ME 201
Engineering Mechanics: Statics
Chapter 6 – Part A
6.1 Simple Trusses
6.2 Method of Joints
6.3 Zero Force Members
Simple Truss
 A structure composed of slender members
joined together at their end points
 “Planar Truss”
Simple Truss
 To Design members and connections of a
truss, necessary to determine forces
developed in each member
 Assumptions:
All loadings are applied at the joints
 Members are joined together by smooth pins
Assumptions satisfactory for bolted or welded joints

Simple Truss
 Each truss member acts as a 2-force member

Force directed along axis of member

Tension – pull, elongation

Compression – push, shorten
 Several analytical approaches to solving
Method of Joints
 If truss is in equilibrium, each joint must also
be in equilibrium
 Approach:



Sketch Free Body Diagram of Entire Truss
Solve for Reactions
Sketch Free Body Diagrams of Each Joint
2 unknown limit per FBD
 ∑ Fx =0
∑ Fy =0

∑ Mo =0
Example Problem
B
F
2m
Given:
F = 500 N
θ = 45º
Find:
Force in each
member
θ
A
2m
C
Example Problem Solution
B
2 m 45º
A
Ax
F
F
2m
2m
Ay
0
Ax  500  0
Ax  500 or 500 N 
2m
θ
Cy
x
M
0
C y  2  500  2  0
C y  500 N 
F
500 N
A
0
Ay  500  0
Ay  500 or 500 N 
y
B
2m
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
B
500 N
2 m 45º
A
C
500 N
500 N
500 N
C
Example Problem Solution
B
Joint A
500 N
2m
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
3-Joint FBDs
2 m 45º
A
C
500 N
500 N
500 N
Joint B
Joint C
AB
500 N
AC
500 N
500 N
45º
45º
AB
BC
BC
AC
500 N
Example Problem Solution
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
3-Joint FBDs
Joint B
Joint A
AB
500 N
45º
AC
500 N
AB
500 N
500 N
F
0
AC  500  0
AC  500 N T
x
F
0
AB  500  0
AB  500 N T
y
BC
F
0
500  BC sin 45  0
BC  707 N C
x
B
500 T
Results shown in a force diagram
A
500 T
C
Zero Force Members
 Zero Force Members support NO loading
 Used for:


Stability
Changing Applied Loads
Zero Force Members
 If only 2 members form a truss joint AND no
external load or support reaction is applied to
the joint, then the members must be Zero
Force Members
X
X
X
X
Zero Force Members
 If 3 members form a truss joint for which 2
members are collinear, the 3rd member is a Zero
Force Member, provided no external force or
support reaction is applied to the joint.
X
X