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Structures

2009-01-19T11:35:00Z

86.96.226.86: /* Lecture */

'''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==
Structural engineering relies heavily on the strengths of materials and their ability to withstand forces of tension, compression & shear. When used in conjunction with each other, as in the case of a truss, individual load bearing members both share and transmit loads, enabling the structure to accomplish much more than any individual member could alone.

===Plane Trusses===
One way of distributing a force across a large distance is by building a ''Plane Truss'', which takes advantage of the principle of Equilibrium to translate forces along a system of interconnecting members.
[[Image:Warren truss.PNG|thumb|400px|left|A Warren Truss]][[Image:Pratt truss.PNG|thumb|400px|right|A Pratt Truss]]
 
[[Image:Simpletruss.PNG|thumb|200px|left|A Simple Triangle Truss]]
 
 
 
 
 
 
The simplest truss is a triangle made of three points: '''A''', '''B''' and '''C''', and three members: '''AB''', '''BC''' and '''CA'''. The method of distributing forces amongst many members relies on the engineer's ability to place a ''tensile'' or ''compressive'' force at any particular location. To properly sum forces at a particular point, one must be able to sum forces into that point and also away from it. Thus, '''AB''' and '''AC''' are in compression while '''BC''' is in tension.
 
 

===Method of Joints===
The principle of equilibrium may be used to solve the loads impinging upon a ''massless'' truss by analyzing the effect of each load at a single point on the truss. Each load is broken down into its <math>\ x</math> and <math>\ y</math> component vectors and these are summed to equal zero at a particular point on the truss (e.g. '''A'''). Similarly, each load creates a moment rotating about that same point '''A''' and these may also be summed together to equal zero. Therefore, given enough information about the loads applied, any of the other loads may be calculated.

Therefore, the Method of Joints may also be applied to a truss joint to determine the force (compressive or tensile) in each member of the truss. A place where the forces and members meet may become the joint to be examined ('''A'''), and the principle of equilibrium is applied, thus solving the question of where the forces are transmitted in that truss around that joint.

'''Example:''' 
Consider a truss bridge under loads <math>\vec F_1</math>, <math>\vec F_2</math> and <math>\vec F_L</math>. What are the forces in each of the members of the loaded truss, under the loads applied?

Assume that <math>\vec F_1 = 3N</math>, <math>\vec F_2 = 7N</math> and <math>\vec F_L = 11N</math>. Also assume that each member '''AB''', '''CE''' etc. is <math>\ 5</math> meters long and that <math>\vec F_L</math> is <math>\frac{2}{3}L</math> from <math>\vec R_1 </math>.
 
[[Image:LoadedTrussBridge.JPG|center|600px|thumb]]

 
'''Solution:''' 
First we must solve the external forces on the truss completely. We do so by analyzing the free body diagram. Equilibrium dictates that <math> \sum \vec F = 0 </math> and <math> \sum \vec M = 0 </math>.

''First'' we sum the ''moments'' about a particular point. In this case, let's use '''A''':

<math> \sum \vec M_A \ = \vec F_1*2L + \vec F_2*3L + \vec F_L*\frac{8L}{3} - \vec R_2*4L = 0</math>
 Or... 
<math> \sum \vec M_A \ = 3N*10m + 7N*15m + 11N*\frac{8*5m}{3} - \vec R_2*20 = 0</math>

<math> \vec R_2 = 14.1 N</math>.

We may sum the forces around an arbitrary point '''A'''. There are no <math>\ x</math> components of the force vectors, so <math> \sum \vec F_x \ = 0 </math>.

<math> \sum \vec F_{yA} \ = \vec R_1 + \vec R_2 - \vec F_1 - \vec F_2 - \vec F_L = 0 </math>.
 Or... 
<math> \sum \vec F_{yA} \ = \vec R_1 + 14.1N - 3N - 7N - 11N = 0 </math> and...

<math> \vec R_1 = 6.9N</math>

[[Image:TrussJointA.JPG|left|200px|thumb]]
Secondly, we may begin to solve for the internal forces within each member by summing the forces around point '''A''' at the location of <math>\vec R_1</math>.

