Discrete tomography - Revision history

en>Trivialist at 17:59, 7 December 2014

2014-12-07T17:59:10Z

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	~~In [[geotechnical engineering]],~~ '~~''bearing capacity''' is the capacity of [[soil]] to support the [[structural load\|loads]] applied to the ground~~. ~~The bearing capacity of soil~~ is the maximum average contact [[pressure]] between the [[foundation (architecture)\|foundation]] and the soil which should not produce [[shear strength (soil)\|shear]] failure in the soil. ''Ultimate bearing capacity'' is the theoretical maximum pressure which can be supported without failure; ''allowable bearing capacity'' is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.		Yoshiko is her name but she doesn't like when people use her complete title. Playing croquet is something I will by no means give up. Managing individuals is what I do in my working day job. Kansas is where her house is but she requirements to move because of her family.<br><br>Also visit my blog :: [http://www.Thehubermangroup.com/ActivityFeed/MyProfile/tabid/60/userId/24292/Default.aspx car warranty]

	~~There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure.~~

	~~== Introduction ==~~
	A foundation is the part of a structure which transmits the weight of the structure to the ground. All structures constructed on land are supported on foundations. A foundation is, therefore, a connecting link between the structure proper and the ground which supports it.

	~~== General shear failure ==~~
	~~The general shear failure case is the one normally analyzed~~. ~~Prevention against other failure modes~~ is ~~accounted for implicitly~~ in settlement calculations.<ref name=coduto>{{Citation\|surname=Coduto\|given=Donald\|author-link=\|year=2001\|title=Foundation Design\|Place=\|publisher=Prentice-Hall\|isbn=0-13-589706-8\|url=}}</ref> There are many different methods for computing when this failure will occur.

	~~== Terzaghi's Bearing Capacity Theory ==~~
	~~[[Karl von Terzaghi]] was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This theory states that a foundation~~ is ~~shallow if its depth~~ is ~~less than or equal~~ to ~~its width.<ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|edition=6th\|year=2007\|title=Principles~~ of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref> Later investigations, however, have suggested that foundations with a depth, measured from the ground surface, equal to 3 to 4 times their width may be defined as shallow foundations(Das, 2007).

	~~Terzaghi developed a method for determining bearing capacity for the general shear failure case in 1943. The equations are given below~~.

	~~For square foundations:~~
	:<~~math~~> ~~q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.4 \gamma ' B N_\gamma \~~ <~~/math>~~

	~~For continuous foundations:~~
	~~:<math> q_{ult} = c' N_c + \sigma '_{zD} N_q + 0.5 \gamma ' B N_\gamma \ </math~~>

	~~For circular foundations:~~
	:~~<math> q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.3 \gamma ' B N_\gamma \ </math>~~

	~~where~~
	:~~<math> N_q = \frac{ e ^{ 2 \pi \left( 0.75 - \phi '/360 \right) \tan \phi ' } }{2 \cos ^2 \left( 45 + \phi '/2 \right) } </math>~~
	~~:<math> N_c = 5.7 \ </math> for φ' = 0~~
	~~:<math> N_c = \frac{ N_q - 1 }{ \tan \phi '} </math> for φ' > 0~~
	~~:<math> N_\gamma = \frac{ \tan \phi ' }{2} \left( \frac{ K_{p \gamma} }{ \cos ^2 \phi ' } - 1 \right) </math>~~
	~~:''c''′ is the effective~~ [~~[cohesion (geology)\|cohesion]].~~
	:~~''σ<sub>zD<~~/~~sub>''′ is the vertical [[effective stress]] at the depth the foundation is laid.~~
	~~:γ''′ is the effective unit weight when saturated or the total unit weight when not fully saturated.~~
	~~:''B'' is the width or the diameter of the foundation.~~
	~~:''φ''′ is the effective internal [[friction#ange of friction\|angle of friction]].~~
	~~:''K<sub>pγ<~~/~~sub>'' is obtained graphically~~. ~~Simplifications have been made to eliminate the need for ''K<sub>pγ</sub>''~~. ~~One such was done by Coduto, given below, and it is accurate to within 10%.<ref name=coduto/>~~
	~~:<math> N_\gamma = \frac{ 2 \left( N_q + 1 \right) \tan \phi ' }{1 + 0.4 \sin 4 \phi ' }</math>~~

	~~For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modifications to the previous equations. The equations are given below.~~

