Intersecting Chords - Revision history

DT Online at 15:22, 4 July 2017

2017-07-04T15:22:56Z

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	* but, for small deflections, Δ<sup>2</sup> will be negligible		* but, for small deflections, Δ<sup>2</sup> will be negligible
	* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''		* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''
	''(see ~~[https://www.amazon.co.uk/gp/~~product~~/0306812835/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN~~=0306812835~~&linkCode~~=~~as2&tag=dton06-21 ''''~~Structures: Or Why Things Don't Fall Down' by J.E.Gordon'''])'' </span>		''(see '''<dtamazon product="0306812835" type="text">Structures: Or Why Things Don't Fall Down by J.E.Gordon</dtamazon>)''''' </span>
	\|[[File:BeamChordsTheorem.png\|400px\|right]]		\|[[File:BeamChordsTheorem.png\|400px\|right]]
	\|}		\|}

DT Online at 10:03, 14 November 2016

2016-11-14T10:03:12Z

← Older revision		Revision as of 10:03, 14 November 2016
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	* but, for small deflections, Δ<sup>2</sup> will be negligible		* but, for small deflections, Δ<sup>2</sup> will be negligible
	* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''		* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''
	''(see ~~‘Structures’ by~~ [~~http~~://en.~~wikipedia~~.~~org~~/~~wiki~~/~~J.E._Gordon~~ J.E.Gordon] ~~ISBN 0 14 02.1961 7~~)'' </span>		''(see [https://www.amazon.co.uk/gp/product/0306812835/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0306812835&linkCode=as2&tag=dton06-21 ''''Structures: Or Why Things Don't Fall Down' by J.E.Gordon'''])'' </span>
	\|[[File:BeamChordsTheorem.png\|400px\|right]]		\|[[File:BeamChordsTheorem.png\|400px\|right]]
	\|}		\|}

DT Online: Removed a category

2015-12-21T11:23:38Z

Removed a category

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	[[Category:Secondary]]		[[Category:Secondary]]
	~~[[Category:Structures and Environments]]~~
	[[Category:Terminology]]		[[Category:Terminology]]

DT Online at 13:41, 2 June 2015

2015-06-02T13:41:46Z

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	[[Category:Secondary]]		[[Category:Secondary]]
	[[Category:Structures]]		[[Category:Structures and Environments]]
	[[Category:Terminology]]		[[Category:Terminology]]

DT Online at 09:06, 27 February 2015

2015-02-27T09:06:32Z

← Older revision		Revision as of 09:06, 27 February 2015
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	* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''		* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''
	''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)'' </span>		''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)'' </span>
	\|[[File:~~DeflectedBeamChords~~.~~jpg~~\|400px\|right]]		\|[[File:BeamChordsTheorem.png\|400px\|right]]
	\|}		\|}

DT Online at 08:34, 27 February 2015

2015-02-27T08:34:03Z

← Older revision		Revision as of 08:34, 27 February 2015
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	* (2R-Δ) x Δ = ½cd x ½cd		* (2R-Δ) x Δ = ½cd x ½cd
	* but, for small deflections, Δ<sup>2</sup> will be negligible		* but, for small deflections, Δ<sup>2</sup> will be negligible
	* so R = cd<sup>2</sup> ÷ 8 x Δ		* so '''Bending Radius ''(R)'' = cd<sup>2</sup> ÷ (8 x Δ)'''
	''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)'' </span>		''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)'' </span>
	\|[[File:DeflectedBeamChords.jpg\|400px\|right]]		\|[[File:DeflectedBeamChords.jpg\|400px\|right]]

DT Online: Improved presentation

2015-02-27T07:59:01Z

Improved presentation

← Older revision		Revision as of 07:59, 27 February 2015
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	[[File:ChordTheorem.jpg\|~~200px~~\|right]]		[[File:ChordTheorem.jpg\|300px\|right]]
	This theorem relates to a characteristic of a [http://en.wikipedia.org/wiki/Cyclic_quadrilateral#Characterizations '''cyclic quadlitateral'''], the diagonals of which are two intersecting chords of the circumscribing circle.		This theorem relates to a characteristic of a [http://en.wikipedia.org/wiki/Cyclic_quadrilateral#Characterizations '''cyclic quadlitateral'''], the diagonals of which are two intersecting chords of the circumscribing circle.

	It can be useful when measuring the radius of bending of a deflected beam~~, for example,~~ if one of the chords is taken to be the length of the beam
	~~[[File:DeflectedBeamChords.jpg\|400px\|right]]~~		The [http://www.mathopenref.com/chordsintersecting.html '''Intersecting Chords Theorem'''] states that the relationship '''''(ao x ob = co x od)''''' is true for <u>'''any'''</u> two intersecting chords, whether or not one of them is a diameter.

			{\| cellpadding="5"
			\|-
			\| '''Measuring Beam Deflections'''
			\| <span style="color:#B00000">
			The theorem can be useful when measuring the radius of bending of a deflected beam if one of the chords is taken to be the length of the beam
	e.g.		e.g.
	# set up a strip of material as a simple beam		* set up a strip of material as a simple beam
	# note the distance between supports '''''(cd)'''''		* note the distance between supports '''''(cd)'''''
	# apply a central load to make it bend - or '''''[[Beam Deflection\|‘deflect’(Δ)]]''''' - therefore '''co = od = ½cd'''		* apply a central load to make it bend - or '''''[[Beam Deflection\|‘deflect’(Δ)]]''''' - therefore '''co = od = ½cd'''
	# measure the deflection '''''(ob)'''''		* measure the deflection '''''(ob)'''''
	Bending Radius (R) can be calculated as follows:		Bending Radius ''(R)'' can be calculated as follows:
	* ao x ob = co x od		* ao x ob = co x od
	* (2R-Δ) x Δ = ½cd x ½cd		* (2R-Δ) x Δ = ½cd x ½cd
	* but, for small deflections, Δ<sup>2</sup> will be negligible		* but, for small deflections, Δ<sup>2</sup> will be negligible
	* so R = cd<sup>2</sup> ÷ 8 x Δ		* so R = cd<sup>2</sup> ÷ 8 x Δ
	''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)''		''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)'' </span>
			\|[[File:DeflectedBeamChords.jpg\|400px\|right]]
			\|}



	~~{{Terminology}}~~		[[Category:Secondary]]
	[[Category:Structures]]		[[Category:Structures]]
			[[Category:Terminology]]

DT Online: Added category link

2014-12-19T15:45:47Z

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	{{Terminology}}		{{Terminology}}
			[[Category:Structures]]

DT Online: Added Template

2014-12-18T18:27:43Z

Added Template

← Older revision		Revision as of 18:27, 18 December 2014
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	* so R = cd<sup>2</sup> ÷ 8 x Δ		* so R = cd<sup>2</sup> ÷ 8 x Δ
	''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)''		''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)''


			{{Terminology}}

DT Online: Added link to J.E.Gordon

2014-11-08T10:04:19Z

Added link to J.E.Gordon

← Older revision		Revision as of 10:04, 8 November 2014
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	* but, for small deflections, Δ<sup>2</sup> will be negligible		* but, for small deflections, Δ<sup>2</sup> will be negligible
	* so R = cd<sup>2</sup> ÷ 8 x Δ		* so R = cd<sup>2</sup> ÷ 8 x Δ
	''(see ‘Structures’ by J.E.Gordon ISBN 0 14 02.1961 7)''		''(see ‘Structures’ by [http://en.wikipedia.org/wiki/J.E._Gordon J.E.Gordon] ISBN 0 14 02.1961 7)''