally, it should be appreciated that items included in a list in the form of “at least one A, B, and C” can mean (A); (B); (C); (A and B); (A and C); (B and C); or (A, B, and C). Similarly, items listed in the form of “at least one of A, B, or C” can mean (A); (B); (C); (A and B); (A and C); (B and C); or (A, B, and C).

[0025] The disclosed embodiments may be implemented, in some cases, in hardware, firmware, software, or any combination thereof. The disclosed embodiments may also be implemented as instructions carried by or stored on a transitory or non-transitory machine-readable (e g., computer-readable) storage medium, which may be read and executed by one or more processors. A machine-readable storage medium may be embodied as any storage device, mechanism, or other physical structure for storing or transmitting information in a form readable by a machine (e.g., a volatile or non-volatile memory, a media disc, or other media device).

[0026] In the drawings, some structural or method features may be shown in specific arrangements and / or orderings. However, it should be appreciated that such specific arrangements and / or orderings may not be required. Rather, in some embodiments, such features may be- 3 -175350189v4MITEK-00019 arranged in a different manner and / or order than shown in the illustrative figures. Additionally, the inclusion of a structural or method feature in a particular figure is not meant to imply that such feature is required in all embodiments and, in some embodiments, may not be included or may be combined with other features.

[0027] Referring now to FIG. 1, a system 100 for analyzing structural wood diaphragms with greater efficiency and accuracy than conventional systems includes an analysis compute device 110 communicatively connected to user compute devices 130, 132 and manufacturing devices 140, 142. In operation, the analysis compute device 110 may obtain (e.g., from a user compute device 130, 132) structural design data 120 which may be embodied as any data (e.g., a computer aided design (CAD) file or three-dimensional building information model) indicative of a structure of a building with one or more wood diaphragms. That is, in the illustrative embodiment, the structural design data represents the design for a building that has yet to be built. A wood diaphragm is a structural element that resists lateral forces acting on a building by transferring the loads (e.g., forces) to vertical lateral force resisting elements (a “vertical lateral system”), such as wood structural panel shear walls or steel moment frames, of the building. As described in more detail herein, the analysis compute device 110, in operation, produces, from the structural design data, mesh data 122 indicative of a mesh that represents an equivalent truss (e.g., equivalent to the wood diaphragm(s) in the structure). The mesh may be embodied as a set of connected cells (e.g., rectangles, trapezoids, and / or triangles) that, together, reflect the shape of the structure, including any irregularities such as openings, cantilevers, out of plane offsets in walls, and / or non-parallel wings. In some embodiments, the mesh may include a combination of four node cells (e.g., rectangles and trapezoid) and three node cells (e.g., triangles).

[0028] Further, in the illustrative embodiment, the analysis compute device 110 assigns properties (e.g., properties data 124) to members (e.g., elements) of the mesh based on a set of factors, including, for example, nail size, nail spacing, type of wood to be used, and / or other factors. Those properties may correspond to considerations (e.g., chord deformation, panel shear and nail slip, and / or chord splice slip) associated with one or more building codes that define requirements associated with wood diaphragms in a given jurisdiction (e.g., country, state, city, etc.). The analysis compute device 110, in the illustrative embodiment, analyzes the mesh as an equivalent truss to determine deflections and forces associated with the wood diaphragm(s) of the structure and produces analysis data 126 indicative of the results of the analysis.- 4 -175350189v4MITEK-00019

[0029] Unlike conventional systems, the analysis compute device 1 10 models the wood diaphragm(s) as semi-rigid, rather than fully flexible or fully rigid. Using a flexible or rigid diaphragm assumption can result in significant error in force estimation in diaphragm components (e.g., axial force in chords and collectors, and diaphragm shear). These assumptions may also lead to underestimation of diaphragms’ shear and torsional deflection. Applying the semi-rigid analysis described herein, on the other hand, provides a more realistic load distribution to chords / collectors and vertical lateral force resisting elements, and estimates the diaphragm deflection more accurately. This allows for generating more optimized and cost-effective designs that could lead to more affordable, yet reliably performing buildings. Further, unlike conventional systems, the analysis compute device 110 accounts for complex diaphragm shapes, out-of-plane offsets of vertical lateral elements, large openings in the diaphragm, or variable nailing patterns and does so without requiring information that is absent in the basic parameters that are typically defined in design standards for wood diaphragms.

[0030] In some embodiments, in response to a determination from the analysis compute device 110 that the structure will not satisfy a set of corresponding requirements (e.g., a building code), a user (e.g., operating a user compute device 130, 132) may modify the design for the building for subsequent analysis by the analysis compute device 110. Further, in some embodiments, after a determination that the structure satisfies the applicable requirements, the analysis compute device 110 may provide information indicative of the structure (e.g., the building) to one or more manufacturing devices 140, 142, which may include robots, saws, presses, conveyors, and / or other machines adapted to construct or assist in the construction of one or more parts of the structure (e.g., the building), such as by cutting lumber, positioning pieces of cut lumber relative to each other, fastening pieces of cut lumber relative to each other with nails or other fastening elements, and / or performing other construction operations.

[0031] While a relatively small number of devices 110, 130, 132, 140, 142 are shown in FIG. 1 for simplicity and clarity, it should be understood that the number of devices, in practice, may range in the tens, hundreds, thousands, or more. Likewise, it should be understood that the devices 110, 130, 132, 140, 142 may be distributed differently or perform different roles than the configuration shown in FIG. 1. Further, though shown as separate devices 110, 130, 132, 140, 142 in some embodiments, the functionality of one or more of the devices 110, 130, 132, 140, 142 may- 5 -175350189v4MITEK-00019 be combined into fewer devices and / or distributed across more devices than those shown in FIG.1.

[0032] Referring now to FIG. 2, an illustrative embodiment of the analysis compute device 110, includes a compute engine 210, an input / output (I / O) subsystem 216, communication circuitry 218, and one or more data storage devices 222. In some embodiments, the analysis compute device 110 may include one or more display devices 224 and / or one or more peripheral devices 226 (e.g., a mouse, a physical keyboard, etc.). In some embodiments, one or more of the illustrative components may be incorporated in, or otherwise form a portion of, another component. The compute engine 210 may be embodied as any type of device or collection of devices capable of performing various compute functions. In some embodiments, the compute engine 210 may be embodied as a single device such as an integrated circuit, an embedded system, a field- programmable gate array (FPGA), a system-on-a-chip (SOC), or other integrated system or device. Additionally, in the illustrative embodiment, the compute engine 210 includes or is embodied as at least one processor 212 and a memory 214. The processor 212 may be embodied as any type of processor capable of performing the functions described herein. For example, the processor 212 may be embodied as a single or multi-core processor(s), a microcontroller, or other processor or processing / controlling circuit. In some embodiments, the processor 212 may be embodied as, include, or be coupled to an FPGA, an application specific integrated circuit (ASIC), one or more graphics processing units (GPUs), neural processing units (NPUs), and / or floating point units (FPUs), reconfigurable hardware or hardware circuitry, or other specialized hardware to facilitate performance of the functions described herein.

