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<h2 id="load-bearing">Load-bearing</h2> <p><a href="/facts/Building/edSjKXje">Buildings</a>, <a href="/facts/Aircraft/EhC4mBep">aircraft</a>, <a href="/facts/Skeleton/FXc9Y2lF">skeletons</a>, <a href="/facts/Ant_colony/jw9KGsex">anthills</a>, <a href="/facts/Beaver_dam/vGE8ee82">beaver dams</a>, <a href="/facts/Bridge/vBJ7Hw8v">bridges</a> and <a href="/facts/Salt_dome/RsPm1A8y">salt domes</a> are all examples of <a href="/facts/Structural_load/MAxjDyhc">load</a>-bearing structures. The results of <a href="/facts/Construction/58eqDhy9">construction</a> are divided into <a href="/facts/Building/edSjKXje">buildings</a> and <a href="/facts/Nonbuilding_structure/We5QqF7Y">non-building structures</a>, and make up the <a href="/facts/Infrastructure/QJvbsSpl">infrastructure</a> of a human society. Built structures are broadly divided by their varying design approaches and standards, into <a href="/facts/Structural_engineering/Wj1vpoGh">categories</a> including building structures, <a href="/facts/Architectural_structure/p66IyqCY">architectural structures</a>, civil engineering structures and mechanical structures. </p><p>The effects of loads on physical structures are determined through <a href="/facts/Structural_analysis/phRJdfup">structural analysis</a>, which is one of the tasks of <a href="/facts/Structural_engineering/Wj1vpoGh">structural engineering</a>. The <a href="/facts/Structural_engineering/Wj1vpoGh">structural elements</a> can be classified as one-dimensional (<a href="/facts/Rope/heTalcCM">ropes</a>, <a href="/facts/Strut/49lYbdrE">struts</a>, <a href="/facts/Beam_(structure)/V9BPDeS8">beams</a>, <a href="/facts/Arch/t9L51pqn">arches</a>), two-dimensional (<a href="/facts/Membrane/FDlaJe23">membranes</a>, plates, <a href="/facts/Concrete_slab/YkVygvIp">slab</a>, <a href="/facts/Shell_(structure)/DBjRqIA1">shells</a>, <a href="/facts/Vault_(architecture)/HjLDot2V">vaults</a>), or three-dimensional (solid masses).<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>: 2 Three-dimensional elements were the main option available to early structures such as <a href="/facts/Chichen_Itza/fUahLnmR">Chichen Itza</a>. A one-dimensional element has one dimension much larger than the other two, so the other dimensions can be neglected in calculations; however, the ratio of the smaller dimensions and the composition can determine the <a href="/facts/Flexural_rigidity/r0wVJ3Em">flexural</a> and <a href="/facts/Compressive_strength/qVWDPDvo">compressive</a> stiffness of the element. Two-dimensional elements with a thin third dimension have little of either but can resist biaxial traction.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>: 2–3 </p><p>The structure elements are combined in <i>structural systems</i>. The majority of everyday load-bearing structures are <i>section-active</i> structures like frames, which are primarily composed of one-dimensional (bending) structures. Other types are <i>Vector-active</i> structures such as <a href="/facts/Truss/bJXJyUtz">trusses</a>, <i>surface-active</i> structures such as shells and folded plates, <i>form-active</i> structures such as cable or membrane structures, and hybrid structures.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>: 134–136 </p><p>Load-bearing biological structures such as bones, teeth, shells, and tendons derive their strength from a multilevel hierarchy of structures employing biominerals and <a href="/facts/Protein/Jxmagu3E">proteins</a>, at the bottom of which are <a href="/facts/Collagen/KsyAb72K">collagen fibrils</a>.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h2 id="biological">Biological</h2> <p>In <a href="/facts/Biology/1M1ee3pB">biology</a>, one of the properties of <a href="/facts/Life/DNw7NUId">life</a> is its highly <i>ordered</i> structure,<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> which can be observed at <a href="/facts/Biological_organisation/CgpMqgys">multiple levels</a> such as in <a href="/facts/Cell_(biology)/bLM9UQvy">cells</a>, <a href="/facts/Tissue_(biology)/H7CpML7A">tissues</a>, <a href="/facts/Organ_(anatomy)/FUYsLaxz">organs</a>, and <a href="/facts/Organism/j8JkL09u">organisms</a>. </p><p>In another context, structure can also observed in <a