COMPOSITE CONCRETE STEEL COLUMN HAVING A FULLY- EMBEDDED X-SHAPE STEEL SECTION

Description

This application claims the benefit of U.S. Provisional Patent Application Ser. No. 63/644,491 filed May 8, 2024 entitled, “Composite Concrete Steel Column Having a Fully-Embedded X-Shape Steel Section,” the disclosure of which is incorporated by reference as if full set forth herein.

BACKGROUND

The demand for cost-effective construction materials has increased in recent years, due to the development of quick and intelligent construction processes. Composite concrete elements are now frequently used, especially in high-rise buildings. To meet high-strength column capacity requirements, a column with large concrete section is necessary, which reduces the available living space in the floor. Larger sections are more expensive, and less spacious floor areas are undesirable. By using composite concrete elements, the regular reinforced concrete column is replaced, and the cross-sectional area is reduced, sustaining acceptable floor areas, a smaller cross-sectional area, and higher strength capacity.

Generally, a composite concrete-steel column refers to a concrete-encased section (“I,” “H” or “W” sections or beams), or a concrete-filled tubular section of hot-rolled steel. The most common section is the “W” section (beam), which includes wider, parallel flanges compared to “I” or “S” beams. “H” beams are often used to support heavier loads and are often found in bearing piles and load bearing columns for skyscrapers and other large buildings. Unlike “W” beams, “H” beams have flanges with widths that are about the same as the length of the beam depth. The composite concrete-steel column may include additional elements, including rebar to provide additional support for the concrete within the column.

Several researchers have studied the steel sections depicted in the American Institute of Steel Construction (AISC) manual with various concrete strengths and cross-sections, focusing on compressive and flexural strength along with shear resistance. In these studies, stress-strain and force-moment diagrams were drawn to compare theoretical and experimental results to find similarities and consistency. Furthermore, theoretical analyses for steel have been conducted based on two main codes: Eurocode 4 and AISC. Eurocode 4 provides more accurate experimental results than conservative AISC results. Finite elements analysis was strongly used in many studies to simulate the behavior of structural elements and compare it with theoretical or experimental data.

Although existing composite concrete-steel columns have proven successful, there is a need for alternative designs that present reduced cross-sectional areas while optimizing load capacities. The present disclosure is directed to these and other deficiencies in the prior art.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more implementations described herein and, together with the description, explain these implementations. The drawings are not intended to be drawn to scale, and certain features and certain views of the figures may be shown exaggerated, to scale or in schematic in the interest of clarity and conciseness. Not every component may be labeled in every drawing.

FIG. 1A presents a transverse section of fully encased composite (FEC) column showing depicting a first embodiment of the x-shaped steel section.

FIG. 1B presents an isolated transverse section of the x-shaped steel section of FIG. 1A.

FIG. 1C presents a perspective view of the FEC column of FIG. 1A with the concrete removed for clarity.

FIG. 2A presents a transverse section of fully encased composite (FEC) column showing depicting a second embodiment of the x-shaped steel section.

FIG. 2B presents an isolated transverse section of the x-shaped steel section of FIG. 2A.

FIG. 2C presents a perspective view of the FEC column of FIG. 2A with the concrete removed for clarity.

FIG. 3A presents a transverse section of fully encased composite (FEC) column showing depicting a third embodiment of the x-shaped steel section.

FIG. 3B presents an isolated transverse section of the x-shaped steel section of FIG. 3A.

FIG. 3C presents a perspective view of the FEC column of FIG. 3A with the concrete removed for clarity.

FIG. 4 shows AISC Compressive Strength Values of the specimens under test.

FIG. 5 shows Eurocode4 Compressive Strength Values of the Specimens.

FIG. 6 shows a comparison of Load vs Deflection of all Specimens.

FIG. 7 depicts the cross-section of each steel beam evaluated in the experiments disclosed herein.