[0033] In embodiments, the processor 212 is capable of receiving, e.g., from the memory 214 or via the I / O subsystem 216, a set of instructions which when executed by the processor 212 cause the analysis compute device 110 to perform one or more operations described herein. In embodiments, the processor 212 is further capable of receiving, e.g., from the memory 214 or via the I / O subsystem 216, one or more signals from external sources, e.g., from the peripheral devices 226 or via the communication circuitry 218 from an external compute device, external source, or external network. As one will appreciate, a signal may contain encoded instructions and / or information. In embodiments, once received, such a signal may first be stored, e.g., in the memory 214 or in the data storage device(s) 222, thereby allowing for a time delay in the receipt by the processor 212 before the processor 212 operates on a received signal. Likewise, the processor 212- 6 -175350189v4MITEK-00019 may generate one or more output signals, which may be transmitted to an external device, e.g., an external memory or an external compute engine via the communication circuitry 218 or, e.g., to one or more display devices 224. In some embodiments, a signal may be subjected to a time shift in order to delay the signal. For example, a signal may be stored on one or more storage devices 222 to allow for a time shift prior to transmitting the signal to an external device. One will appreciate that the form of a particular signal will be determined by the particular encoding a signal is subject to at any point in its transmission (e.g., a signal stored will have a different encoding than a signal in transit, or, e.g., an analog signal will differ in form from a digital version of the signal prior to an anal og-to-digi tai (A / D) conversion).

[0034] The main memory 214 may be embodied as any type of volatile (e.g., dynamic random access memory (DRAM), etc.) or non-volatile memory or data storage capable of performing the functions described herein. Volatile memory may be a storage medium that requires power to maintain the state of data stored by the medium. In some embodiments, all or a portion of the main memory 214 may be integrated into the processor 212. In operation, the main memory 214 may store various software and data used during operation such as structural design data, mesh data, properties data, analysis data, applications, libraries, and drivers.

[0035] The compute engine 210 is communicatively coupled to other components of the analysis compute device 110 via the I / O subsystem 216, which may be embodied as circuitry and / or components to facilitate input / output operations with the compute engine 210 (e.g., with the processor 212 and the main memory 214) and other components of the analysis compute device 110. For example, the I / O subsystem 216 may be embodied as, or otherwise include, memory controller hubs, input / output control hubs, integrated sensor hubs, firmware devices, communication links (e.g., point-to-point links, bus links, wires, cables, light guides, printed circuit board traces, etc ), and / or other components and subsystems to facilitate the input / output operations. In some embodiments, the VO subsystem 216 may form a portion of a system-on-a- chip (SoC) and be incorporated, along with one or more of the processor 212, the main memory 214, and other components of the analysis compute device 110, into the compute engine 210.

[0036] The communication circuitry 218 may be embodied as any communication circuit, device, or collection thereof, capable of enabling communications over a network between the analysis compute device 110 and another device (e.g., a device 130, 132, 140, 142, etc.). The communication circuitry 218 may be configured to use any one or more communication- 7 -175350189v4MITEK-00019 technology (e.g., wired or wireless communications) and associated protocols (e.g., Ethernet, WiFi®, WiMAX, Bluetooth®, etc.) to effect such communication.

[0037] The illustrative communication circuitry 218 includes a network interface controller (NIC) 220. The NIC 220 may be embodied as one or more add-in-boards, daughter cards, network interface cards, controller chips, chipsets, or other devices that may be used by the analysis compute device 110 to connect with another device (e.g., a device 130, 132, 140, 142, etc.). In some embodiments, the NIC 220 may be embodied as part of a system-on-a-chip (SoC) that includes one or more processors, or included on a multichip package that also contains one or more processors. In some embodiments, the NIC 220 may include a local processor (not shown) and / or a local memory (not shown) that are both local to the NIC 220. Additionally or alternatively, in such embodiments, the local memory of the NIC 220 may be integrated into one or more components of the analysis compute device 110 at the board level, socket level, chip level, and / or other levels.

[0038] Each data storage device 222, may be embodied as any type of device configured for short-term or long-term storage of data such as, for example, memory devices and circuits, memory cards, hard disk drives, solid-state drives, or other data storage device. Each data storage device 222 may include a system partition that stores data and firmware code for the data storage device 222 and one or more operating system partitions that store data files and executables for operating systems.

[0039] Each display device 224 may be embodied as any device or circuitry (e.g., a liquid crystal display (LCD), a light emitting diode (LED) display, a cathode ray tube (CRT) display, etc.) configured to display visual information (e.g., text, graphics, etc.) to a user. In some embodiments, a display device 224 may be embodied as atouch screen (e.g., a screen incorporating resistive touchscreen sensors, capacitive touchscreen sensors, surface acoustic wave (SAW) touchscreen sensors, infrared touchscreen sensors, optical imaging touchscreen sensors, acoustic touchscreen sensors, and / or other type of touchscreen sensors) to detect selections of on-screen user interface elements or gestures from a user.

[0040] In the illustrative embodiment, the components of the analysis compute device 110 are housed in a single unit. However, in other embodiments, the components may be in separate housings. The other devices 130, 132, 140, 142 may include components similar to those of the analysis compute device 110 and / or other components (e.g., end effectors, motors, servos, saws,- 8 -175350189v4MITEK-00019 etc ). Further, the devices 110, 130, 132, 140, 142 may include other components, sub-components, and devices commonly found in a computing device, which are not discussed above in reference to the analysis compute device 110 and not discussed herein for clarity of the description.

[0041] In the illustrative embodiment, the devices 110, 130, 132, 140, 142 are in communication via a network 150, which may be embodied as any type of wired or wireless communication network, including global networks (e.g., the internet), wide area networks (WANs), local area networks (LANs), digital subscriber line (DSL) networks, cable networks (e g., coaxial networks, fiber networks, etc.), cellular networks (e.g., Global System for Mobile Communications (GSM), Long Term Evolution (LTE), Worldwide Interoperability for Microwave Access (WiMAX), 3G, 4G, 5G, etc.), a radio area network (RAN), or any combination thereof.

[0042] Referring now to FIG. 3, the system 100 (e.g., the analysis compute device 110) may perform a method 300 for analyzing, with enhanced efficiency and accuracy, one or more structural wood diaphragms. The method 300, in the illustrative embodiment, begins with block 302 in which the analysis compute device 110 obtains (e.g., from another compute device, such as a user compute device 130, 132) structural design data indicative of a structure of a building with one or more wood diaphragms. In doing so, and as indicated in block 304, the analysis compute device 110 may obtain data indicative of a floor plan of a building. The analysis compute device 110 may also obtain data indicative of one or more walls of the building, as indicated in block 306. Further, the analysis compute device 110 may obtain data indicative of a roof of the building, as indicated in block 308. In some embodiments, the analysis compute device 110, in obtaining the structural design data, may obtain data indicative of one or more irregularities such as irregularly shaped diaphragm(s) (e.g., not perfectly rectangular), one or more openings, one or more cantilevers, one or more out of plane offsets in walls, and / or one or more non-parallel wings, as indicated in block 310. The analysis compute device 110 may also obtain data indicative of a geographic location for the building, as indicated in block 312. From the geographic location, the analysis compute device 110 may determine (e.g., from a data set indexed by geographic locations) one or more environmental factors that may contribute to loads on the building, such as wind speeds (e.g., based on historical patterns, forecasts, and location relative to other objects that may block or impede the wind) and / or seismic activity (e.g., occurrences and magnitudes of seismic activity). The analysis compute device 110 may also obtain (e.g., as part of the structural design- 9 -175350189v4MITEK-00019 data) data indicative of nail size, nail spacing, and / or properties of the wood to be used (e.g., the type of wood), as indicated in block 314.

