Reconfigurable precast concrete construction system

Abstract

Embodiments implement an apparatus for use in a building structure. Embodiments include at least two structural modules having a convex side oriented towards the common axis and a concave side oriented away from a common axis. Further, embodiments include member element defined by the at least two structural modules in coupled arrangement, the member element comprising a first end and a second end. A post-tensioning assembly is utilized including: (i) at least two anchors coupled to the member element at distinct locations at or between the first end and the second end, and (ii) a tensile element coupled to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis.

Description

RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 499,222 filed on Apr. 29, 2023. The entire teachings of the above application are incorporated herein by reference.BACKGROUND

[0002] Concrete is one of the most common building materials, with demand expected to rise due to a growing urban population. Cementitious materials are responsible for 8% of anthropogenic greenhouse gas emissions, over 60% of which result from the energy-intensive process of cement production-about half of which is used in the construction of buildings, which are typically overdesigned [2]. Despite its ubiquity, concrete is perceived as a low-value material, accounting for 80% of construction and demolition waste by weight [3,4]. Most of this waste is downcycled in an energy-intensive process [5], despite its reuse potential, especially for concrete of high compressive strength [6].

[0003] In recent years, interest in the geometric computational optimization of structural modules has grown. Material savings of upwards of 60% can be accomplished by using computation to optimize floor slabs [7, 8]. Computation has also gained traction as a strategy to facilitate salvage reuse, emphasizing the introduction of irregular, non-standard or waste materials into a constrained design process [9]. ‘Design for reuse’ has been posited as a strategy for the reduction of embodied carbon (EC) in structural modules [6,10] but reusability often ends at demountability, without any other consideration of future use cases.

[0004] Research on the reduction or replacement of cement content is relatively mature, yet recent work suggests that equally significant carbon savings exist along the rest of the value chain [2]. Two promising approaches are material reduction, which uses computation to optimally allocate material, and circularity, a strategy to reduce EC through reuse. However, these two strategies are often mutually exclusive, as optimization produces highly specific elements that are difficult to reuse outside of identical geometric and loading scenarios, and circularity demands a degree of standardization for components to be reusable, creating a tradeoff between flexibility and efficiency.SUMMARY

[0005] Embodiments relate to a unique geometry, with varying concrete strength, arranged in some configurations around a core to form distinct column and beam cross-sections that are stacked and internally axially post-tensioned to ensure monolithic behavior.

[0006] An example embodiment is directed to an apparatus for use in a building structure. The apparatus includes at least two structural modules, each having a convex side oriented toward a common axis and a concave side oriented away from the common axis. The apparatus also includes a member element defined by the at least two structural modules in coupled arrangement, the member element comprising a first end and a second end. The member includes a post-tensioning assembly including: (i) at least two anchors coupled to the member element at distinct locations at or between the first end and the second end; and (ii) a tensile element coupled to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors. The post-tensioning force has a force substantially in parallel with or coincident with the common axis. For brevity, “along the common axis” is used herein to refer to either or both locations of the force as is relative to the common axis.

[0007] In another embodiment, the convex side of each structural module defines a first complementary coupling feature. The apparatus further includes a core module having a length, the core module defining a second complementary coupling feature along at least a portion of the length. The member element is further defined by the core module in coupled arrangement with the structural modules via the first and second complementary coupling features.

[0008] In another embodiment, intermediate plates are configured to be spaced between adjacent structural modules and in coupled arrangement with the core module.

[0009] In still another embodiment, the intermediate plates are configured to couple to any one of: a post-tensioning element, a different member element, or a connection node configured to couple at least two member elements.

[0010] In another embodiment, the post-tensioning assembly further includes the intermediate plate that is configured to couple additional elements to a tensile element and provide external post-tensioning.

[0011] In a further embodiment, the second complementary coupling feature is positioned on or defined by the core module at a location that orients two or more structural modules to be coupled radially around the core module.

[0012] In another embodiment, the core module includes concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

[0013] In still another embodiment, the tensile element includes steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof.

[0014] In another embodiment, the at least two anchors are coupled to end bearing plates and, in combination with the tensile element, are configured to hold the structural modules in coupled arrangement.

[0015] In another embodiment, the structural module consists of concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

[0016] In yet another embodiment, the structural module's composition varies according to at least one of: cement content, fiber dosage, admixtures, aggregate content, or any combination thereof.

[0017] Another embodiment includes a connection node component configured to couple multiple member elements together to form a connection node.

[0018] Another embodiment includes a plurality of member elements coupled to a plurality of connection node components arranged to form a structure.

[0019] Another embodiment includes at least one planar element configured to be coupled to the structure, the at least one planar element, in coupled arrangement with the structure, defining at least one of a floor, roof, or wall.

[0020] In an embodiment, the planar element further comprises an independent interface component configured to couple the planar element to at least one member element.

[0021] Another example embodiment is directed toward a method of assembling a building structure. The method includes orienting a convex side of a structural module toward a common axis and orienting a concave side of the structural moule away from the common axis. The method further includes coupling and arranging at least two structural modules to define a member element, the member element having a first end and a second end. The method also includes assembling a post-tensioning assembly by: (i) coupling at least two anchors to the member element at distinct locations at or between the first and the second end, and (ii) coupling a tensile element to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis.

[0022] In an embodiment, the convex side of each structural module defines a first complementary coupling feature, the method further includes coupling the first complementary coupling feature of each structural module to a core module coupled thereto or defining (“having” as used herein covering either or both cases) a second complementary coupling feature and a length, wherein the second complementary coupling feature is along at least a portion of the length. The method further includes coupling and arranging the core module with the structural modules via the first and second complementary coupling features to compose the member element.

[0023] In another embodiment, the method further includes spacing intermediate plates between adjacent structural modules, which in some embodiments is in coupled arrangement with the core module.

[0024] In another embodiment, the method further includes spacing intermediate plates between adjacent structural modules, in coupled arrangement with the core module.

[0025] Yet another embodiment is directed to an apparatus for use in a building structure. The apparatus providing means for interconnecting structural modules in a manner that enables reversible construction. The apparatus also providing means for assembling of a member element with at least two structural modules. The apparatus further providing means for applying post-tensioning for maintaining structural integrity of the member element.

[0026] In an embodiment, the structural modules have a concave side and a convex side. The apparatus further includes means for coupling the structural modules together with at least two adjacent structural modules. The structural modules having respective convex sides oriented toward a common axis, and respective concave sides oriented away from the common axis.

[0027] It is noted that the apparatus, means for building a structure, and method of building a structure may be configured to implement any embodiments, or combinations of embodiments, described herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0029] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0030] FIG. 1 is a diagram of a flow of graphical renderings and photos showing an overview of an example “Pixelframe” embodiment of at least two structural modules and a post-tensioning assembly that defines a Pixelframe system embodiment.

[0031] FIG. 2 is a flow diagram for an apparatus for use in a building structure, according to embodiments.

[0032] FIGS. 3A-3B are graphical representations showing how the Pixelframe system and apparatus may assembled, according to embodiments.

[0033] FIGS. 4A-4C are graphical representations of isometric and top-down views of the core modules and member elements, according to embodiments.

[0034] FIG. 5 is a photo showing an end bearing plate and tensile element being coupled to a structural module, according to an embodiment.

[0035] FIGS. 6A-6C are graphical representations of embodiments that show how several member elements may be coupled together in order to form a building structure.

[0036] FIGS. 7A and 7B show a graphical representation of how member elements may be coupled to form a structure, according to embodiments.

[0037] FIG. 7C is a graphical representation of a geometry of a planar element configured to couple to a member element, according to an embodiment.

[0038] FIGS. 8A-8C are plots of demand sampling and internal force distributions for embodiments.

[0039] FIG. 9 is a graphical representation of a primary beam and associated external post-tensioning assembly.

[0040] FIGS. 10A and 10B are photos of the external post-tensioning assembly for embodiments.

[0041] FIGS. 11A and 11B are graphical representations of both the internal and external post-tensioning systems for a primary beam and a secondary beam, according to embodiments.

[0042] FIGS. 12A and 12B are graphical representations highlighting the differences in external post-tensioning between primary and secondary beams in embodiments.

[0043] FIG. 13 is a graphical representation of a comparison of reconfiguration potential, utilization and EC across different approaches.DETAILED DESCRIPTION

[0044] A description of example embodiments follows.

[0045] Demand to build structures, such as housing, for a growing urban population is in conflict with a preference to reduce contributions to global CO2 emissions from the Architectural Engineering and Construction (AEC) sector. Structural systems are a factor in this challenge, as they contribute substantially to a building's mass and are typically overdesigned. Two strategies for reducing the embodied carbon of structural systems are (i) geometric optimization, which can reduce structural mass but limits reusability, and (ii) circular material reuse, which is most successful when building components are standardized, often resulting in poor utilization.

[0046] To improve reuse potential while maintaining flexibility and efficiency, embodiments of the present invention leverage standardization and optimization by discretizing structural modules into precast modules with variable mix designs. An algorithmic design strategy may be implemented and allows for a discrete optimization approach that can meet demands of variable load cases, utilizes element types and spans with one base geometry, resulting in a system and apparatus that is reversible and reconfigurable. The system may utilize a data-driven approach to determine design loads and criteria, and a bidirectional algorithmic approach to match precast modules to optimized building frames.

[0047] The selection of unique concrete mixes for open-ended design applications is informed by the rationalization of anticipated structural demands across varying structural geometries and building programs. Rationalization in structural design is most often deployed in the context of manufacturing and procurement complexity reduction [15-17]. To extend this process to the rationalization of structural demands, embodiments build upon metrics and clustering algorithms that consider the directions of comparisons between structural demand and module capacity [18,19].

[0048] Disclosed herein are embodiments directed to an apparatus for use in a building structure which uses structural modules (herein referred to as “Pixels”) in a system referred to as to as “Pixelframe.” Embodiments implement a new precast concrete structural system that is designed to be reused. Embodiments achieve a high reuse potential for structural modules through building load demand analysis, a segmental externally post-tensioned design, and an integrated optimal assignment strategy. Compared to previous work in this area, embodiments contribute an original bidirectional algorithmic approach; both the target building structure and the circular material inventory may be computationally generated to achieve versatility with minimal emissions.

