Truss Analysis
description
Transcript of Truss Analysis
Truss AnalysisTruss AnalysisEngineeringEngineering
Mr. CumberMr. Cumber
20092009
BellworkBellwork
What are two applications of trusses What are two applications of trusses besides bridges?besides bridges?
Non-Bridge TrussesNon-Bridge Trusses
Non-Bridge TrussesNon-Bridge Trusses
Non-Bridge TrussesNon-Bridge Trusses
StaticsStatics
Not MovingNot Moving Forces in X and Y directions = 0Forces in X and Y directions = 0 Newton’s 2Newton’s 2ndnd Law Law
a
P
c
b
ImportanceImportance
MethodsMethods
Method of JointsMethod of Joints
Method of SectionsMethod of Sections
Pa
P
b
c
FbcFac
Fbc
Fab
P
Rx
Ry
Method of JointsMethod of Joints
Good when few membersGood when few members When all forces are neededWhen all forces are needed To check Method of Sections dataTo check Method of Sections data
ExecutionExecution
Cut each joint, draw forcesCut each joint, draw forces Fill in anglesFill in angles Break down forces into X and Y Break down forces into X and Y
componentscomponents Add like forces, solve for unknownsAdd like forces, solve for unknowns
Class ExampleClass Example
If P = 300 N, If P = 300 N, = 60, = 60, = 30, what is the = 30, what is the force on member [bc]?force on member [bc]?
a
P
b
c
ExampleExample
Step One: Cut JointStep One: Cut Joint Step Two: Fill in ForcesStep Two: Fill in Forces Step Three: Fill in AnglesStep Three: Fill in Angles
300
Fbc
Fac
6030
ExampleExample
Step Four: Break Forces into X and Y Step Four: Break Forces into X and Y componentscomponents
300
Fbc
Fac
6030
3060Fxac = Fac cos 60
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fybc = Fbc sin 30
Fxac
Fyac
Fxbc
Fybc
ExampleExample
Step Five: Sum like forces and set = to 0, Step Five: Sum like forces and set = to 0, solve!solve!
FFxx = 0 = -F = 0 = -Fxacxac + F + Fxbc xbc
(right is positive)(right is positive)
FFyy = 0 = 300 + F = 0 = 300 + Fyacyac + F + Fybcybc
(down is positive)(down is positive)
Complete w/Mr. Cumber on boardComplete w/Mr. Cumber on board
Fxac = Fac cos 60
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fybc = Fbc sin 30
PracticePractice
If P = 500 N, If P = 500 N, = 72, = 72, = 18, what is the = 18, what is the force on member [ac]?force on member [ac]?
a
P
b
c
Method of SectionsMethod of Sections
Good when there are lots of membersGood when there are lots of members When only one specific member force is When only one specific member force is
neededneeded
ExecutionExecution
Cut truss into two sections (through the Cut truss into two sections (through the member you need)member you need)
Treat section as a single rigid bodyTreat section as a single rigid body Draw Forces and AnglesDraw Forces and Angles Determine X and Y ComponentsDetermine X and Y Components
Solve for Solve for FFxx and and FFyy = 0 = 0
Class ExampleClass Example
If P = 300 N, If P = 300 N, = 60, = 60, = 30, what is the = 30, what is the force on member [bc]?force on member [bc]?
a
P
b
cab = 20 cm
ac = 10 cm
bc = 17.3 cm
ExampleExample
Step One: Cut TrussStep One: Cut Truss Step Two: Draw Forces and AnglesStep Two: Draw Forces and Angles Step Three: Determine componentsStep Three: Determine components
Fbc
Fab
300
Rx
Ry
30
Fxbc
Fybc
Fxbc = Fbc cos 30Fybc = Fbc sin 30
ExampleExample
Step Four: Sum like forces and set = to 0, Step Four: Sum like forces and set = to 0, solve!solve!
FFxx = 0 = F = 0 = Fxbcxbc + F + Fabab + R + Rxx
(right is positive)(right is positive)
FFyy = 0 = 300 + F = 0 = 300 + Fybc ybc + R+ Ryy
(down is positive)(down is positive)
M = 0 (New Equation! – for RM = 0 (New Equation! – for Rxx and R and Ryy))
Complete w/Mr. Cumber on boardComplete w/Mr. Cumber on board
Important NotesImportant Notes
Either method should give the same Either method should give the same answeranswer Use to checkUse to check
Choosing a method wisely will save lots of Choosing a method wisely will save lots of workwork
Figure out reaction forces first - you might Figure out reaction forces first - you might need them later.need them later.