COURSE:
CE 201 (STATICS)
LECTURE NO.:
18
FACULTY:
DR. SHAMSHAD AHMAD
DEPARTMENT:
CIVIL ENGINEERING
UNIVERSITY:
KING FAHD UNIVERSITY OF PETROLEUM
& MINERALS, DHAHRAN, SAUDI ARABIA
TEXT BOOK:
ENGINEERING MECHANICS-STATICS
by R.C. HIBBELER, PRENTICE HALL
LECTURE NO. 18
EQUILIBRIUM OF RIGID BODIES
Objectives:
►
To develop the equations of equilibrium for a
rigid body
►
To introduce the concept of the free-body
diagram for a rigid body
LAWS OF EQUILIBRIUM
It is necessary and sufficient condition for the
equilibrium of rigid bodies that the summation
of forces is equal to zero and that moments taken
about any point inside or outside the body are
zero.
CONDITIONS FOR RIGID BODIES
EQUILIBRIUM
Let us consider various forces acting on a rigid
body as shown in the following figure:
According to the law of equilibrium, we have
following conditions for the equilibrium:
ΣF = 0
ΣMo = 0
FREE BODY DIAGRAMS:
SUPPORT REACTIONS
FREE BODY DIAGRAMS:
EXTERNAL AND INTERNAL FORCES
• Only show the external forces, F, on the FBD
because the net effect of the internal forces, f,
is found to be zero
• If a portion of the body is separated for
drawing the FBD, show the internal forces
also at the cut section
FREE BODY DIAGRAMS:
WEIGHT AND THE CENTER OF GRAVITY
• Apply the weight, W, of a body at its
center of gravity, G
• For a uniform body, the G is located
on its geometric center or centroid
FREE BODY DIAGRAMS:
DRAWING PROCEDURE
• Draw outlined shape
• Show all forces
• Identify each loading and give dimensions
PROBLEM SOLVING: Example # 1
Draw the free-body diagram of the 50 Kg paper
roll, which has a center of mass at G and rests on
the smooth hauler. Explain the significance of each
force, acting on the diagram.
PROBLEM SOLVING: Example # 1
The free-body diagram of the paper roll is drawn
as shown below:
In the free-body diagram:
G
B
F
60
o
30o
A
F
B
A
50 kg
Free-body diagram of the paper roll
FA = reaction of the blade at A
FB = reaction of the blade at B
50 kg = weight of the paper roll
concentrating at the centroid (G) of
the paper roll.
PROBLEM SOLVING: Example # 2
Draw the free-body diagram of member
AB, which is supported by a roller at A and
a pin at B. Explain the significance of each
force, acting on the diagram.
PROBLEM SOLVING: Example # 2
The free-body diagram of member AB is drawn as
shown below:
800 llb-ft
A
60o
FA
30o
4ft
8ft
390lb
13 12
5
B
FHB
FVB
Free-body diagram of member AB
In the free-body diagram:
FA = Reaction of roller support at A.
FHB = Horizontal reaction of pin support at B
FVB = Vertical reaction of pin support at B
390lb = Inclined external force on the member.
800lb-ft = Counterclockwise external couple on the
member
PROBLEM SOLVING: Example # 3
Draw the free-body diagram of the crane boom AB
which has a weight of 650 lb and center of gravity at
G. The boom is supported by a pin at A and cable
BC. The load of 1250 lb is suspended from cable
attached at B. Explain the significance of each force,
acting on the diagram.
PROBLEM SOLVING: Example # 3
TBC
13
12
5
G
FHA
A
ft
18
B
60o
ft
12 1250 lb
650 lb
FVA
Free-body diagram of the crane boom AB
FHA & FVA = reactions of pin support at A
650 lb
= Weight of the crane boom
1250 lb
= load suspended from cable at B
TBC
= Tension in cable BC
PROBLEM SOLVING: Example # 4
Draw the free-body diagram of the spanner wrench
subjected to the 20 lb force, as shown in the
following figure. The support at A can be considered
a pin, and surface of contact at B is smooth. Explain
the significance of each force, acting on the diagram.
PROBLEM SOLVING: Example # 4
FVA
A
FHA
inch
1
20 lb
B FB
1 inch
6 inch
FHA & FVA = Horizontal and vertical reaction at pin support ‘A’
FB = Reaction at contact point B
20 lb = Vertical force on the spanner wrench
Multiple Choice Problems
1. The number of unknown to be shown in the free-body diagram of
member AB, as shown in the following figure, would be:
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (c)
Feedback:
The hinge support at A will have two reactions and roller support
at B will have one reaction.
Multiple Choice Problems
2. The number of unknown to be shown in the free-body diagram of
member AB, as shown in the following figure, would be:
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (c)
Feedback:
The hinge support at A will have two reactions and the rope at B
will have tension.