<math> \sum \vec F_{yA} \ = \vec R_1 - \vec F_{AB} * cos{30} = 0 </math>
 Or... 
<math> \vec F_{AB} = \frac{\vec R_1}{cos{30}} = \frac{6.9N}{cos{30}} = 7.97N </math> ''(in Compression)''

 
<math> \sum \vec F_{xA} \ = \vec F_{AC} - \vec F_{AB} * sin{30} = 0 </math>
 Or... 
<math> \vec F_{AC} = \vec F_{AB} * sin{30} = 7.97N * sin{30} = 3.99N </math> ''(in Tension)''

Each successive member may be analyzed for its internal forces, be they ''compressive'' or ''tensile'' in a similar manner. For a successful analysis of every member of the truss, it is imperative that every external force be included. Therefore it is advised that the engineer begin analysis by the method of joints at each joint where external forces have been resolved and work his or her way inward towards the center.

===Method of Sections===
If every joint in a structure does not need to be analyzed, yet the internal forces of some members need to be resolved, a potential shortcut method is the method of sections. The method of sections involves cutting a truss into a smaller part, thus changing the internal forces in the members in question to external forces, which may easily be solved by the method of Equilibrium.

[[Image:LoadedTrussSection.JPG|200px|thumb|left]]
'''Example:''' 
If the truss shown here were to need analysis for the internal forces on one particular member, '''EF''', the method of sections could be used. Here we use the previous values for <math>\vec F_1 = 3N</math> and <math>\vec R_2 = 14N</math>. Also assume that each member is <math>\ 5</math> meters long.

'''Solution:''' 
We solve the external forces on the truss completely. Equilibrium dictates that <math> \sum \vec F = 0 </math> and <math> \sum \vec M = 0 </math>.

Once again, we first sum the ''moments'' about a particular point. In this case, let's use '''I''':

<math> \sum \vec M_I \ = -\vec F_1*L + \vec F_{EH}*cos{30} = 0</math>
 Or... 
<math> \sum \vec M_I \ = -3N*5m + \vec F_{EH}*cos{30} = 0</math>

<math> \vec F_{EH} = 17.3 N</math> (in tension).

===Space Trusses===
[[Image:SpaceTruss.png|thumb|300px|left|A Triangle Space Truss]]
A Space Truss is a 3D plane truss. Made up of similar structural forms, the space truss is a much more realistic form of truss thatn the Plane Truss. Calculation and resolution of loads, external and internal forces is performed the same way, however, care must be made to ensure that all three dimensions are correctly examined and properly resolved. Once again <math> \sum \vec F = 0 </math> and <math> \sum \vec M = 0 </math>.
 

==Assignments==
'''Activities:'''
* Create an [[Structures/activity|activity]]

'''Readings:'''
* Peruse the appropriate sections of [[Wikibooks:Statics]]
* [http://urban.arch.virginia.edu/%7Ekm6e/arch324/highlights/home.html Introduction to Structural Design, Virginia Tech.]

'''Study guide:'''
# Wikipedia article:[[w:Plane Truss|Plane Truss]]
# Wikipedia article:[[w:Tension|Tension]]
# Wikipedia article:[[w:Compression|Compression]]
# Wikipedia article:[[w:Method of Joints|Method of Joints]]
# Wikipedia article:[[w:Method of Sections|Method of Sections]]
# Wikipedia article:[[w:Space Truss|Space Truss]]

[[Category:Statics]]
[[Category:Advanced Classical Mechanics]]
[[Category:Applied Mechanics]]
[[Category:Mechanical engineering]]
[[Category:Engineering]]

Aerospace engineering

2009-01-03T03:38:20Z

86.96.226.86: /* Topics */

{{RightTOC}}
Welcome to the Department of Aerospace Engineering.

Aerospace engineering deals with aircraft and spacecraft, and any other types of machine that can fly. Topics within aerospace engineering include, but are not limited to: ''aerodynamics', structural dynamics, ''fluid'' mechanics, '''[[orbital mechanics]]''', ''[[flight dynamics]]'', propulsion, and control systems. These topics can be applied to ''missiles'', [[space structures]], satellites, and all aspects related to atmosphere and space flight.

Aerospace engineers design, develop, and [[test aircraft]], [[spacecraft]], and missiles and supervise the production of these products. Those who work with aircraft are called aeronautical engineers, and those working specifically with spacecraft are astronautical engineers. Aerospace engineers develop new technologies for use in aviation, defense systems, and [[space exploration]], often specializing in areas such as structural design, guidance, [[navigation and control]], [[instrumentation and communication]], or production methods. They also may specialize in a particular type of aerospace product, such as commercial aircraft, military fighter jets, helicopters, spacecraft, or missiles and rockets, and may become experts in aerodynamics, thermodynamics, celestial mechanics, propulsion, acoustics, or [[guidance and control systems]].

