Calculating Forces in Beams - Revision history

DT Online at 14:53, 31 May 2019

2019-05-31T14:53:05Z

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	In the case of a '''[[Class 2 Lever\|Second Class Lever]]''' as shown.		In the case of a '''[[Class 2 Lever\|Second Class Lever]]''' as shown.

	::::::::::'''Load x distance d1 = Effort x distance d2'''		::::::::::'''Load x distance d1 = Effort x distance (d1 + d2)'''
	[[File:WheelbarrowLabelled.png \|300px\|left]]		[[File:WheelbarrowLabelled.png \|300px\|left]]

DT Online at 07:23, 19 September 2018

2018-09-19T07:23:37Z

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	In the examples of a flag on a flagpole, or a sail on a yacht mast, the force of the wind can be assumed to act through the '''Centre of Area''' or '''Centroid'''.		In the examples of a flag on a flagpole, or a sail on a yacht mast, the force of the wind can be assumed to act through the '''Centre of Area''' or [https://en.wikipedia.org/wiki/Centroid '''Centroid'''].


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	The magnitude of the '''[[Wind Load]]''' is less easy to determine but can be derived from tables - obtained by connecting a test flag to a tow line, which is then connected through a load cell to an airplane!		The magnitude of the '''[[Wind Load]]''' is less easy to determine but can be derived from tables ''(obtained by connecting a test flag to a tow line, which is then connected through a load cell to an airplane!)''

DT Online at 15:29, 4 July 2017

2017-07-04T15:29:38Z

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	For more information on this topic see - ~~[http://www.amazon.co.uk/gp/~~product~~/0140135979/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN~~=0140135979~~&linkCode~~=~~as2&tag=dton06-21 '''~~'The New Science of Strong Materials: Or Why You Don't Fall Through the Floor' by J.E.Gordon''']		For more information on this topic see - '''<dtamazon product="0140135979" type="text">'The New Science of Strong Materials: Or Why You Don't Fall Through the Floor' by J.E.Gordon</dtamazon>'''

DT Online at 10:23, 1 March 2017

2017-03-01T10:23:56Z

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	[[File:Stonehenge Closeup.jpg\|400px\|right\|Stonehenge, Wiltshire, UK\|link=~~https~~://en.wikipedia.org/wiki/Stonehenge]]		[[File:Stonehenge Closeup.jpg\|400px\|right\|Stonehenge, Wiltshire, UK\|link=http://en.wikipedia.org/wiki/Stonehenge]]

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	[[File:BeamForceDiagram.png\|200px\|right]]		[[File:BeamForceDiagram.png\|200px\|right]]
	Forces are known as [~~https~~://en.wikipedia.org/wiki/Euclidean_vector '''vector quantities'''] because they not only have magnitude but also direction.		Forces are known as [http://en.wikipedia.org/wiki/Euclidean_vector '''vector quantities'''] because they not only have magnitude but also direction.


	[~~https~~://en.wikipedia.org/wiki/Euclidean_vector '''Vectors'''] can be represented by drawing arrows. The length is equal to its magnitude and the arrow points in the direction the force is acting.		[http://en.wikipedia.org/wiki/Euclidean_vector '''Vectors'''] can be represented by drawing arrows. The length is equal to its magnitude and the arrow points in the direction the force is acting.


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	The total length of the downward pointing line is equal to the sum of all the downward forces and is known as the [~~https~~://en.wikipedia.org/wiki/Resultant_force '''Resultant'''].		The total length of the downward pointing line is equal to the sum of all the downward forces and is known as the [http://en.wikipedia.org/wiki/Resultant_force '''Resultant'''].


	The total length of the upward pointing line is equal to the sum of all the upward forces and is known as the [~~https~~://en.wikipedia.org/wiki/Equilibrant_Force '''Equilibrant'''] - because it is the force required to balance the two loads and maintain balance or equilibrium		The total length of the upward pointing line is equal to the sum of all the upward forces and is known as the [http://en.wikipedia.org/wiki/Equilibrant_Force '''Equilibrant'''] - because it is the force required to balance the two loads and maintain balance or equilibrium


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	As before, the [~~https~~://en.wikipedia.org/wiki/Resultant_force '''Resultant'''] ''''ac'''' can be measured downwards and the [~~https~~://en.wikipedia.org/wiki/Equilibrant_Force '''Equilibrant'''] ''''ca'''' measured upwards ''(note that small letters are now used to name the vectors in '''Force Diagrams''')''.		As before, the [http://en.wikipedia.org/wiki/Resultant_force '''Resultant'''] ''''ac'''' can be measured downwards and the [http://en.wikipedia.org/wiki/Equilibrant_Force '''Equilibrant'''] ''''ca'''' measured upwards ''(note that small letters are now used to name the vectors in '''Force Diagrams''')''.