The following abbreviations and units may be used herein:

• • AISC: American Institute of Steel Construction,
  • CCSC: Composite concrete steel column,
  • FEC: fully encased composite,
  • br: flange (leg) plate width,
  • d: core plate width,
  • t_f: flange (leg) plate thickness,
  • t_w: core plate thickness,
  • f_cu: Ultimate stress,
  • E_c: Modulus of elasticity,
  • ε_cu: Ultimate strain,
  • γ: Poisson ratio,
  • F_y: Yield stress,
  • F_sh: Shrinkage stress,
  • F_w: Ultimate stress,
  • ε_y: Yield strain,
  • ε_sh: Shrinkage strain,
  • ε_u: Ultimate strain

DETAILED DESCRIPTION

The present disclosure describes a composite concrete-steel column having a structural steel section having a novel “X” shape in cross-section embedded therein lengthwise. In one non-limiting embodiment, the X-type steel section is formed as a unitary, integrally-constructed member through hot-rolling, cold-rolling, extrusion, or casting. In another non-limiting embodiment, the X-type steel section is constructed by joining two beams with an “L-shaped” cross-section together by welding or other means such that there is a single longitudinal axis along the length of X-type steel beam. In yet another non-limiting embodiment, the steel section is constructed by joining together four beams each with an L-shaped cross-section together to form an X shape. Analyses showed that the compressive strength capacities of the novel composite concrete-steel column with X-type steel sections were comparable to that of conventional W-type steel sections.

In some embodiments, the present disclosure is directed to a composite concrete-steel column that includes a concrete matrix and a steel beam fully encased within the concrete matrix, wherein the steel beam has an X-shaped cross-section.

In other embodiments, the present disclosure is directed to a method for constructing a composite concrete-steel column that includes the steps of obtaining a beam with an X-shaped cross-section with four legs, obtaining a form that matches an outer perimeter of the composite concrete-steel column, wherein the form includes at least four corners, and placing the beam into the form such that the beam is centered within the form. The method continues with the steps of orienting the beam such that each of the four legs of the beam are directed towards a different one of the at least four corners of the form. The method continues with the step of pouring concrete into the form around the beam to create a concrete matrix around the beam.

In yet other embodiments, the present disclosure is directed to a composite concrete-steel column that includes a concrete matrix that has a cross-section with a plurality of corners and a steel beam encased within the concrete matrix. The steel beam includes a plurality of legs and wherein each of the plurality of legs extends distally away from a common proximal portion toward a corresponding one of the plurality of corners of the concrete matrix.

Before further describing various embodiments of the apparatus, component parts, and methods of the present disclosure in more detail by way of exemplary description, examples, and results, it is to be understood that the embodiments of the present disclosure are not limited in application to the details of apparatus, component parts, and methods as set forth in the following description. The embodiments of the apparatus, component parts, and methods of the present disclosure are capable of being practiced or carried out in various ways not explicitly described herein. For example, the various apparatus and devices of the various embodiments described herein may be constructed using various off-the shelf components, such as other mechanical and electrical components which perform the same function as the particular components described herein. As such, the language used herein is intended to be given the broadest possible scope and meaning; and the embodiments are meant to be exemplary, not exhaustive. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting unless otherwise indicated as so. Moreover, in the following detailed description, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to a person having ordinary skill in the art that the embodiments of the present disclosure may be practiced without these specific details. In other instances, features which are well known to persons of ordinary skill in the art have not been described in detail to avoid unnecessary complication of the description. While the apparatus, component parts, and methods of the present disclosure have been described in terms of particular embodiments, it will be apparent to those of skill in the art that variations may be applied to the apparatus, component parts, and/or methods and in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit, and scope of the inventive concepts as described herein. All such similar substitutes and modifications apparent to those having ordinary skill in the art are deemed to be within the spirit and scope of the inventive concepts as disclosed herein.

All patents, published patent applications, and non-patent publications referenced or mentioned in any portion of the present specification are indicative of the level of skill of those skilled in the art to which the present disclosure pertains, and are hereby expressly incorporated by reference in their entireties to the same extent as if the contents of each individual patent or publication was specifically and individually incorporated herein.