[0049] Pixelframe includes of V-shaped fiber-reinforced concrete structural modules (pixels) of varying strength and local geometry. Pixels are reversibly connected in varying quantities and orientations to form a structural cross-section (member element), and axially aligned member elements are post-tensioned to form dry-jointed structural modules. The structural module's intermediate and end bearing plates are fabricated out of metallic sheets and are fully reusable, as is all connecting hardware such as cables and bolts. Pixelframe's discretized nature allows for precast modules to be assembled on site, improving the transportation and labor (assembly) logistics for the use of precast concrete modules. At the end of use, a member element can be disassembled into its constituent pixels, which can be reconfigured into new modules of diverse length, cross-section, and mechanical load-carrying capacity due to the discretized nature of the system. This research introduces at least three principles useful for success of this system: demand forecasting, segmental post-tensioned concrete design, and constrained inventory matching and target structure optimization.

[0050] Pixelframe integrates proven engineering analysis and workflows from bridge design, modern fabrication technology, and computation to develop a discrete structural system for building applications. Analysis of Pixelframe encompass one-way concrete structures (primary beams, secondary beams, and columns) with span ranges from 4-12 m, column heights of 3-5 m and a maximum of 6 stories, with application targeting mid-rise residential, commercial, and single-story industrial building typologies. Embodiments are designed to integrate with common prefabricated floor systems to maintain the discrete logic of assembly; an example being hollow-core slabs, which have been shown to be more efficient than cast-in-place slabs and present the possibility of reuse

[20] .

[0051] FIG. 1 is a diagram of a flow of renderings and photos showing an overview of an example of the Pixelframe system embodiment 100. In this embodiment, a base unit of the Pixelframe system is a single, V-shaped concrete structural module 101, or “pixel.” Example lengths of structural module 101 are 0.5 m and 1.0 m. The structural module 101 has a convex side 121a and a concave side 121b. The pixel geometry is held constant, while a fiber-reinforced concrete (FRC) mix used to make this embodiment is varied to provide a range of compressive strength (f′c) and EC (CO2e) values (both positively correlate with cement content).

[0052] Developed from a modified t-beam divided into thirds with radial symmetry, pixels may connect around a core 102a-b (“core module”) in varying quantities and orientations to form a structural cross-section (member element 103a-b), in a simple piecewise ‘sliding’ assembly. A core module 102a allowing for three structural modules 101 to be oriented radially around the core module 102a, and a core module 102b allowing for at least two structural modules 101 to be oriented radially around the core module 102b are shown.

[0053] In some embodiments, the core module 102a may be used for primary or secondary beams (“member elements”) 103b of a structure, whereas the core module 102b may be used for columns 103a of a structure 104 and 105. A primary beam 104a of a structure 104 is a primary structural member which may connect to connection nodes 104c coupled to at least one column 104b of the same structure. A secondary beam 104d is a secondary structural member which may connect to one or more primary beams 104a. A column 104b is a vertical structural support which supports the structure 104.

[0054] In some embodiments, multiple structures 104 may be coupled together, along with their respective primary beams 104a, secondary beams 104d, columns 104b, and connection nodes 104c to construct a larger structure 105.

[0055] Axially aligned member elements 103a-b are post-tensioned with both internal and / or external steel cables (not shown) to form dry-jointed, reversibly connected member elements 103a-b. Here, a conventionally fused assembly of steel and concrete is separated, allowing each material to respond independently to tensile and compressive forces without impeding longevity or function of the other. At the end of use, a member element 103a-b may be disassembled into its respective structural modules 101, core modules 102a-b, and associated hardware (not shown), which can then be reconfigured into new member elements of variable length, cross-section, and overall capacity.

[0056] FIG. 2 is a flow diagram 200 depicting a method for assembling a building structure according to embodiments implemented herein. Embodiments interconnect structural modules in a manner that enables construction and deconstruction (also referred to as “reversible construction”) of a building structure by building reversibly constructed beams 103b and columns 103a. (See FIG. 1) At least two structural modules may be interconnected 201 by orienting a convex side of each structural module toward a common axis, as described in more detail below in reference to FIGS. 3A and 3B. A portion of the structural modules 101 in coupled arrangement may be substantially parallel to, or in some embodiments, coincident with a common axis. Further, in embodiments, the convex side 121a of each structural module 101 defines a first complementary coupling feature 122a. In this embodiment, a core module 102a-b is also employed. The core module has a length and defines a second complementary coupling feature 122b along at least a portion of the length. (See FIGS. 3A and 3B and FIGS. 4A-4C) The core module 102a-b, or the structural module 101, may include concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof. The structural module's 101 composition may vary according to at least one of: cement content, fiber dosage, admixtures, aggregate content, or any combination thereof. The second complementary coupling feature 122b may be positioned on the core module 102a-b at a location that orients two or more structural modules 101 to be coupled radially around the core module 102a-b. (See FIGS. 4A-4C)

[0057] Still referring to FIG. 2, a member element 103a-b is assembled (202) by coupling and arranging at least two structural modules 101 onto a core module 102a-b. (See FIGS. 3A and 3B and FIGS. 4A-4C) This combination of the structural modules 101 and the core module 102a-b results in the member element 103a-b.

[0058] Next, still referring to FIG. 2, the structural integrity of the member element 103a-b is maintained by assembling (230) a post-tensioning assembly. (See FIG. 5, FIG. 9-FIG. 12B) The post-tensioning assembly may be assembled by coupling at least two anchors to the member element 103a-b at distinct locations, and coupling a tensile element to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis. The anchors may be end bearing plates and, in combination with the tensile element, configured to hold the structural modules 101 in coupled arrangement, i.e., as a member element 103a-b. Some embodiments also include intermediate plates (See FIG. 10B) configured to be spaced between adjacent structural modules 101 in coupled arrangement with the core module. The intermediate plates may be configured to couple to any one of: a post-tensioning element, a different member element, or a connection node component configured to couple at least two member elements. The post-tensioning assembly may further include the intermediate plates being configured to couple additional elements to a tensile element and provide external post-tensioning. (See FIG. 10A) The tensile element may include steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof. The member elements may be coupled to connection nodes, which allow multiple member elements to be coupled together. (See FIGS. 7A and 7B) A plurality of member elements may be coupled to a plurality of connection nodes and arranged to form a structure. A planar element may be configured to be coupled to the structure, the planar element may be a floor, roof, or wall. (See FIG. 7B) The planar element may include an independent interface component configured to couple the planar element to at least one member element. (See FIG. 7C)

[0059] Pixelframe embodiments are designed to be reused, addressing the poor reuse potential of precast concrete modules in the building industry today. Embodiments achieve a high reuse potential for structural modules through building load demand analysis, a segmental externally post-tensioned design, and an integrated optimal assignment strategy.

[0060] The use of discretization (modularity) in the fabrication of long-span, large-scale concrete structures dates to the mid-twentieth century, where developments in pre-stressing technology were applied to rationalize construction by linking together precast structural modules

[11] . Today, post-tensioned box girders are common in road and bridge infrastructure, but this approach is not typically used in building construction. Previous research that models these systems suggests that their flexural behavior can be understood computationally with high fidelity, and that they behave similarly to monolithic beams, allowing for an abstracted analysis of such a system [12-14].

[0061] FIGS. 3A and 3B are graphical representations 300 and 310, respectively, showing how the Pixelframe system and apparatus may assembled. FIG. 3A includes three isometric views 300a-c of three different configurations of a member element assembly. In the member element 300a, a structural module 301a is shown being slid over a core module 302. In this embodiment, the core module 302 has complementary coupling features configured to allow for two structural modules 301a-b to be oriented radially around a center axis 303a. These structural modules may be stacked to produce a member element 300a of variable length. In the member element 300b, a structural module 304a is shown being slid over a core module 305. In this embodiment, the core module 305 has complementary coupling features to allow for four structural modules 304a-d to be oriented radially around a center axis 303b. These structural modules may be stacked to produce a member element 300b of variable length. In the member element 300c, a structural module 306a is shown being slid over a core module 307. In this embodiment, the core module 307 has complementary coupling features to allow for three structural modules 308a-c to be oriented around a center axis 303c. These structural modules may be stacked to produce a member element 300c of variable length.

[0062] FIG. 3B is a graphical representation 310 of bottom views of member elements 300a-c from FIG. 3A. Specifically, FIG. 3B illustrates the shape of the core modules 302, 305, and 307, that include the complementary coupling features to adhere structural modules to the respective core modules.

[0063] FIGS. 4A-4B are graphical representations 400a-c, respectively, of isometric and top-down views of the core modules and member elements from FIGS. 3A and 3B.

[0064] Embodiments provided herein allow for several different configurations of member elements, which are enabled via core modules of different shapes. In FIG. 4A, the box column embodiment 400a is comprised of a core module 401 with four complementary coupling features 402a-d. These allow for the complementary coupling features 403a-d of the structural modules 404a-d to attach to the core module 401. In FIG. 4B, the x-column embodiment 400b is comprised of a core module 405 with two complementary coupling features 406a-b. These allow for the complementary coupling features 407a-b of the structural modules 408a-b to attach to the core module 405. In FIG. 4C, the beam embodiment is comprised of a core module 409 with three complementary coupling features 410a-c. These allow for the complementary coupling features 411a-c of the structural modules 412a-c to attach to the core module 409.

[0065] FIG. 5 is a photo 500 of a beam member element embodiment of the Pixelframe system and apparatus receiving an end bearing plate 501 during assembly. The end bearing plate 501 is coupled to the first / last set of structural modules 502a-c slid onto the core module 503 of the beam member element. The beam member element is secured in part by the tensile element 504 that, in this embodiment, is one or more threaded steel rods inserted into the core module 503 and runs the length of the member element. The tensile element 504 is then screwed into place with hardware (not shown) on both ends. This provides post-tensioning to the member element, as well as holds the structural modules 502a-c in place.