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	For more information on this topic see - [~~https~~://www.amazon.co.uk/gp/product/0140135979/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0140135979&linkCode=as2&tag=dton06-21 ''''The New Science of Strong Materials: Or Why You Don't Fall Through the Floor' by J.E.Gordon''']		For more information on this topic see - [http://www.amazon.co.uk/gp/product/0140135979/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0140135979&linkCode=as2&tag=dton06-21 ''''The New Science of Strong Materials: Or Why You Don't Fall Through the Floor' by J.E.Gordon''']


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	<big>'''[[Wind Load]]''' (N/m<sup>2</sup>) = <big>½</big> x [~~https~~://en.wikipedia.org/wiki/Density_of_air 1.25] (kg/m) x [~~https~~://en.wikipedia.org/wiki/Wind_speed Wind Speed] (m/s<sup>2</sup>) x '''Area''' (m<sup>2</sup>)</big>		<big>'''[[Wind Load]]''' (N/m<sup>2</sup>) = <big>½</big> x [http://en.wikipedia.org/wiki/Density_of_air 1.25] (kg/m) x [http://en.wikipedia.org/wiki/Wind_speed Wind Speed] (m/s<sup>2</sup>) x '''Area''' (m<sup>2</sup>)</big>

DT Online at 09:25, 6 January 2017

2017-01-06T09:25:22Z

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	This total downward force must be resisted by upward forces which together are equal and opposite to it. In the diagram these are shown as '''Reactions R1 and R2'''		This total downward force must be resisted by upward forces which together are equal and opposite to it. In the diagram these are shown as '''[[Reactions (structures)\|Reactions]] R1 and R2'''


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	=====Moments of a Force=====		=====Moments of a Force=====
	[[File:MeasuringTorque.png\|300px\|left]]		[[File:MeasuringTorque.png\|300px\|left]]
	If either of the two ~~'''[[Reactions (structures)\|~~reactions~~]]'''~~ were to be removed, the beam can be imagined to pivot on the one remaining. It follows that each '''Reaction''' must be providing a turning force or '''[[Torque]]''' to keep the beam in position.		If either of the two reactions were to be removed, the beam can be imagined to pivot on the one remaining. It follows that each '''[[Reactions (structures)\|Reaction]]''' must be providing a turning force or '''[[Torque]]''' to keep the beam in position.


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	'''Torque''' and '''Moments''' are not quite the same thing but both are measured in '''[[newton\|newtons]]''' x metres '''(NM)'''		'''Torque''' and '''Moments''' are not quite the same thing but both are measured in '''[[newton\|newtons]]''' x metres '''(Nm)'''


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	[[File:BeamForce2.png\|300px\|right]]		[[File:BeamForce2.png\|300px\|right]]
	This gives a way of calculating how much force a bridge support (or ~~reaction~~) has to provide if the bridge is to stay up - very useful since bridges are usually too big to just ''try it and see''!		This gives a way of calculating how much force a bridge support ''(or '''[[Reactions (structures)\|Reaction]]''')'' has to provide if the bridge is to stay up - very useful since bridges are usually too big to just ''try it and see''!


	The moment of the load on the beam '''(F)''' must be balanced by the moment of the ~~reaction~~ at the support '''(R2)''' :		The moment of the load on the beam '''(F)''' must be balanced by the moment of the '''Reaction''' at the support '''(R2)''' :


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	[[File:BeamForce3.png \|300px\|left]]		[[File:BeamForce3.png \|300px\|left]]
	It can be seen that this is so if we imagine taking away the ~~reaction~~ '''R2'''.		It can be seen that this is so if we imagine taking away the '''Reaction''' '''R2'''.