[0043] Continuing the method 300 in block 316, the analysis compute device 110, in the illustrative embodiment, constructs, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm(s) as semi-rigid (rather than fully rigid or fully flexible). In the illustrative embodiment, in constructing the mesh, the analysis compute device 110 subdivides the structure (e.g., as defined in the structural design data from block 302) into a set of cells (e.g., four node cells, such as rectangles or trapezoids and / or three node cells, such as triangles), as indicated in block 318. FIG. 5 illustrates an example embodiment of a mesh 500 that may be produced by the analysis compute device 110 representing a wall and a sloped roof. FIG. 6 illustrates an example embodiment of a mesh 600 that may be produced by the analysis compute device 110 representing a set of walls and an attached surface (e.g., a floor). Referring back to FIG. 3, as indicated in block 320, the analysis compute device 110, in the illustrative embodiment, assigns properties to members of the mesh based on the obtained structural design data. In doing so, and as indicated in block 322, the analysis compute device 110 may assign properties based on nail size, nail spacing, and / or properties of the wood (e.g., the type of structural sheathing) to be used. As indicated in block 324, the analysis compute device 110 may assign one or more properties corresponding with one or more building code(s) (e.g., properties for which requirements are defined in one or more building codes). In block 326, the analysis compute device 110 may assign one or more properties for chord deformation, panel shear and nail slip, and / or chord splice slip. The above properties correspond with terms of Equation 1 below, in which the first term represents chord deformation (excluding slip), the second term represents panel shear and nail slip, and the third term represents chord splice slip.„ 5vL3.1 Aonjn= -Ula+ (Equation 1). 8EAHv 1 7

[0044] Equation 1 above corresponds with a formulation for diaphragm deflection provided by the American Wood Council’s Special Design Provisions for Wind and Seismic (SDPWS). Referring briefly to FIG. 7, an example assignment 700 of properties to members of the mesh is shown. In particular, the outer perimeter of the mesh accounts for deflection due to bending from chord deformation. The elements 710 of the outer perimeter represent chord members and may be modeled with material properties of the actual chord member they represent. The elements 710 may also represent drag or collector members since a chord may also serve as a- 10 -175350189v4MITEK-00019 drag / col lector, depending on the direction of loading. Chords are structural members, such as beams, that extend along the edges of the diaphragm and resist tension and compression forces caused by the lateral loads. Collectors or drag struts (“drags”) are structural members, such as beams, that extend parallel to the direction of the lateral load. Collectors connect to the diaphragm and transfer the shear forces to the shear walls or other vertical elements of the lateral force resisting system. Axial load in the elements 710 can be used to design drags, chords, and / or collector members. Diagonal brace elements 712 in the mesh correspond with shear deflection including panel shear and nail slip. Brace elements represent the shear resistance of diaphragms which are designed to transfer lateral forces such as wind or seismic activity. The material properties and geometry of the elements 712 are selected based on the diaphragm specification and an apparent shear stiffness (e.g., as defined by SDPWS). Axial forces in the elements 712 reflect shear forces in the diaphragm. The analysis compute device 110, in the illustrative embodiment, accounts for bending deflection due to chord splice slip by modifying the chord members where splices 714 exist. The modification, in the illustrative embodiment, depends on the type of splices 714. For example, a nailed splice in an overlapped joint may have a different stiffness than a bolted splice or a strap splice. The analysis compute device 110 may utilize axial forces in the modified elements for verifying the design of the chord splices. Further, in FIG. 7, non-brace elements 716 indicate where no chord / drag / collector is present. The elements 716 are designated as internal elements and may be included to prevent instability in modeling the behavior of the structure. Further, in the illustrative embodiment, the analysis compute device 110 assigns relatively low stiffness to the elements 716 to prevent them from contributing to modeled bending behavior of the diaphragm. The elements 716 may also be used to model floor joist contributions to stiffness.

[0045] Referring now to FIG. 4, continuing the method 300, the analysis compute device 110 analyzes the mesh as an equivalent truss to determine deflection(s) and force(s) associated with the wood diaphragm(s) of the structure (e.g., the building), as indicated in block 328. In doing so, and as indicated in block 330, the analysis compute device 110 may populate one or more matrices associated with elements of the mesh based on Hooke’s law (e.g., treating elements as springs), set forth below in Equation 2.Fs= kx (Equation 2).- 11 -175350189v4MITEK-00019

[0046] As indicated in block 332, to improve computational efficiently (e.g., reduce processing time, reduce memory mapping operations, etc.) the analysis compute device 110, in the illustrative embodiment, positions values within the matrices to approximate positions of corresponding elements in the actual structure (e.g., such that elements that are adjacent to each other in the physical structure have values stored at adjacent positions within the matrices). In the illustrative embodiment, applied loads are distributed depending on the type of the loading. Seismic loads, in the illustrative embodiment, are distributed to each node based on the tributary area of the node in relation to adjacent nodes. Wind loads, in the illustrative embodiment, are distributed to each node at the edges of the diaphragm based on tributary width. Since the properties of all elements are intended to represent the actual behavior of the horizontal and vertical lateral elements, the default analysis of the model represents a semi-rigid diaphragm analysis. However, the operations can also be used to analyze a model with flexible or rigid diaphragm assumptions.

[0047] The analysis compute device 110 may determine whether results of the analysis satisfy applicable building codes (e.g., whether a determined deflection exceeds a maximum allowable deflection defined in a building code associated with the intended location for the building), as indicated in block 334. Further, as indicated in block 336, the analysis compute device 110, in the illustrative embodiment, provides (e.g., via a user interface) results of the analysis to a user (e.g., operating a user compute device 130, 132) for review (e.g., indicating the determined deflections and forces, indicating whether the design satisfies applicable building code(s), etc.).

[0048] In response to a determination that the design for the structure is not satisfactory (e.g., that an applicable building code would not be satisfied), the method 300 advances from block 338 to block 340, in which the design of the structure may be adjusted (e.g., by a user operating a user compute device 130, 132, by the analysis compute device 110, etc.). Afterwards, the method 300 may loop back to block 302, in which the analysis compute device 110 may perform the abovedescribed operations on the adjusted design. Otherwise, in response to a determination that the structure is satisfactory, the method 300 may proceed to block 342, in which the system 100 may build the structure. In doing so, the system 100 may utilize one or more of the manufacturing device(s) 140, 142 to build the structure (or components thereof), as indicated in block 344.

[0049] As compared to conventional methods of diaphragm analysis, which are either based on overly simplistic analytical methods, such as rigid body or equivalent deep beam analysis,- 12 -175350189v4MITEK-00019 or computationally expensive finite element analysis (FEA), the equivalent truss method (ETM) described herein provides a computationally efficient and accurate approach for semi-rigid analysis of wood diaphragms. The ETM employs truss elements to simulate panel shear stiffness and nail slip, beam elements for chords and drags, and stiffness modifiers for chord splices. The approach enables accurate analysis of irregular diaphragms with relatively large openings, cantilevers, out-of-plane offsets in walls, or buildings with non-parallel wings. The outputs of the analysis include panel unit shear forces, chords / collectors axial forces, and diaphragm deflections while accounting for torsional effects and force transfer around openings. Further, the methodology can be adjusted to capture non-linear behavior of diaphragms.

