Structural engineering theory: Difference between revisions

Revision as of 22:47, 11 January 2012

Revision as of 11:13, 9 May 2012

Line 1:

[[ImageFile:bolt-in-shear.PNG|thumb|right|Figure of a [[Screw|bolt]] in [[Shear stress|shear]]. Top figure illustrates single shear, bottom figure illustrates double shear.]]

[[Structural engineering]] depends upon a detailed knowledge of [[Structural load|loads]], [[physics]] and [[materials]] to understand and predict how structures support and resist self-weight and imposed loads. To apply the knowledge successfully a structural engineer will need a detailed knowledge of [[mathematics]] and of relevant empirical and theoretical [[design codes]]. He will also need to know about the [[corrosion]] resistance of the materials and structures, especially when those structures are exposed to the external environment.

Line 92:

<math>r + b = 2j</math>

It should be noted that even if this relationship does hold, a structure can be arranged in such a way as to be statically indeterminate.<ref>{{cite book|title=Structural Modeling and Analysis|author=Dym, Clive L.|publisher=Cambridge University Press|date=1997|isbn=05214953690-521-49536-9|pages=98}}</ref>

==Elasticity==

Line 108:

==Plasticity==

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

{{Main|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=05216224920-521-62249-2}}</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.

Plasticity theory states that the point at which a structure collapses (reaches yield) lies between an upper and a lower bound on the load, defined as follows:

Line 119:

*If, for a small increment of displacement, the internal work done by the structure, assuming that the moment at every plastic hinge is equal to the yield moment and that the boundary conditions are satisfied, is equal to the external work done by the given load for that same small increment of displacement, then that load is an '''upper bound''' on the collapse load.

If the correct collapse load is found, the two methods will give the same result for the collapse load.<ref>{{cite book|title=Design of Concrete Structures|author=Nilson, Arthur H.; Darwin, David; Dolan, Charles W.|publisher=McGraw-Hill Professional|date=2004|isbn=00724830590-07-248305-9|pages=486}}</ref>

Plasticity theory depends upon a correct understanding of when yield will occur. A number of different models for stress distribution and approximations to the [[yield surface]] of plastic materials exist:<ref name=Heyman>{{cite book|title=The Science of Structural Engineering|author=Heyman, Jacques|url=http://books.google.co.uk/books?id=Au34lwRovHIC&dq=Leonhard+Euler+Daniel+Bernoulli+Beam+equation|date=1999|publisher=Imperial College Press|isbn=18609418931-86094-189-3}}</ref>

*[[Mohr's circle]]

Line 128:

==The Euler-Bernoulli beam equation==

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

{{Main|Euler-Bernoulli beam equation}}

Line 164:

==Buckling==

{{Main|Buckling}}

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

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.

Line 196:

<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 05214953690-521-49536-9.

* Dugas, René (1988). ''A History of Mechanics''. Courier Dover Publications. ISBN 04866563220-486-65632-2.

* Hewson, Nigel R. (2003). ''Prestressed Concrete Bridges: Design and Construction''. Thomas Telford. ISBN 07277277450-7277-2774-5.

* Heyman, Jacques (1998). ''Structural Analysis: A Historical Approach''. Cambridge University Press. ISBN 05216224920-521-62249-2.

* Heyman, Jacques (1999). ''The Science of Structural Engineering''. Imperial College Press. ISBN 18609418931-86094-189-3.

* 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 9780415268431978-0-415-26843-1.

* 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 08247916220-8247-9162-2.

* 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 04191970010-419-19700-1.

* 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 00724830590-07-248305-9.

* 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 04150206380-415-02063-8

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

* Scott, Richard (2001). ''In the Wake of Tacoma: Suspension Bridges and the Quest for Aerodynamic Stability''. ASCE Publications. ISBN 07844054250-7844-0542-5.

* Turner, J.; Clough, R.W.; Martin, H.C.; Topp, L.J. (1956). "Stiffness and Deflection of Complex Structures". ''Journal of Aeronautical Science'' '''Issue 23'''.

* Virdi, K.S. (2000). ''Abnormal Loading on Structures: Experimental and Numerical Modelling''. Taylor & Francis. ISBN 04192596000-419-25960-0.

{{DEFAULTSORT:Structural Engineering Theory}}