href="/facts/Macromolecule/039ULSLg">macromolecules</a>, particularly <a href="/facts/Protein/Jxmagu3E">proteins</a> and <a href="/facts/Nucleic_acid/2tTgcI0v">nucleic acids</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> The function of these molecules is determined by their shape as well as their composition, and their structure has multiple levels. <a href="/facts/Protein_structure/BptnTs9X">Protein structure</a> has a four-level hierarchy. The <i><a href="/facts/Protein_primary_structure/QNBoERdu">primary structure</a></i> is the sequence of <a href="/facts/Amino_acid/WDxYwBny">amino acids</a> that make it up. It has a <a href="/facts/Peptide/C4ltc7UG">peptide</a> backbone made up of a repeated sequence of a nitrogen and two carbon atoms. The <i><a href="/facts/Protein_secondary_structure/MMgXXbQ2">secondary structure</a></i> consists of repeated patterns determined by <a href="/facts/Hydrogen_bonding/85V86IIg">hydrogen bonding</a>. The two basic types are the <a href="/facts/Alpha_helix/7CESPIYJ">α-helix</a> and the <a href="/facts/Beta_sheet/B6mwwR6H">β-pleated sheet</a>. The <i><a href="/facts/Protein_tertiary_structure/1QJVj1V1">tertiary structure</a></i> is a back and forth bending of the polypeptide chain, and the <i><a href="/facts/Protein_quaternary_structure/ukuyKJfj">quaternary structure</a></i> is the way that tertiary units come together and interact.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> <a href="/facts/Structural_biology/XRkPtHYv">Structural biology</a> is concerned with <a href="/facts/Biomolecular_structure/VaN6MEYh">biomolecular structure</a> of macromolecules.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <h2 id="chemical">Chemical</h2> <p class="note">Main article: <a href="/facts/Chemical_structure/r5rT1Lj4">Chemical structure</a></p> <p>Chemical structure refers to both molecular geometry and electronic structure. The structure can be represented by a variety of diagrams called <a href="/facts/Structural_formula/XRTmvINB">structural formulas</a>. <a href="/facts/Lewis_structure/PTgB3gtW">Lewis structures</a> use a dot notation to represent the <a href="/facts/Valence_electron/mXPA15VP">valence electrons</a> for an atom; these are the electrons that determine the role of the atom in chemical reactions.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a>: 71–72 Bonds between atoms can be represented by lines with one line for each pair of electrons that is shared. In a simplified version of such a diagram, called a <a href="/facts/Skeletal_formula/RFcmIenv">skeletal formula</a>, only carbon-carbon bonds and functional groups are shown.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p><p>Atoms in a crystal have a <a href="/facts/Crystal_structure/bJ4bCeHd">structure</a> that involves repetition of a basic unit called a <i>unit cell</i>. The atoms can be modeled as points on a <a href="/facts/Bravais_lattice/7gQKTsXk">lattice</a>, and one can explore the effect of <a href="/facts/Symmetry/hpu7DK8p">symmetry</a> operations that include rotations about a point, reflections about a symmetry planes, and <i><a href="/facts/Translation_(geometry)/KlpWmnfX">translations</a></i> (movements of all the points by the same amount). Each crystal has a finite group, called the <a href="/facts/Space_group/2XQx0J7M">space group</a>, of such operations that map it onto itself; there are 230 possible space groups.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a>: 125–126 By <a href="/facts/Neumann%2527s_law/p8YH6XYP">Neumann's law</a>, the symmetry of a crystal determines what physical properties, including <a href="/facts/Piezoelectricity/65k6BDqx">piezoelectricity</a> and <a href="/facts/Ferromagnetism/fH3HFnSl">ferromagnetism</a>, the crystal can have.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a>: 34–36, 91–92, 168–169 </p> <h2 id="mathematical">Mathematical</h2> <p class="note">Main article: <a href="/facts/Mathematical_structure/6CXReUNv">Mathematical structure</a></p> <h2 id="musical">Musical</h2> <p class="note">See also: <a href="/facts/Musical_form/JrnVvFDq">Musical form</a></p> <p>A large part of <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a> involves identifying and interpreting the structure of musical works. Structure can be found at the level of part of a work, the entire work, or a group of works.