	~~For square foundations:~~
	~~:<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.4 \gamma ' B N '_\gamma \ </math>~~

	~~For continuous foundations:~~
	~~:<math> q_{ult} = \frac{2}{3} c' N '_c + \sigma '_{zD} N '_q + 0.5 \gamma ' B N '_\gamma \ </math>~~

	~~For circular foundations:~~
	~~:<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.3 \gamma ' B N '_\gamma \ <~~/~~math>~~

	~~<math> N '_c, N '_q and N '_y <~~/~~math>, the modified bearing capacity factors, can be calculated by using the bearing capacity factors equations(for <math> N_c, N_q, and N_y<~~/~~math>, respectively) by replacing the effective internal angle of friction<math>(\phi ')<~~/~~math> by a value equal to <math> : tan^{-1}\, (\frac{2}{3} tan \phi ') <~~/~~math> <ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|edition=6th\|year=2007\|title=Principles of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref>~~

	~~== Factor of Safety ==~~
	~~Calculating the gross allowable-load bearing capacity of shallow foundations requires the application of a factor of safety(FS) to the gross ultimate bearing capacity, or:~~

	<math> q_{all} = \frac{q_{ult}}{FS} </math> <ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|year=2007\|title=Principles of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref>

	~~== Meyerhofs's Bearing Capacity theory ==~~
	~~In 1951, Meyerhof published a bearing capacity theory which could be applied to rough shallow and deep foundations.<ref name=Das2>{{\|publisher=CRC Press LLC\|id=\|}}</ref>~~

	~~==See also==~~
	*[[Geotechnical engineering]]
	*[[Foundation (architecture)]]
	*[[Soil mechanics]]

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

	~~==External links==~~
	*[http://~~www~~.~~geotechnicalinfo.com/bearing_capacity_factors.html Bearing Capacity Factors related to the angle of internal friction]~~
	~~{{Geotechnical engineering}}~~

	~~[[Category:Soil mechanics]]~~

	~~[[nl:Draagkracht (constructie)]~~]

Deltahedron: /* Theory */ cite Brualdi (2006)

2013-04-13T18:24:42Z

Theory: cite Brualdi (2006)

← Older revision		Revision as of 20:24, 13 April 2013
Line 1:		Line 1:
	~~Wilber Berryhill~~ is ~~what his wife enjoys~~ to ~~call him~~ and ~~he completely loves this name~~. ~~Mississippi~~ is ~~exactly where her home~~ is ~~but her spouse desires them to transfer~~. ~~What me~~ and ~~my family members love~~ is to ~~climb but I'm thinking~~ on ~~starting something new~~. ~~My day job~~ is ~~an invoicing~~ [~~http~~://~~brazil~~.~~amor~~-~~amore~~.~~com~~/~~irboothe psychics online] officer but I~~'~~ve currently applied~~ for ~~an additional~~ 1.<br><br>~~Visit my blog~~ ... ~~free~~ [~~http~~://~~www~~.~~taehyuna~~.~~net~~/xe/~~?document_srl~~=~~78721 psychic phone~~] ~~readings;~~ [http://~~isaworld~~.pe.kr/~~?document_srl=392088 isaworld~~.~~pe.kr~~],		In [[geotechnical engineering]], '''bearing capacity''' is the capacity of [[soil]] to support the [[structural load\|loads]] applied to the ground. The bearing capacity of soil is the maximum average contact [[pressure]] between the [[foundation (architecture)\|foundation]] and the soil which should not produce [[shear strength (soil)\|shear]] failure in the soil. ''Ultimate bearing capacity'' is the theoretical maximum pressure which can be supported without failure; ''allowable bearing capacity'' is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

			There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure.

			== Introduction ==
			A foundation is the part of a structure which transmits the weight of the structure to the ground. All structures constructed on land are supported on foundations. A foundation is, therefore, a connecting link between the structure proper and the ground which supports it.

			== General shear failure ==
			The general shear failure case is the one normally analyzed. Prevention against other failure modes is accounted for implicitly in settlement calculations.<ref name=coduto>{{Citation\|surname=Coduto\|given=Donald\|author-link=\|year=2001\|title=Foundation Design\|Place=\|publisher=Prentice-Hall\|isbn=0-13-589706-8\|url=}}</ref> There are many different methods for computing when this failure will occur.