[0066] Pixelframe embodiments integrate proven engineering analysis and workflows from bridge construction and engineering, modern fabrication technology and computation to develop a discrete structural system for building applications. Embodiments present an original solution with a combination of a modular design strategy with the express goal of reuse, which informs both the design and engineering process. This analysis encompasses one-way concrete structures (primary beams, secondary beams, and columns) with span ranges from 4 meters (m) to 12 m, column heights of 3 m-5 m and a maximum of six stories, with application targeting mid-rise residential, commercial, and single-story industrial building typologies.

[0067] To determine the appropriate cross-sectional geometry and structural capacity of each pixel, a large-scale structural demand forecasting of 1000 buildings was performed, which determined the distribution of anticipated internal loads experienced by structural members. Using a database of concrete mixes that included strength, embodied carbon, and cost, the concrete chemistry and local geometry of each pixel can be customized, creating a high-resolution structural system that reduces two common issues with concrete structures: structural overdesign, and high embodied carbon.

[0068] The success of a reconfigurable structural system depends on the minimization of the number of unique components, the minimization of embodied carbon, and the maximization of the reuse potential, i.e., its versatility. To determine a suitable number of unique pixel geometries and concrete strengths and geometries, Monte Carlo sampling of typical building geometries and load combinations was performed to determine the distribution of anticipated internal loads experienced by structural members. The sampled loads are then clustered into a reduced set of design loads with a modified K-Means clustering algorithm using an asymmetric distance metric between design loads and sampled demands.

[0069] The use of a single geometry with variable mix designs allows for optimization without pre-determined span lengths or column heights, which can be a hindrance to reuse.

[0070] While this system is designed to maximize reuse potential, it also presents significant upfront CO2e savings. A comparative volumetric analysis between a conventional prismatic reinforced concrete (RC) beam and embodiments' Pixelframe primary beam demonstrates a 61% reduction in embodied CO 2e.

[0071] FIGS. 6A-6C are graphical representations of embodiments which show how several member elements may be coupled together in order to form a building structure. FIG. 6A shows two box column member elements 601a-b, with end bearing plates 606a-b and connection node components 602a-b. The beam member element 605 is also shown, with end bearing plates 604a-b that are configured to couple to connection node components 602a-b. Additionally, beam member element 605 contains an-external post-tensioning assembly 603, which provides external post-tensioning to the beam 605.

[0072] FIG. 6B shows a graphical representation of the embodiment from FIG. 6A. Specifically, FIG. 6B shows how the external post-tensioning assembly 603 may connect to an intermediate plate 608 positioned between two structural modules of a primary beam 610. The intermediate plate 608 may include a piece of the post-tensioning assembly 606 as part of the intermediate plate construction. In some embodiments, the intermediate plate may also allow for the connection of a secondary beam 609 of the structure to couple to a primary beam of the structure. (Not shown)

[0073] FIG. 6C shows a graphical representation of a profile view of a structure. FIG. 6C shows two box column member elements 611a-b, supporting a primary beam 621. The member elements 611a-b include connection node components 612a-b atop the member elements to allow for coupling to the primary beam 621. The member elements 611a-b also include intermediate plates 613a-n spaced between each structural module (not labeled for clarity), each intermediate plate 613a-n is not individually labeled for clarity. Additionally, the primary beam 621 includes intermediate plates 614a-n also spaced between each structural module, each intermediate plate 614a-n is not individually labeled for clarity. The primary beam 621 includes intermediate plates 615a-c, which are different from the remaining intermediate plates in that they contain additional elements 622a-c configured to attach to the post-tensioning system 616. FIG. 6C also includes a generic representation of a primary beam 619, with end plates 618a-b configured to couple to connection nodes, as well as a generic representation of a secondary beam 620, which h6as end plates 617a-b configured to couple to intermediate plates of a primary beam.

[0074] FIGS. 7A and 7B show a graphical representation of how member elements may be coupled to form a structure. FIG. 7A shows a structure 700. The structure 700 includes four column member elements 701a-c, four primary beams 703a-d, as well as three secondary beams 704a-c. The primary beams 703a-d are coupled by utilizing connection nodes 702a-d. The secondary beams 704a-c are coupled to primary beams 703a and 703c by respective intermediate plates having additional coupling features configured to couple secondary beams to primary beams. Primary beams 703a and 703c also include an external post-tensioning assembly 705a-b.

[0075] FIG. 7B shows an additional structure 710. The structure 710 includes columns 711, primary beams 712, secondary beams 713 and connection node components 714, similar to FIG. 7A. Structure 710 also includes a planar element 715, that in this embodiment is being utilized as a floor. In some embodiments planar elements may be utilized as a roof or a wall.

[0076] FIG. 7C shows a graphical representation 720 of how a planar element 721 may couple to a primary or secondary beam 723. In this embodiment, the planar element 721 includes a geometry 724 which is configured to couple to the shape a structural module of a primary or secondary beam 723.Demand Analysis and Regularization

[0077] Determining the number of unique concrete mixes assigned to pixels is a mediation between reuse potential, logistical complexity, and EC efficiency. A demand analysis is performed to investigate the distribution of anticipated loads across varying structural geometries and programs, and demand regularization to identify a set of representative design loads for concrete mix specification.

[0078] To determine the range and frequency of unique internal force demands, a parametric structural model was developed that includes variable bay dimensions, floor heights, number of stories, and load magnitudes. These parameters are uniformly sampled to generate 1000 framing models; the three primary internal forces (axial, shear, and moment) are then extracted from each element at 0.25 m increments, resulting in 28 million sampled force demands represented as points in 3D. Demand points are categorized by their primary structural role: secondary beams with uniformly distributed loads, primary beams with point loads at joist locations, and columns with up to a 10% eccentric axial force. These points are weighted by their frequency of occurrence, e.g., the number of beams with the same loading condition in each structure.

[0079] FIGS. 8A-8C are plots 800, 810, and 820, respectively, of demand sampling and internal force distributions for embodiments. Plot 800 shows a computer-generated building for the purpose of simulation. Plot 810 represents the internal force demands for member elements of the building in the simulation. Plot 810 compares the moment 811 (rotational force when a perpendicular pressure is applied), the shear force 812 and the axial pressure 813 of a beam in the simulation. Plot 820 represents the beam demands for primary and secondary beams, plotting the moment 821 against the shear force 822.

[0080] The sampled data is reduced to a set of n representative design loads for concrete mix specification through an asymmetric distance clustering algorithm. As the cluster “center” is considered the representative load for all demand conditions within the cluster, it must necessarily be the supremum of all load values within the set. This contrasts with conventional clustering algorithms such as K-means, which takes the geometric mean of a cluster as its center, consequently setting a design load that does not fully cover the entire group. A modified version of the asymmetric Expectile Regression loss function

[18] is used as the basis for clustering.

[0081] These representative demands are the basis for capacity analysis and optimal concrete mix design. The distance from a demand point to its cluster center is a proxy for the degree of overdesign caused by assigning a higher-than-necessary capacity. As the capacity of a pixel is directly tied to concrete mix, it is also a measure of the excess EC associated with assignment. The choice of the number of unique concrete mixes is then a decision left to the stakeholders-designers, fabricators, building owners-based on an acceptable compromise between overdesign and logistical complexity.Engineering Analysis

[0082] Embodiments are original in their combination of a modular design strategy with the express goal of reuse, which informs both the design and engineering process. To ensure the safety and serviceability of the structural system, the engineering analysis is based on ACI 318-19

[20] code standards, with FRC providing the required shear demand, calculated from fib Model Code 2010

[21] . FRC eliminates embedded steel reinforcement which improves durability

[22] and extends module lifespans. The system is categorized into three types of member elements: secondary beams, primary beams, and columns.

[0083] The secondary beams, where shear and flexural forces are dominant, are idealized as simply supported beams with uniform loads from the floor system. The shear capacity is provided by FRC, and the flexural capacity is analyzed based on the ultimate post-tensioned stress under the equations in ACI table 20.3.2.4.1

[21] . Moment-axial force diagrams are used to determine the ultimate axial and flexural strength of the concrete section, which are calculated based on existing standards. Currently, the eccentricity of the post-tensioned system of the primary beams is determined by the physical constraints of the available space below the beams, but it is possible to vary the eccentricity to give flexibility to the section capacity. While columns have less eccentricity and different cross sections from the primary beams, they follow the same behavioral assumptions.

[0084] There are many models that can be used to predict the force-deflection behavior of externally post-tensioned beams

[24] . In half-scale load testing of a primary beam, the load-deflection curve could be accurately described by assuming virtual cracks between the structural modules of the member element due to the segmental nature of the beam. Therefore, the elastic post-cracking and the effective moment of inertia model proposed by Ng and Tan

[13] were chosen to calculate the curve. The half-scale test results also suggest that the segmental design of the beam mitigates cracking in the loading stage through strain localization at the dry joints, improving the long-term durability of Pixelframe embodiments (thorough exposition of physical testing of the Pixelframe system is reserved for future publications).

[0085] FIG. 9 shows a graphical representation of a primary beam 900 and associated external post-tensioning assembly. The primary beam 900 includes two end bearing plats 901a-b, which are configured to support the external post-tensioning assembly at the ends of the beam 900. Intermediate plates 904a-b are spaced at distinct intervals and include support members 903a-b of the post-tensioning assembly, which allow for the appropriate angle on the tensile element 902. The tensile element 902 may be steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof. The primary beam 900 also includes intermediate plates 905a-n between each set of structural modules 906a-n, each structural module is not labeled for clarity, which are different than intermediate plates 904a-b in that they do not include the support members for the external post-tensioning assembly. Though an intermediate plate is spaced between each set of structural modules, each intermediate plate is not labeled for clarity.