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> Elements of music such as <a href="/facts/Pitch_(music)/fQAK0JsC">pitch</a>, <a href="/facts/Duration_(music)/8RsxXLrH">duration</a> and <a href="/facts/Timbre/lVXB949E">timbre</a> combine into small elements like <a href="/facts/Motif_(music)/Bag88j9V">motifs</a> and <a href="/facts/Phrase_(music)/bteKoAt6">phrases</a>, and these in turn combine in larger structures. Not all music (for example, that of <a href="/facts/John_Cage/L8UuNbIY">John Cage</a>) has a <a href="/facts/Hierarchical_organization/Edj1h0RE">hierarchical organization</a>, but hierarchy makes it easier for a listener to understand and remember the music.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a>: 80 </p><p>In analogy to <a href="/facts/Linguistics/oQuamvf2">linguistic</a> terminology, motifs and phrases can be combined to make complete musical ideas such as <a href="/facts/Sentence_(music)/LM4PYUEz">sentences</a> and <a href="/facts/Phrase_(music)/bteKoAt6">phrases</a>.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a><a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> A larger form is known as the <a href="/facts/Period_(music)/TjUMAVQc">period</a>. One such form that was widely used between 1600 and 1900 has two phrases, an <i>antecedent</i> and a <i>consequent</i>, with a half <a href="/facts/Cadence_(music)/9AuxqJD4">cadence</a> in the middle and a full cadence at the end providing punctuation.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a>: 38–39 On a larger scale are single-movement forms such as the <a href="/facts/Sonata_form/xgVobu3o">sonata form</a> and the <a href="/facts/Counterpoint/9yd8pKzN">contrapuntal form</a>, and multi-movement forms such as the <a href="/facts/Symphony/mwmt5ndW">symphony</a>.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> </p> <h2 id="social">Social</h2> <p class="note">Main article: <a href="/facts/Social_structure/MyCzKt4H">Social structure</a></p> <p>A social structure is a pattern of relationships. They are social <a href="/facts/Organization/CR83f1Rn">organizations</a> of individuals in various life situations. Structures are applicable to people in how a society is as a system organized by a characteristic pattern of relationships. This is known as the social organization of the group.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a>: 3 Sociologists have studied the changing structure of these groups. <a href="/facts/Structure_and_agency/7DvqIwf1">Structure and agency</a> are two confronted theories about human behaviour. The debate surrounding the influence of structure and agency on human thought is one of the central issues in sociology. In this context, <i>agency</i> refers to the individual human capacity to act independently and make free choices. <i>Structure</i> here refers to factors such as <a href="/facts/Social_class/gJbHDVNc">social class</a>, <a href="/facts/Religion/cxntrD0R">religion</a>, <a href="/facts/Gender/LfjRHcJy">gender</a>, <a href="/facts/Ethnic_group/XSp5l24t">ethnicity</a>, customs, etc. that seem to limit or influence individual opportunities. </p> <h2 id="data">Data</h2> <p class="note">Main article: <a href="/facts/Data_structure/yNsNvL1I">Data structure</a></p> <p>In <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, a data structure is a way of organizing information in a <a href="/facts/Computer/SQe1aK05">computer</a> so that it can be used efficiently.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> Data structures are built out of two basic types: An <a href="/facts/Array_data_structure/BKGvF8AM">array</a> has an index that can be used for immediate access to any data item (some <a href="/facts/Programming_language/cWTYbgWa">programming languages</a> require array size to be <a href="/facts/Initialization_(programming)/rFtbHWvF">initialized</a>). A <a href="/facts/Linked_list/Ik4JTgJW">linked list</a> can be reorganized, grown or shrunk, but its elements must be accessed with a <a href="/facts/Reference_(computer_science)/1vm2Bph1">pointer</a> that links them together in a particular order.