[0050] As described above, in wood light frame construction, diaphragms are structural elements that form part of the lateral force resisting system in a building. Diaphragms typically include wood structural panels (WSP) made of plywood or oriented strand board (OSB) and are used to resist wind and seismic loads, by transferring those loads to vertical lateral force resisting elements of a building. In wood construction, the vertical elements are typically wood structural panel shear walls. For wood light-framed diaphragms, the capacity, stiffness, and deflection of the diaphragm depend on the sheathing thickness and material properties, panel nail slip, chord splice slip, and chord deformation. To distribute lateral forces to the vertical elements, diaphragms may be idealized as either a flexible beam or as a rigid body, in conventional systems. However, as described above, in light-frame buildings, particularly in multi-family dwellings, diaphragms may be neither fully flexible nor fully rigid. Further, conventional modeling equations, such as those provided by the American Wood Council’s Special Design Provisions for Wind and Seismic (SDPWS) are specific to overly simplistic conditions and can be inadequate for capturing the behavior of conditions such as complex diaphragm shapes, out-of-plane offsets of vertical lateral elements, large opening in the diaphragm, or variable nailing patterns. As described herein, for increased accuracy and precision, the diaphragms should be analyzed as semi-rigid and the load should be distributed horizontally, taking into account the relative stiffness of diaphragms and vertical lateral elements. Such an analysis not only captures the distribution of the lateral load more accurately, but it also captures the internal elemental forces and diaphragm deformation more accurately, even for more complex irregular diaphragms.

[0051] As stated above, conventional systems for analyzing diaphragms are overly complex and require a large amount of computational resources and modelling expertise. In- 13 -175350189v4MITEK-00019 addition, such systems typical require inputs that are beyond the available parameters that are defined in design standards for wood diaphragms. Accordingly, additional efforts are usually required to obtain those inputs, or the resulting models are incorrect. When shell elements are used in modelling, interpreting the results to meet design requirements can also be challenging. The equivalent truss method described herein provides a practical analytical process that is computationally efficient and enables analysis of light-framed wood diaphragms while explicitly analyzing stiffness (i.e., a semi-rigid modeling assumptions).

[0052] As an example implementation of the equivalent truss method, a simply supported diaphragm 810 is shown in FIG. 8. A corresponding ETM model 820 is also shown in FIG. 8. Loading is first distributed based on tributary area of each line of nodes. The load distributed to each line is then evenly divided between each node of that line. Referring now to FIG. 9, three variations 910, 920, 930 of an ETM model, the respective model deflections, and a comparison to SDPWS calculated deflection for different terms of Equation 1 are shown. The model 910 represents rigid properties for the chord element and no chord splice elements, which isolates the deformation to just shear deformation. The model 920 utilizes the actual chord properties and no chord splice elements to include both shear and bending due to chord deformation. The model 930 utilizes the actual chord properties and includes chord splice elements to represent all of the contributing deformations. As shown in the comparison, the ETM model prediction of the diaphragm is almost identical to calculated values in SDPWS. In the example implementation, total mid-span deflection is determined by summing deflection components from the first, second, and third terms of Equation 1 represented above. Again, the first term represents bending, the second term represents shear, and the third term represents chord splice slip. The total mid-span deflection determined with the ETM model is 0.454” while the total mid-span deflection determined according to Equation 1 is 0.456”. Accordingly, the difference between the result determined with the ETM model and the result determined with Equation 1 is less than 1%.

[0053] Referring now to a set of diagrams 1010, 1020, 1030 in FIG. 10, a set of method validation operations are performed. Multiple diaphragms are tested using cyclic displacements to determine the effect of various construction details on lateral stiffness of the diaphragms. The diaphragm dimensions, are 16 x 20 ft in the diagrams 1010, 1020 and 10 x 40 ft in the diagram 1030. Further, 2x12 Douglas-fir joists are spaced at 16 inches on center and nailed with three 16d nails at each end to a 2 x 12 Douglas-fir rim joist. The structures are sheathed with 4 x 8 ft. 23 / 32”- 14 -175350189v4MITEK-00019 thick plywood sheets in a staggered configuration. Further, 1 Od nails are spaced at 6 inches around the perimeter and 12 inches in the interior supports of the panels. In the structure associated with diagrams 1010, 1020, no splices are present. In the structure associated with the diagram 1030, a bolted splice is present at the middle of 40 ft. long rim joists / chords. Two loading cases are investigated. The load protocol is five sinusoidal cycles at a predetermined deflection. The deflection is plus and minus 0.25 inches for the structure associated with the diagram 1010. For the structure associated with the diagram 1020, the deflection is plus and minus 0.20 inches. Further, for the structure associated with the diagram 1030, the deflection is 0.80 inches. In one case, load is oriented parallel to the joists and perpendicular to the continuous joint in the sheathing. In a second case, load is oriented perpendicular to the joists and parallel to the continuous joints in the sheathing. The investigated construction details include blocking, presence of designated chord members, and openings (center and corner). For each diaphragm, the stiffness is calculated and compared to a benchmark diaphragm (i.e., a diaphragm with designated chords, blocking, and no openings) to determine the reduction in stiffness if any of those construction details are omitted.

[0054] Referring now to FIG. 11, a similar analysis is performed through modeling reference diaphragm configurations using the equivalent truss method. In FIG. 11, one ETM model 1110 represents a benchmark diaphragm and an ETM model 1120 of a variation with an opening at the center. The reduction in stiffness due to the center opening is estimated to be approximately 40% by the ETM, which is close to the calculated tested value of 44%. The modeling and comparisons are repeated for other test configurations. The results of the models and their corresponding test are summarized in FIG. 12, with bars 1210 representing average test results and lines 1220 representing the range of test results. Several pairs of test specimens are used to calculate an effect of each parameter on the diaphragm stiffness. Points 1230 represent estimated stiffness reduction from the ETM models. For the models investigating the effect of blocking, the shear stiffness properties of the unblocked model are multiplied by 0.6 for a first case and by 0.4 for other cases based on SDPWS provisions for unblocked diaphragms. Overall, the model stiffness reductions fall within test ranges with several being similar to the average test value.

[0055] Referring now to FIG. 13, in another example implementation, diaphragms are tested with varying details based on reference data. The varying details include openings and variable nail spacing. A diaphragm 1310 is utilized as a control specimen. Diaphragms 1320,- 15 -175350189v4MITEK-000191330 are tested with different openings. Further, diaphragms 1340 are tested with multiple rows of nails and varying nail spacing through a span of the diaphragms 1340. An ETM model is generated for each diaphragm 1310, 1320, 1330, 1340 and the loads are distributed to each node such that the total load is equal to the applied load from the test. To accommodate varying nail spacing in the ETM model for diaphragms, the brace properties are calibrated for the stiffness based on the nailing used in the different sections of the diaphragm.

[0056] As another point of comparison, the deflection is also hand calculated using equations provided by SDPWS. The SDPWS deflections are not included for diaphragms with openings because the equations are no longer valid when openings are present. Additionally, for diaphragms with variable nailing, the deflection is determined assuming the support nailing for the whole diaphragm. FIG. 14 represents a chart 1400 of resulting deflections from the tests, ETM models, and manual calculations. Overall, the ETM models are able to estimate the deflections more accurately than the SDPWS equations.

