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* 1941: [[Alexander Hrennikoff]] solved the discretization of plane elasticity problems using a lattice framework.
* 1942: [[Richard Courant]] divided a ___domain into finite subregions.
* 1956: J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp's paper on the "Stiffness and Deflection of Complex Structures" introduces the name "[[finite-element method]]" and is widely recognized as the first comprehensive treatment of the method as it is known today.
===Structural failure===
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[[File:Bolt-in-shear.svg|thumb|Figure of a [[Screw|bolt]] in [[shear stress]]. Top figure illustrates single shear, bottom figure illustrates double shear.]]
Structural engineering depends upon a detailed knowledge of [[applied mechanics]], [[materials science]], and [[applied mathematics]] to understand and predict how structures support and resist self-weight and imposed loads. To apply the knowledge successfully a structural engineer generally requires detailed knowledge of relevant empirical and theoretical [[design codes]], the techniques of [[structural analysis]], as well as some knowledge of the [[corrosion]] resistance of the materials and structures, especially when those structures are exposed to the external environment. Since the 1990s, specialist software has become available to aid in the design of structures, with the functionality to assist in the drawing, analyzing and designing of structures with maximum precision; examples include [[AutoCAD]], StaadPro, [[Computers and Structures|ETABS]], Prokon, Revit Structure, Inducta RCB, etc. Such software may also take into consideration environmental loads, such as earthquakes and winds.{{cn|date=February 2024}}
==Profession==
{{Main|Structural engineer}}
Structural engineers are responsible for engineering design and structural analysis. Entry-level structural engineers may design the individual structural elements of a structure, such as the beams and columns of a building. More experienced engineers may be responsible for the structural design and integrity of an entire system, such as a building.{{cn|date=February 2024}}
Structural engineers often specialize in particular types of structures, such as buildings, bridges, pipelines, industrial, tunnels, vehicles, ships, aircraft, and spacecraft. Structural engineers who specialize in buildings
Structural engineering has existed since humans first started to construct their structures. It became a more defined and formalized profession with the emergence of architecture as a distinct profession from engineering during the industrial revolution in the late 19th century. Until then, the architect and the structural engineer were usually one and the same thing – the master builder. Only with the development of specialized knowledge of structural theories that emerged during the 19th and early 20th centuries, did the professional structural engineers come into existence.{{cn|date=February 2024}}
The role of a structural engineer today involves a significant understanding of both static and dynamic loading and the structures that are available to resist them. The complexity of modern structures often requires a great deal of creativity from the engineer in order to ensure the structures support and resist the loads they are subjected to. A structural engineer will typically have a four or five-year undergraduate degree, followed by a minimum of three years of professional practice before being considered fully qualified.
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[[File:Burjdubaiaug92007.jpg|thumb|upright|[[Burj Khalifa]], in [[Dubai]], the [[world's tallest building]], shown under construction in 2007 (since completed)]]
Structural building engineering is primarily driven by the creative manipulation of materials and forms and the underlying mathematical and scientific ideas to achieve an end that fulfills its functional requirements and is structurally safe when subjected to all the loads it could reasonably be expected to experience. This is subtly different from architectural design, which is driven by the creative manipulation of materials and forms, mass, space, volume, texture, and light to achieve an end which is aesthetic, functional, and often artistic.
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Civil engineering structures are often subjected to very extreme forces, such as large variations in temperature, dynamic loads such as waves or traffic, or high pressures from water or compressed gases. They are also often constructed in corrosive environments, such as at sea, in industrial facilities, or below ground.
===Mechanical structures===▼
▲===Mechanical engineering structures===
The forces which parts of a machine are subjected to can vary significantly and can do so at a great rate. The forces which a boat or aircraft are subjected to vary enormously and will do so thousands of times over the structure's lifetime. The structural design must ensure that such structures can endure such loading for their entire design life without failing.
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==Structural elements==
{{main|
[[File:Bending.svg|thumb|right|A [[statically determinate]] simply supported beam, bending under an evenly distributed load]]
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===Columns===
{{Main|Column}}
Columns are elements that carry only axial force (compression) or both axial force and bending (which is technically called a beam-column but practically, just a column). The design of a column must check the axial capacity of the element and the buckling capacity.
The [[buckling]] capacity is the capacity of the element to withstand the propensity to buckle. Its capacity depends upon its geometry, material, and the effective length of the column, which depends upon the restraint conditions at the top and bottom of the column. The effective length is <math>K*l</math> where <math>l</math> is the real length of the column and K is the factor dependent on the restraint conditions.
The capacity of a column to carry axial load depends on the degree of bending it is subjected to, and vice versa. This is represented on an interaction chart and is a complex non-linear relationship.
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{{Main|Plate (structure)}}
Plates carry bending in two directions. A concrete flat slab is an example of a plate.
They can also be designed with yield line theory, where an assumed collapse mechanism is analyzed to give an upper bound on the collapse load. This technique is used in practice<ref>{{cite web |title=Assessment of a Pair of Reinforced Concrete Roof Slabs |url=http://www.ramsay-maunder.co.uk/downloads/precast_roof_slabs.pdf |website=Ramsay-Maunder.co.uk |publisher=Ramsay Maunder Associates |date=2011 |access-date=2022-03-08 }}</ref> but because the method provides an upper-bound (i.e. an unsafe prediction of the collapse load) for poorly conceived collapse mechanisms, great care is needed to ensure that the assumed collapse mechanism is realistic.<ref>{{cite web |url=http://www.ramsay-maunder.co.uk/downloads/l_shaped_landing.pdf |title=Reappraisal of a Simply Supported Landing Slab |website=Ramsay-Maunder.co.uk |publisher=Ramsay Maunder Associates |url-status=live |archive-url=https://web.archive.org/web/20160304071038/http://www.ramsay-maunder.co.uk/downloads/l_shaped_landing.pdf |date=2011 |archive-date=2016-03-04 |access-date=2022-03-08 }}</ref>
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===Shells===
{{Main|Thin-shell structure}}
{{See also|Gridshell|Space frame}}
Shells derive their strength from their form and carry forces in compression in two directions. A dome is an example of a shell. They can be designed by making a hanging-chain model, which will act as a catenary in pure tension and inverting the form to achieve pure compression.
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* [[List of bridge disasters]]
* [[List of structural engineers]]
* [[List of structural engineering software]]
* [[Mechanical engineering]]
* [[Nanostructure]]
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