Statics:Hibbeler 1

RealReal--WorldWorld

Why do we study free-body diagrams and use equilibrium to find unknown forces?

Results of the Kansas City Hotel disaster

33rdrd Floor Walkway Floor Walkway (Independent of 2(Independent of 2ndnd and 4and 4thth Floor Floor

Walkways)Walkways)

Design of Design of WalkwayWalkway

There was a modification of the

lkwalkway design.

4th Floor Walkway Beam4th Floor Walkway Beam View of View of Hanger Hanger Rods for Rods for 44thth FloorFloor

CloseClose--up of Rod, up of Rod, Washer, and BoltWasher, and Bolt

Statics:Hibbeler 2

Free-body

diagrams of

Design of Design of WalkwayWalkway

the 2nd and 4th

floor

walkways

Notice the free-body diagram of the 4th floor

Design of Design of WalkwayWalkway

the 4 floor walkway shows that the force at B and E doubles in the modified structure.

33rdrd Floor Floor Walkway BeamWalkway Beam

EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS

Identify the force and moment reaction components on a rigid body for a specific connection type, including (but not limited to): smooth surfaces, roller supports, link supports, cable supports, fixed supports.

Draw free body diagrams for 2D rigid bodies, labeling all external forces and moments, known or unknown

CONDITIONS FOR RIGID-BODY EQUILIBRIUM (Section 5.1)

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

For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be equal to zero.

F = 0 and MO = 0

Forces on a rigid body

p

Statics:Hibbeler 3

THE PROCESS OF SOLVING RIGID BODY EQUILIBRIUM PROBLEMS

For analyzing an actual physical system, first we need to create an idealized model.Then we need to draw a free-body diagram showing all the external (active and reactive) forces.Finally, we need to apply the equations of equilibrium to solve for any unknowns.

SUPPORT REACTIONS IN 2-D

As a general rule, if a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction. Similarly, if rotation is prevented, a couple moment is exerted on the body.

A few examples are shown above. Other support reactions are given in your textbook (in Table 5-1).

Action vs. ReactionAction vs. Reaction

Statics:Hibbeler 4

Flexible Cord, Rope, Chain, CableFlexible Cord, Rope, Chain, Cable Rigid LinkRigid Link Ball, Roller, RockerBall, Roller, Rocker

Smooth SurfacesSmooth Surfaces Smooth PinSmooth Pin Pin in Smooth GuidePin in Smooth Guide

Statics:Hibbeler 5

Collar on Smooth ShaftCollar on Smooth Shaft Smooth Collar with Fixed Smooth Collar with Fixed ConnectionConnection Fixed SupportFixed Support

Linear Elastic SpringLinear Elastic Spring Idealized PulleyIdealized Pulley WellWell--supported Rigid Bodysupported Rigid Body