			== Terzaghi's Bearing Capacity Theory ==
			[[Karl von Terzaghi]] was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This theory states that a foundation is shallow if its depth is less than or equal to its width.<ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|edition=6th\|year=2007\|title=Principles of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref> Later investigations, however, have suggested that foundations with a depth, measured from the ground surface, equal to 3 to 4 times their width may be defined as shallow foundations(Das, 2007).

			Terzaghi developed a method for determining bearing capacity for the general shear failure case in 1943. The equations are given below.

			For square foundations:
			:<math> q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.4 \gamma ' B N_\gamma \ </math>

			For continuous foundations:
			:<math> q_{ult} = c' N_c + \sigma '_{zD} N_q + 0.5 \gamma ' B N_\gamma \ </math>

			For circular foundations:
			:<math> q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.3 \gamma ' B N_\gamma \ </math>

			where
			:<math> N_q = \frac{ e ^{ 2 \pi \left( 0.75 - \phi '/360 \right) \tan \phi ' } }{2 \cos ^2 \left( 45 + \phi '/2 \right) } </math>
			:<math> N_c = 5.7 \ </math> for φ' = 0
			:<math> N_c = \frac{ N_q - 1 }{ \tan \phi '} </math> for φ' > 0
			:<math> N_\gamma = \frac{ \tan \phi ' }{2} \left( \frac{ K_{p \gamma} }{ \cos ^2 \phi ' } - 1 \right) </math>
			:''c''′ is the effective [[cohesion (geology)\|cohesion]].
			:''σ<sub>zD</sub>''′ is the vertical [[effective stress]] at the depth the foundation is laid.
			:γ''′ is the effective unit weight when saturated or the total unit weight when not fully saturated.
			:''B'' is the width or the diameter of the foundation.
			:''φ''′ is the effective internal [[friction#ange of friction\|angle of friction]].
			:''K<sub>pγ</sub>'' is obtained graphically. Simplifications have been made to eliminate the need for ''K<sub>pγ</sub>''. One such was done by Coduto, given below, and it is accurate to within 10%.<ref name=coduto/>
			:<math> N_\gamma = \frac{ 2 \left( N_q + 1 \right) \tan \phi ' }{1 + 0.4 \sin 4 \phi ' }</math>

			For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modifications to the previous equations. The equations are given below.

			For square foundations:
			:<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.4 \gamma ' B N '_\gamma \ </math>

			For continuous foundations:
			:<math> q_{ult} = \frac{2}{3} c' N '_c + \sigma '_{zD} N '_q + 0.5 \gamma ' B N '_\gamma \ </math>

			For circular foundations:
			:<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.3 \gamma ' B N '_\gamma \ </math>

			<math> N '_c, N '_q and N '_y </math>, the modified bearing capacity factors, can be calculated by using the bearing capacity factors equations(for <math> N_c, N_q, and N_y</math>, respectively) by replacing the effective internal angle of friction<math>(\phi ')</math> by a value equal to <math> : tan^{-1}\, (\frac{2}{3} tan \phi ') </math> <ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|edition=6th\|year=2007\|title=Principles of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref>

			== Factor of Safety ==
			Calculating the gross allowable-load bearing capacity of shallow foundations requires the application of a factor of safety(FS) to the gross ultimate bearing capacity, or:

			<math> q_{all} = \frac{q_{ult}}{FS} </math> <ref name=Das>{{Citation\|surname=Das\|given=Braja\|author-link=\|year=2007\|title=Principles of Foundation Engineering\|place=Stamford, CT\|publisher=Cengage Publisher\|id=}}</ref>

			== Meyerhofs's Bearing Capacity theory ==
			In 1951, Meyerhof published a bearing capacity theory which could be applied to rough shallow and deep foundations.<ref name=Das2>{{\|publisher=CRC Press LLC\|id=\|}}</ref>

			==See also==
			*[[Geotechnical engineering]]
			*[[Foundation (architecture)]]
			*[[Soil mechanics]]

			==References==
			{{reflist}}

			==External links==
			*[http://www.geotechnicalinfo.com/bearing_capacity_factors.html Bearing Capacity Factors related to the angle of internal friction]
			{{Geotechnical engineering}}

			[[Category:Soil mechanics]]

			[[nl:Draagkracht (constructie)]]

143.169.49.163: /* Algorithms */

2012-07-31T21:50:32Z

Algorithms

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