IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
AR 231
Structures in Architecture I
Fall 2012-2013
13.12.2015
Dr. Engin Aktaş
1
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
1.0 Introduction
13.12.2015
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: [email protected]
Web : http://www.iyte.edu.tr/~enginaktas
13.12.2015
Dr. Engin Aktaş
3
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
13.12.2015
Dr. Engin Aktaş
4
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.
13.12.2015
Dr. Engin Aktaş
5
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.
13.12.2015
Dr. Engin Aktaş
6
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Grading
•
•
•
•
13.12.2015
Quizzes
10%
1st Midterm Exam 25%
2nd Midterm Exam 25%
Final Exam
40%
Dr. Engin Aktaş
7
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.
13.12.2015
Dr. Engin Aktaş
8
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Mechanics
Mechanics of Rigid Bodies
Statics
Bodies at rest
(AR231)
13.12.2015
Mechanics of Deformable Bodies
(AR232)
Mechanics of Fluids
Dynamics
Bodies in motion
Dr. Engin Aktaş
9
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.
13.12.2015
Dr. Engin Aktaş
10
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.
13.12.2015
Dr. Engin Aktaş
11
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.
13.12.2015
Dr. Engin Aktaş
12
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
UNITS
SI – The International Symbol of Units
Dimensional
Quantity
Symbol
Unit
Symbol
Mass
M
Kilogram
Kg
Length
L
meter
m
Time
T
second
s
Force
F
Newton
N
13.12.2015
Dr. Engin Aktaş
13
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)
13.12.2015
Dr. Engin Aktaş
14
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Scalars and Vectors
13.12.2015
Scalars
Magnitude only
time
Vectors
Magnitude and direction
displacement
volume
velocity
density
acceleration
speed
force
energy
moment
mass
momentum
Dr. Engin Aktaş
15
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
VECTOR
q
-V
Magnitude
13.12.2015
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
13.12.2015
Dr. Engin Aktaş
17
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Vector Subtraction
V2
V1
V
-V2
V1
V=V1-V2
13.12.2015
Dr. Engin Aktaş
18
IZMIR INSTITUTE OF TECHNOLOGY
Department of Architecture
AR231 Fall 2012-13
Components of a Vector
y
V
Vy
q
Vx
x
VX and VY are rectangular components of V
q  tan
1
Vy
Vx
13.12.2015
Dr. Engin Aktaş
19
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
13.12.2015
Dr. Engin Aktaş
20
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
13.12.2015
Vy=V cos qy
Dr. Engin Aktaş
i
Vz=V cos qz
21
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
13.12.2015
Dr. Engin Aktaş
22
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
n 
V
V
13.12.2015
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
13.12.2015
10.35 kN
Dr. Engin Aktaş
24
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.
y
tan
q=?
q’
n
V 
V
V
13.12.2015

 10 i  24 j

1
24
 10
  67 . 4 
q  180  67 . 4  112 . 6 
x
Vx
Vy
Vx
Vy= 24 j
Vy
V
q   tan
Vx= -10 i
1
10 
2
  24   26
2
  0 . 385 i  0 . 923 j
26
Dr. Engin Aktaş
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AR 231 Structures in Architecture I