[0057] The above example implementations provide validation for deflection and stiffness. In another example implementation, the equivalent truss method is tested with regard to internal forces in diaphragm components. With regard to a reference manual calculation method for analyzing diaphragm shears and chord and collector forces in complex diaphragms, FIG. 15 represents a diaphragm 1500 with an opening. Equivalent forces can be reported from the ETM analysis using the axial forces in the elements as shown in FIG. 15. The diaphragm shear forces near the opening and the chord / collector axial forces are shown in FIG. 16, as representations 1610, 1620 respectively. Despite some differences, the overall load distribution within the diaphragm using the ETM is close to the manually calculated distribution. For the values that show greater differences, part of the discrepancy can be attributed to variations between the model behavior and assumptions used in the manual calculations. The manual calculation assumes that sections above and below the opening have points of contraflexure at their midlength. Therefore, the collector forces in the middle of the members at the edge of the opening are zero. In the ETM model, the load is distributed based on the actual relative stiffness of the diaphragm sections around the opening. Since the sections above, below, and on the sides have different dimensions in the example, their stiffnesses are different and points of contraflexure would not occur at the midpoint. Stated differently, the ETM will estimate the load distribution around the opening more accurately than the manual calculations by accounting for the actual stiffness of diaphragm segments.- 16 -175350189v4MITEK-00019

[0058] Referring now to FIG. 17, in another example implementation, a simple rectangular building with walls 1730 of various lengths is analyzed. A building plan 1710 of the rectangular building and a corresponding ETM model 1720 are shown in FIG. 17. The diaphragm design is assumed to be 19 / 32” plywood with nailing at 6” o.c. As shown in FIG. 18, the building is modeled with actual diaphragm properties (i.e., semi-rigid) in the representation 1810, as well as rigid properties in the representation 1830, and flexible properties in the representation 1820. Plywood shear walls are represented in the model 1720 of FIG. 17 with equivalent X braces. The braces are calibrated to have lateral stiffness as defined by SDPWS. The flexible diaphragm deforms between the supports and the rigid diaphragm moves together as one body. The semi-rigid diaphragm, in the representation 1810, exhibits a behavior that is between the flexible and rigid representations 1820, 1830.

[0059] FIG. 19 represents a set of charts 1910, 1920 indicative of a normalized shear force distribution to each wall line for loading in the x and y directions. That is, the chart 1910 represents x direction loading and the chart 1920 represents y direction loading. The results indicate a pattern similar to a pattern exhibited in the deformed shapes. That is, using the actual properties of the diagram in the analysis typically provides results between flexible and rigid behavior. Due to a lack of a practical method for semi-rigid analysis of wood diaphragms, it is common for engineers to use an envelope method. The envelope method utilizes maximum forces from both flexible and rigid diagraph analysis for the design of the lateral systems. However, the chart 1910 suggests that an envelope approach can significantly overestimate the force in lines A, C, and E. Further, the envelope approach can potentially underestimate the force, as demonstrated with lines B and D.

[0060] Referring now to FIG. 20, in another example implementation, a large building that has a more complex shape than those discussed above and that includes cantilevered diaphragms is analyzed. A building plan 2010 of the complex building and a corresponding ETM model 2020 are shown in FIG. 20. The building includes internal walls 2030 and openings 2040. The diaphragm design is assumed to be 19 / 32” plywood with nailing at 6” o.c. The building is used to observe torsional effects, cantilevered diaphragm behavior, and a difference in force distribution in the chord elements between different analysis methos. Shear walls are simulated using X braces, as described above. Referring now to FIG. 21, a diagram 2110 represents a rigid model with x direction load, a diagram 2120 represents a semi-rigid model with x direction load, a diagram 2130 represents a rigid model with y direction load, and a diagram 2140 represents a semi-rigid model- 17 -175350189v4MITEK-00019 with y direction load. Tn assigning rigid properties for the diaphragm, diagrams 2110, 2130 illustrate rotational deformation due to torsion without any deformation of the diaphragm between supports. In the semi-rigid model represented in diagrams 2120, 2140, some torsional deformation is present, but the torsional deformation is significantly less noticeable than the rigid model due to the significantly larger deformation of the diaphragm between walls. Due to the cantilever diaphragms, the model cannot be analyzed as flexible. However, there are differences between fully flexible and semi-rigid behavior that can still be observed. In the diagram 2120, it can bee seen that the right wing has close to fully flexible behavior between the supporting wall lines. However, in the left wing, some short walls are on gridlines 8 and 9, as shown in the building plan 2010 in FIG. 20. Due to the lower stiffness at those lines, the diaphragm appears to behave like a flexible diaphragm that is supported only at lines 7 and 10.

[0061] Referring now to FIG. 22, a diagram 2210 represents a rigid model with x direction load, a diagram 2220 represents a semi-rigid model with x direction load, a diagram 2230 represents a rigid model with y direction load, and a diagram 2240 represents a semi-rigid model with y direction load. Further, axial forces in chords and collectors are represented. FIG. 22 illustrates that there is a large increase in axial forces when assuming a rigid diaphragm, not only in the chord members but also in other collector members that are normally not considered as chords. The effect is most apparent in the right wing for x direction loading, in wall lines L, M, O, P, and Q, and the top wing for y direction loading, in wall lines 1, 4, and 5, and the cantilevered edge of the diaphragm. However, performing semi-rigid analysis would provide a more realistic representation of load distribution to chords and collectors. Doing so can be followed by a more efficient design of the elements, in terms of resources utilized to produce the building.

[0062] As described above, the system 100 utilizes a discretized model of truss elements with various stiffness properties to more accurately represent the behavior of diaphragms, including deflections and internal elemental forces. The models, based on tests such as those described above, confirm that the method performed by the system 100 is capable of accurately estimating stiffness and deflections for diaphragms. Further, as described above, the system 100 is capable of determining force distributions that are similar to those of significantly more computationally resource intensive approaches that typically require additional input data beyond the data that is provided in design standards for wood diaphragms. The system 100 enables determination of stiffness and deflection for diaphragms beyond the scope of standard systems,- 18 -175350189v4MITEK-00019 such as analysis of diaphragms with openings, variable nail spacings, and other factors. Further, the example implementations described above demonstrate that using a flexible or rigid diaphragm assumption, such as in typical systems, can result in significant error in force estimation in diaphragm components and can also lead to underestimation of the local and torsional deflection of diaphragms. Semi-rigid analysis enabled by the system 100 on the other hand, provides a more realistic load distribution to chords / collectors and shear walls, and estimates the diaphragm deflection more accurately. That is, the system 100 enables more accurate determination of forces in diaphragm components, including axial forces in chords and collectors, and shear in diaphragm sheathing. Further, the system enables more accurate determination of local and torsional deflection. Accordingly, the system 100 enables the generation of more optimized and cost- effective designs that allow for more affordable and more reliably-performing buildings. As such, the system 100 addresses shortcomings of conventional systems for designing, analyzing, and constructing buildings with modern light-frame wood construction.

[0063] While certain illustrative embodiments have been described in detail in the drawings and the foregoing description, such an illustration and description is to be considered as exemplary and not restrictive in character, it being understood that only illustrative embodiments have been shown and described and that all changes and modifications that come within the spirit of the disclosure are desired to be protected. Additional embodiments may be described in the attached appendix. There exist a plurality of advantages of the present disclosure arising from the various features of the apparatus, systems, and methods described herein. It will be noted that alternative embodiments of the apparatus, systems, and methods of the present disclosure may not include all of the features described, yet still benefit from at least some of the advantages of such features. Those of ordinary skill in the art may readily devise their own implementations of the apparatus, systems, and methods that incorporate one or more of the features of the present disclosure.EXAMPLES

[0064] Illustrative examples of the technologies disclosed herein are provided below. An embodiment of the technologies may include any one or more, and any combination of, the examples described below.- 19 -175350189v4MITEK-00019

[0065] Example 1 includes a system comprising circuitry configured to obtain structural design data indicative of a structure of a building with at least one wood diaphragm; construct, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm as semi-rigid; and analyze the mesh as the equivalent truss to determine deflections and forces associated with the wood diaphragm, thereby providing computationally efficient and accurate semi-rigid analysis of the wood diaphragm to improve reliability of the structure of the building.

