Beams - Revision history

wikademia>Wikademia: Text replace - 'w:' to 'Wikipedia:'

2009-04-11T18:13:12Z

Text replace - 'w:' to 'Wikipedia:'

← Older revision		Revision as of 18:13, 11 April 2009
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	===Centroids===		===Centroids===
	If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by the following equations. (Also see the [[w:List_of_centroids\|List of Centroids]] on Wikipedia.)		If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by the following equations. (Also see the [[Wikipedia:List_of_centroids\|List of Centroids]] on Wikipedia.)
	<BR>		<BR>
	<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)		<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)
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	===Bending===		===Bending===
	[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]		[[Wikipedia:List_of_area_moments_of_inertia\|List of area moments of inertia]]
	A bending beam is <math>\ w</math>.		A bending beam is <math>\ w</math>.
	<BR>		<BR>
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	'''Study guide:'''		'''Study guide:'''
	# Wikipedia article:[[w:Distributed force\|Distributed force]]		# Wikipedia article:[[Wikipedia:Distributed force\|Distributed force]]
	# Wikipedia article:[[w:Center_of_mass\|Center of mass]]		# Wikipedia article:[[Wikipedia:Center_of_mass\|Center of mass]]
	# Wikipedia article:[[w:Centroid\|Centroid]]		# Wikipedia article:[[Wikipedia:Centroid\|Centroid]]
	# Wikipedia article:[[w:List of centroids\|List of centroids]]		# Wikipedia article:[[Wikipedia:List of centroids\|List of centroids]]
	# Wikipedia article:[[w:Pappus's centroid theorem\|Pappus's centroid theorem]]		# Wikipedia article:[[Wikipedia:Pappus's centroid theorem\|Pappus's centroid theorem]]
	# Wikipedia article:[[w:Beam (structure)\|Beam (structure)]]		# Wikipedia article:[[Wikipedia:Beam (structure)\|Beam (structure)]]
	# Wikipedia article:[[w:Beam theory\|Beam theory]]		# Wikipedia article:[[Wikipedia:Beam theory\|Beam theory]]
	# Wikipedia article:[[w:Statically indeterminate\|Statically indeterminate]]		# Wikipedia article:[[Wikipedia:Statically indeterminate\|Statically indeterminate]]
	# Wikipedia article:[[w:Torsion\|Torsion]]		# Wikipedia article:[[Wikipedia:Torsion\|Torsion]]
	# Wikipedia article:[[w:Shear_stress\|Shear]]		# Wikipedia article:[[Wikipedia:Shear_stress\|Shear]]
	# Wikipedia article:[[w:Bending\|Bending]]		# Wikipedia article:[[Wikipedia:Bending\|Bending]]
	# Wikipedia article:[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]		# Wikipedia article:[[Wikipedia:List_of_area_moments_of_inertia\|List of area moments of inertia]]

	[[Category:Statics]]		[[Category:Statics]]

wikademia>Wikademia at 00:56, 11 April 2009

2009-04-11T00:56:44Z

← Older revision		Revision as of 00:56, 11 April 2009
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			{{ntnes}}
	==Lecture==		==Lecture==
	Distributed forces are very common in the design and analysis of structures themselves, while point forces are often what structures are designed to withstand. The weight of a stationary car on a bridge should be interpreted as four point forces at the point of contact of each tire with the bridge, while the weight of a long train could be interpreted as a distributed force along the length of the train.		Distributed forces are very common in the design and analysis of structures themselves, while point forces are often what structures are designed to withstand. The weight of a stationary car on a bridge should be interpreted as four point forces at the point of contact of each tire with the bridge, while the weight of a long train could be interpreted as a distributed force along the length of the train.

wikademia>Wikademia at 21:13, 10 April 2009

2009-04-10T21:13:01Z

← Older revision		Revision as of 21:13, 10 April 2009
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	'''Part of the [[Topic:Statics\|Statics]] course offered by the ''[[Topic:Applied Mechanics\|Division of Applied Mechanics]]'', ''[[School:Engineering\|School of Engineering]]'' and the ''[[Portal:Engineering and Technology\|Engineering and Technology Portal]]'''''

