Augmented sixth chord - Revision history

en>Jerome Kohl: /* Tristan chord */ looks like OR

2014-09-15T16:38:36Z

Tristan chord: looks like OR

← Older revision		Revision as of 18:38, 15 September 2014
Line 1:		Line 1:


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71.31.4.90: /* Standard harmonic function */

2014-03-02T00:00:05Z

Standard harmonic function

← Older revision		Revision as of 02:00, 2 March 2014
Line 1:		Line 1:
	~~{{refimprove\|date=November 2010}}~~

	An '''elastic modulus''', or '''modulus of elasticity''', is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a [[force]] is applied to it. The elastic modulus of an object is defined as the [[slope]] of its [[stress–strain curve]] in the elastic deformation region:<ref>{{cite book \| last = Askeland \| first = Donald R. \| last2 = Phulé \| first2 = Pradeep P. \| title = The science and engineering of materials \| year = 2006 \| publisher = Cengage Learning \| page = 198 \| edition = 5th \| url = http://books.google.com/books?id=fRbZslUtpBYC&pg=PA198 \| isbn = 978-0-534-55396-8}}</ref> As such, a stiffer material will have a higher elastic modulus.

	~~:<math>\lambda \ \stackrel{\text{def}}{=}\ \frac {\text{stress}} {\text{strain}}</math>~~		Dalton is what's written across his birth certificate but he never really liked that name. The precious hobby for him also his kids is [http://Www.dailymail.co.uk/home/search.html?sel=site&searchPhrase=growing+plants growing plants] but he's been bringing on new things a short time ago. Auditing is where his primary income originates from. Massachusetts is where that he and his [http://Search.Un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=wife+stay&Submit=Go wife stay]. He's not godd at design but may also want to check their website: http://prometeu.net<br><br>My weblog - [http://prometeu.net clash of clans hack cydia]

	~~where lambda (<var>λ</var>)~~ is ~~the elastic modulus; <var>~~[~~[stress (physics)\|stress]]<~~/~~var> is the restoring force caused due to the deformation divided by the area to which the force is applied; and <var>[[strain (materials science)\|strain]]<~~/~~var> is the ratio of the change caused by the stress to the original state of the object~~. ~~If stress is measured in [[pascal (unit)\|pascal]]s, since strain is a dimensionless quantity, then the units of <var>λ</var> are pascals as well~~.~~<ref>{{cite book \| last = Beer \| first = Ferdinand P~~. ~~\| last2 = Johnston \| first2 = E~~. ~~Russell \| last3~~ = ~~Dewolf \| first3~~ = ~~John \| last4 = Mazurek \| first4 = David \| title = Mechanics of Materials \| year = 2009 \| publisher = McGraw Hill \| page = 56 \| isbn = 978-0-07-015389-9}}</ref>~~

	Since the denominator turns into unity if length is doubled, the elastic modulus becomes the stress induced in the material, when the sample of the material turns double of its original length on applying external force. While this endpoint is not realistic because most materials will fail before reaching it, it is practical, in that small fractions of the defining load will operate in exactly the same ratio. Thus, for steel with a [[Young's ~~modulus]] of 30 million psi, a 30 thousand psi load will elongate~~ a 1 inch bar by one thousandth of an inch; similarly, for metric units, a load of one-thousandth of the modulus (now measured in gigapascals) will change the length of a one-meter rod by a millimeter.

	~~Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined.~~
	~~The three~~ primary ~~ones are:~~

	* ''[[Young's modulus]]'' (<var>E</var>) describes tensile [[Elasticity (physics)\|elasticity]], or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of [[tensile stress]] to [[Tension (physics)\|tensile]] strain. It is ~~often referred to simply as the ''elastic modulus''.~~
	* The ''[~~[shear modulus]]'' or ''modulus of rigidity'' (<var>G<~~/~~var> or <math>\mu \,<~~/~~math>) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as [[shear stress]] over [[shear strain]]~~. ~~The shear modulus is part of the derivation of [[viscosity]]~~.
	* The ''[[bulk modulus]]'' (<var>K</var>) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as [[Stress (physics)#Stress deviator tensor\|volumetric stress]] over volumetric strain, and is the inverse of [[compressibility]]. The bulk modulus is an extension of Young's modulus to three dimensions.

	~~Three other elastic moduli are [[Axial Modulus]], [[Lamé's first parameter]], and [[P-wave modulus]].~~

	Homogeneous and [[isotropic]] (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.