[0066] Example 2 includes the subject matter of Example 1, and wherein to obtain structural design data comprises to obtain data indicative of one or more of a floor plan, a wall, or a roof of the building; and obtain data indicative a nail size, nail spacing, or type of wood to be utilized in construction of the building.

[0067] Example 3 includes the subject matter of any of Examples 1 and 2, and wherein to obtain structural design data further comprises to obtain data indicative of one or more irregularities including one or more of an irregular diaphragm, an opening, a cantilever, an out-of- plane offset, or a non-parallel wing of the structure of the building.

[0068] Example 4 includes the subject matter of any of Examples 1-3, and wherein to obtain structural design data further comprises to obtain data indicative of a geographic location of the building; and to analyze the mesh to determine deflections and forces comprises to determine a design load associated with wind or seismic activity based on the geographical location of the building and determine deflections and forces associated with wind or seismic activity associated with the geographic location of the building.

[0069] Example 5 includes the subject matter of any of Examples 1-4, and wherein to construct, from the structural design data, the mesh comprises to subdivide the structure into a set of multiple cells, in which each cell includes multiple nodes.

[0070] Example 6 includes the subject matter of any of Examples 1-5, and wherein the circuitry is further configured to assign properties to members of the mesh based on the obtained structural design data, including one or more of nail size, nail spacing, or structural sheathing to be utilized in the construction of one or more components of the building.

[0071] Example 7 includes the subject matter of any of Examples 1-6, and wherein the circuitry is further configured to assign properties to members of the mesh to represent one or more of chord deformation, panel shear, nail slip, or chord splice slip.- 20 -175350189v4MITEK-00019

[0072] Example 8 includes the subject matter of any of Examples 1-7, and wherein the circuitry is further configured to assign properties to one or more members of the mesh as a function of one or more building codes applicable to the building.

[0073] Example 9 includes the subject matter of any of Examples 1-8, and wherein to analyze the mesh as the equivalent truss comprises to populate one or more matrices associated with elements of the mesh based on a representation of a stiffness of each element.

[0074] Example 10 includes the subject matter of any of Examples 1-9, and wherein to analyze the mesh further comprises to position numeric values within the one or more matrices as a function of positions of corresponding elements of the structure of the building as represented in the structural design data, wherein adjacent elements in the structure are represented with corresponding numeric values in adjacent positions within the one or more matrices, to reduce memory mapping operations for computational efficiency.

[0075] Example 11 includes the subject matter of any of Examples 1-10, and wherein to analyze the mesh further comprises to distribute applied loads represented in the one or more matrices as a function of a type of loading, including distributing seismic loads to nodes represented within the one or more matrices as a function of a tributary area of a node relative to one or more adjacent nodes, distributing wind loads to nodes represented in the one or more matrices to edge nodes as a function of a tributary width, and adjusting the distributed loads to the nodes to account for torsion.

[0076] Example 12 includes the subject matter of any of Examples 1-11, and wherein the circuitry is further configured to determine deflection of the wood diaphragm as a function of bending from chord deformation along an outer perimeter of the mesh.

[0077] Example 13 includes the subject matter of any of Examples 1-12, and wherein the circuitry is further configured to determine shear deflection of the wood diaphragm as a function of panel shear and nail slip based on material properties and geometries of brace elements in the mesh.

[0078] Example 14 includes the subject matter of any of Examples 1-13, and wherein the circuitry is further configured to analyze bending and deflection due to chord splice slip by modifying one or more chord members represented in the mesh as a function of a splice type represented in the structural design data.- 21 -175350189v4MITEK-00019

[0079] Example 15 includes the subject matter of any of Examples 1 -14, and wherein the circuitry is further configured to determine the splice type by determining whether a splice represented in the structural design data is indicative of a nailed splice, a bolted splice, or a strap splice; and assign, as a function of the determined splice type, a corresponding stiffness to the splice in the corresponding chord member.

[0080] Example 16 includes the subject matter of any of Examples 1-15, and wherein the circuitry is further configured to analyze axial forces in a modified chord member to verify a design of the one or more splices.

[0081] Example 17 includes the subject matter of any of Examples 1-16, and wherein the circuitry is further configured to identify one or more non-brace elements indicative of a location where no chord, drag, or collector is present in the structure; designate each non-brace element as an internal element; and assign a stiffness value to each non-brace element that is determined to prevent the identified one or more non-brace elements from contributing to modeled bending behavior of the wood diaphragm.

[0082] Example 18 includes the subject matter of any of Examples 1-17, and wherein the circuitry is embedded in a first compute device, the first compute device is in communication with a second compute device that is configured to fabricate one or more components of the structure, and the circuitry embedded in the first compute device is further configured to provide the structural design data to the second compute device to fabricate the one or more components of the structure.

[0083] Example 19 includes the subject matter of any of Examples 1-18, and wherein the circuitry is further configured to identify a building code applicable to the structure; and determine, as a function of the analysis of the mesh, whether the identified building code is satisfied; and wherein to provide the structural design data to the second compute device comprises to provide, in response to a determination that the identified building code is satisfied, the structural design data to the second compute device to fabricate the one or more components of the structure.

[0084] Example 20 includes the subject matter of any of Examples 1-19, and wherein to analyze the mesh further comprises to analyze the mesh based on a relative stiffness of the wood diaphragm and a vertical lateral system including determining a distribution of a lateral load in the vertical lateral system based on the relative stiffness of the wood diaphragm and the vertical lateral system.- 22 -175350189v4MITEK-00019

[0085] Example 21 includes a method comprising obtaining, by a compute device, structural design data indicative of a structure of a building with at least one wood diaphragm; constructing, by the compute device, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm as semi-rigid; and analyzing, by the compute device, the mesh as the equivalent truss to determine deflections and forces associated with the wood diaphragm, thereby providing computationally efficient and accurate semi-rigid analysis of the wood diaphragm to improve reliability of the structure of the building.

[0086] Example 22 includes the subject matter of Example 21, and wherein obtaining structural design data comprises obtaining data indicative of one or more of a floor plan, a wall, or a roof of the building; and obtaining data indicative a nail size, nail spacing, or type of wood to be utilized in construction of the building.

[0087] Example 23 includes the subject matter of any of Examples 21 and 22, and wherein obtaining structural design data further comprises obtaining data indicative of one or more irregularities including one or more of an irregular diaphragm, an opening, a cantilever, an out-of- plane offset, or a non-parallel wing of the structure of the building.

[0088] Example 24 includes the subject matter of any of Examples 21-23, and wherein obtaining structural design data further comprises obtaining data indicative of a geographic location of the building; and analyzing the mesh to determine deflections and forces comprises determining a design load associated with wind or seismic activity based on the geographical location of the building and determining deflections and forces associated with wind or seismic activity associated with the geographic location of the building.

[0089] Example 25 includes the subject matter of any of Examples 21-24, and wherein constructing, from the structural design data, the mesh comprises subdividing the structure into a set of multiple cells, in which each cell includes multiple nodes.