[0086] FIGS. 10A and 10B are photos 1001 and 1002 of the external post-tensioning assembly. Photo 1001 shows a primary beam 1002 with an external post-tensioning assembly. The assembly includes the tensile element 1003, as well as the intermediate plates 1004a-c which are configured to support the tensile element. FIG. 10B shows a photo 1002 of a side of the primary beam 1002 from photo 1001. The tensile element 1003 is coupled to hardware 1005 which connects to the end bearing plate 1006. An intermediate plate 1007 which is not used to support the external post-tensioning assembly is also shown.

[0087] FIGS. 11A and 11B are graphical representations of both the internal and external post-tensioning assemblies for a primary beam 1110 and a secondary beam 1100. FIG. 11A shows a secondary beam 1100. The secondary beam 1100 is internally post-tensioned via a tensile element 1101 connected to an end bearing plate 1105 and secured with associated hardware 1102. Additionally, the secondary beam 1100 is externally post-tensioned via a tensile element 1103 and associated hardware 1104. It should be noted that the secondary beam 1100 is also similarly secured and connected at a second end of the beam, which is not shown for clarity. The end bearing plate 1105 is configured to attach to an intermediate plate of a primary beam.

[0088] FIG. 11B shows a primary beam 1110. The primary beam 1110 is internally post-tensioned via a tensile element 1111 connected to an end bearing plate 1115 and secured with associated hardware 1112. Additionally, the primary beam 1110 is externally post-tensioned via a tensile element 1113 and associated hardware 1114. It should be noted that the primary beam 1110 is also similarly secured and connected at a second end of the beam, which is not shown for clarity. The end bearing plate 1115 is configured to attach to a connection node component.

[0089] FIGS. 12A and 12B are graphical representations 1200 and 1210, respectively, highlighting the differences in external post-tensioning between primary and secondary beams. FIG. 12A shows primary beam 1200 including internal axial post-tensioning 1201 and external deviated post-tensioning 1202. FIG. 12B shows secondary beam 1210 including internal axial post-tensioning 1211 and external axial post-tensioning 1212.High Resolution, Semi-Constrained Inventory Assignment

[0090] To design a structure with Pixelframe embodiments, a design tool was created to solve a balanced assignment problem between the strength capacities of a pixel inventory and the demands of an interactive, discretized structural framing model, while minimizing EC and maximizing average structural utilization (avg. util). Traditional structural design is iterative and specific, with design decisions made case by case—the design process itself must adapt to support flexible, adaptable, reusable systems

[10] . In a circular building economy, building parameters such as spans and floor heights become variables to optimize matches between pixel inventory and structural demand.

[0091] Users input a building footprint and set design constraints to define all possible structural configurations and determine constraints such as bay spacing, column height and secondary span. The structural demands of potential target structures may not always be supported by inventory pixels; to eliminate structural underdesign, new perfect-match pixels are added, generating a semi-constrained inventory. The EC of all pixels is calculated using an estimation of kgCO2e based on percent cement content. For reused pixels, a small portion of their EC is used as a proxy for the carbon associated with deconstruction and transportation.

[0092] All possible 3D models within the design space are generated, divided into segments, and undergo a finite element analysis using, for example, Karamba3D. From this analysis, structural demands under the governing load combination and translate demands are extracted into optimal concrete strengths for each structural module. To compare inventory to demand, the Hungarian matching algorithm

[25] is used with a custom combined cost matrix that acts as a single objective proxy of the two primary design goals: maximizing average utilization and minimizing EC. The resultant matching score is used to generate matching indices, which assign inventory structural modules to demand locations. Using optimization, the lowest carbon, highest average utilization solution within the given user-input parameters can be located within the design space. The adjustable, semi-constrained inventory developed for this design method prioritizes the use of existing pixels while allowing for the introduction of new pixels with a higher EC cost, managed by a user input that determines the frequency with which new structural modules are introduced.

[0093] FIG. 13 is a graphical representation 1300 of a comparison of reconfiguration potential, utilization and EC across different approaches. Representation 1300 shows three approaches, prismatic cast on-site 1301, Pixelframe single mix 1302, and Pixelframe using ten unique mixes 1303 for a first structure 1304 and a second structure 1305. The second structure 1305 embodies the deconstruction of the first structure 1304 and subsequent construction of a second structure 1305.

[0094] Building with reusable structural modules can present a trade-off between design freedom and embodied carbon: the Pixelframe system is developed to maintain flexibility and efficiency while maximizing reuse potential. Up front, the system allows for a 77% reduction in EC in comparison to typical cast on-site RC frame construction. The modular, adaptable design strategy enables the specification of structural modules with variable compressive strength capacities and is informed by statistical analysis of common internal load demands to ensure that high strength, high carbon pixels are only assigned where needed, optimizing the distribution of EC within the structure. Preliminary flexural testing shows structural behavior can be effectively represented by linear elastic post-crack models. These virtual cracks between pixel segments eliminate localized damage and ensures prolongation of structural life. In combination, these strategies enable the reuse of precast components in diverse loading and geometric conditions, making possible even higher CO2e savings in future life cycles.

[0095] It should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific implementations described above. The specific implementations described above are disclosed as examples only.REFERENCES[1] Van Damme H 2018 Concrete material science: Past, present, and future innovations Cem Concr Res 112 5-24

[0097] [2] Favier A, De Wolf C, Scrivener K and Habert G 2018 A sustainable future for the European Cement and Concrete Industry: Technology assessment for full decarbonisation of the industry by 2050 (ETH Zurich)

[0098] [3] Marsh ATM, Velenturf APM and Bernal SA 2022 Circular Economy strategies for concrete: implementation and integration J Clean Prod 362 132486

[0099] [4] Zhang C, Hu M, Yang X, Miranda-Xicotencatl B, Sprecher B, Di Maio F, et al 2020 Upgrading construction and demolition waste management from downcycling to recycling in the Netherlands J Clean Prod 266 121718

[0100] [5] Margareta Wahlstrüm, Jef Bergmans, Tuuli Teittinen, John Bachér, Anse Smeets and Anne Paduart 2020 Construction and Demolition Waste: challenges and opportunities in a circular economy European Environment Agency

[0101] [6] Bertin I, Saadé M, Le Roy R, Jaeger J-M, and Feraille A 2022 Environmental impacts of Design for Reuse practices in the building sector JClean Prod 349 131228

[0102] [7] Ismail MA and Mueller CT 2021 Minimizing embodied energy of reinforced concrete floor systems in developing countries through shape optimization Eng Struct 246 112955.

[0103] [8] Lopez D, Veenendaal D, Akbarzadeh M and Block P 2014 Prototype of an ultra-thin, concrete vaulted floor system Proceedings of the UASS-SLTE Symposium (Brasilia)

[0104] [9] Brütting J, Senatore G, Schevenels M, and Fivet C 2020 Optimum Design of Frame Structures From a Stock of Reclaimed Elements Front Built Environ 6 57

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[10] Gorgolewski M 2008 Designing with reused building components: some challenges Build Res Inf 36 175-88

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[11] G Sauvageot 2000 Segmental Concrete Bridges in Bridge Engineering Handbook ed Chen WF and Duan L (Boca Raton CRC Press) 236-87

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[12] Eakarat W, Aravinthan T, Mutsuyoshi H and Watanabe M 2000 Analysis of the Flexural Behavior of Externally Prestressed Concrete Beams with Large Eccentricities Jpn Concr Inst 22 817-22

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[13] Aravinthan T, Mutsuyoshi H, Niitsu T and Chen A 1998 Flexural Behavior of Externally Prestressed Beams with Large Eccentricities Jpn Concr Inst 20 673-8

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[15] Flory S, and Pottmann H 2010 Ruled Surfaces for Rationalization and Design in Architecture Proceedings to Acadia 2010 (New York USA) 103-9

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[17] Koronaki A, Shepherd P and Evernden M 2020 Rationalization of freeform space-frame structures: Reducing variability in the joints. Int J Archit Comput 18 84-99

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[20] Wang J, Tingley DD, Mayfield M, Wang Y 2018 Life cycle impact comparison of different concrete floor slabs considering uncertainty and sensitivity analysis. J Clean Prod 189 374-85.

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[21] ACI Committee 318 2019 Building Code Requirements for Structural Concrete and Commentary

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[22] ACI Committee 544 2018 Guide to design with fiber-reinforced concrete

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[23] Ahmad J, González-Lezcano RA, Majdi A, Ben Kahla N, Deifalla AF and El-Shorbagy MA, 2022 Glass Fibers Reinforced Concrete: Overview on Mechanical, Durability and Microstructure Analysis Materials 15 5111

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[24] Alqam M and Alkhairi F 2019 Numerical and Analytical Behavior of Beams Prestressed with Unbonded Internal or External Steel Tendons: A State-of-the-Art Review Arab J Sci Eng 44 8149-70

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[25] Kuhn HW 1955 The Hungarian method for the assignment problem Nav Res Logist Q 2 83-97

[0121] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[0122] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Examples

Embodiment Construction

[0044]A description of example embodiments follows.

[0045]Demand to build structures, such as housing, for a growing urban population is in conflict with a preference to reduce contributions to global CO2 emissions from the Architectural Engineering and Construction (AEC) sector. Structural systems are a factor in this challenge, as they contribute substantially to a building's mass and are typically overdesigned. Two strategies for reducing the embodied carbon of structural systems are (i) geometric optimization, which can reduce structural mass but limits reusability, and (ii) circular material reuse, which is most successful when building components are standardized, often resulting in poor utilization.

[0046]To improve reuse potential while maintaining flexibility and efficiency, embodiments of the present invention leverage standardization and optimization by discretizing structural modules into precast modules with variable mix designs. An algorithmic design strategy may be impl...

RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 499,222 filed on Apr. 29, 2023. The entire teachings of the above application are incorporated herein by reference.BACKGROUND

[0002] Concrete is one of the most common building materials, with demand expected to rise due to a growing urban population. Cementitious materials are responsible for 8% of anthropogenic greenhouse gas emissions, over 60% of which result from the energy-intensive process of cement production-about half of which is used in the construction of buildings, which are typically overdesigned [2]. Despite its ubiquity, concrete is perceived as a low-value material, accounting for 80% of construction and demolition waste by weight [3,4]. Most of this waste is downcycled in an energy-intensive process [5], despite its reuse potential, especially for concrete of high compressive strength [6].

