Relaxation methods applied to engineering problems I—The deflexion of beams under transverse loading

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Abstract

I—According to the approximate theory of flexure, the transverse loading and deflexion of a girder initially straight are related by the equations ω = d 2 M / dx 2 , (1) B d 2 y / dx 2 = M , (2) whence we have on elimination of M ω = d 2 / dx 2 ( B d 2 y / dx 2 ). (3) In (l)-(3), ω, y and M relate to a section of the girder distant x from one end; M is the bending moment at this section, y the deflexion of the central line from its initial (unstrained) position, and ω the line intensity of the transverse loading. B ( = El ) denotes the flexural rigidity. 2—The solution of (3) entails four arbitrary constants, which can be used to satisfy two imposed conditions at each end of the girder.

Publisher

The Royal Society

Subject

Pharmacology (medical)

Reference3 articles.

1. H opkins H . J . 1937 Engineering 143 469.

2. a Proc. Roy;Southwell R .;Soc. A,1935

3. W h ittak er E . T. an d R obinson G. 1926 " The Calculus of O bservations" 2nd ed. L o n d o n : Blackie and Son.

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Richard Vynne Southwell, 1888-1970;Biographical Memoirs of Fellows of the Royal Society;1972-11

2. Recent Mathematical Tables;Mathematics of Computation;1943

3. I. Numerical differentiation near the limits of a difference table;The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science;1942-01

4. Formulae for Numerical Differentiation;The Mathematical Gazette;1941-02

5. Formulae for Numerical Differentiation;The Mathematical Gazette;1941-02

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