Structural engineering theory: Difference between revisions

Revision as of 23:06, 20 June 2010

Revision as of 01:03, 5 December 2010

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See also:

{{seeSee also|Tensile strength|Compressive strength|Shear strength}}

==Stiffness==

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The inverse of stiffness is [[flexibility (engineering)|flexibility]].

{{seeSee also|Flexibility method|Direct stiffness method}}

==Safety factors==

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The job of the structural engineer is to ensure that the chance of overlap between the distribution of loads on a structure and the distribution of material strength of a structure is acceptably small (it is impossible to reduce that chance to zero).

It is normal to apply a ''[[safety factor|partial safety factor]]'' to the loads and to the material strengths, to design using 95th percentiles (two [[standard deviations]] from the [[mean]]). The safety factor applied to the load will typically ensure that in 95% of times the actual load will be smaller than the design load, while the factor applied to the strength ensures that 95% of times the actual strength will be higher than the design strength.

The safety factors for material strength vary depending on the material and the use it is being put to and on the design codes applicable in the country or region.

===Load cases===

{{Globalize|date=December 2010}}

A '''load case''' is a combination of different types of loads with safety factors applied to them. A structure is checked for strength and serviceability against all the load cases it is likely to experience during its lifetime.

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: ''1.0 x Dead Load + 1.0 x Live Load''

Different load cases would be used for different loading conditions. For example, in the case of design for fire a load case of ''1.0 x Dead Load + 0.8 x Live Load'' may be used, as it is reasonable to assume everyone has left the building if there is a fire.

In multi-story buildings it is normal to reduce the total live load depending on the number of stories being supported, as the probability of maximum load being applied to all floors simultaneously is negligibly small.

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==Newton's laws of motion==

{{mainMain|Newton's laws of motion}}

The most important natural laws for structural engineering are [[Newton's Laws of Motion]]

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With these laws it is possible to understand the forces on a structure and how that structure will resist them. The Third Law requires that for a structure to be stable all the internal and external forces must be in [[Mechanical equilibrium|equilibrium]]. This means that the sum of all internal and external forces on a ''[[free-body diagram]]'' must be zero:

* <math> \sum \vec F = 0 </math>: the vectorial sum of the [[force]]s acting on the body equals zero. This translates to

::Σ ''H'' = 0: the sum of the horizontal components of the forces equals zero;

::Σ ''V'' = 0: the sum of the vertical components of forces equals zero;

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==Statical determinacy==

{{mainMain|Statically indeterminate}}

A structural engineer must understand the internal and external forces of a structural system consisting of structural elements and nodes at their intersections.

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==Elasticity==

{{mainMain|Elasticity (physics)|l1=Elasticity}}

{{seeSee also|Hooke's Law}}

Much engineering design is based on the assumption that materials behave elastically. For most materials this assumption is incorrect, but empirical evidence has shown that design using this assumption can be safe. Materials that are elastic obey Hooke's Law, and plasticity does not occur.

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==Plasticity==

[[Image:Tresca stress 2D.png|right|thumb|Comparison of Tresca and Von Mises Criteria]]

{{mainMain|Plasticity (physics)|l1=Plasticity}}

Some design is based on the assumption that materials will behave [[Plasticity (physics)|plastically]].<ref name=Heyman1>{{cite book|title=Structural Analysis: A Historical Approach|author=Heyman, Jacques|publisher=Cambridge University Press|date=1998|isbn=0521622492}}</ref> A plastic material is one which does not obey Hooke's Law, and therefore deformation is not proportional to the applied load. Plastic materials are [[ductile]] materials. Plasticity theory can be used for some reinforced concrete structures assuming they are underreinforced, meaning that the steel reinforcement fails before the concrete does.

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==The Euler-Bernoulli beam equation==

[[Image:deflection.svg|thumb|right|Deflection of a cantilever under a point load (f) in engineering]]

{{mainMain|Euler-Bernoulli beam equation}}

The Euler-Bernoulli beam equation defines the behaviour of a beam element (see below). It is based on five assumptions:

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==Buckling==

{{mainMain|Buckling}}

[[Image:Buckled column.png|thumb|A column under a centric axial load exhibiting the characteristic deformation of buckling.]]