	~~[[Inviscid fluids]] are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus is always zero.~~

	==~~Estimating value~~==
	E=~~33w^1.5*sqrt(f'c)~~
	w=~~density of concrete~~
	~~f'c~~=~~fracture stress~~

	E=~~57000sqrt(f'c)~~
	~~f'c=fracture stress~~
	~~(these are both only good up to 6000psi)~~

	==~~See also==~~
	* [[Bending stiffness]]
	* [[Dynamic modulus]]
	* [[Elastic limit]]
	* [[Elastic wave]]
	* [[Flexural modulus]]
	* [[Hooke's ~~Law]]~~
	* [[Impulse excitation technique]]
	* [[Proportional limit]]
	* [[Stiffness]]
	* [[Tensile strength]]
	* [[Transverse isotropy]]

	~~==References==~~
	~~{{reflist}}~~

	~~==Further reading==~~
	*{{cite book
	~~\| last = Hartsuijker~~
	~~\| first = C~~.
	~~\| last2 = Welleman~~
	~~\| first2 = J. W.~~
	~~\| title = Engineering Mechanics~~
	~~\| series = Volume 2~~
	~~\| year = 2001~~
	~~\| publisher = Springer~~
	~~\| isbn = 978~~-~~1-4020-4123-5}}~~

	~~{{Elastic moduli}}~~

	~~{{DEFAULTSORT:Elastic Modulus}}~~
	[~~[Category~~:~~Elasticity (physics)]]~~
	~~[[Category:Deformation]]~~

	~~[[de:Elastizitätsmodul]]~~
	~~[[simple:Elastic modulus]~~]

24.127.68.167: /* Extended functions */

2013-08-14T03:28:18Z

Extended functions

← Older revision		Revision as of 05:28, 14 August 2013
Line 1:		Line 1:
	~~More mature video games ought not~~ to be [http://~~Www~~.~~adobe~~.com/~~cfusion/search/index.cfm~~?~~term~~=&~~discarded&loc~~=~~en_us&siteSection~~=~~home discarded]~~. ~~When you loved this post along with you would like~~ to ~~be given more info concerning~~ [~~http:~~/~~/circuspartypanama.com clash~~ of ~~clans cheats ipod] kindly go~~ to ~~our own page~~. ~~They happen to be worth some money at several video retailers. While you buy and sell~~ a ~~number~~ of ~~game titles, you might even get your upcoming reputation at no cost!~~<br><br>~~Lee~~ are ~~able to assist those gems to [http://Www~~.~~Bing~~.~~com/search?q~~=~~instantly+fortify&form~~=~~MSNNWS&mkt~~=~~en-us&pq~~=~~instantly+fortify instantly fortify] his army. He tapped 'Yes,'" probably without thinking. Within just under a month to do with walking around a small number~~ of ~~hours on a daily basis, he''d spent well~~-~~nigh 1000 dollars.~~<br>~~<br>clash of clans~~ is ~~a ideal game~~, ~~which usually requires one to build your personal village~~, ~~discover warriors, raid funds and build your own clan and so~~ on. ~~there~~ is a ~~lot~~ a ~~lot good deal to this video sports and~~ for ~~every~~ one of ~~these you require jewels~~ to ~~play~~, ~~as you really like. Clash of Clans hack~~ allows ~~you to obtain as~~ many ~~jewels as you like. There is an unlimited regarding gems you could yield with all the Clash~~ of ~~Clans cheats you can get online, however you need~~ to be ~~specific about the weblink you~~ are ~~using for some of them exclusively waste materials your serious amounts of also dont get you actually anything more.~~<br><br>~~Collide~~ of ~~Clans is definitely a popular sport made~~ to ~~end up being experienced on multiple systems, for the most part iOS and also android. The overall game~~ is ~~incredibly intriguing but presently and also comes a spot on legend, where~~ the ~~character gets trapped because using not enough gems~~. ~~However, this problem~~ is ~~becoming able~~ to ~~easily turn into resolved~~.<br><br>~~While~~ the ~~game is per mobile edition,~~ it is ~~performing not lack substance comparable to many mobile games~~. ~~So, defragging~~ the ~~course~~ of ~~action registry will boost specific system overall performance within order to a fantastic extent. I usually get anywhere from 4000 to 6000 m - Points from a day ($4 to $5 for Amazon~~. The ~~showed off the massively anticipated i - Blackberry 5 for the first time in San Francisco on Wednesday morning~~ (~~September 12, 2012). There is a huge demand during some i - Mobile device 4 application not sole promoting business but also helps users to receive extra money.~~<br><br>~~Ought to you are~~ the ~~proud holder~~ of an ~~ANY transportable device that runs on iOS or android~~ as ~~a a touchscreen tablet computer or a smart phone~~, ~~then you definitely definitely have already been sensitive of~~ the ~~revolution using place right now a world~~ of ~~mobile personal game "~~The ~~Clash Having~~ to ~~do with Clans"~~, and ~~you would be~~ in ~~demand pointing to conflict of families totally free of charge jewels compromise because a bit more gems~~, ~~elixir~~ and ~~gold are needed seriously on acquire every battle~~.~~<br><br>If you're are playing~~ a ~~flaunting activity~~, ~~and you equally don't possess knowledge including it, establish~~ the ~~problem stage to rookie~~. ~~This should help the customer pick-up~~ in ~~the outstanding options~~ that ~~come when using~~ the ~~game and discover closer round the field~~. ~~Should you set it more than~~ that~~, in all probability you~~'~~ll get frustrated and suggests possess fun~~.		{{refimprove\|date=November 2010}}

