Truss Analysis
Engineering
Mr. Cumber
2009
Bellwork
 What are two applications of trusses
besides bridges?
Non-Bridge Trusses
Non-Bridge Trusses
Non-Bridge Trusses
Statics
 Not Moving
 Forces in X and Y directions = 0
 Newton’s 2nd Law
c
P
a
a
q
b
Importance
Methods
c
 Method of Joints
P
Fbc
Fac
P
q
a
a
 Method of Sections
P
Fbc
Rx
Ry
Fab
b
Method of Joints
 Good when few members
 When all forces are needed
 To check Method of Sections data
Execution
 Cut each joint, draw forces
 Fill in angles
 Break down forces into X and Y
components
 Add like forces, solve for unknowns
Class Example
 If P = 300 N, a = 60, q = 30, what is the
force on member [bc]?
c
P
a
a
q
b
Example
 Step One: Cut Joint
 Step Two: Fill in Forces
 Step Three: Fill in Angles
60
30
Fbc
Fac
300
Example
 Step Four: Break Forces into X and Y
components
Fxac
Fxbc
60
30
60
Fyac
Fxac = Fac cos 60
Fybc
30
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fbc
Fac
300
Fybc = Fbc sin 30
Example
 Step Five: Sum like forces and set = to 0,
solve!
 SFx = 0 = -Fxac + Fxbc
 (right is positive)
 SFy = 0 = 300 + Fyac + Fybc
 (down is positive)
Fxac = Fac cos 60
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fybc = Fbc sin 30
 Complete w/Mr. Cumber on board
Practice
 If P = 500 N, a = 72, q = 18, what is the
force on member [ac]?
c
a
a
P
q
b
Method of Sections
 Good when there are lots of members
 When only one specific member force is
needed
Execution
 Cut truss into two sections (through the




member you need)
Treat section as a single rigid body
Draw Forces and Angles
Determine X and Y Components
Solve for SFx and SFy = 0
Class Example
 If P = 300 N, a = 60, q = 30, what is the
force on member [bc]?
ab = 20 cm
c
ac = 10 cm
bc = 17.3 cm
P
a
a
q
b
Example
 Step One: Cut Truss
 Step Two: Draw Forces and Angles
 Step Three: Determine components
Fxbc
30
300
Fybc
Fbc
Rx
Ry
Fab
Fxbc = Fbc cos 30
Fybc = Fbc sin 30
Example
 Step Four: Sum like forces and set = to 0,
solve!
 SFx = 0 = Fxbc + Fab + Rx
 (right is positive)
 SFy = 0 = 300 + Fybc + Ry
 (down is positive)
 SM = 0 (New Equation! – for Rx and Ry)
 Complete w/Mr. Cumber on board
Important Notes
 Either method should give the same
answer
 Use to check
 Choosing a method wisely will save lots of
work
 Figure out reaction forces first - you might
need them later.