Republic of the Philippines
ISABELA STATE UNIVERSITY
Echague, Isabela
Title:
Chapter 1 – Principles of Statics
Overview/Introduction
Engineering Mechanics may be defined as the science which considers the
effects of forces on rigid bodies.
Learning Outcome/Objective
At the end of this chapter, students are expected to be able to:
1. Differentiate statics and dynamics;
2. Understand the different axioms of mechanics;
3. Differentiate the use and concepts of parallelogram law and triangle law;
4. Familiarize the different units use in statics; and
5. Solve conversion of units.
Learning Content/Topic
Lesson 1-1 – Branches of Mechanics
The branches and sub-branches of mechanics are presented below.
Engineering Mechanics
Statics
Force Systems
Concurrent
Parallel
Non-Concurrent
Applications
Structures
Friction
Dynamics
Kinematics
Translation
Rotation
Plane Motion
Kinetics
Translation
Rotation
Plane Motion
Fundamental Concepts (Definition of Terms)
Rigid Body. A definite amount of matter the parts of which are fixed in
position relative to each other.
Statics of Rigid Bodies. A branch of mechanics that deals with the effect
and distribution of forces on rigid bodies which are and remain at rest.
Dynamics of Rigid Bodies. A branch of mechanics that considers the
motion of rigid bodies caused by the forces acting upon them.
Force. Force may be defined as that which changes, or tends to change
the state of motion of a body.
Inertia. A property of matter that resist the change in motion of a body.
Mass. The quantitative measure of inertia.
Principle of Transmissibility. The external effect of force on a body is the
same for all points of applications along its line of action.
Lesson 1-2 – Axioms of Mechanics
The axioms of mechanics are stated in lengthy discussion in subsequent
articles. At this time we shall merely collate them for reference and state them
I the following form:
1. Parallelogram Law states that the resultant of two forces is the
diagonal of the parallelogram formed on the vectors of these forces.
2. Two forces are in equilibrium only when equal on magnitude, opposite
in direction, and collinear in action.
3. A set of forces in equilibrium may be added to any system of forces
without changing the effect of the original system.
4. Action and reaction forces are equal but oppositely directed.
Lesson 1-3 – Parallelogram and Triangle Law
Parallelogram Law states that the sum of the squares of the lengths of the
four sides of a parallelogram equals the sum of the squares of the lengths of
the two diagonals. Consider the illustration below:
Y
F1
F2
X
Given the two forces above, the resultant or the vector sum of two forces
may be can be determined by parallelogram law as shown below.
Y
R
F2
F1
F1
F2
X
Triangle Law of forces addition states that when two forces are represented
as two sides of the triangle with the order of magnitude and direction, then the
third side of the triangle represents the magnitude and direction of the
resultant force.
Y
F1
F2
X
Given the two forces above, the resultant or the vector sum of two forces
may be can be determined by triangle law in two ways as shown below.
Y
R
F1
F2
X
Y
F2
R
F1
X
Example Solve 1
Solve for the resultant force of the two forces shown below.
Y
F2
F1
X
Solution A: by parallelogram law
Y
F1
F2
R
F2
F1
X
Solution B: by triangle law
Y
F1
R
F2
X
Example Solve 2
Solve for the resultant force of the three forces shown below.
Y
F3
F2
F1
X
Solution A: by parallelogram law
Step 1: Solve for the resultant of F1 and F2 and label R1
Y
F1
F2
R1
F2
F1
X
Step 2: Solve for the resultant of R1 and F3
Y
R
F3
R1
R1
F3
X
Solution B: by triangle law
Y
F2
R
F1
F3
X
Lesson 1-4 – Units and Conversion
Unit of Mass
The common unit of mass for metric system is kilogram (kg) and gram (g)
while the uncommon unit of mass in English system is slug. The unit slug
is rarely used in mechanics; the unit Pound (lb) is often used.
Units of Force and Weight
The common units used for force are Newton (N) for metric system of unit
and Pound Force (lb) for English system of unit. Newton is a combination
of units of kg-m/s2. Another unit use for force in metric system is Dyne
(dyn) a combination of g-cm/s2. Pound force (lb) is a English system has
another unit for large forces: Kips (kip) which is equal to 1000 pound force.
Units of Length
The common units for length used in mechanics Meter (m) and Centimeter
(cm) for metric and Feet (ft) and Inch (in) for English system.
Units of Moment
The unit used for moment is a combination of unit of for e and length such
as Newton-Meter (Nm) and Pound-Feet (lb-ft).
Units of Angle
There are two common units of angle used in mechanics: Degrees and
Radians.
Conversion of Units
Below are the equivalents of each unit in metric and English system of
unit.
1m = 3.28ft
1kg = 2.204lbm
1N = 0.2248lbf
1° = 0.0175rad
1ft = 0.305m
1lbm =0.4545kg
1lbf = 4.4482N
1rad = 180°/π
Example Solve 1
Convert 10kg to lbm
Example Solve 2
Convert 10N to lbf
Example Solve 3
Convert 10Nm to lb-ft
Teaching and Learning Activities
Activity 1
Answer the following questions:
1. Differentiate Statics and Dynamics.
2. Relate the axioms of mechanics to the laws of motion.
3. Convert 19lb-ft to Nm.
4. Convert 12lbm to kg.