[0090] Example 26 includes the subject matter of any of Examples 21-25, and further including assigning, by the compute device, properties to members of the mesh based on the obtained structural design data, including one or more of nail size, nail spacing, or structural sheathing to be utilized in the construction of one or more components of the building.

[0091] Example 27 includes the subject matter of any of Examples 21-26, and further including assigning, by the compute device, properties to members of the mesh to represent one or more of chord deformation, panel shear, nail slip, or chord splice slip.- 23 -175350189v4MITEK-00019

[0092] Example 28 includes the subject matter of any of Examples 21-27, and further including assigning, by the compute device, properties to one or more members of the mesh as a function of one or more building codes applicable to the building.

[0093] Example 29 includes the subject matter of any of Examples 21-28, and wherein analyzing the mesh as the equivalent truss comprises populating one or more matrices associated with elements of the mesh based on a representation of a stiffness of each element.

[0094] Example 30 includes the subject matter of any of Examples 21-29, and wherein analyzing the mesh further comprises positioning numeric values within the one or more matrices as a function of positions of corresponding elements of the structure of the building as represented in the structural design data, wherein adjacent elements in the structure are represented with corresponding numeric values in adjacent positions within the one or more matrices, to reduce memory mapping operations for computational efficiency.

[0095] Example 31 includes the subject matter of any of Examples 21-30, and wherein analyzing the mesh further comprises distributing applied loads represented in the one or more matrices as a function of a type of loading, including distributing seismic loads to nodes represented within the one or more matrices as a function of a tributary area of a node relative to one or more adjacent nodes, distributing wind loads to nodes represented in the one or more matrices to edge nodes as a function of a tributary width, and adjusting the distributed loads to the nodes to account for torsion.

[0096] Example 32 includes the subject matter of any of Examples 21-31, and further including determining, by the compute device, deflection of the wood diaphragm as a function of bending from chord deformation along an outer perimeter of the mesh.

[0097] Example 33 includes the subject matter of any of Examples 21-32, and further including determining, by the compute device, shear deflection of the wood diaphragm as a function of panel shear and nail slip based on material properties and geometries of brace elements in the mesh.

[0098] Example 34 includes the subject matter of any of Examples 21-33, and further including analyzing, by the compute device, bending and deflection due to chord splice slip by modifying one or more chord members represented in the mesh as a function of a splice type represented in the structural design data.- 24 -175350189v4MITEK-00019

[0099] Example 35 includes the subject matter of any of Examples 21-34, and further including determining, by the compute device, the splice type by determining whether a splice represented in the structural design data is indicative of a nailed splice, a bolted splice, or a strap splice; and assigning, by the compute device and as a function of the determined splice type, a corresponding stiffness to the splice in the corresponding chord member.

[0100] Example 36 includes the subject matter of any of Examples 21-35, and further including analyzing, by the compute device, axial forces in a modified chord member to verify a design of the one or more splices.

[0101] Example 37 includes the subject matter of any of Examples 21-36, and further including identifying, by the compute device, one or more non-brace elements indicative of a location where no chord, drag, or collector is present in the structure; designating, by the compute device, each non-brace element as an internal element; and assigning, by the compute device, a stiffness value to each non-brace element that is determined to prevent the identified one or more non-brace elements from contributing to modeled bending behavior of the wood diaphragm.

[0102] Example 38 includes the subject matter of any of Examples 21-37, and wherein the compute device is a first compute device, the method further comprising providing, by the first compute device and to a second compute device that is in communication with the first compute device and that is configured to fabricate one or more components of the structure, the structural design data to fabricate the one or more components of the structure.

[0103] Example 39 includes the subject matter of any of Examples 21-38, and further including identifying, by the first compute device, a building code applicable to the structure; and determining, by the first compute device and as a function of the analysis of the mesh, whether the identified building code is satisfied; and wherein providing the structural design data to the second compute device comprises providing, in response to a determination that the identified building code is satisfied, the structural design data to the second compute device to fabricate the one or more components of the structure.

[0104] Example 40 includes the subject matter of any of Examples 21-39, and wherein analyzing the mesh further comprises analyzing the mesh based on a relative stiffness of the wood diaphragm and a vertical lateral system including determining a distribution of a lateral load in the vertical lateral system based on the relative stiffness of the wood diaphragm and the vertical lateral system.- 25 -175350189v4MITEK-00019

[0105] Example 41 includes one or more machine-readable storage media comprising a plurality of instructions stored thereon that, in response to being executed, cause a compute device to perform the method of any of Examples 21-40.- 26 -175350189v4

Claims

1. MITEK-00019CLAIMS:

1. A system comprising: circuitry configured to: obtain structural design data indicative of a structure of a building with at least one wood diaphragm; construct, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm as semi-rigid; and analyze the mesh as the equivalent truss to determine deflections and forces associated with the wood diaphragm, thereby providing computationally efficient and accurate semi-rigid analysis of the wood diaphragm to improve reliability of the structure of the building.

2. The system of claim 1, wherein to obtain structural design data comprises to: obtain data indicative of one or more of a floor plan, a wall, or a roof of the building; and obtain data indicative a nail size, nail spacing, or type of wood to be utilized in construction of the building.

3. The system of claim 2, wherein to obtain structural design data further comprises to: obtain data indicative of one or more irregularities including one or more of an irregular diaphragm, an opening, a cantilever, an out-of-plane offset, or a non-parallel wing of the structure of the building.

4. The system of claim 1, wherein: to obtain structural design data further comprises to obtain data indicative of a geographic location of the building; and to analyze the mesh to determine deflections and forces comprises to determine a design load associated with wind or seismic activity based on the geographical location of the building and determine deflections and forces associated with wind or seismic activity associated with the geographic location of the building.- 27 -175350189v4MITEK-000195. The system of claim 1, wherein to construct, from the structural design data, the mesh comprises to subdivide the structure into a set of multiple cells, in which each cell includes multiple nodes.

6. The system of claim 5, wherein the circuitry is further configured to: assign properties to members of the mesh based on the obtained structural design data, including one or more of nail size, nail spacing, or structural sheathing to be utilized in the construction of one or more components of the building.

7. The system of claim 6, wherein the circuitry is further configured to: assign properties to members of the mesh to represent one or more of chord deformation, panel shear, nail slip, or chord splice slip.

8. The system of claim 5, wherein the circuitry is further configured to: assign properties to one or more members of the mesh as a function of one or more building codes applicable to the building.

9. The system of claim 1, wherein to analyze the mesh as the equivalent truss comprises to: populate one or more matrices associated with elements of the mesh based on a representation of a stiffness of each element.

10. The system of claim 9, wherein to analyze the mesh further comprises to: position numeric values within the one or more matrices as a function of positions of corresponding elements of the structure of the building as represented in the structural design data, wherein adjacent elements in the structure are represented with corresponding numeric values in adjacent positions within the one or more matrices, to reduce memory mapping operations for computational efficiency.

11. The system of claim 9, wherein to analyze the mesh further comprises to: distribute applied loads represented in the one or more matrices as a function of a type of loading, including distributing seismic loads to nodes represented within the one or more- 28 -175350189v4MITEK-00019 matrices as a function of a tributary area of a node relative to one or more adjacent nodes, distributing wind loads to nodes represented in the one or more matrices to edge nodes as a function of a tributary width, and adjusting the distributed loads to the nodes to account for torsion.

12. The system of claim 9, wherein the circuitry is further configured to: determine deflection of the wood diaphragm as a function of bending from chord deformation along an outer perimeter of the mesh.

