Truss Analysis –Identifying Zero- Force Members Finding... · 2018-08-15 · Zero-Force Members in Trusses Under certain truss geometries and loading conditions, there can be truss

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)