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.