Unless otherwise defined herein, scientific and technical terms used in connection with the present disclosure shall have the meanings that are commonly understood by those having ordinary skill in the art. Further, unless otherwise required by context, singular terms shall include pluralities and plural terms shall include the singular.

As utilized in accordance with the methods and compositions of the present disclosure, the following terms and phrases, unless otherwise indicated, shall be understood to have the following meanings: The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and/or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and/or” unless explicitly indicated to refer to alternatives only or when the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and/or.” The use of the term “at least one” will be understood to include one as well as any quantity more than one, including but not limited to, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 100, or any integer inclusive therein. The phrase “at least one” may extend up to 100 or 1000 or more, depending on the term to which it is attached; in addition, the quantities of 100/1000 are not to be considered limiting, as higher limits may also produce satisfactory results. In addition, the use of the term “at least one of X, Y and Z” will be understood to include X alone, Y alone, and Z alone, as well as any combination of X, Y and Z.

As used in this specification and claims, the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of including, such as “includes” and “include”) or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open-ended and do not exclude additional, unrecited elements or method steps.

The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof” is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AAB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

Throughout this application, the terms “about” or “approximately” are used to indicate that a value includes the inherent variation of error for the apparatus, composition, or the methods or the variation that exists among the objects, or study subjects. As used herein the qualifiers “about” or “approximately” are intended to include not only the exact value, amount, degree, orientation, or other qualified characteristic or value, but are intended to include some slight variations due to measuring error, manufacturing tolerances, stress exerted on various parts or components, observer error, wear and tear, and combinations thereof, for example. The terms “about” or “approximately”, where used herein when referring to a measurable value such as an amount, percentage, temporal duration, and the like, is meant to encompass, for example, variations of +20% or +10%, or +5%, or #1%, or +0.1% from the specified value, as such variations are appropriate to perform the disclosed methods and as understood by persons having ordinary skill in the art. As used herein, the term “substantially” means that the subsequently described event or circumstance completely occurs or that the subsequently described event or circumstance occurs to a great extent or degree. For example, the term “substantially” means that a thing possesses or occurs in an amount, duration, degree or other measure or parameter value that is 90% to 99% of which the thing is being compared to.

As used herein any reference to “one embodiment” or “an embodiment” means that a particular element, feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment.

As used herein, all numerical values or ranges include fractions of the values and integers within such ranges and fractions of the integers within such ranges unless the context clearly indicates otherwise. Thus, to illustrate, reference to a numerical range, such as 1-10 includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, as well as 1.1, 1.2, 1.3, 1.4, 1.5, etc., and so forth. Reference to a range of 1-50 therefore includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc., up to and including 50, as well as 1.1, 1.2, 1.3, 1.4, 1.5, etc., 2.1, 2.2, 2.3, 2.4, 2.5, etc., and so forth. Reference to a series of ranges includes ranges which combine the values of the boundaries of different ranges within the series. Thus, to illustrate reference to a series of ranges, for example, a range of 1-1,000 includes, for example, 1-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-75, 75-100, 100-150, 150-200, 200-250, 250-300, 300-400, 400-500, 500-750, 750-1,000, and includes ranges of 1-20, 10-50, 50-100, 100-500, and 500-1,000. The range 100 units to 2000 units therefore refers to and includes all values or ranges of values of the units, and fractions of the values of the units and integers within said range, including for example, but not limited to 100 units to 1000 units, 100 units to 500 units, 200 units to 1000 units, 300 units to 1500 units, 400 units to 2000 units, 500 units to 2000 units, 500 units to 1000 units, 250 units to 1750 units, 250 units to 1200 units, 750 units to 2000 units, 150 units to 1500 units, 100 units to 1250 units, and 800 units to 1200 units. Any two values within the range of about 100 units to about 2000 units therefore can be used to set the lower and upper boundaries of a range in accordance with the embodiments of the present disclosure. More particularly, a range of 10-12 units includes, for example, 10, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 11.0, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9, and 12.0, and all values or ranges of values of the units, and fractions of the values of the units and integers within said range, and ranges which combine the values of the boundaries of different ranges within the series, e.g., 10.1 to 11.5.

