AR%20231%20Structures%20in%20Architecture%20I

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AR 231 Structures in Architecture I

• Fall 2012-2013

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1.0 Introduction
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Instructor

• Dr. Engin AKTAS 
•   Department of Civil Engineering 
• Mechanical Eng. Build. Z16  
• Tel [phone]  
• E-mail enginaktas_at_iyte.edu.tr
• Web http//www.iyte.edu.tr/enginaktas 

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Time and Location

• Time
• Friday 13.30 16.15   
•   
•  Place
• Architecture B Z08
• TA Yelin Demir
• Architecture A 107

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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.
•    

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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.
•  

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Grading

• Quizzes 10 
•  1st Midterm Exam 25 
•  2nd Midterm Exam 25  
• Final Exam 40

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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.

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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, DAlambert,
  Lagrange, Laplace, etc.

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Newtons 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.

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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.

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UNITSSI The International Symbol of Units
Quantity Dimensional Symbol Unit Symbol
Mass M Kilogram Kg
Length L meter m
Time T second s
Force F Newton N
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• Relationship between units is based on the
  equation
• F m a
• 1 N (1 kg) (1 m/s2)

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Scalars and Vectors
Scalars Magnitude only Vectors Magnitude and direction
time displacement
volume velocity
density acceleration
speed force
energy moment
mass momentum
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VECTOR
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Vector Addition
VV1V2
V
Parallelogram Law
V
VV1V2
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Vector Subtraction
VV1-V2
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Components of a Vector
V
Vy
q
Vx
VX and VY are rectangular components of V
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Unit Vector

• A vector V can be expressed mathematically as

V
VV n
n
vector
unit vector
magnitude
ns magnitude is one and direction coincides with
Vs direction
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j
k
Vzk
qy
Vyj
qz
qx
i
Vxi
VVxiVyjVzk
VxV cos qx
VyV cos qy
VzV cos qz
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Direction cosines
n cos qz
m cos qy
l cos qx
VznV
VymV
Vxl V
V 2Vx2Vy2Vz2
l 2 m 2 n 21
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B(xB, yB, zB)
V
n
A(xA, yA, zA)
(xB-xA)
(yB-yA)
i
V

j
(zB-zA)

k
Unit vector along AB
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Numerical Accuracy
In engineering calculations three significant
figure accuracy is sufficient for results
25646 N
25600 N
3.29 m
3.285714 m
an exception is for the results starting with the
digit 1, four significant figures used for such a
case
10.34628 kN
10.35 kN
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Example (Meriam and Krieg prob.1/1)

• Determine the angle made by the vector
• V -10 i24 j with the positive x-axis. Write
  the unit vector n in the direction of V.

y
Vx -10 i
Vy 24 j
Vy
V
q ?
q
x
Vx