===[[/Areas of study/]]===


==Topics==
{{Col list|3|
* [[Topic:Fluid mechanics]]
* [[Topic:Aerodynamics]]
* [[Topic:Aeronautics]]
* [[Topic:Astrodynamics]]
* [[Topic:Orbital mechanics]]
* [[Topic:Statics]]
* [[Topic:Engineering mechanics]]
* [[School:Mathematics]]
* [[Topic:Electrotechnology]]
* [[Topic:Propulsion]]
* [[Topic:Control engineering]]
* [[Topic:Aircraft flight control systems]]
* [[Topic:Aircraft structures]]
* [[Topic:Materials science]]
* [[Topic:Solid mechanics]]
* [[Topic:Aeroelasticity]]
* [[Topic:Avionics]]
* [[Topic:Reliability engineering]]
* [[Topic:Noise control]]
* [[Topic:Flight testing]]
}}

==Additional readings==
* [[Wikipedia: Astronautics]]
* [[Wikipedia: Spacecraft design]]

== External links ==
[[Image:Dn8310-2_700.jpg|300px|right|thumb|‘Blended wing’ craft prototype]]
* [http://cafefoundation.org/v2/pav_home.php Personal Air Vehicle Page at Cafe Foundation (in affiliation with NASA)]
* [http://psas.pdx.edu/ Open avionics]
* [http://aerospace.me/ Aerospace Engineering - Students]
* [http://seattlepi.nwsource.com/business/130398_electplane11.html Boeing's electric plane using fuelcells.]
* [http://sourceforge.net/projects/openavionics/ OpenAvionics]
* [http://www.aiaa.org/ American Institute of Aeronautics and Astronautics]
* [http://aero.stanford.edu/adgprojects.html Projects at Standford's Aerodynamics Design Group]
* [http://dthrocket.blogspot.com/ A Project to create a supersonic homebrew rocket]
* [http://rgl.faa.gov/ U.S. Federal Aviation Administration (FAA) Regulatory and Guidance Library]

===Books===
* [http://books.google.com/books?vid=ISBN1428996389&id=mViQar7gcfkC&dq=nanotechnology&as_brr=1 Research opportunities in advanced aerospace concepts]

*[[Wikibooks:Astrodynamics|Astrodynamics]]

*[[Wikibooks:Jet_Propulsion|Jet Propulsion]]

===Videos===
*[http://www.youtube.com/view_play_list?p=A481C3DD60812502 MIT 16.01 Unified Engineering - Video Lecture]
*[http://www.youtube.com/view_play_list?p=35721A60B7B57386 MIT 16.885J Aircraft Systems Engineering - Video Lecture]

===Pictures===
* [http://www.darpa.mil/body/news/2007/Hyper_Test_6_20_07.html Pictures of the HyCAUSE Mach 10 test flight] - Collaboration between Australia and DARPA, 6/20/07

===Related news===
* September 2008 ''[http://www.physorg.com/news141922847.html Micro honeycomb materials enable new physics in aicraft sound reduction]
* August 2008 ''[http://www.markstechnologynews.com/2008/08/sikorsky-x2-helicopter-at-288mph-is.html Sikorsky X2 Helicopter: At 288mph Is World's Fastest]
* April 2008 ''[http://www.physorg.com/news127060603.html Avoiding wind tunnels, computer simulations pave way for hypersonic flight]
* April 2007 [http://www.newscientist.com/channel/fundamentals/mg18925331.200-take-a-leap-into-hyperspace.html Paper on hyperdrive system wins award at conference and is examined by US Government researchers...][http://www.theregister.co.uk/2006/01/06/hyperdrive/]
* March 2007 [http://www.physorg.com/news94233194.html NASA seeks research proposals.]
* March 2007 [http://www.physorg.com/news93631842.html Private company to launch rocket.]

[[Category:Engineering]]
[[Category:Mechanical engineering]]
[[Category:Aerospace engineering]]
[[Category:Engineering departments]]
[[Category:Departments]]

Aerospace engineering

2009-01-03T03:37:20Z

86.96.226.86: /* Books */

{{RightTOC}}
Welcome to the Department of Aerospace Engineering.

Aerospace engineering deals with aircraft and spacecraft, and any other types of machine that can fly. Topics within aerospace engineering include, but are not limited to: ''aerodynamics', structural dynamics, ''fluid'' mechanics, '''[[orbital mechanics]]''', ''[[flight dynamics]]'', propulsion, and control systems. These topics can be applied to ''missiles'', [[space structures]], satellites, and all aspects related to atmosphere and space flight.