Beginning with FIGS. 1A-1C, shown therein are various depictions of a first embodiment of a composite concrete-steel column 100 that includes a substantially rectangular cross-section. When fully formed, the composite concrete-steel column 100 includes a section (beam) 102 embedded within a poured concrete matrix 104. The composite concrete-steel column 100 can also include auxiliary structural members 106, such as reinforcing bars (rebars). The rebars 106 can be banded together with stirrups or bands 108 to hold the rebars 106 in place while pouring the concrete matrix 104. The rebars 106 are generally oriented in longitudinal, parallel alignment with the beam 102 in the composite concrete-steel column 100. The rebars 106 can optionally be connected or tied to the beam 102. The composite concrete-steel column 100 may include an external form 128 around the exterior of the concrete matrix 104, which may be removed or retained after the composite concrete-steel column 100 is fabricated. Although the beam 102 is constructed from steel in the exemplary embodiments, it will be appreciated that in certain applications the beam 102 can be manufactured from other metals (e.g., aluminum) or materials (e.g., composites).

In the embodiment depicted in FIGS. 1A-1C, the beam 102 is steel and includes four legs 110 that extend distally outward from a common proximal portion 112, which may be integral with one or more of the four legs 110. The distal ends of the four legs 110 are located in proximity to a separate corner of the composite concrete-steel column 100 to give the steep beam 102 an “X-shape” cross-section. The steel beam 102 can be fabricated by hot-rolling, cold-rolling, extrusion, or casting. Alternatively, the steel beam 102 can be prepared by welding or otherwise attaching the proximal ends of the legs 110 together to form the proximal portion 112.

Turning to FIGS. 2A-2C, shown therein are various depictions of a second embodiment of the composite concrete-steel column 100. In this embodiment, the beam 102 is formed by joining together two L-shaped steel beams 114 that each include first and second flanges 116, 118 that are joined together in a substantially orthogonal relationship. The two L-shaped beams 114 can be joined together with longitudinal welds 120. The first and second flanges 116, 118 form the legs 110 of the beam 102 and extend outward from the center of the composite concrete-steel column 100 toward a separate corner of the composite concrete-steel column 100.

As best illustrated in FIG. 2B, the L-shaped beams 114 can be welded together such that the first flanges 116 of each of the L-shaped beams 114 are substantially co-planar and aligned with one another, while the second flanges 118 are offset by the width of the second flanges 118. In other embodiments, the two L-shaped beams 114 can be joined together in a more compact arrangement in which the first flanges 116 are more offset because the second flanges 118 are more overlapped. In some embodiments, the second flanges 118 are overlapped by between about 5% and 60% of the length of the second flanges 118. In some embodiments, the second flanges 118 are overlapped by between about 10% and 40% of the length of the second flanges 118. In some embodiments, the second flanges 118 are overlapped by between about 10% and 30% of the length of the second flanges 118. As depicted, the second flanges 118 are overlapped by about 20% of the length of the second flanges 118. In some embodiments, the L-shaped beams 114 have different dimensions from one another.

The beam 102 depicted in FIGS. 2A-2C can be prepared by undertaking the following steps. First, the cross-sectional shape and size of the intended composite concrete-steel column 100 is determined. Next, the L-shaped beams 114 are selected. In many cases, the L-shaped beams 114 can be selected from commonly produced and stocked beams. Next, the second flanges 118 of the L-shaped beams 114 are approximated with one another to form an X-shaped beam 102, where the first and second flanges 116, 118 of each L-shaped beam 114 form the legs 110 of the beam 102. In this step, the L-shaped beams 114 are positioned such that the first and second flanges 116, 118 of each L-shaped beam 114 are directed at a separate corner of the intended composite concrete-steel column 100, which requires overlapping the second flanges 118 of the L-shaped beams 114 as discussed. Once the desired configuration of the L-shaped beams 114 has been determined, the two L-shaped beams 114 are fastened together with the appropriate overlap by welding or other fastening mechanisms. This manufacturing process is cost-effective because common and inexpensive L-shaped beams 114 can be sourced and arranged to create the novel X-shape steel beam 102, which presents a significant cost savings over other complicated steel sections that require more complicated fabrication processes.