[0003] In recent years, interest in the geometric computational optimization of structural modules has grown. Material savings of upwards of 60% can be accomplished by using computation to optimize floor slabs [7, 8]. Computation has also gained traction as a strategy to facilitate salvage reuse, emphasizing the introduction of irregular, non-standard or waste materials into a constrained design process [9]. ‘Design for reuse’ has been posited as a strategy for the reduction of embodied carbon (EC) in structural modules [6,10] but reusability often ends at demountability, without any other consideration of future use cases.

[0004] Research on the reduction or replacement of cement content is relatively mature, yet recent work suggests that equally significant carbon savings exist along the rest of the value chain [2]. Two promising approaches are material reduction, which uses computation to optimally allocate material, and circularity, a strategy to reduce EC through reuse. However, these two strategies are often mutually exclusive, as optimization produces highly specific elements that are difficult to reuse outside of identical geometric and loading scenarios, and circularity demands a degree of standardization for components to be reusable, creating a tradeoff between flexibility and efficiency.SUMMARY

[0005] Embodiments relate to a unique geometry, with varying concrete strength, arranged in some configurations around a core to form distinct column and beam cross-sections that are stacked and internally axially post-tensioned to ensure monolithic behavior.

[0006] An example embodiment is directed to an apparatus for use in a building structure. The apparatus includes at least two structural modules, each having a convex side oriented toward a common axis and a concave side oriented away from the common axis. The apparatus also includes a member element defined by the at least two structural modules in coupled arrangement, the member element comprising a first end and a second end. The member includes a post-tensioning assembly including: (i) at least two anchors coupled to the member element at distinct locations at or between the first end and the second end; and (ii) a tensile element coupled to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors. The post-tensioning force has a force substantially in parallel with or coincident with the common axis. For brevity, “along the common axis” is used herein to refer to either or both locations of the force as is relative to the common axis.

[0007] In another embodiment, the convex side of each structural module defines a first complementary coupling feature. The apparatus further includes a core module having a length, the core module defining a second complementary coupling feature along at least a portion of the length. The member element is further defined by the core module in coupled arrangement with the structural modules via the first and second complementary coupling features.

[0008] In another embodiment, intermediate plates are configured to be spaced between adjacent structural modules and in coupled arrangement with the core module.

[0009] In still another embodiment, the intermediate plates are configured to couple to any one of: a post-tensioning element, a different member element, or a connection node configured to couple at least two member elements.

[0010] In another embodiment, the post-tensioning assembly further includes the intermediate plate that is configured to couple additional elements to a tensile element and provide external post-tensioning.

[0011] In a further embodiment, the second complementary coupling feature is positioned on or defined by the core module at a location that orients two or more structural modules to be coupled radially around the core module.

[0012] In another embodiment, the core module includes concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

[0013] In still another embodiment, the tensile element includes steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof.

[0014] In another embodiment, the at least two anchors are coupled to end bearing plates and, in combination with the tensile element, are configured to hold the structural modules in coupled arrangement.

[0015] In another embodiment, the structural module consists of concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

[0016] In yet another embodiment, the structural module's composition varies according to at least one of: cement content, fiber dosage, admixtures, aggregate content, or any combination thereof.

[0017] Another embodiment includes a connection node component configured to couple multiple member elements together to form a connection node.

[0018] Another embodiment includes a plurality of member elements coupled to a plurality of connection node components arranged to form a structure.

[0019] Another embodiment includes at least one planar element configured to be coupled to the structure, the at least one planar element, in coupled arrangement with the structure, defining at least one of a floor, roof, or wall.

[0020] In an embodiment, the planar element further comprises an independent interface component configured to couple the planar element to at least one member element.

[0021] Another example embodiment is directed toward a method of assembling a building structure. The method includes orienting a convex side of a structural module toward a common axis and orienting a concave side of the structural moule away from the common axis. The method further includes coupling and arranging at least two structural modules to define a member element, the member element having a first end and a second end. The method also includes assembling a post-tensioning assembly by: (i) coupling at least two anchors to the member element at distinct locations at or between the first and the second end, and (ii) coupling a tensile element to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis.

[0022] In an embodiment, the convex side of each structural module defines a first complementary coupling feature, the method further includes coupling the first complementary coupling feature of each structural module to a core module coupled thereto or defining (“having” as used herein covering either or both cases) a second complementary coupling feature and a length, wherein the second complementary coupling feature is along at least a portion of the length. The method further includes coupling and arranging the core module with the structural modules via the first and second complementary coupling features to compose the member element.

[0023] In another embodiment, the method further includes spacing intermediate plates between adjacent structural modules, which in some embodiments is in coupled arrangement with the core module.

[0024] In another embodiment, the method further includes spacing intermediate plates between adjacent structural modules, in coupled arrangement with the core module.

[0025] Yet another embodiment is directed to an apparatus for use in a building structure. The apparatus providing means for interconnecting structural modules in a manner that enables reversible construction. The apparatus also providing means for assembling of a member element with at least two structural modules. The apparatus further providing means for applying post-tensioning for maintaining structural integrity of the member element.

[0026] In an embodiment, the structural modules have a concave side and a convex side. The apparatus further includes means for coupling the structural modules together with at least two adjacent structural modules. The structural modules having respective convex sides oriented toward a common axis, and respective concave sides oriented away from the common axis.

[0027] It is noted that the apparatus, means for building a structure, and method of building a structure may be configured to implement any embodiments, or combinations of embodiments, described herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0029] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0030] FIG. 1 is a diagram of a flow of graphical renderings and photos showing an overview of an example “Pixelframe” embodiment of at least two structural modules and a post-tensioning assembly that defines a Pixelframe system embodiment.

[0031] FIG. 2 is a flow diagram for an apparatus for use in a building structure, according to embodiments.

[0032] FIGS. 3A-3B are graphical representations showing how the Pixelframe system and apparatus may assembled, according to embodiments.

[0033] FIGS. 4A-4C are graphical representations of isometric and top-down views of the core modules and member elements, according to embodiments.

[0034] FIG. 5 is a photo showing an end bearing plate and tensile element being coupled to a structural module, according to an embodiment.

[0035] FIGS. 6A-6C are graphical representations of embodiments that show how several member elements may be coupled together in order to form a building structure.

[0036] FIGS. 7A and 7B show a graphical representation of how member elements may be coupled to form a structure, according to embodiments.

[0037] FIG. 7C is a graphical representation of a geometry of a planar element configured to couple to a member element, according to an embodiment.

[0038] FIGS. 8A-8C are plots of demand sampling and internal force distributions for embodiments.

[0039] FIG. 9 is a graphical representation of a primary beam and associated external post-tensioning assembly.

[0040] FIGS. 10A and 10B are photos of the external post-tensioning assembly for embodiments.

[0041] FIGS. 11A and 11B are graphical representations of both the internal and external post-tensioning systems for a primary beam and a secondary beam, according to embodiments.

[0042] FIGS. 12A and 12B are graphical representations highlighting the differences in external post-tensioning between primary and secondary beams in embodiments.

[0043] FIG. 13 is a graphical representation of a comparison of reconfiguration potential, utilization and EC across different approaches.DETAILED DESCRIPTION

[0044] A description of example embodiments follows.

[0045] Demand to build structures, such as housing, for a growing urban population is in conflict with a preference to reduce contributions to global CO2 emissions from the Architectural Engineering and Construction (AEC) sector. Structural systems are a factor in this challenge, as they contribute substantially to a building's mass and are typically overdesigned. Two strategies for reducing the embodied carbon of structural systems are (i) geometric optimization, which can reduce structural mass but limits reusability, and (ii) circular material reuse, which is most successful when building components are standardized, often resulting in poor utilization.

[0046] To improve reuse potential while maintaining flexibility and efficiency, embodiments of the present invention leverage standardization and optimization by discretizing structural modules into precast modules with variable mix designs. An algorithmic design strategy may be implemented and allows for a discrete optimization approach that can meet demands of variable load cases, utilizes element types and spans with one base geometry, resulting in a system and apparatus that is reversible and reconfigurable. The system may utilize a data-driven approach to determine design loads and criteria, and a bidirectional algorithmic approach to match precast modules to optimized building frames.

[0047] The selection of unique concrete mixes for open-ended design applications is informed by the rationalization of anticipated structural demands across varying structural geometries and building programs. Rationalization in structural design is most often deployed in the context of manufacturing and procurement complexity reduction [15-17]. To extend this process to the rationalization of structural demands, embodiments build upon metrics and clustering algorithms that consider the directions of comparisons between structural demand and module capacity [18,19].

[0048] Disclosed herein are embodiments directed to an apparatus for use in a building structure which uses structural modules (herein referred to as “Pixels”) in a system referred to as to as “Pixelframe.” Embodiments implement a new precast concrete structural system that is designed to be reused. Embodiments achieve a high reuse potential for structural modules through building load demand analysis, a segmental externally post-tensioned design, and an integrated optimal assignment strategy. Compared to previous work in this area, embodiments contribute an original bidirectional algorithmic approach; both the target building structure and the circular material inventory may be computationally generated to achieve versatility with minimal emissions.

[0049] Pixelframe includes of V-shaped fiber-reinforced concrete structural modules (pixels) of varying strength and local geometry. Pixels are reversibly connected in varying quantities and orientations to form a structural cross-section (member element), and axially aligned member elements are post-tensioned to form dry-jointed structural modules. The structural module's intermediate and end bearing plates are fabricated out of metallic sheets and are fully reusable, as is all connecting hardware such as cables and bolts. Pixelframe's discretized nature allows for precast modules to be assembled on site, improving the transportation and labor (assembly) logistics for the use of precast concrete modules. At the end of use, a member element can be disassembled into its constituent pixels, which can be reconfigured into new modules of diverse length, cross-section, and mechanical load-carrying capacity due to the discretized nature of the system. This research introduces at least three principles useful for success of this system: demand forecasting, segmental post-tensioned concrete design, and constrained inventory matching and target structure optimization.

