Statics

Professor: Dr. Miguel Alonso Jr.

Outline

IntroductionForcesMomentsResultantsEquilibrium

Introduction

Statics is concerned with the equilibrium of bodies subjected to force systems

Forces and Moments

Forces

A force is the manifestation of the action of one body upon another

Can arise from the direct action of two bodies in contact with one anotherYou pushing on the wall

Or from the “action at a distance” of one body upon anotherGravityMagnetism

Forces can be either body forces or surface forces

Mathematically, forces are represented as vectorsA directed line segment having a tail and a headDefined by a magnitude and direction

Moments

In addition to the pushing, or pulling effect on the point at which it acts, a force creates a moment about axes passing through the body

Moments can be thought of as a tendency to rotate the body upon which it acts around a certain axis

Computed as the cross product between the component of the force perpendicular to the axis and the distance from the component to the axis

Resultant Force

Resultant force of a system is the equivalent force of the total system. It is the vector sum of the individual forces.

Example 18.1 and 18.2

Equilibrium

Any body is in equilibrium ( that is there is 0 movement) when the resultant force on the body is absolutely zeroVector sum of all forces is zeroResultant moment of the forces about each of the

axes is zero

∑ F x=0

∑ F y=0

∑ F z=0

∑ M x=0

∑ M y=0

∑ M z=0

If all of the forces act in only one plane, (lets say the x-y plane), then equilibrium is met by

Free body diagrams help in solving these types of problems

An FBD is a neat sketch of the body showing all forces and moments acting on the body with all important linear and angular dimensions

∑ F x=0

∑ F y=0

∑ M z=0

Example 18.3 and 18.4

Practice Problems

Chapter 18 18.1 18.3 18.9 18.10 18.12