IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
AR 231
Structures in Architecture I
Fall 2012-2013
23.3.2016
Dr. Engin Aktaş
1
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
1.0 Introduction
23.3.2016
Dr. Engin Aktaş
2
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Instructor
Dr. Engin AKTAŞ
Department of Civil Engineering
Mechanical Eng. Build. #Z16
Tel: (232) 750 6809
E-mail: enginaktas@iyte.edu.tr
Web : http://www.iyte.edu.tr/~enginaktas
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Time and Location
Time
Friday 13.30 – 16.15
Place
Architecture B Z08
TA: Yelin Demir
Architecture A 107
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Course Description
Rigid body concept is introduced.
Equilibrium conditions and equivalent force
systems are discussed.
Analysis of rigid structures by their free body
diagrams is performed.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Text Book
Beer, F. P. and Johnston, Jr., E. R., Eisenberg,
E.R., Mazurek, D.F. (2007). Vector Mechanics for
Engineers: Statics, Eight Edition. McGraw-Hill, Inc
Reference Book
Meriam, J.L. and Kraige, L.G.(2002). Engineering
Mechanics, Statics Fifth Edition.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Grading
•
•
•
•
23.3.2016
Quizzes
10%
1st Midterm Exam 25%
2nd Midterm Exam 25%
Final Exam
40%
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
What is Mechanics?
• Mechanics can be defined as the science
which describes the condition of rest or
motion of bodies under the action of forces.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Mechanics
Mechanics of Rigid Bodies
Statics
Bodies at rest
(AR231)
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Mechanics of Deformable Bodies
(AR232)
Mechanics of Fluids
Dynamics
Bodies in motion
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Contributions
• Aristotle (384-322 BC)
• Archimedes (287-212 BC) Principle of lever,
principle of buoyancy
• Stevinus (1548-1620) Law of vector combination,
principles of statics
• Galileo (1564-1642) Dynamics
• Newton (1642-1727) Law of motion, law of
gravitation
• Also Vinci, Varignon, Euler, D’Alambert,
Lagrange, Laplace, etc.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Newton’s Laws
• A particle remains at rest or continues to move with
uniform velocity (in a straight line with a constant
speed) if there is no unbalanced force acting on it.
• The acceleration of a particle is proportional to the
vector sum of forces acting on it, and in the direction
of vector sum.
• The forces of action and reaction between bodies are
equal in magnitude, opposite in direction and collinear.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Basic Concepts
• Space:
The geometric region where bodies position are
represented by linear and angular measurements relative to a
coordinate system.
•
•
•
•
•
Time: Measure of succession of events.
Mass: Measure of the inertia of the body.
Force: Action of one body to another.
Particle: A body of negligible dimension.
Rigid Body: Deformation under forces is negligible.
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
UNITS
SI – The International Symbol of Units
Dimensional
Quantity
Symbol
23.3.2016
Unit
Symbol
Mass
M
Kilogram
Kg
Length
L
meter
m
Time
T
second
s
Force
F
Newton
N
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
• Relationship between units is based on the
equation
F = m a
1 N= (1 kg) (1 m/s2)
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Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Scalars and Vectors
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Scalars
Magnitude only
time
Vectors
Magnitude and direction
displacement
volume
velocity
density
acceleration
speed
force
energy
moment
mass
momentum
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
VECTOR
q
-V
Magnitude
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Dr. Engin Aktaş
V
V or V
V V
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Vector Addition
V=V1+V2
V2
V2
V
V1
V=V1+V2
Parallelogram
Law
V1
V
V2
V1
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Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Vector Subtraction
V2
V1
V
-V2
V1
V=V1-V2
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Components of a Vector
y
Vy
V
q
Vx
x
VX and VY are rectangular components of V
q  tan
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1
Vy
Vx
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Unit Vector
A vector V can be expressed mathematically as
V
V=V n
n
vector
unit vector
magnitude
n’s magnitude is one and direction coincides with V’s
direction
23.3.2016
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
z
Department of Architecture
y AR231 Fall 2012-13
j
V
k
Vzk
Vyj qy
qz
qx
x
Vxi
V=Vxi+Vyj+Vzk
Vx=V cos qx
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Vy=V cos qy
Dr. Engin Aktaş
i
Vz=V cos qz
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Direction cosines
l = cos qx
m = cos qy
n = cos qz
Vx=l V
Vy=mV
Vz=nV
V 2=Vx2+Vy2+Vz2
l 2 + m 2 + n 2=1
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Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
z
Department of Architecture
y AR231 Fall 2012-13
B(xB, yB, zB)
V
A(xA, yA, zA)
n
V= (xB-xA) i + (yB-yA) j + (zB-zA) k
x
Unit vector along AB
23.3.2016
V
n
V
Dr. Engin Aktaş
23
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Numerical Accuracy
In engineering calculations three significant figure
accuracy is sufficient for results
25646 N
3.285714 m
25600 N
3.29 m
an exception is for the results starting with the digit 1,
four significant figures used for such a case
10.34628 kN
23.3.2016
10.35 kN
Dr. Engin Aktaş
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IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Example
(Meriam and Krieg prob.1/1)
Determine the angle made by the vector
V = -10 i+24 j with the positive x-axis. Write the
unit vector n in the direction of V.
V
1 y
y
q   tan

Vx= -10 i
Vx
Vy= 24 j
Vy
1 24
tan
 67.4
 10
V
q=?
q’
q  180  67.4  112.6
x
Vx
2
2
V  10  24  26
V  10i  24 j
n 
 0.385i  0.923 j
V
26
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Dr. Engin Aktaş
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