IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 1 AR 231 Structures in Architecture I Fall

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş Introduction

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 3 Instructor Dr. Engin AKTAŞ Department of Civil Engineering Mechanical Eng. Build. #Z16 Tel: (232) Web :

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 4 Time and Location Time Friday – Place Architecture B Z08 TA: Yelin Demir Architecture A 107

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 5 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 TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 6 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 TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 7 Grading Quizzes 10% 1st Midterm Exam 25% 2nd Midterm Exam 25% Final Exam 40%

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 8 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 TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 9 Mechanics Mechanics of Rigid Bodies Statics Bodies at rest (AR231) Dynamics Bodies in motion Mechanics of Deformable Bodies (AR232) Mechanics of Fluids

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 10 Contributions Aristotle ( BC) Archimedes ( BC) Principle of lever, principle of buoyancy Stevinus ( ) Law of vector combination, principles of statics Galileo ( ) Dynamics Newton ( ) Law of motion, law of gravitation Also Vinci, Varignon, Euler, D’Alambert, Lagrange, Laplace, etc.

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 11 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 TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 12 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 TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 13 UNITS SI – The International Symbol of Units Quantity Dimensional Symbol UnitSymbol MassMKilogramKg LengthLmeterm TimeTseconds ForceFNewtonN

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 14 Relationship between units is based on the equation F = m a 1 N= (1 kg) (1 m/s 2 )

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 15 Scalars and Vectors Scalars Magnitude only Vectors Magnitude and direction timedisplacement volumevelocity densityacceleration speedforce energymoment massmomentum

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 16 VECTOR -V V  Magnitude

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 17 Vector Addition V1V1 V2V2 V1V1 V2V2 V V1V1 V2V2 V V=V 1 +V 2 Parallelogram Law V=V 1 +V 2

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 18 Vector Subtraction V1V1 V2V2 V1V1 -V 2 V=V 1 -V 2 V

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 19 Components of a Vector x y V VxVx VyVy V X and V Y are rectangular components of V 

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 20 Unit Vector A vector V can be expressed mathematically as V=V nV=V n vector magnitude unit vector n’s magnitude is one and direction coincides with V’s direction V n

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 21 x y z V VzkVzk k j iVxiVxi VyjVyj xx yy zz V=Vxi+Vyj+VzkV=Vxi+Vyj+Vzk V x = V cos  x V y = V cos  y V z = V cos  z

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 22 Direction cosines l = cos  x m = cos  y n = cos  z V x = l V V y = mV V z = nV V 2 = V x 2 + V y 2 + V z 2 l 2 + m 2 + n 2 =1

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 23 x y z B( x B, y B, z B ) A( x A, y A, z A ) V V= ( x B -x A ) i + ( y B -y A ) j + ( z B -z A ) k n Unit vector along AB

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 24 Numerical Accuracy In engineering calculations three significant figure accuracy is sufficient for results N N m 3.29 m kN kN 1 an exception is for the results starting with the digit 1, four significant figures used for such a case

IZMIR INSTITUTE OF TECHNOLOGY Department of Architecture AR231 Fall Dr. Engin Aktaş 25 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. x y  = ? V x = - 10 i V y = 24 j VxVx VyVy V ’’