Engineering Mechanics: Statics

Chapter 3: Equilibrium

Equilibrium Part A: Equilibrium in Two Dimensions

Equilibrium  In equilibrium,

R

0

M

0    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)

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 

M O

 0

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 0; 0, 0, 0 

M

 0; 

M x

 0, 

M y

 0, 

M z

 0  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

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.