[0050] Pixelframe integrates proven engineering analysis and workflows from bridge design, modern fabrication technology, and computation to develop a discrete structural system for building applications. Analysis of Pixelframe encompass one-way concrete structures (primary beams, secondary beams, and columns) with span ranges from 4-12 m, column heights of 3-5 m and a maximum of 6 stories, with application targeting mid-rise residential, commercial, and single-story industrial building typologies. Embodiments are designed to integrate with common prefabricated floor systems to maintain the discrete logic of assembly; an example being hollow-core slabs, which have been shown to be more efficient than cast-in-place slabs and present the possibility of reuse

[20] .

[0051] FIG. 1 is a diagram of a flow of renderings and photos showing an overview of an example of the Pixelframe system embodiment 100. In this embodiment, a base unit of the Pixelframe system is a single, V-shaped concrete structural module 101, or “pixel.” Example lengths of structural module 101 are 0.5 m and 1.0 m. The structural module 101 has a convex side 121a and a concave side 121b. The pixel geometry is held constant, while a fiber-reinforced concrete (FRC) mix used to make this embodiment is varied to provide a range of compressive strength (f′c) and EC (CO2e) values (both positively correlate with cement content).

[0052] Developed from a modified t-beam divided into thirds with radial symmetry, pixels may connect around a core 102a-b (“core module”) in varying quantities and orientations to form a structural cross-section (member element 103a-b), in a simple piecewise ‘sliding’ assembly. A core module 102a allowing for three structural modules 101 to be oriented radially around the core module 102a, and a core module 102b allowing for at least two structural modules 101 to be oriented radially around the core module 102b are shown.

[0053] In some embodiments, the core module 102a may be used for primary or secondary beams (“member elements”) 103b of a structure, whereas the core module 102b may be used for columns 103a of a structure 104 and 105. A primary beam 104a of a structure 104 is a primary structural member which may connect to connection nodes 104c coupled to at least one column 104b of the same structure. A secondary beam 104d is a secondary structural member which may connect to one or more primary beams 104a. A column 104b is a vertical structural support which supports the structure 104.

[0054] In some embodiments, multiple structures 104 may be coupled together, along with their respective primary beams 104a, secondary beams 104d, columns 104b, and connection nodes 104c to construct a larger structure 105.

[0055] Axially aligned member elements 103a-b are post-tensioned with both internal and / or external steel cables (not shown) to form dry-jointed, reversibly connected member elements 103a-b. Here, a conventionally fused assembly of steel and concrete is separated, allowing each material to respond independently to tensile and compressive forces without impeding longevity or function of the other. At the end of use, a member element 103a-b may be disassembled into its respective structural modules 101, core modules 102a-b, and associated hardware (not shown), which can then be reconfigured into new member elements of variable length, cross-section, and overall capacity.

[0056] FIG. 2 is a flow diagram 200 depicting a method for assembling a building structure according to embodiments implemented herein. Embodiments interconnect structural modules in a manner that enables construction and deconstruction (also referred to as “reversible construction”) of a building structure by building reversibly constructed beams 103b and columns 103a. (See FIG. 1) At least two structural modules may be interconnected 201 by orienting a convex side of each structural module toward a common axis, as described in more detail below in reference to FIGS. 3A and 3B. A portion of the structural modules 101 in coupled arrangement may be substantially parallel to, or in some embodiments, coincident with a common axis. Further, in embodiments, the convex side 121a of each structural module 101 defines a first complementary coupling feature 122a. In this embodiment, a core module 102a-b is also employed. The core module has a length and defines a second complementary coupling feature 122b along at least a portion of the length. (See FIGS. 3A and 3B and FIGS. 4A-4C) The core module 102a-b, or the structural module 101, may include concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof. The structural module's 101 composition may vary according to at least one of: cement content, fiber dosage, admixtures, aggregate content, or any combination thereof. The second complementary coupling feature 122b may be positioned on the core module 102a-b at a location that orients two or more structural modules 101 to be coupled radially around the core module 102a-b. (See FIGS. 4A-4C)

[0057] Still referring to FIG. 2, a member element 103a-b is assembled (202) by coupling and arranging at least two structural modules 101 onto a core module 102a-b. (See FIGS. 3A and 3B and FIGS. 4A-4C) This combination of the structural modules 101 and the core module 102a-b results in the member element 103a-b.

[0058] Next, still referring to FIG. 2, the structural integrity of the member element 103a-b is maintained by assembling (230) a post-tensioning assembly. (See FIG. 5, FIG. 9-FIG. 12B) The post-tensioning assembly may be assembled by coupling at least two anchors to the member element 103a-b at distinct locations, and coupling a tensile element to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis. The anchors may be end bearing plates and, in combination with the tensile element, configured to hold the structural modules 101 in coupled arrangement, i.e., as a member element 103a-b. Some embodiments also include intermediate plates (See FIG. 10B) configured to be spaced between adjacent structural modules 101 in coupled arrangement with the core module. The intermediate plates may be configured to couple to any one of: a post-tensioning element, a different member element, or a connection node component configured to couple at least two member elements. The post-tensioning assembly may further include the intermediate plates being configured to couple additional elements to a tensile element and provide external post-tensioning. (See FIG. 10A) The tensile element may include steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof. The member elements may be coupled to connection nodes, which allow multiple member elements to be coupled together. (See FIGS. 7A and 7B) A plurality of member elements may be coupled to a plurality of connection nodes and arranged to form a structure. A planar element may be configured to be coupled to the structure, the planar element may be a floor, roof, or wall. (See FIG. 7B) The planar element may include an independent interface component configured to couple the planar element to at least one member element. (See FIG. 7C)

[0059] Pixelframe embodiments are designed to be reused, addressing the poor reuse potential of precast concrete modules in the building industry today. Embodiments achieve a high reuse potential for structural modules through building load demand analysis, a segmental externally post-tensioned design, and an integrated optimal assignment strategy.

[0060] The use of discretization (modularity) in the fabrication of long-span, large-scale concrete structures dates to the mid-twentieth century, where developments in pre-stressing technology were applied to rationalize construction by linking together precast structural modules

[11] . Today, post-tensioned box girders are common in road and bridge infrastructure, but this approach is not typically used in building construction. Previous research that models these systems suggests that their flexural behavior can be understood computationally with high fidelity, and that they behave similarly to monolithic beams, allowing for an abstracted analysis of such a system [12-14].

[0061] FIGS. 3A and 3B are graphical representations 300 and 310, respectively, showing how the Pixelframe system and apparatus may assembled. FIG. 3A includes three isometric views 300a-c of three different configurations of a member element assembly. In the member element 300a, a structural module 301a is shown being slid over a core module 302. In this embodiment, the core module 302 has complementary coupling features configured to allow for two structural modules 301a-b to be oriented radially around a center axis 303a. These structural modules may be stacked to produce a member element 300a of variable length. In the member element 300b, a structural module 304a is shown being slid over a core module 305. In this embodiment, the core module 305 has complementary coupling features to allow for four structural modules 304a-d to be oriented radially around a center axis 303b. These structural modules may be stacked to produce a member element 300b of variable length. In the member element 300c, a structural module 306a is shown being slid over a core module 307. In this embodiment, the core module 307 has complementary coupling features to allow for three structural modules 308a-c to be oriented around a center axis 303c. These structural modules may be stacked to produce a member element 300c of variable length.

[0062] FIG. 3B is a graphical representation 310 of bottom views of member elements 300a-c from FIG. 3A. Specifically, FIG. 3B illustrates the shape of the core modules 302, 305, and 307, that include the complementary coupling features to adhere structural modules to the respective core modules.

[0063] FIGS. 4A-4B are graphical representations 400a-c, respectively, of isometric and top-down views of the core modules and member elements from FIGS. 3A and 3B.

[0064] Embodiments provided herein allow for several different configurations of member elements, which are enabled via core modules of different shapes. In FIG. 4A, the box column embodiment 400a is comprised of a core module 401 with four complementary coupling features 402a-d. These allow for the complementary coupling features 403a-d of the structural modules 404a-d to attach to the core module 401. In FIG. 4B, the x-column embodiment 400b is comprised of a core module 405 with two complementary coupling features 406a-b. These allow for the complementary coupling features 407a-b of the structural modules 408a-b to attach to the core module 405. In FIG. 4C, the beam embodiment is comprised of a core module 409 with three complementary coupling features 410a-c. These allow for the complementary coupling features 411a-c of the structural modules 412a-c to attach to the core module 409.

[0065] FIG. 5 is a photo 500 of a beam member element embodiment of the Pixelframe system and apparatus receiving an end bearing plate 501 during assembly. The end bearing plate 501 is coupled to the first / last set of structural modules 502a-c slid onto the core module 503 of the beam member element. The beam member element is secured in part by the tensile element 504 that, in this embodiment, is one or more threaded steel rods inserted into the core module 503 and runs the length of the member element. The tensile element 504 is then screwed into place with hardware (not shown) on both ends. This provides post-tensioning to the member element, as well as holds the structural modules 502a-c in place.

[0066] Pixelframe embodiments integrate proven engineering analysis and workflows from bridge construction and engineering, modern fabrication technology and computation to develop a discrete structural system for building applications. Embodiments present an original solution with a combination of a modular design strategy with the express goal of reuse, which informs both the design and engineering process. This analysis encompasses one-way concrete structures (primary beams, secondary beams, and columns) with span ranges from 4 meters (m) to 12 m, column heights of 3 m-5 m and a maximum of six stories, with application targeting mid-rise residential, commercial, and single-story industrial building typologies.

[0067] To determine the appropriate cross-sectional geometry and structural capacity of each pixel, a large-scale structural demand forecasting of 1000 buildings was performed, which determined the distribution of anticipated internal loads experienced by structural members. Using a database of concrete mixes that included strength, embodied carbon, and cost, the concrete chemistry and local geometry of each pixel can be customized, creating a high-resolution structural system that reduces two common issues with concrete structures: structural overdesign, and high embodied carbon.

