Statics - STA 201E
Week-1
Introduction, fundamental concepts and general principles
Dr. Samet Ceri
Dept. of Aeronautical Engineering
Faculty of Aeronautics & Astronautics
Why Statics? (Motivation)
Engineering Statics is the foundation of all engineering mechanics.
•Before motion, vibration, or failure, every system must satisfy static equilibrium
•Aircraft structures, landing gear, satellite panels, and joints are all designed starting from Statics
•This course teaches you how engineers simplify real systems and reason correctly
Statics is where you start thinking like an engineer - not just solving equations.
What You Will Learn in This Course
By the end of this course, you will be able to:
•
Model physical systems using free-body diagrams
•
Analyze forces, moments, and reactions
•
Determine equilibrium of particles and rigid bodies
Solve basic structural problems (trusses, frames, machines)
How to Succeed
Most students struggle with Statics because of thinking, not mathematics.
To succeed:
•Attend lectures regularly
•Practice problems every week
•Ask questions early — confusion compounds fast
If you master Statics:
•Dynamics becomes easier
•Mechanics of Materials makes sense
•Structural and aerospace courses become manageable
Statics is difficult only when ignored.
Introduction
What is mechanics and why do we need this subject as an Aerospace Engineer?
Mechanics is a physical science concerned with the conditions of the rest or motion of bodies under the action of
forces.
Statics
Undeformable
(rigid) bodies
Dynamics
MECHANICS
Deformable
bodies
Strength of
materials
Fluids
Fluid
Mechanics
Fundamental concepts
Hence, we have to learn Statics before anything else and we have to do it very well!
Mass
Definition
&
purpose
SI units
Force
Quantity of the matter.
Push or pull action exerted
from one body on another.
gram (g)
kilogram (kg)
Newton (N)
kiloNewton (kN)
Plane
Space
This concept is associated
This concept is associated
with the position of an
with the position of an
arbitrary point P with respect arbitrary point P with respect
We use mass to compare
This interaction can occur with or
to a reference point (or
to a reference point (or
a body with another. Also,
without direct contact between
origin).
origin).
the mass provides
the bodies. The latter type
resistance against the
include gravitational, electrical
Two coordinates are
Three coordinates are
change in velocity.
and magnetical forces.
required.
required.
millimetre (mm),
millimetre (mm),
metre (m), degree (°), radian metre (m), degree (°), radian
(rad)
(rad)
Newton’s Laws of Motion
We will make use of Newtonian mechanics in this course.
Isaac Newton (1643-1727)
First Law
Second Law
Third Law
A particle that has no accelaration (i.e. at rest
or moving with a constant velocity) tends to
remain its state as long as the acting loads are
in equilibrium.
A particle acted by an unbalanced force (𝐹)
experiences an accelaration (𝑎) that has the
same direction of the force;
The mutual forces of action and reaction
between two particles are
• equal,
• opposite,
• colinear.
𝐅1
accelerates
Unbalanced
force
𝐅
𝐚
Force of A on B.
𝑚
the mass.
𝐅B
𝐅A
Force of B on A.
𝐅2
𝐅3
Equilibrium
෍𝐅 = 0
and the magnitude of the acceleration is
proportional to the force.
Action-reaction
𝐅=𝑚×𝐚
FA = −FB
Idealisations (Assumptions)
Engineering is sometimes defined as «the art of making the correct assumptions».
What are the most important assumptions we have in Statics?
Particle
Rigid Body
Concentrated Force
Particle has a mass but its geometry has no
A rigid body can be considered as a combination of a
Represents the effect of a loading
significance (the size can be neglected or large number of particles in which all the particles remain which is assumed to act at a point on
represented as a point). This assumption is
at a fixed distance from one another (undeformable),
a body.
particularly useful when all the forces meet
both before and after applying a load.
at a single point.
Example: the contact force between
Example: the wing of an aircraft with the engines
a landing gear and the ground.
Example: a hot air balloon tied to the
mounted on.
ground with ropes
Lift
force
Wing-fuselage
joint (connection)
Wing
Ground
Rope
Ground
(Courtesy: Google images)
Rope
Balloon’s
weight
Force
Weight of
the engine-1
Weight of
the engine-2
Anka UAV/UCAV (Courtesy: TAI/TUSAŞ)
Newton’s Law of Gravitational Attraction
Following the formulation of the Laws of Motion,
Newton postulated a law governing the gravitational attraction between any two particles.
Hence, the weight of a particle on Earth is
Mathematically;
Masses of the two particles.
Radius of the Earth: 𝑟
𝑚1 𝑚2
𝐹=𝐺
(𝑟)2
𝑀𝑒 𝑚
𝐹=𝐺
(𝑟)2
All constants
𝐺𝑀𝑒
𝑔=
𝑟 2
Force of gravitation
between two particles.
Universal constant of gravitation;
measured experimentally
Length of the line connecting
the centres of two particles.
Mass of the particle: 𝑚
or
−11
𝐺 = 6.67343 × 10
m3
kgΤs 2
simply, the distance
between two particles.
Mass of the Earth: 𝑀𝑒
𝑊 = 𝑚𝑔
Weight
gravitational
acceleration
Units of Measurement and Dimensional Homogeneity
To carry out our calculations and compare with the findings of
the others, we have to use a system that is consistent and
comparable.
We will use the International System of Units (SI Units).
SI base units are tabulated below:
Exponential form
Prefix
SI symbol
1 000 000 000
109
G
giga
1 000 000
106
M
mega
1 000
103
k
kilo
0.001
10-3
m
milli
0.000 001
10-6
𝜇
micro
0.000 000 001
10-9
n
nano
Symbol
Name
Quantity
s
second
time
m
metre
length
kg
kilogram
mass
Let’s calculate the universal constant of gravitation and pay attention
to the dimensional homogeneity.
The units must be
consistent on both sides
Gravitational acceleration; 𝑔 ≅ 9.807 m/s 2
of the equation!!!
Mass of the Earth: 𝑀𝑒 ≅ 5.972 × 1024 kg
A
Ampere
electric current
Radius of the Earth: 𝑟 ≅ 6371 km
K
Kelvin
thermodynamic temperature
𝑔 = 𝑟 2𝑒 rearrange the equation:
mol
mole
amount of substance
cd
candela
luminous intensity
Exercise: show that this is equal to
𝐺𝑀
𝐺=
𝑔 𝑟 2
𝑀𝑒
=
9.807 (6371)2
5.972 × 1024
m
2
∙ s
103 m 2
kg
≅
6.67343 × 10−11
m3
kg ∙ s2
𝑁𝑚2
𝑘𝑔2
Importance of unit inconsistency
•In 1999, NASA lost the Mars Climate Orbiter
•Not due to hardware failure or bad physics — but due to unit inconsistency
SI units (N) and Imperial
units (lbf) were mixed
without conversion
Statics begins with correct
assumptions, correct
models, and correct units
Engineering does not forgive sloppiness.
Chapter References
• Beer, F.P. and Johnston Jr, E.R; “Vector mechanics for engineers: Statics”, 8th edition, McGraw-Hill, 2007.
• Hibbeler, R.C., “Statics and Mechanics of Materials”, 5th edition, Pearson Press, 2019.
• Hibbeler, R.C., “Engineering Mechanics: Statics”, 12th edition, Pearson Press, 2009.