Engineering Mechanics: Statics

1
Engineering Mechanics Statics

• Chapter 3 Equilibrium

2
Equilibrium
Part A Equilibrium in Two Dimensions
3
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)

4
Free-Body Diagram
5
Free-Body Diagram
6
Free-Body Diagram
7
Free-Body Diagram
8
Free-Body Diagram
9
Free-Body Diagram
10
Equilibrium Conditions

• In two dimensions, equations of equilibrium may
  be written as

11
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

12
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.
13
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.
14
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.
15
Equilibrium
Part A Equilibrium in Three Dimensions
16
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

17
Free-Body Diagram
18
Free-Body Diagram
19
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.
20
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.