13. The system of claim 9, wherein the circuitry is further configured to: determine shear deflection of the wood diaphragm as a function of panel shear and nail slip based on material properties and geometries of brace elements in the mesh.

14. The system of claim 9, wherein the circuitry is further configured to: analyze bending and deflection due to chord splice slip by modifying one or more chord members represented in the mesh as a function of a splice type represented in the structural design data.

15. The system of claim 14, wherein the circuitry is further configured to: determine the splice type by determining whether a splice represented in the structural design data is indicative of a nailed splice, a bolted splice, or a strap splice; and assign, as a function of the determined splice type, a corresponding stiffness to the splice in the corresponding chord member.

16. The system of claim 15, wherein the circuitry is further configured to: analyze axial forces in a modified chord member to verify a design of the one or more splices.

17. The system of claim 9, wherein the circuitry is further configured to: identify one or more non-brace elements indicative of a location where no chord, drag, or collector is present in the structure; designate each non-brace element as an internal element; and- 29 -175350189v4MITEK-00019 assign a stiffness value to each non-brace element that is determined to prevent the identified one or more non-brace elements from contributing to modeled bending behavior of the wood diaphragm.

18. The system of claim 1, wherein the circuitry is embedded in a first compute device, the first compute device is in communication with a second compute device that is configured to fabricate one or more components of the structure, and the circuitry embedded in the first compute device is further configured to provide the structural design data to the second compute device to fabricate the one or more components of the structure.

19. The system of claim 18, wherein the circuitry is further configured to: identify a building code applicable to the structure; and determine, as a function of the analysis of the mesh, whether the identified building code is satisfied; and wherein to provide the structural design data to the second compute device comprises to provide, in response to a determination that the identified building code is satisfied, the structural design data to the second compute device to fabricate the one or more components of the structure.

20. The system of claim 1, wherein to analyze the mesh further comprises to: analyze the mesh based on a relative stiffness of the wood diaphragm and a vertical lateral system including determining a distribution of a lateral load in the vertical lateral system based on the relative stiffness of the wood diaphragm and the vertical lateral system.

21. A method comprising: obtaining, by a compute device, structural design data indicative of a structure of a building with at least one wood diaphragm; constructing, by the compute device, from the structural design data, a mesh that serves as an equivalent truss that models the wood diaphragm as semi-rigid; and analyzing, by the compute device, the mesh as the equivalent truss to determine deflections and forces associated with the wood diaphragm, thereby providing computationally- 30 -175350189v4MITEK-00019 efficient and accurate semi-rigid analysis of the wood diaphragm to improve reliability of the structure of the building.

22. The method of claim 21, wherein obtaining structural design data comprises: obtaining data indicative of one or more of a floor plan, a wall, or a roof of the building; and obtaining data indicative a nail size, nail spacing, or type of wood to be utilized in construction of the building.

23. The method of claim 22, wherein obtaining structural design data further comprises: obtaining data indicative of one or more irregularities including one or more of an irregular diaphragm, an opening, a cantilever, an out-of-plane offset, or a non-parallel wing of the structure of the building.

24. The method of claim 21, wherein: obtaining structural design data further comprises obtaining data indicative of a geographic location of the building; and analyzing the mesh to determine deflections and forces comprises determining a design load associated with wind or seismic activity based on the geographical location of the building and determining deflections and forces associated with wind or seismic activity associated with the geographic location of the building.

25. The method of claim 21, wherein constructing, from the structural design data, the mesh comprises subdividing the structure into a set of multiple cells, in which each cell includes multiple nodes.

26. The method of claim 25, further comprising: assigning, by the compute device, properties to members of the mesh based on the obtained structural design data, including one or more of nail size, nail spacing, or structural sheathing to be utilized in the construction of one or more components of the building.- 31 -175350189v4MITEK-0001927. The method of claim 26, further comprising: assigning, by the compute device, properties to members of the mesh to represent one or more of chord deformation, panel shear, nail slip, or chord splice slip.

28. The method of claim 25, further comprising: assigning, by the compute device, properties to one or more members of the mesh as a function of one or more building codes applicable to the building.

29. The method of claim 21, wherein analyzing the mesh as the equivalent truss comprises: populating one or more matrices associated with elements of the mesh based on a representation of a stiffness of each element.

30. The method of claim 29, wherein analyzing the mesh further comprises: positioning numeric values within the one or more matrices as a function of positions of corresponding elements of the structure of the building as represented in the structural design data, wherein adjacent elements in the structure are represented with corresponding numeric values in adjacent positions within the one or more matrices, to reduce memory mapping operations for computational efficiency.

31. The method of claim 29, wherein analyzing the mesh further comprises: distributing applied loads represented in the one or more matrices as a function of a type of loading, including distributing seismic loads to nodes represented within the one or more matrices as a function of a tributary area of a node relative to one or more adjacent nodes, distributing wind loads to nodes represented in the one or more matrices to edge nodes as a function of a tributary width, and adjusting the distributed loads to the nodes to account for torsion.

32. The method of claim 29, further comprising: determining, by the compute device, deflection of the wood diaphragm as a function of bending from chord deformation along an outer perimeter of the mesh.

33. The method of claim 29, further comprising:- 32 -175350189v4MITEK-00019 determining, by the compute device, shear deflection of the wood diaphragm as a function of panel shear and nail slip based on material properties and geometries of brace elements in the mesh.

34. The method of claim 29, further comprising: analyzing, by the compute device, bending and deflection due to chord splice slip by modifying one or more chord members represented in the mesh as a function of a splice type represented in the structural design data.

35. The method of claim 34, further comprising: determining, by the compute device, the splice type by determining whether a splice represented in the structural design data is indicative of a nailed splice, a bolted splice, or a strap splice; and assigning, by the compute device and as a function of the determined splice type, a corresponding stiffness to the splice in the corresponding chord member.

36. The method of claim 35, further comprising: analyzing, by the compute device, axial forces in a modified chord member to verify a design of the one or more splices.

37. The method of claim 29, further comprising: identifying, by the compute device, one or more non-brace elements indicative of a location where no chord, drag, or collector is present in the structure; designating, by the compute device, each non-brace element as an internal element; and assigning, by the compute device, a stiffness value to each non-brace element that is determined to prevent the identified one or more non-brace elements from contributing to modeled bending behavior of the wood diaphragm.

38. The method of claim 21, wherein the compute device is a first compute device, the method further comprising:- 33 -175350189v4MITEK-00019 providing, by the first compute device and to a second compute device that is in communication with the first compute device and that is configured to fabricate one or more components of the structure, the structural design data to fabricate the one or more components of the structure.

39. The method of claim 38, further comprising: identifying, by the first compute device, a building code applicable to the structure; and determining, by the first compute device and as a function of the analysis of the mesh, whether the identified building code is satisfied; and wherein providing the structural design data to the second compute device comprises providing, in response to a determination that the identified building code is satisfied, the structural design data to the second compute device to fabricate the one or more components of the structure.

40. The method of claim 21, wherein analyzing the mesh further comprises: analyzing the mesh based on a relative stiffness of the wood diaphragm and a vertical lateral system including determining a distribution of a lateral load in the vertical lateral system based on the relative stiffness of the wood diaphragm and the vertical lateral system.

41. One or more machine-readable storage media comprising a plurality of instructions stored thereon that, in response to being executed, cause a compute device to perform the method of any of claims 21-40.- 34 -175350189v4

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