	==Lecture==		==Lecture==
	Distributed forces are very common in the design and analysis of structures themselves, while point forces are often what structures are designed to withstand. The weight of a stationary car on a bridge should be interpreted as four point forces at the point of contact of each tire with the bridge, while the weight of a long train could be interpreted as a distributed force along the length of the train.		Distributed forces are very common in the design and analysis of structures themselves, while point forces are often what structures are designed to withstand. The weight of a stationary car on a bridge should be interpreted as four point forces at the point of contact of each tire with the bridge, while the weight of a long train could be interpreted as a distributed force along the length of the train.

wikademia>Wikademia: 14 revisions

2009-04-10T20:00:15Z

14 revisions

← Older revision	Revision as of 20:00, 10 April 2009
(No difference)

wikademia>Gustable at 01:20, 6 July 2008

2008-07-06T01:20:59Z

← Older revision		Revision as of 01:20, 6 July 2008
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	[[Category:Statics]]		[[Category:Statics]]
	~~[[Category:Advanced Classical Mechanics]]~~
	~~[[Category:Applied Mechanics]]~~
	~~[[Category:Mechanical Engineering]]~~
	~~[[Category:Engineering]]~~

wikademia>CommonsDelinker: Replacing Image:Beam_in_Bending.png with Image:Bending.png (by Rlevse because: Was in category "Duplicate", exact duplicate).

2008-03-02T18:58:17Z

Replacing Image:Beam_in_Bending.png with Image:Bending.png (by Rlevse because: Was in category "Duplicate", exact duplicate).

← Older revision		Revision as of 18:58, 2 March 2008
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	===Distributed Forces===		===Distributed Forces===
	[[Image:~~Beam_in_Bending~~.png\|thumb\|250px\|left\|A Beam Bending Under a Distributed Force]]		[[Image:Bending.png\|thumb\|250px\|left\|A Beam Bending Under a Distributed Force]]
	A distributed force is a force applied over a length, area or volume. A line-distributed force such as the weight of a bridge suspended off of a single tension wire, is measured in units of force per unit of length (Newtons/meter). An area-distributed force such as the weight of a ship's hull against the body of water it floats in, is measured in units of force per unit of area (Newtons/m<sup>2</sup>) and is referred to as ''pressure'' when associated with the force of water and ''stress'' when associated with the internal forces affecting solids (such as those invoked by tension or compression). A volume-distributed force such as the force of gravity affecting a mass within the gravity field of a celestial body, is measured in units of force per unit of volume (Newtons/m<sup>3</sup>) and is often called a ''body force''. A distributed force, like any force, may be simplified into a resultant point force <math>\ R</math>, which acts at the ''centroid'' of the function described by the resultant force <math>\ w</math>.		A distributed force is a force applied over a length, area or volume. A line-distributed force such as the weight of a bridge suspended off of a single tension wire, is measured in units of force per unit of length (Newtons/meter). An area-distributed force such as the weight of a ship's hull against the body of water it floats in, is measured in units of force per unit of area (Newtons/m<sup>2</sup>) and is referred to as ''pressure'' when associated with the force of water and ''stress'' when associated with the internal forces affecting solids (such as those invoked by tension or compression). A volume-distributed force such as the force of gravity affecting a mass within the gravity field of a celestial body, is measured in units of force per unit of volume (Newtons/m<sup>3</sup>) and is often called a ''body force''. A distributed force, like any force, may be simplified into a resultant point force <math>\ R</math>, which acts at the ''centroid'' of the function described by the resultant force <math>\ w</math>.
	<math>\bar x = \frac{\int x w dx}{R}</math>		<math>\bar x = \frac{\int x w dx}{R}</math>

70.133.76.196: /* Assignments */

2008-02-13T06:39:22Z

Assignments

← Older revision		Revision as of 06:39, 13 February 2008
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	# Wikipedia article:[[w:Torsion\|Torsion]]		# Wikipedia article:[[w:Torsion\|Torsion]]
	# Wikipedia article:[[w:Shear_stress\|Shear]]		# Wikipedia article:[[w:Shear_stress\|Shear]]
			# Wikipedia article:[[w:Bending\|Bending]]
			# Wikipedia article:[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]

	[[Category:Statics]]		[[Category:Statics]]