[[Image:Ltb.PNG|thumb|right|Lateral-torsional buckling of an aluminium alloy plate girder designed and built by students at [http://www.imperial.ac.uk Imperial College London].]]

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When subjected to compressive forces it is possible for structural elements to deform significantly due to the destabilising effect of that load. The effect can be initiated or exacerbated by possible inaccuracies in manufacture or construction.

The Euler buckling formula defines the axial compression force which will cause a [[strut]] (or column) to fail in buckling.

:<math>F=\frac{\pi^2 EI}{(Kl)^2}</math>

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Other forms of buckling include lateral torsional buckling, where the compression flange of a beam in bending will buckle, and buckling of plate elements in plate girders due to compression in the plane of the plate.

== References ==

<References/>

* Castigliano, Carlo Alberto (translator: Andrews, Ewart S.) (1966). [http://books.google.co.uk/books?id=wU1CAAAAIAAJ&q=The+Theory+of+Equilibrium+of+Elastic+Systems+and+Its+Applications&dq=The+Theory+of+Equilibrium+of+Elastic+Systems+and+Its+Applications&pgis=1 ''The Theory of Equilibrium of Elastic Systems and Its Applications'']. Dover Publications.

* Dym, Clive L. (1997). ''Structural Modeling and Analysis''. Cambridge University Press. ISBN 0521495369.

* Dugas, René (1988). ''A History of Mechanics''. Courier Dover Publications. ISBN 0486656322.

* Hewson, Nigel R. (2003). ''Prestressed Concrete Bridges: Design and Construction''. Thomas Telford. ISBN 0727727745.

* Heyman, Jacques (1998). ''Structural Analysis: A Historical Approach''. Cambridge University Press. ISBN 0521622492.

* Heyman, Jacques (1999). ''The Science of Structural Engineering''. Imperial College Press. ISBN 1860941893.

* Hognestad, E. ''A Study of Combined Bending and Axial Load in Reinforced Concrete Members''. University of Illinois, Engineering Experiment Station, Bulletin Series N. 399.

* Jennings, Alan (2004) [http://www.amazon.co.uk/dp/0415268435 ''Structures: From Theory to Practice'']. Taylor & Francis. ISBN 9780415268431.

* Leonhardt, A. (1964). ''Vom Caementum zum Spannbeton, Band III (From Cement to Prestressed Concrete)''. Bauverlag GmbH.

* MacNeal, Richard H. (1994). ''Finite Elements: Their Design and Performance''. Marcel Dekker. ISBN 0824791622.

* Mörsch, E. (Stuttgart, 1908). ''Der Eisenbetonbau, seine Theorie und Anwendung, (Reinforced Concrete Construction, its Theory and Application)''. Konrad Wittwer, 3rd edition.

* Nedwell, P.J.; Swamy, R.N.(ed) (1994). ''Ferrocement:Proceedings of the Fifth International Symposium''. Taylor & Francis. ISBN 0419197001.

* Newton, Isaac; Leseur, Thomas; Jacquier, François (1822). [http://books.google.co.uk/books?id=TA-l3gysWaUC&printsec=frontcover&dq=Philosophi%C3%A6+Naturalis+Principia+Mathematica ''Philosophiæ Naturalis Principia Mathematica'']. Oxford University.

* Nilson, Arthur H.; Darwin, David; Dolan, Charles W. (2004). ''Design of Concrete Structures''. McGraw-Hill Professional. ISBN 0072483059.

* Rozhanskaya, Mariam; Levinova, I. S. (1996). "Statics" in Morelon, Régis & Rashed, Roshdi (1996). ''Encyclopedia of the History of Arabic Science'', '''vol. 2-3''', Routledge. ISBN 0415020638

* Schlaich, J., K. Schäfer, M. Jennewein (1987). "Toward a Consistent Design of Structural Concrete". ''PCI Journal'', Special Report, Vol. 32, No. 3.

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* Virdi, K.S. (2000). ''Abnormal Loading on Structures: Experimental and Numerical Modelling''. Taylor & Francis. ISBN 0419259600.

[[Category{{DEFAULTSORT: Structural engineering]]Engineering Theory}}

[[Category:Structural engineering]]