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Truss Analysis – Identifying Zero-Force MembersStevenVukazich
SanJoseStateUniversity
Zero-Force Members in Trusses
Under certain truss geometries and loading conditions, there can be truss members that carry zero load.
Identifying these zero-force members (ZFM) can make truss analysis more efficient
Identifying ZFMs consists of identifying a few special joint conditions illustrated in the following slides.
Case 1
Look for:• An unloaded joint;• Connecting exactly three members;• Two of the members are collinear (lie along the same line).
F1
F2
F3
!𝐹#
�
�
= 0+
F1
F2y
x𝐹( cos 𝜃𝐹( sin 𝜃
F3 = 0
Case 2
Look for:• An unloaded joint;• Connecting exactly two members;• The two members are not collinear.
F1
F2
!𝐹#
�
�
= 0+
F1
y x𝐹/ cos 𝜃𝐹/ sin 𝜃
F1 = 0
!𝐹0
�
�
= 0+F2 = 0
Case 3 (Similar to Case 1)
Look for:• A loaded joint (the load can be due to an applied load or
a support reaction);• Connecting exactly two members;• One member is in the same line as the load.
F1
F2
!𝐹#
�
�
= 0+F1
y x𝐹/ cos 𝜃𝐹/ sin 𝜃
F2 = 0
P P
1. Check truss for Cases 1, 2, and 3 and identify each zero-force member (ZFM);
2. Considering ZFMs found in Step 1 as not being present, check for Cases 1, 2, and 3 and identify each ZFM;
3. Repeat Step 2 until all ZFMs are found.
General Procedure for IdentifyingZero-Force Members in Trusses
A
B
G I
Example
For the truss, find all zero-force members (ZFMs).
CD
E
F
HJ
P1
P2
P3
A
B
G I
Check Cases for ZFMs
CD
E
F
HJ
1. Check truss for Cases 1, 2, and 3 and identify each zero-force member (ZFM);
Case 1
Case 2
Ax
AyDy
Case 3
P1
P2P3
HJ = 0JI = 0
CD = 0BE = 0
A
B
G I
Step 2
CD
E
F
H
J
2. Considering ZFMs found in Step 1 as not being present, check for Cases 1, 2, and 3 and identify each ZFM;
Case 1Ax
AyDyP1
P2
P3
(0)(0)
(0)
(0)HF = 0
A
B
G I
Repeat Step 2
CD
E
F
H
J
3. Repeat Step 2 until all ZFMs are found.
Case 1
Ax
Ay DyP1
P2P3
(0)(0)
(0)
(0)
(0)
GF = 0
A
B
G I
All ZFMs Shown in Blue
CD
E
F
H
J
Ax
Ay DyP1
P2
P3
(0)(0)
(0)
(0)
(0)
(0)