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	Self-weight can be assumed to be the same as a single point load acting on the centre of a beam or the cantilever. In the case of this cantilever example, self-weight would be acting therefore a quarter of the way along the beam - or '''Length = L/4''' and the '''Maximum BM. = W/2 x L/4 = WL/8'''		Self-weight can be assumed to be the same as a single point load acting on the centre of a beam or the cantilever. In the case of this cantilever example, self-weight would be acting therefore a quarter of the way along the beam - or '''Length = L/4''' and the '''Maximum BM. = W/2 x L/4 = WL/8'''


			For more information on this topic see - [https://www.amazon.co.uk/gp/product/0140135979/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0140135979&linkCode=as2&tag=dton06-21 ''''The New Science of Strong Materials: Or Why You Don't Fall Through the Floor' by J.E.Gordon''']


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	From this, the force at the point of attachment (A) can be calculated and a '''Force Diagram''' drawn around point A to determine the tension in the guy line.		From this, the force at the point of attachment (A) can be calculated and a '''[[Force Diagrams\|Force Diagram]]''' drawn around point A to determine the tension in the guy line.


	[[Category:Beams]]		[[Category:Beams]]

DT Online at 15:26, 12 November 2016

2016-11-12T15:26:16Z

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	=====Beam Deflection=====		=====Beam Deflection=====
	The deflection of a beam under load may be measured using a ~~dial gauge~~ for example but may also be calculated.		The deflection of a beam under load may be measured using a '''[[Precision Marking and Measuring\|Dial Gauge]]''' for example but may also be calculated.
	[[File:DeflectionCalc.png \|300px\|right]]		[[File:DeflectionCalc.png \|300px\|right]]
	'''Deflection (Δ)''' of a simply supported beam loaded in the centre:		'''Deflection (Δ)''' of a simply supported beam loaded in the centre:

DT Online at 15:19, 12 November 2016

2016-11-12T15:19:27Z

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	When a beam is simply supported at each end, all the downward forces are balanced by equal and opposite upward forces and the beam is said to be held in '''[[Equilibrium]]''' ''(i.e. the total load exerted by the beam's own weight plus any additional applied load are completely balanced by the sum of the two '''[[Reactions (structures)\|reactions]]''' at the two supports)''.		When a beam is simply supported at each end, all the downward forces are balanced by equal and opposite upward forces and the beam is said to be held in '''[[Equilibrium]]''' ''(i.e. the total load exerted by the beam's own weight plus any additional applied load are completely balanced by the sum of the two '''[[Reactions (structures)\|reactions]]''' at the two supports)''.

	*Place a length of timber, say 1 metre long, between two sets of kitchen scales as ~~show~~		*Place a length of timber, say 1 metre long, between two sets of kitchen scales as shown.
	*Adjust the scales until they both read zero - this will take away the weight of the timber itself.		*Adjust the scales until they both read zero - this will take away the weight of the timber itself.
	*Place a 2kg mass directly above each of the scales in turn and note the readings - it should be 2kg each time		*Place a 2kg mass directly above each of the scales in turn and note the readings - it should be 2kg each time

DT Online at 08:36, 29 October 2016

2016-10-29T08:36:06Z

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	So from '''[[:Category:Levers\|Levers]]''', '''Wind ~~Force~~ x height = F x d'''		So from '''[[:Category:Levers\|Levers]]''', '''[[Wind Load]] x height = F x d'''

DT Online at 08:34, 29 October 2016

2016-10-29T08:34:42Z

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	[[File:BeamOnScales.png\|300px\|right]]		[[File:BeamOnScales.png\|300px\|right]]

DT Online at 08:32, 29 October 2016

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	<big>'''[[Wind Load]]''' (N/m<sup>2</sup>) = <big>½</big> x [https://en.wikipedia.org/wiki/Density_of_air 1.25] (kg/m) x [https://en.wikipedia.org/wiki/Wind_speed Wind Speed] (m/s<sup>2</sup>)~~</big>~~ x '''Area''' (m<sup>2</sup>)		<big>'''[[Wind Load]]''' (N/m<sup>2</sup>) = <big>½</big> x [https://en.wikipedia.org/wiki/Density_of_air 1.25] (kg/m) x [https://en.wikipedia.org/wiki/Wind_speed Wind Speed] (m/s<sup>2</sup>) x '''Area''' (m<sup>2</sup>)</big>