Engineering Mechanics: Statics

Chapter 3: Equilibrium

Equilibrium

Part A: Equilibrium in Two Dimensions

Equilibrium

In equilibrium,

Before applying the equation, we must define the

mechanical system to be analyzed and represent all forces acting on the body

To do that, the body has to be isolated from all

surrounding bodies

A diagramatic representation of the isolated system treated as a single body = free-body diagram (FBD)

0 0R F M M

FBD is the most important step in the solution of problems in mechanics!

Free-Body Diagram

Free-Body Diagram

Free-Body Diagram

Free-Body Diagram

Free-Body Diagram

Free-Body Diagram

Equilibrium Conditions

In two dimensions, equations of equilibrium may be written as

0 0 0x y OF F M

Two- and Three-Force Members

A body under the action of two forces only = two-force member

For a two-force member to be in equilibrium, the forces

must be equal, opposite and collinear

For a three-force member, equilibrium requires the lines of action of the three forces to be concurrent

Sample Problem 3/4

Determine the magnitude T of the tension in the

supporting cable and the magnitude of the force

on the pin at A for the jib crane shown. The beam

AB is a standard 0.5-m I-Beam with a mass of 95

kg per meter of length.

Problem 3/24

A block placed under the head of the claw hammer as

shown greatly facilitates the extraction of the nail. If a 200-

N pull on the handle is required to pull the nail, calculate

the tension T in the nail.

Problem 3/48

The small crane is mounted on one side of the bed of a

pickup truck. For the position q = 40º, determine the

magnitude of the force supported by the pin at O and the

force p against the hydraulic cylinder BC.

Equilibrium

Part A: Equilibrium in Three Dimensions

Equilibrium Conditions

In three dimensions, equations of equilibrium may be written as

Statical determinacy

The supporting constraints are not more than the number

required to establish equilibrium condition

If the supports are redundant, the body is statically

indeterminate

0; 0, 0, 0

0; 0, 0, 0

x y z

x y z

F F F F

M M M M

Free-Body Diagram

Free-Body Diagram

Sample Problem 3/5

The uniform 7-m steel shaft has a mass of 200

kg and is supported by a ball-and-socket

joint at A in the horizontal floor. The ball end B

rests against the smooth vertical walls as

shown. Compute the forces exerted by the

walls and the floor on the ends of the shaft.

Problem 3/67

The light right-angle boom which supports the

400-kg cylinder is supported by three cables

and a ball-and-socket joint at O attached to

the vertical x-y surface. Determine the

reactions at O and the cable tensions.