Turning to FIGS. 3A-3C, shown therein are various depictions of a third embodiment of the composite concrete-steel column 100. In this embodiment, the beam 102 is formed by joining together four L-shaped beams 122 that each include first and second flanges 124, 126 that are joined together in a substantially orthogonal relationship. The first and second flanges 124, 126 combine to form the legs 110 of the beam 102. In this embodiment, the first and second flanges 124, 126 can be approximately the same width and the four L-shaped beams 122 can be joined together with welds, rivets, a combination of welds and rivets, or other fastening mechanisms. The ends of each of the combined first and second flanges 124, 126 extend outward from the center of the composite concrete-steel column 100 toward a separate corner of the composite concrete-steel column 100.

In each of the embodiments depicted in FIGS. 1A-1C, 2A-2C, and 3A-3C, the beam 102 approximates an “X-shape” within a square or rectangular column, with the ends of the legs 110 extending toward a separate corner of the rectangular composite concrete-steel column 100, such that distal ends of the legs 110 are closer in proximity to the corners of the composite concrete-steel column 100 than midpoints of the sides of the composite concrete-steel column 100. Orienting the beam 102 in the X-shape configuration places more of the beam 102 closer to the perimeter of the composite concrete-steel column 100 than conventional S, I, H, W or cross-shaped beams located within the center of a rectangular composite concrete-steel column.

According to AISC conventions, compressive strength calculations in columns should be considered on a major (strong) x-axis and a minor (weak) y-axis to prevent a potential failure due to weak axis geometric properties. In some embodiments, the X-shape beam 102 has symmetrical dimensions with four congruent angles having vertices which intersect lengthwise, forming a central longitudinal axis, which not only increases column strength of the steel beam, but also eliminates the steel beam from having one strong axis and one weak axis. In these exemplary embodiments, the beam 102 does not include any flanges or plates secured at the distal end of each leg 110 opposite the proximal portion 112, which would require additional fabrication steps.

Thus, in one aspect, embodiments disclosed herein include a composite concrete-steel column 100 that includes a cross-section with a plurality of corners and an internal beam 102 that includes a plurality of legs or flanges, with each of the plurality of legs or flanges extending outward form the central portion of the composite concrete-steel column 100 to a corresponding corner of the composite concrete-steel column 100. If, for example, the composite concrete-steel column 100 included a pentagonal, hexagonal or octagonal cross-section, the corresponding beam 102 would include five, six or eight legs or flanges, each directed at a corresponding corner of the composite concrete-steel column 100.

The composite concrete-steel column 100 can be constructed by placing the selected beam 102 into the form 128 such that the beam 102 is centered in the form 128. The beam 102 can be oriented such that the legs 110 of the beam 102 are directed at the corners of the form 128. In this configuration, the distal ends of the legs 110 are located closer to the corners of the form 128 than the midpoint of the sides of the form 128. Rebars 106 can be placed into the form 128 before or after the beam 102. Next, concrete is poured into the form 128 around the beam 102 and rebars 106. Once the concrete has cured into the concrete matrix 104, the form 128 can be removed from the composite concrete-steel column 100. In exemplary embodiments, the beam 102 is fully encased within the concrete matrix 104.

