IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

11.04.23 Dr. Engin Aktaş 1

AR 231 Structures in Architecture I

Fall 2012-2013

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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1.0 Introduction

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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 

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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.

   

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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Text Book

Meriam, J.L. and Kraige, L.G.(2002). Engineering Mechanics, Statics Fifth Edition.

 

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

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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Grading

• Quizzes 10% 

•  1st Midterm Exam 25% 

•  2nd Midterm Exam 25%  

• Final Exam 40%

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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.

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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Mechanics

Mechanics of Rigid BodiesMechanics of Deformable Bodies

(AR232) Mechanics of Fluids

StaticsBodies at rest

(AR231)

DynamicsBodies in motion

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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, D’Alambert,

Lagrange, Laplace, etc.

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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.

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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.

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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UNITSSI – The International Symbol of Units

QuantityDimensional

SymbolUnit 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 VectorsScalars

Magnitude only

Vectors

Magnitude and direction

time displacement

volume velocity

density acceleration

speed force

energy moment

mass momentum

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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VECTOR

-V

V

VVMagnitude

VorV

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Vector Addition

V1

V2

V1

V2

V

V1

V2

V

V=V1+V2

Parallelogram Law

V=V1+V2

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Vector Subtraction

V1

V2 V1-V2

V=V1-V2

V

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Components of a Vector

x

y

V

Vx

Vy

VX and VY are rectangular components of V

x

y

V

V1tan

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Unit VectorA vector V can be expressed mathematically as

V=V n

vectormagnitude

unit vector

n’s magnitude is one and direction coincides with V’s direction

V

n

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x

yz

V

Vzk

k

j

iVxi

Vyj

x

y

z

V=Vxi+Vyj+Vz

kVx=V cos x Vy=V cos y Vz=V cos z

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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Direction cosines

l = cos x m = cos y n = cos z

Vx=l V Vy=mV Vz=nV

V 2=Vx

2+Vy2+Vz

2

l 2 + m 2 + n 2=1

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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x

yz

B(xB, yB, zB)

A(xA, yA, zA)V

V= (xB-xA)i

+ (yB-yA) j

+ (zB-zA)k

n

V

Vn Unit vector along AB

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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Numerical Accuracy

In engineering calculations three significant figure accuracy is sufficient for results

25646 N 25600 N

3.285714 m 3.29 m

10.34628 kN

10.35 kN

an exception is for the results starting with the digit 11, four significant figures used for such a case

IZMIR INSTITUTE OF TECHNOLOGYIZMIR INSTITUTE OF TECHNOLOGY Department of ArchitectureDepartment of Architecture AR23AR2311 Fall 2012-13Fall 2012-13

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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.

4.6710

24tan

tan

1

1

x

y

V

V

x

y

= ?

Vx= -10 i

Vy= 24 j

Vx

Vy

V’ 6.1124.67180

V

Vn

262410 22 V

jiji

923.0385.026

2410