Aerospace engineers design, develop, and [[test aircraft]], [[spacecraft]], and missiles and supervise the production of these products. Those who work with aircraft are called aeronautical engineers, and those working specifically with spacecraft are astronautical engineers. Aerospace engineers develop new technologies for use in aviation, defense systems, and [[space exploration]], often specializing in areas such as structural design, guidance, [[navigation and control]], [[instrumentation and communication]], or production methods. They also may specialize in a particular type of aerospace product, such as commercial aircraft, military fighter jets, helicopters, spacecraft, or missiles and rockets, and may become experts in aerodynamics, thermodynamics, celestial mechanics, propulsion, acoustics, or [[guidance and control systems]].

===[[/Areas of study/]]===


==Topics==
{{Col list|3|
* [[Topic:Fluid mechanics]]
* [[Topic:Aerodynamics]]
* [[Topic:Aeronautics]]
* [[Topic:Astrodynamics]]
* [[Topic:Orbital mechanics]]
* [[Topic:Statics]]
* [[Topic:Engineering mechanics]]
* [[School:Mathematics]]
* [[Topic:Electrotechnology]]
* [[Topic:Turbomachinery]]
* [[Topic:Control engineering]]
* [[Topic:Aircraft flight control systems]]
* [[Topic:Aircraft structures]]
* [[Topic:Materials science]]
* [[Topic:Solid mechanics]]
* [[Topic:Aeroelasticity]]
* [[Topic:Avionics]]
* [[Topic:Reliability engineering]]
* [[Topic:Noise control]]
* [[Topic:Flight testing]]
}}

==Additional readings==
* [[Wikipedia: Astronautics]]
* [[Wikipedia: Spacecraft design]]

== External links ==
[[Image:Dn8310-2_700.jpg|300px|right|thumb|‘Blended wing’ craft prototype]]
* [http://cafefoundation.org/v2/pav_home.php Personal Air Vehicle Page at Cafe Foundation (in affiliation with NASA)]
* [http://psas.pdx.edu/ Open avionics]
* [http://aerospace.me/ Aerospace Engineering - Students]
* [http://seattlepi.nwsource.com/business/130398_electplane11.html Boeing's electric plane using fuelcells.]
* [http://sourceforge.net/projects/openavionics/ OpenAvionics]
* [http://www.aiaa.org/ American Institute of Aeronautics and Astronautics]
* [http://aero.stanford.edu/adgprojects.html Projects at Standford's Aerodynamics Design Group]
* [http://dthrocket.blogspot.com/ A Project to create a supersonic homebrew rocket]
* [http://rgl.faa.gov/ U.S. Federal Aviation Administration (FAA) Regulatory and Guidance Library]

===Books===
* [http://books.google.com/books?vid=ISBN1428996389&id=mViQar7gcfkC&dq=nanotechnology&as_brr=1 Research opportunities in advanced aerospace concepts]

*[[Wikibooks:Astrodynamics|Astrodynamics]]

*[[Wikibooks:Jet_Propulsion|Jet Propulsion]]

===Videos===
*[http://www.youtube.com/view_play_list?p=A481C3DD60812502 MIT 16.01 Unified Engineering - Video Lecture]
*[http://www.youtube.com/view_play_list?p=35721A60B7B57386 MIT 16.885J Aircraft Systems Engineering - Video Lecture]

===Pictures===
* [http://www.darpa.mil/body/news/2007/Hyper_Test_6_20_07.html Pictures of the HyCAUSE Mach 10 test flight] - Collaboration between Australia and DARPA, 6/20/07

===Related news===
* September 2008 ''[http://www.physorg.com/news141922847.html Micro honeycomb materials enable new physics in aicraft sound reduction]
* August 2008 ''[http://www.markstechnologynews.com/2008/08/sikorsky-x2-helicopter-at-288mph-is.html Sikorsky X2 Helicopter: At 288mph Is World's Fastest]
* April 2008 ''[http://www.physorg.com/news127060603.html Avoiding wind tunnels, computer simulations pave way for hypersonic flight]
* April 2007 [http://www.newscientist.com/channel/fundamentals/mg18925331.200-take-a-leap-into-hyperspace.html Paper on hyperdrive system wins award at conference and is examined by US Government researchers...][http://www.theregister.co.uk/2006/01/06/hyperdrive/]
* March 2007 [http://www.physorg.com/news94233194.html NASA seeks research proposals.]
* March 2007 [http://www.physorg.com/news93631842.html Private company to launch rocket.]

[[Category:Engineering]]
[[Category:Mechanical engineering]]
[[Category:Aerospace engineering]]
[[Category:Engineering departments]]
[[Category:Departments]]