EXPERIMENTAL

Three 6-ft long composite concrete-steel columns 100 were analyzed: one conventional W-type section (W100×330) (the “control”), a composite concrete-steel column 100 with an X-shaped beam 102 section formed by two L-shaped beams 114 welded together lengthwise (2L 89×76.5×8), and a composite concrete-steel column 100 with an X-shaped beam 102 formed by four L-shaped beams 122 welded together lengthwise (4L 50×50×6.5). Each composite concrete-steel column 100 was characterized by a 200 mm×200 mm transverse cross-section and a length of 1830 mm. All specimens had four axial rebars 106 of #10 mm, and all beams 102 were positioned in the center of the corresponding composite concrete-steel column 100. The section dimensions of each composite concrete-steel column 100 were chosen to have a failure load of less than 1333 KN, although this is not to be considered to be a limiting feature of the embodiments of the present disclosure. Table 1 and FIG. 7, show transverse cross-sections of each specimen, where FIG. 7(a) shows the first specimen of a conventional column with a W-type steel column embedded (control), FIG. 7(b) shows composite concrete-steel column 100 with two fused steel “L” beams 114 embedded, and FIG. 7(c) shows another composite concrete-steel column 100 with 4 fused steel “L” beams 122 embedded.

AISC 360 (chapter I, section 12) equations “1” and “2” were used to calculate the design compressive strength ØcPn, and allowable compressive strength Pn/Ωc for axially loaded encased composite members for the three specimens.

∅ ⁢ c = 0.75 ( LRFD ) , Ω ⁢ c = 2. ( ASD ) . When ⁢ Pno / Pe ≤ 2.25 Pn = Pno * ( 0.658 ( Pno / Pe ) ) Eq . ( 1 ) When ⁢ Pno / Pe > 2.25 Pn = 0.877 * Pe Eq . ( 2 ) Where : Pno = Fy * As + Fysr * Asr + 0.85 * fc ′ * Ac

The AISC equations are described further below:

Pn = Pno * ( 0.658 ( Pno / Pe ) ) Eq . ( A .1 ) Pn = 0.877 * Pe Eq . ( A .2 ) Pno = Fy * As + Fysr * Asr + 0.85 * fc ′ * Ac Eq . ( A .3 ) Pe = π 2 ( EIeff ) / Lc 2 Eq . ( A .4 ) Ec = wc 1.5 * fc ′ , ksi ( 0.043 * wc 1.5 * fc ′ ⁢ MPa Eq . ( A .5 ) EIeff = Es * Is + Es * Isr + C ⁢ 1 * Ec * Ic Eq . ( A .6 ) C ⁢ 1 = 0.25 + 3 * ( As + Asr / Ag ) ≤ 0.7 Eq . ( A .7 ) Npl , Rd = Aa * fyd + 0.85 * Ac * fcd + As * fsd Eq . ( A .8 )
Pe=elastic critical buckling load=π²(EIeff)/Lc²  Eq. (A.4)

• • Ac=area of concrete, in². (mm²).

As=cross-sectional area of steel section, in². (mm²).

Ec=modulus of elasticity of concrete=wc^1.5*√{square root over (fc′)},ksi(0.043*wc^1.5*√{square root over (fc′)}MPa  Eq. (A.5).

EIeff=effective stiffness of composite section,kip-in².(N-mm²).=Es*Is+Es*Isr+C1*Ec*Ic  Eq. (A.6).

C1=coefficient for calculation of effective rigidity of an encased composite compression member=0.25+3*(As+Asr/Ag)≤0.7  Eq. (A.7).

• • Es=modulus of elasticity of steel=29,000 ksi (200,000 MPa).
  • Fy=specified minimum yield stress of steel section, ksi (MPa).
  • Fysr=specified minimum yield stress of reinforcing bars, ksi (MPa).
  • Ic=moment of inertia of the concrete section about the elastic neutral axis of the composite section, in⁴ (mm⁴).
  • Is=moment of inertia of steel shape about the elastic neutral axis if the composite section, in⁴ (mm⁴).
  • Isr=moment of inertia of reinforcing bars about the elastic neutral axis of the composite section, in⁴ (mm⁴).
  • K=effective length factor.
  • L=laterally unbraced length of the member, in. (mm).
  • Lc=K*L=effective length of the member, in. (mm).
  • fc′=specified compressive strength of concrete, ksi (MPa).
  • wc=weight of concrete per unit volume (90≤wc≤155 Ib/ft³ or 1500≤wc≤2800 kg/m³).