[0068] The success of a reconfigurable structural system depends on the minimization of the number of unique components, the minimization of embodied carbon, and the maximization of the reuse potential, i.e., its versatility. To determine a suitable number of unique pixel geometries and concrete strengths and geometries, Monte Carlo sampling of typical building geometries and load combinations was performed to determine the distribution of anticipated internal loads experienced by structural members. The sampled loads are then clustered into a reduced set of design loads with a modified K-Means clustering algorithm using an asymmetric distance metric between design loads and sampled demands.

[0069] The use of a single geometry with variable mix designs allows for optimization without pre-determined span lengths or column heights, which can be a hindrance to reuse.

[0070] While this system is designed to maximize reuse potential, it also presents significant upfront CO2e savings. A comparative volumetric analysis between a conventional prismatic reinforced concrete (RC) beam and embodiments' Pixelframe primary beam demonstrates a 61% reduction in embodied CO 2e.

[0071] FIGS. 6A-6C are graphical representations of embodiments which show how several member elements may be coupled together in order to form a building structure. FIG. 6A shows two box column member elements 601a-b, with end bearing plates 606a-b and connection node components 602a-b. The beam member element 605 is also shown, with end bearing plates 604a-b that are configured to couple to connection node components 602a-b. Additionally, beam member element 605 contains an-external post-tensioning assembly 603, which provides external post-tensioning to the beam 605.

[0072] FIG. 6B shows a graphical representation of the embodiment from FIG. 6A. Specifically, FIG. 6B shows how the external post-tensioning assembly 603 may connect to an intermediate plate 608 positioned between two structural modules of a primary beam 610. The intermediate plate 608 may include a piece of the post-tensioning assembly 606 as part of the intermediate plate construction. In some embodiments, the intermediate plate may also allow for the connection of a secondary beam 609 of the structure to couple to a primary beam of the structure. (Not shown)

[0073] FIG. 6C shows a graphical representation of a profile view of a structure. FIG. 6C shows two box column member elements 611a-b, supporting a primary beam 621. The member elements 611a-b include connection node components 612a-b atop the member elements to allow for coupling to the primary beam 621. The member elements 611a-b also include intermediate plates 613a-n spaced between each structural module (not labeled for clarity), each intermediate plate 613a-n is not individually labeled for clarity. Additionally, the primary beam 621 includes intermediate plates 614a-n also spaced between each structural module, each intermediate plate 614a-n is not individually labeled for clarity. The primary beam 621 includes intermediate plates 615a-c, which are different from the remaining intermediate plates in that they contain additional elements 622a-c configured to attach to the post-tensioning system 616. FIG. 6C also includes a generic representation of a primary beam 619, with end plates 618a-b configured to couple to connection nodes, as well as a generic representation of a secondary beam 620, which h6as end plates 617a-b configured to couple to intermediate plates of a primary beam.

[0074] FIGS. 7A and 7B show a graphical representation of how member elements may be coupled to form a structure. FIG. 7A shows a structure 700. The structure 700 includes four column member elements 701a-c, four primary beams 703a-d, as well as three secondary beams 704a-c. The primary beams 703a-d are coupled by utilizing connection nodes 702a-d. The secondary beams 704a-c are coupled to primary beams 703a and 703c by respective intermediate plates having additional coupling features configured to couple secondary beams to primary beams. Primary beams 703a and 703c also include an external post-tensioning assembly 705a-b.

[0075] FIG. 7B shows an additional structure 710. The structure 710 includes columns 711, primary beams 712, secondary beams 713 and connection node components 714, similar to FIG. 7A. Structure 710 also includes a planar element 715, that in this embodiment is being utilized as a floor. In some embodiments planar elements may be utilized as a roof or a wall.

[0076] FIG. 7C shows a graphical representation 720 of how a planar element 721 may couple to a primary or secondary beam 723. In this embodiment, the planar element 721 includes a geometry 724 which is configured to couple to the shape a structural module of a primary or secondary beam 723.Demand Analysis and Regularization

[0077] Determining the number of unique concrete mixes assigned to pixels is a mediation between reuse potential, logistical complexity, and EC efficiency. A demand analysis is performed to investigate the distribution of anticipated loads across varying structural geometries and programs, and demand regularization to identify a set of representative design loads for concrete mix specification.

[0078] To determine the range and frequency of unique internal force demands, a parametric structural model was developed that includes variable bay dimensions, floor heights, number of stories, and load magnitudes. These parameters are uniformly sampled to generate 1000 framing models; the three primary internal forces (axial, shear, and moment) are then extracted from each element at 0.25 m increments, resulting in 28 million sampled force demands represented as points in 3D. Demand points are categorized by their primary structural role: secondary beams with uniformly distributed loads, primary beams with point loads at joist locations, and columns with up to a 10% eccentric axial force. These points are weighted by their frequency of occurrence, e.g., the number of beams with the same loading condition in each structure.

[0079] FIGS. 8A-8C are plots 800, 810, and 820, respectively, of demand sampling and internal force distributions for embodiments. Plot 800 shows a computer-generated building for the purpose of simulation. Plot 810 represents the internal force demands for member elements of the building in the simulation. Plot 810 compares the moment 811 (rotational force when a perpendicular pressure is applied), the shear force 812 and the axial pressure 813 of a beam in the simulation. Plot 820 represents the beam demands for primary and secondary beams, plotting the moment 821 against the shear force 822.

[0080] The sampled data is reduced to a set of n representative design loads for concrete mix specification through an asymmetric distance clustering algorithm. As the cluster “center” is considered the representative load for all demand conditions within the cluster, it must necessarily be the supremum of all load values within the set. This contrasts with conventional clustering algorithms such as K-means, which takes the geometric mean of a cluster as its center, consequently setting a design load that does not fully cover the entire group. A modified version of the asymmetric Expectile Regression loss function

[18] is used as the basis for clustering.

[0081] These representative demands are the basis for capacity analysis and optimal concrete mix design. The distance from a demand point to its cluster center is a proxy for the degree of overdesign caused by assigning a higher-than-necessary capacity. As the capacity of a pixel is directly tied to concrete mix, it is also a measure of the excess EC associated with assignment. The choice of the number of unique concrete mixes is then a decision left to the stakeholders-designers, fabricators, building owners-based on an acceptable compromise between overdesign and logistical complexity.Engineering Analysis

[0082] Embodiments are original in their combination of a modular design strategy with the express goal of reuse, which informs both the design and engineering process. To ensure the safety and serviceability of the structural system, the engineering analysis is based on ACI 318-19

[20] code standards, with FRC providing the required shear demand, calculated from fib Model Code 2010

[21] . FRC eliminates embedded steel reinforcement which improves durability

[22] and extends module lifespans. The system is categorized into three types of member elements: secondary beams, primary beams, and columns.

[0083] The secondary beams, where shear and flexural forces are dominant, are idealized as simply supported beams with uniform loads from the floor system. The shear capacity is provided by FRC, and the flexural capacity is analyzed based on the ultimate post-tensioned stress under the equations in ACI table 20.3.2.4.1

[21] . Moment-axial force diagrams are used to determine the ultimate axial and flexural strength of the concrete section, which are calculated based on existing standards. Currently, the eccentricity of the post-tensioned system of the primary beams is determined by the physical constraints of the available space below the beams, but it is possible to vary the eccentricity to give flexibility to the section capacity. While columns have less eccentricity and different cross sections from the primary beams, they follow the same behavioral assumptions.

[0084] There are many models that can be used to predict the force-deflection behavior of externally post-tensioned beams

[24] . In half-scale load testing of a primary beam, the load-deflection curve could be accurately described by assuming virtual cracks between the structural modules of the member element due to the segmental nature of the beam. Therefore, the elastic post-cracking and the effective moment of inertia model proposed by Ng and Tan

[13] were chosen to calculate the curve. The half-scale test results also suggest that the segmental design of the beam mitigates cracking in the loading stage through strain localization at the dry joints, improving the long-term durability of Pixelframe embodiments (thorough exposition of physical testing of the Pixelframe system is reserved for future publications).

[0085] FIG. 9 shows a graphical representation of a primary beam 900 and associated external post-tensioning assembly. The primary beam 900 includes two end bearing plats 901a-b, which are configured to support the external post-tensioning assembly at the ends of the beam 900. Intermediate plates 904a-b are spaced at distinct intervals and include support members 903a-b of the post-tensioning assembly, which allow for the appropriate angle on the tensile element 902. The tensile element 902 may be steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof. The primary beam 900 also includes intermediate plates 905a-n between each set of structural modules 906a-n, each structural module is not labeled for clarity, which are different than intermediate plates 904a-b in that they do not include the support members for the external post-tensioning assembly. Though an intermediate plate is spaced between each set of structural modules, each intermediate plate is not labeled for clarity.

[0086] FIGS. 10A and 10B are photos 1001 and 1002 of the external post-tensioning assembly. Photo 1001 shows a primary beam 1002 with an external post-tensioning assembly. The assembly includes the tensile element 1003, as well as the intermediate plates 1004a-c which are configured to support the tensile element. FIG. 10B shows a photo 1002 of a side of the primary beam 1002 from photo 1001. The tensile element 1003 is coupled to hardware 1005 which connects to the end bearing plate 1006. An intermediate plate 1007 which is not used to support the external post-tensioning assembly is also shown.

[0087] FIGS. 11A and 11B are graphical representations of both the internal and external post-tensioning assemblies for a primary beam 1110 and a secondary beam 1100. FIG. 11A shows a secondary beam 1100. The secondary beam 1100 is internally post-tensioned via a tensile element 1101 connected to an end bearing plate 1105 and secured with associated hardware 1102. Additionally, the secondary beam 1100 is externally post-tensioned via a tensile element 1103 and associated hardware 1104. It should be noted that the secondary beam 1100 is also similarly secured and connected at a second end of the beam, which is not shown for clarity. The end bearing plate 1105 is configured to attach to an intermediate plate of a primary beam.

