ME 201Engineering Mechanics: Statics

Chapter 6 – Part A6.1 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

Given:

F = 500 N

θ = 45º

Find:

Force in each member

θ

2 m

B

CA2 m

F

Example Problem Solution

Given:F = 500 Nθ = 45º

Find:Force in each member

Solution:1-FBD2-Support Reactions

45º

2 m

B

Ax

2 m

500 N

AyCy

0 yF

0 AM

0 xF

θ

2 m

B

CA2 m

F

0500 xA NorAx 500500

025002 yC NCy 500

0500 yA NorAy 500500

45º

2 m

B

500 N

2 m

500 N

500 N 500 N

A C

Example Problem Solution

Given:F = 500 Nθ = 45º

Find:Force in each member

Solution:1-FBD2-Support Reactions3-Joint FBDs

500 N

500 N

AC

AB

45º

2 m

B

500 N

2 m

500 N

500 N 500 N

A C

Joint A Joint B

500 N

BCAB

45º

Joint C

500 N

BC

AC45º

Example Problem Solution

Given:F = 500 Nθ = 45º

Find:Force in each member

Solution:1-FBD2-Support Reactions3-Joint FBDs

0 yF

0 xF

500 N

500 N

AC

AB

Joint A500 N

BCAB

500 N

Joint B

45º

0 xF

B

A C

500 T

500 T

707 C

Results shown in a force diagram

0500 ACTNAC 500

0500 ABTNAB 500

045sin500 BCCNBC 707

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

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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.

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