Eurocode4 section 6.7, equation “3” was used to calculate the plastic resistance to compression for encased concrete-encased composite members Npl, Rd.

Npl , Rd = Aa * fyd + 0.85 * Ac * fcd + As * fsd Eq . ( 3 )

Finite element analysis was performed using ABAQUS software to apply an axial concentric load on the three specimens and draw force-deflection graph, following the same methodology described elsewhere herein. All angles of “L” section were assumed to form an X-type section, with the dimensions of the angles equivalent to those used in the theoretical analysis. The force-deflection graphs were compared to determine which section had the greatest compressive strength capacity. The deflection control analysis using ABAQUS was validated first on samples from a previously published experimental study conducted in the laboratory, and results from ABAQUS were well aligned with the experimental study outcomes. While in the present work steel “L” shape angle sections were used to represent the X-type shape, instead, X-type steel sections can be made as integral, single-piece, sections using a pre-made steel mold for this shape.

Results and Discussion

Table 2 below shows the values of compressive strength of all three specimens of conventional steel section W100×330, two angles 2L 89×76.5×8, and four angles 4L 50×50×6.5.

FIG. 4 shows that the compressive strength of the 2L section (specimen 2) is greater than the compressive strength of the W and 4 L section, with a capacity around 20 MPa higher than the W section and higher than 4L section. The W section shows a 62 MPa higher capacity than the 4L section, which can be considered comparable and similar values. It is worth noting that increasing the area of steel or modifying the “X” shape can lead to a stronger section.

Table 3 below shows the material properties as per Eurocode 4, and values of compressive strength of all three specimens of conventional steel section W100×330, two angles 2L 89×76.5×8 and four angles 4L 50×50×6.5.

FIG. 5 shows that 2L and W sections have approximately the same compressive strength and are larger with a 6.9 MPa difference than the 4L section.

Table 4 and FIG. 6 show the reaction forces representing the compressive strength of the three specimens after reaching the 25.4 mm (1-inch) deflection.

The specimens did not reach failure due to the displacement control approach that was used in ABAQUS. This is because these forces were applied to reach a displacement of 25.4 mm only. The goal of the simulation was to find the load which would cause 25.4 mm displacement, then calculate the reaction force.

The beam 102 with four fused L-shaped beams 122 showed similar or less compressive strength than the conventional “W” section, while the beam 102 with two fused L-shaped beams 114 showed greater compressive strength than the conventional “W” section. Although these experiments suggest that usng two L-shaped beams is better based on the software analysis, it should be noted that the 2L beam 102 may require a larger sectional depth and could limit the size of the composite concrete-steel column 100. For example, the tested 2L steel beam 102 was 150 mm in depth and width while the “W” and 4L steel beams 102 were 100 mm in depth and width, respectively.

In summary, the present disclosure describes a new X-type beam 102 for use in a composite concrete-steel column 100. The experimental results indicate that the novel X-type beam 102, with four angles welded together to form an “X” shape has an increased strength capacity as compared to conventional steel sections used to construct composite columns. The symmetrical X-type steel section was compared against the conventional W-type steel section by running a theoretical analysis using AISC and Eurocode 4 and software simulation using ABAQUS. In this way, the X-shape steel section was determined to be a successful alternative to conventional W-shape steel sections.

It is clear that the present invention is well adapted to carry out its objectives and attain the ends and advantages mentioned above as well as those inherent therein. While embodiments of the invention have been described in varying detail for purposes of disclosure, it will be understood that numerous changes may be made which will readily suggest themselves to those skilled in the art and which are encompassed within the spirit of the invention disclosed herein and in the associated drawings and appended claims.