[0088] FIG. 11B shows a primary beam 1110. The primary beam 1110 is internally post-tensioned via a tensile element 1111 connected to an end bearing plate 1115 and secured with associated hardware 1112. Additionally, the primary beam 1110 is externally post-tensioned via a tensile element 1113 and associated hardware 1114. It should be noted that the primary beam 1110 is also similarly secured and connected at a second end of the beam, which is not shown for clarity. The end bearing plate 1115 is configured to attach to a connection node component.

[0089] FIGS. 12A and 12B are graphical representations 1200 and 1210, respectively, highlighting the differences in external post-tensioning between primary and secondary beams. FIG. 12A shows primary beam 1200 including internal axial post-tensioning 1201 and external deviated post-tensioning 1202. FIG. 12B shows secondary beam 1210 including internal axial post-tensioning 1211 and external axial post-tensioning 1212.High Resolution, Semi-Constrained Inventory Assignment

[0090] To design a structure with Pixelframe embodiments, a design tool was created to solve a balanced assignment problem between the strength capacities of a pixel inventory and the demands of an interactive, discretized structural framing model, while minimizing EC and maximizing average structural utilization (avg. util). Traditional structural design is iterative and specific, with design decisions made case by case—the design process itself must adapt to support flexible, adaptable, reusable systems

[10] . In a circular building economy, building parameters such as spans and floor heights become variables to optimize matches between pixel inventory and structural demand.

[0091] Users input a building footprint and set design constraints to define all possible structural configurations and determine constraints such as bay spacing, column height and secondary span. The structural demands of potential target structures may not always be supported by inventory pixels; to eliminate structural underdesign, new perfect-match pixels are added, generating a semi-constrained inventory. The EC of all pixels is calculated using an estimation of kgCO2e based on percent cement content. For reused pixels, a small portion of their EC is used as a proxy for the carbon associated with deconstruction and transportation.

[0092] All possible 3D models within the design space are generated, divided into segments, and undergo a finite element analysis using, for example, Karamba3D. From this analysis, structural demands under the governing load combination and translate demands are extracted into optimal concrete strengths for each structural module. To compare inventory to demand, the Hungarian matching algorithm

[25] is used with a custom combined cost matrix that acts as a single objective proxy of the two primary design goals: maximizing average utilization and minimizing EC. The resultant matching score is used to generate matching indices, which assign inventory structural modules to demand locations. Using optimization, the lowest carbon, highest average utilization solution within the given user-input parameters can be located within the design space. The adjustable, semi-constrained inventory developed for this design method prioritizes the use of existing pixels while allowing for the introduction of new pixels with a higher EC cost, managed by a user input that determines the frequency with which new structural modules are introduced.

[0093] FIG. 13 is a graphical representation 1300 of a comparison of reconfiguration potential, utilization and EC across different approaches. Representation 1300 shows three approaches, prismatic cast on-site 1301, Pixelframe single mix 1302, and Pixelframe using ten unique mixes 1303 for a first structure 1304 and a second structure 1305. The second structure 1305 embodies the deconstruction of the first structure 1304 and subsequent construction of a second structure 1305.

[0094] Building with reusable structural modules can present a trade-off between design freedom and embodied carbon: the Pixelframe system is developed to maintain flexibility and efficiency while maximizing reuse potential. Up front, the system allows for a 77% reduction in EC in comparison to typical cast on-site RC frame construction. The modular, adaptable design strategy enables the specification of structural modules with variable compressive strength capacities and is informed by statistical analysis of common internal load demands to ensure that high strength, high carbon pixels are only assigned where needed, optimizing the distribution of EC within the structure. Preliminary flexural testing shows structural behavior can be effectively represented by linear elastic post-crack models. These virtual cracks between pixel segments eliminate localized damage and ensures prolongation of structural life. In combination, these strategies enable the reuse of precast components in diverse loading and geometric conditions, making possible even higher CO2e savings in future life cycles.

[0095] It should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific implementations described above. The specific implementations described above are disclosed as examples only.REFERENCES[1] Van Damme H 2018 Concrete material science: Past, present, and future innovations Cem Concr Res 112 5-24

[0097] [2] Favier A, De Wolf C, Scrivener K and Habert G 2018 A sustainable future for the European Cement and Concrete Industry: Technology assessment for full decarbonisation of the industry by 2050 (ETH Zurich)

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[10] Gorgolewski M 2008 Designing with reused building components: some challenges Build Res Inf 36 175-88

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[11] G Sauvageot 2000 Segmental Concrete Bridges in Bridge Engineering Handbook ed Chen WF and Duan L (Boca Raton CRC Press) 236-87

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[21] ACI Committee 318 2019 Building Code Requirements for Structural Concrete and Commentary

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[22] ACI Committee 544 2018 Guide to design with fiber-reinforced concrete

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[23] Ahmad J, González-Lezcano RA, Majdi A, Ben Kahla N, Deifalla AF and El-Shorbagy MA, 2022 Glass Fibers Reinforced Concrete: Overview on Mechanical, Durability and Microstructure Analysis Materials 15 5111

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[24] Alqam M and Alkhairi F 2019 Numerical and Analytical Behavior of Beams Prestressed with Unbonded Internal or External Steel Tendons: A State-of-the-Art Review Arab J Sci Eng 44 8149-70

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[25] Kuhn HW 1955 The Hungarian method for the assignment problem Nav Res Logist Q 2 83-97

[0121] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[0122] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Examples

Embodiment Construction

[0044]A description of example embodiments follows.

[0045]Demand to build structures, such as housing, for a growing urban population is in conflict with a preference to reduce contributions to global CO2 emissions from the Architectural Engineering and Construction (AEC) sector. Structural systems are a factor in this challenge, as they contribute substantially to a building's mass and are typically overdesigned. Two strategies for reducing the embodied carbon of structural systems are (i) geometric optimization, which can reduce structural mass but limits reusability, and (ii) circular material reuse, which is most successful when building components are standardized, often resulting in poor utilization.

[0046]To improve reuse potential while maintaining flexibility and efficiency, embodiments of the present invention leverage standardization and optimization by discretizing structural modules into precast modules with variable mix designs. An algorithmic design strategy may be impl...

Claims

1. An apparatus for use in a building structure, the apparatus comprising:at least two structural modules having a convex side oriented toward a common axis and a concave side oriented away from the common axis;a member element defined by the at least two structural modules in coupled arrangement, the member element comprising a first end and a second end; anda post-tensioning assembly including: (i) at least two anchors coupled to the member element at distinct locations at or between the first end and the second end, and (ii) a tensile element coupled to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis.

2. The apparatus of claim 1, wherein the convex side of each structural module defines a first complementary coupling feature, the apparatus further comprising:a core module having a length, the core module defining a second complementary coupling feature along at least a portion of the length; and whereinthe member element is further defined by the core module in coupled arrangement with the structural modules via the first and second complementary coupling features.

3. The apparatus of claim 1, further comprising intermediate plates configured to be spaced between adjacent structural modules, in coupled arrangement with the core module.

4. The apparatus of claim 3, wherein the intermediate plates are configured to couple to any one of: a post-tensioning element, a different member element, or a connection node configured to couple at least two member elements.

5. The apparatus of claim 2, wherein the post-tensioning assembly further includes the intermediate plate that is configured to couple additional elements to a tensile element and provide external post-tensioning.

6. The apparatus of claim 2, wherein the second complementary coupling feature is positioned on, or defined by, the core module at a location that orients two or more structural modules to be coupled radially around the core module.

7. The apparatus of claim 2, wherein the core module includes concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

8. The apparatus of claim 1, wherein the tensile element includes steel, fiber, cable, wire, braided material, natural material, synthetic material, or any combination thereof.

9. The apparatus of claim 1, wherein the at least two anchors are coupled to end bearing plates and, in combination with the tensile element are configured to hold the structural modules in coupled arrangement.

10. The apparatus of claim 1, wherein the structural module consists of concrete, cement, plastic, fibers, metal, natural materials, or any combination thereof.

11. The apparatus of claim 1, wherein the structural module's composition varies according to at least one of: cement content, fiber dosage, admixtures, aggregate content, or any combination thereof.

12. The apparatus of claim 1, further comprising a connection node configured to couple multiple member elements together.

13. The apparatus of claim 12, further comprising a plurality of member elements coupled to a plurality of connection nodes arranged to form a structure.

14. The apparatus of claim 13, further comprising at least one planar element configured to be coupled to the structure, the at least one planar element defining at least one of a floor, roof, or wall.

15. The apparatus of claim 14, wherein the planar element further comprises an independent interface component configured to couple the planar element to at least one member element.

16. A method of assembling a building structure, the method comprising:orienting a convex side of a structural module toward a common axis and orienting a concave side of the structural moule away from the common axis;coupling and arranging at least two structural modules to define a member element, the member element having a first end and a second end; andassembling a post-tensioning assembly by: (i) coupling at least two anchors to the member element at distinct locations at or between the first end and the second end, and (ii) coupling a tensile element to the at least two anchors in a manner providing a post-tensioning force between the at least two anchors and along the common axis.

17. The method of assembling a building structure of claim 16, wherein the convex side of each structural module defines a first complementary coupling feature, the method further comprising:coupling the first complementary coupling feature of each structural module to a core module having a second complementary coupling feature and a length, wherein the second complementary coupling feature is along at least a portion of the length; andthe member element being further defined by coupling and arranging the core module with the structural modules via the first and second complementary coupling features.

18. The method of assembling a building structure of claim 16, further comprising:spacing an intermediate plate between adjacent structural modules, in coupled arrangement with the core module.

19. An apparatus for use in a building structure, the apparatus comprising:means for interconnecting structural modules in a manner that enables reversible construction;means for assembling a member element with the at least two structural modules; andmeans for applying post-tensioning for maintaining structural integrity of the member element.

20. The apparatus for use in a building structure of claim 19, wherein the structural modules have a concave side and a convex side, and wherein the apparatus further comprising:means for coupling the structural modules together with at least two adjacent structural modules having respective convex sides oriented toward a common axis and respective concave sides oriented away from the common axis.

Images