70.133.76.196: /* Bending */

2008-02-13T06:36:34Z

Bending

← Older revision		Revision as of 06:36, 13 February 2008
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	===Bending===		===Bending===
			[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]
	A bending beam is <math>\ w</math>.		A bending beam is <math>\ w</math>.
	<BR>		<BR>
	<BR>		<BR>

	==Assignments==		==Assignments==
	'''Activities:'''		'''Activities:'''

70.133.76.196: /* Centroids */

2008-02-13T06:25:45Z

Centroids

← Older revision		Revision as of 06:25, 13 February 2008
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	===Centroids===		===Centroids===
	If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by:		If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by the following equations. (Also see the [[w:List_of_centroids\|List of Centroids]] on Wikipedia.)
	<BR>		<BR>
	<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)		<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)

wikademia>Mu301: /* Assignments */ name

2008-01-08T03:21:37Z

Assignments: name

← Older revision		Revision as of 03:21, 8 January 2008
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	==Assignments==		==Assignments==
	'''Activities:'''		'''Activities:'''
	* Create an [[activity]]		* Create an [[Beams/activity\|activity]]

	'''Readings:'''		'''Readings:'''

← Older revision		Revision as of 18:13, 11 April 2009
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	===Centroids===		===Centroids===
	If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by the following equations. (Also see the [[w:List_of_centroids\|List of Centroids]] on Wikipedia.)		If a body has a uniform density, then as we may see in equation (2) above, the density cancels out, and we are left with a resulting '''COM''' that is determined as a geometric analysis and is called a '''centroid'''. The '''centroid''' of a volume may be calculated by the following equations. (Also see the [[Wikipedia:List_of_centroids\|List of Centroids]] on Wikipedia.)
	<BR>		<BR>
	<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)		<math>\bar x = \frac{\int x dV}{V}</math>, <math>\bar y = \frac{\int y dV}{V}</math>, <math>\bar z = \frac{\int z dV}{V}</math> (4)
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	===Bending===		===Bending===
	[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]		[[Wikipedia:List_of_area_moments_of_inertia\|List of area moments of inertia]]
	A bending beam is <math>\ w</math>.		A bending beam is <math>\ w</math>.
	<BR>		<BR>
Line 53:		Line 53:

	'''Study guide:'''		'''Study guide:'''
	# Wikipedia article:[[w:Distributed force\|Distributed force]]		# Wikipedia article:[[Wikipedia:Distributed force\|Distributed force]]
	# Wikipedia article:[[w:Center_of_mass\|Center of mass]]		# Wikipedia article:[[Wikipedia:Center_of_mass\|Center of mass]]
	# Wikipedia article:[[w:Centroid\|Centroid]]		# Wikipedia article:[[Wikipedia:Centroid\|Centroid]]
	# Wikipedia article:[[w:List of centroids\|List of centroids]]		# Wikipedia article:[[Wikipedia:List of centroids\|List of centroids]]
	# Wikipedia article:[[w:Pappus's centroid theorem\|Pappus's centroid theorem]]		# Wikipedia article:[[Wikipedia:Pappus's centroid theorem\|Pappus's centroid theorem]]
	# Wikipedia article:[[w:Beam (structure)\|Beam (structure)]]		# Wikipedia article:[[Wikipedia:Beam (structure)\|Beam (structure)]]
	# Wikipedia article:[[w:Beam theory\|Beam theory]]		# Wikipedia article:[[Wikipedia:Beam theory\|Beam theory]]
	# Wikipedia article:[[w:Statically indeterminate\|Statically indeterminate]]		# Wikipedia article:[[Wikipedia:Statically indeterminate\|Statically indeterminate]]
	# Wikipedia article:[[w:Torsion\|Torsion]]		# Wikipedia article:[[Wikipedia:Torsion\|Torsion]]
	# Wikipedia article:[[w:Shear_stress\|Shear]]		# Wikipedia article:[[Wikipedia:Shear_stress\|Shear]]
	# Wikipedia article:[[w:Bending\|Bending]]		# Wikipedia article:[[Wikipedia:Bending\|Bending]]
	# Wikipedia article:[[w:List_of_area_moments_of_inertia\|List of area moments of inertia]]		# Wikipedia article:[[Wikipedia:List_of_area_moments_of_inertia\|List of area moments of inertia]]

	[[Category:Statics]]		[[Category:Statics]]