EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS, Summaries of Physics

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EQUILIBRIUM OF A RIGID BODY & FREE-BODY

DIAGRAMS

Today’s Objectives

:

Students will be able to:a) Identify support reactions, and,b) Draw a free-body diagram.

CONDITIONS FOR RIGID-BODY EQUILIBRIUM

Section 5.1)

In contrast to the forces on a particle, theforces on a rigid-body are not usuallyconcurrent and may cause rotation of thebody (due to the moments created by theforces).

For a rigid body to be in equilibrium, thenet force as well as the net momentabout any arbitrary point O must beequal to zero. 

F

= 0 and

M

O

Forces on a particle Forces on a rigid body

FREE-BODY DIAGRAMS

(Section 5.2)

Draw an outlined shape. Imagine the body to be isolatedor cut

“free” from its constraints and draw its outlined

shape.

Show all the external forces and couple moments. Thesetypically include: a) applied loads, b) the weight of thebody,

and c) support reactions (can be difficult).

Idealized model

Free-body diagram

FREE-BODY DIAGRAMS

(continued)

Label loads and dimensions: All known forces andcouple moments should be labeled with theirmagnitudes and directions. For the unknown forcesand couple moments, use letters like A

x

, A

y

, M

A

, etc..

Indicate any necessary dimensions.

Idealized model

Free-body diagram

CONCEPT QUIZ

1. The beam and the cable (with a frictionless pulley at D) support an

80 kg load at C. In a FBD of only the beam, there are how manyunknowns?1) 2 forces and 1 couple moment2) 3 forces and 1 couple moment3) 3 forces4) 4 forces

CONCEPT QUIZ

If the directions of the force and the couple moments arereversed, then what will happen to the beam?A)

The beam will lift from A.

B)

The beam will lift at B.

C)

The beam will be restrained.

D)

The beam will break.

IMPORTANT NOTE

A single bearing or hinge can prevent rotation by providing aresistive couple moment. However, it is usually preferred to usetwo or more properly aligned bearings or hinges. Thus, in thesecases, only force reactions are generated and there are nomoment reactions created.

Reaction Couple Moment

To support weight ofsign, hinge exertsupward force.

H

y

W

Reaction

couple

Weight twists hinge.So wall exerts reactionforce distribution. Thenet force is zero butthere is a non-zerocouple moment.

Improperly Aligned Supports

An improperlyaligned supportdoes nothing toprevent thetwisting of thehinge or makesthe twistingworse.

H

y

W

T

H

x

Are the Supports Properly Aligned?

• The problem says so.• Are there more unknowns than

equations?

• If we drop the reaction couple

moments, do we have enoughequations?