			An '''elastic modulus''', or '''modulus of elasticity''', is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a [[force]] is applied to it. The elastic modulus of an object is defined as the [[slope]] of its [[stress–strain curve]] in the elastic deformation region:<ref>{{cite book \| last = Askeland \| first = Donald R. \| last2 = Phulé \| first2 = Pradeep P. \| title = The science and engineering of materials \| year = 2006 \| publisher = Cengage Learning \| page = 198 \| edition = 5th \| url = http://books.google.com/books?id=fRbZslUtpBYC&pg=PA198 \| isbn = 978-0-534-55396-8}}</ref> As such, a stiffer material will have a higher elastic modulus.

			:<math>\lambda \ \stackrel{\text{def}}{=}\ \frac {\text{stress}} {\text{strain}}</math>

			where lambda (<var>λ</var>) is the elastic modulus; <var>[[stress (physics)\|stress]]</var> is the restoring force caused due to the deformation divided by the area to which the force is applied; and <var>[[strain (materials science)\|strain]]</var> is the ratio of the change caused by the stress to the original state of the object. If stress is measured in [[pascal (unit)\|pascal]]s, since strain is a dimensionless quantity, then the units of <var>λ</var> are pascals as well.<ref>{{cite book \| last = Beer \| first = Ferdinand P. \| last2 = Johnston \| first2 = E. Russell \| last3 = Dewolf \| first3 = John \| last4 = Mazurek \| first4 = David \| title = Mechanics of Materials \| year = 2009 \| publisher = McGraw Hill \| page = 56 \| isbn = 978-0-07-015389-9}}</ref>

			Since the denominator turns into unity if length is doubled, the elastic modulus becomes the stress induced in the material, when the sample of the material turns double of its original length on applying external force. While this endpoint is not realistic because most materials will fail before reaching it, it is practical, in that small fractions of the defining load will operate in exactly the same ratio. Thus, for steel with a [[Young's modulus]] of 30 million psi, a 30 thousand psi load will elongate a 1 inch bar by one thousandth of an inch; similarly, for metric units, a load of one-thousandth of the modulus (now measured in gigapascals) will change the length of a one-meter rod by a millimeter.

			Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined.
			The three primary ones are:

			* ''[[Young's modulus]]'' (<var>E</var>) describes tensile [[Elasticity (physics)\|elasticity]], or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of [[tensile stress]] to [[Tension (physics)\|tensile]] strain. It is often referred to simply as the ''elastic modulus''.
			* The ''[[shear modulus]]'' or ''modulus of rigidity'' (<var>G</var> or <math>\mu \,</math>) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as [[shear stress]] over [[shear strain]]. The shear modulus is part of the derivation of [[viscosity]].
			* The ''[[bulk modulus]]'' (<var>K</var>) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as [[Stress (physics)#Stress deviator tensor\|volumetric stress]] over volumetric strain, and is the inverse of [[compressibility]]. The bulk modulus is an extension of Young's modulus to three dimensions.

			Three other elastic moduli are [[Axial Modulus]], [[Lamé's first parameter]], and [[P-wave modulus]].

			Homogeneous and [[isotropic]] (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.

			[[Inviscid fluids]] are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus is always zero.

			==Estimating value==
			E=33w^1.5*sqrt(f'c)
			w=density of concrete
			f'c=fracture stress

			E=57000sqrt(f'c)
			f'c=fracture stress
			(these are both only good up to 6000psi)

			==See also==
			* [[Bending stiffness]]
			* [[Dynamic modulus]]
			* [[Elastic limit]]
			* [[Elastic wave]]
			* [[Flexural modulus]]
			* [[Hooke's Law]]
			* [[Impulse excitation technique]]
			* [[Proportional limit]]
			* [[Stiffness]]
			* [[Tensile strength]]
			* [[Transverse isotropy]]

			==References==
			{{reflist}}

			==Further reading==
			*{{cite book
			\| last = Hartsuijker
			\| first = C.
			\| last2 = Welleman
			\| first2 = J. W.
			\| title = Engineering Mechanics
			\| series = Volume 2
			\| year = 2001
			\| publisher = Springer
			\| isbn = 978-1-4020-4123-5}}

			{{Elastic moduli}}

			{{DEFAULTSORT:Elastic Modulus}}
			[[Category:Elasticity (physics)]]
			[[Category:Deformation]]

			[[de:Elastizitätsmodul]]
			[[simple:Elastic modulus]]

70.169.149.207: /* Double-diminished triad */

2012-08-07T19:42:04Z

Double-diminished triad

New page

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