<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a>: 156 Out of these any number of other data structures can be created such as <a href="/facts/Stack_(abstract_data_type)/bj7l94v1">stacks</a>, <a href="/facts/Queue_(abstract_data_type)/hVPjPXus">queues</a>, <a href="/facts/Tree_(data_structure)/RcXz9noF">trees</a> and <a href="/facts/Hash_table/Ht4ptDPF">hash tables</a>.<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> </p><p>In solving a problem, a data structure is generally an integral part of the <a href="/facts/Algorithm/fnl5NmRt">algorithm</a>.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a>: 5 In modern programming style, algorithms and data structures are <a href="/facts/Encapsulation_(computer_programming)/kzDnbHPe">encapsulated</a> together in an <a href="/facts/Abstract_data_type/BaVGSHNP">abstract data type</a>.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a>: ix </p> <h2 id="software">Software</h2> <p class="note">Main article: <a href="/facts/Software_architecture/1Hokp0Ed">Software architecture</a></p> <p>Software architecture is the specific choices made between possible alternatives within a framework. For example, a framework might require a database and the architecture would specify the type and manufacturer of the database. The <a href="/facts/Structure_chart/XIQPexYe">structure</a> of software is the way in which it is partitioned into interrelated components. A key structural issue is minimizing dependencies between these components. This makes it possible to change one component without requiring changes in others.<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a>: 3 The purpose of structure is to <a href="/facts/Program_optimization/nXz6RpRM">optimise</a> for (brevity, readability, traceability, isolation and encapsulation, maintainability, extensibility, performance and efficiency), examples being: <a href="/facts/Computer_language/n3L56qdP">language choice</a>, <a href="/facts/Indentation_style/m1DGdgyC">code</a>, <a href="/facts/API/GMlN4vUr">functions</a>, <a href="/facts/Class_browser/LTnqBswK">libraries</a>, <a href="/facts/Makefile/5q1DQ4ot">builds</a>, <a href="/facts/Package_manager/kEX4kx7g">system evolution</a>, or diagrams for <a href="/facts/Control_structure_diagram/sJW3aAC3">flow logic</a> and <a href="/facts/Nassi%25E2%2580%2593Shneiderman_diagram/zqzSRRM6">design</a>.<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a> Structural elements reflect the requirements of the application: for example, if the system requires a high fault tolerance, then a redundant structure is needed so that if a component fails it has backups.<a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a> A high redundancy is an essential part of the design of several systems in the <a href="/facts/Space_Shuttle/7BoyetEv">Space Shuttle</a>.<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a> </p> <h2 id="logical">Logical</h2> <p>As a branch of philosophy, <a href="/facts/Logic/8JnpJLtt">logic</a> is concerned with distinguishing good arguments from poor ones. A chief concern is with the structure of arguments.<a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> An argument consists of one or more <a href="/facts/Premise/HluL8lcd">premises</a> from which a conclusion is <a href="/facts/Inference/RBbe95bP">inferred</a>.<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a> The steps in this inference can be expressed in a formal way and their structure analyzed. Two basic types of inference are <a href="/facts/Deductive_reasoning/HadA1zWS">deduction</a> and <a href="/facts/Inductive_reasoning/EJ992JJ9">induction</a>. In a <a href="/facts/Validity_(logic)/oMGkywGC">valid</a> deduction, the conclusion necessarily follows from the premises, regardless of whether they are true or not. An invalid deduction contains some error in the analysis. An inductive argument claims that if the premises are true, the conclusion is likely.<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Abstract_structure/EkSkcwdQ">Abstract structure</a></li> <li><a href="/facts/Mathematical_structure/6CXReUNv">Mathematical structure</a></li> <li><a href="/facts/Structural_geology/e6tGSc6K">Structural geology</a></li> <li><a href="/facts/Structure_(mathematical_logic)/GsMx1fEb">Structure (mathematical logic)</a></li> <li><a href="/facts/Structuralism_(philosophy_of_science)/z9UnsqFW">Structuralism (philosophy of science)</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Carpi, A.; Brebbia, C.A. (2010). <i>Design & nature V : comparing design in nature with science and engineering</i>. Southampton: WIT. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9781845644543.</li> <li><a href="/facts/Wendy_Pullan_(academic)/hYsnd421">Pullan, Wendy</a> (2000). <i>Structure</i>. Cambridge: Cambridge University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-78258-9.</li> <li>Rottenberg, Annette T.; Winchell, Donna Haisty (2012). <i>The structure of argument</i> (7th ed.). Boston: Bedford/St. Martins. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780312650698.</li> <li>Schlesinger, Izchak M.; Keren-Portnoy, Tamar; Parush, Tamar (2001). <i>The structure of arguments</i>. Amsterdam: J. Benjamins. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9789027223593.</li></ul> <h2 id="external-links">External links</h2> <ul><li>Wüthrich, Christian. <a href="https://web.archive.org/web/20160304214729/http://philosophyfaculty.ucsd.edu/faculty/wuthrich/teaching/2010_246/246Syllabus_2010.pdf">"Structure in philosophy, mathematics and physics (Phil 246, Spring 2010)"</a> (PDF). University of California San Diego. Archived from <a href="http://philosophyfaculty.ucsd.edu/faculty/wuthrich/teaching/2010_246/246Syllabus_2010.pdf">the original</a> (PDF) on 4 March 2016. Retrieved 1 October 2015. (syllabus and reading list)</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"structure, n.". Oxford English Dictionary (Online ed.). Archived from the original on 14 June 2024. Retrieved 1 October 2015. <a href="http://www.oed.com/view/Entry/191895?rskey=pTgPk1&result=1" target="_blank">http://www.oed.com/view/Entry/191895?rskey=pTgPk1&result=1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Carpinteri, Alberto (2002). Structural Mechanics: A unified approach. CRC Press. ISBN 9780203474952. <a href="9780203474952" target="_blank">9780203474952</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Carpinteri, Alberto (2002). Structural Mechanics: A unified approach. CRC Press. ISBN 9780203474952. <a href="9780203474952" target="_blank">9780203474952</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Knippers, Jan; Cremers, Jan; Gabler, Markus; Lienhard, Julian (2011). Construction manual for polymers + membranes : materials, semi-finished products, form-finding design (Engl. transl. of the 1. German ed.). München: Institut für internationale Architektur-Dokumentation. ISBN 9783034614702. <a href="9783034614702" target="_blank">9783034614702</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Zhang, Z.; Zhang, Y.-W.; Gao, H. (1 September 2010). "On optimal hierarchy of load-bearing biological materials". Proceedings of the Royal Society B: Biological Sciences. 278 (1705): 519–525. doi:10.1098/rspb.2010.1093. PMC 3025673. PMID 20810437. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3025673" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3025673</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Urry, Lisa; Cain, Michael; Wasserman, Steven; Minorsky, Peter; Reece, Jane (2017). "Evolution, the themes of biology, and scientific inquiry". Campbell Biology (11th ed.). New York: Pearson. pp. 2–26. ISBN 978-0134093413. <a href="978-0134093413" target="_blank">978-0134093413</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Banaszak, Leonard J. (2000). Foundations of Structural Biology. Burlington: Elsevier. ISBN 9780080521848. <a href="9780080521848" target="_blank">9780080521848</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Purves, William K.; Sadava, David E.; Orians, Gordon H.; H. Craig, Heller (2003). Life, the science of biology (7th ed.). Sunderland, Mass.: Sinauer Associates. pp. 41–44. ISBN 9780716798569. <a href="9780716798569" target="_blank">9780716798569</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Banaszak, Leonard J. (2000). Foundations of Structural Biology. Burlington: Elsevier. ISBN 9780080521848. <a href="9780080521848" target="_blank">9780080521848</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>DeKock, Roger L.; Gray, Harry B. (1989). Chemical structure and bonding (2nd ed.). Mill Valley, Calif.: University Science Books. 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