ARCH 231

Architectural Engineering I:

Statics and Strength What is Mechanics? Deals with the response of

particles and rigid bodies

to mechanical disturbances It is an "Applied Science" that investigates equilibrium and motion conditions of bodies under the action of forces. In other words... Newtonian (Classical)

Mechanics Large objects

Speeds do not approach

speed of light Relativistic Mechanics Quantum Mechanics Surprisingly sexy Sir Isaac Newton! Mechanics of Rigid Bodies Statics: Deals with Bodies at rest

but there is also...

Dynamics: Bodies in Motion (we will skip the fun) No Real Life Object is Undeformable! we will study... However... Mechanics of

Deformable Bodies Deals with..

Distribution of internal forces and material failures hence, we will study the basics of... Another branch of mechanics is... Fluid Mechanics Incompressible Fluids

Compressible Fluids Applications for Civil Engineering,

Water distribution systems,

Open Channel Hydraulics,

Pressurized Pipe Systems etc... The Study of Mechanics, goes back to time of Aristotle (384-322 B.C.) and Archimedes (287-212 B.C.) Formulations

by Isaac Newton (1642-1727) "I can calculate the motion of heavenly bodies,

but not the madness of people." 400 BC Archytus of Tarentum - Theory of Pulleys

287-212 BC Archimedes - Lever equilibrium, buoyancy principle

1452-1519 Leonardo da Vinci - Equilibrium, concept of moments

1473-1543 Copernicus - Proposed that the earth revolves around the sun

1548-1620 Stevinus - Inclined planes, parallelogram law for addition of forces

1564-1642 Stevinus, Galileo - Virtual work principles

1564-1642 Galileo - Dynamics of pendulums, falling bodies

1629-1695 Huygens - Accurate measurement o fthe acceleration due to gravity

1642-1727 Newton - Law of universal gravitation, laws of motion

1654-1722 Varignon - Work with moment and force relationships

1667-1748 Bernoulli - Application of virtual work to equilibrium

1707-1793 Euler - Rigid body systems, moments of inertia

1717-1783 D'Alembert - Concept of inertia force

1736-1813 Lagrange - Formalized generalized equations of motion

1792-1843 Coriolis - Work with moving frames of reference

1858-1947 Planck - Quantum mechanics

1879-1955 Einstein - Theory of relativity Principles were later expressed in a modified form by D'Alembert, Lagrange and Hamilton

Validity remained unchallenged until Theory of Relativity by Einstein (1905)

"Newtonian Mechanics" still remains the basis of today's engineering applications. Basic Concepts Used In Mechanics Space

Time

Mass

Force Position of a

point P

(Coordinates) A measure

of resistance to Acceleration Force represents the

action of one body on another

Actual Contact or,

at a distance (gravitational and magnetic) Fundamental Principles Addition of Forces:

Parallelogram Law Two forces acting on a particle may be replaced by a single force called their RESULTANT obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces. A B R = A + B The Principle of Transmissibility the conditions of equilibrium (uniform motion) of a rigid body will remain unchanged if a force acting at a given point of the rigid body is transmitted along its line of action to another point with the same magnitude and same direction. F F Newton's First Law Of Motion (Law Of Inertia) If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) Newton's Second Law of Motion If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to magnitude of resultant and in the direction of resultant force F = m.a Newton's Third Law of Motion For every action there is an equal and opposite reaction Action:

Weight of the apple Reaction:

Force exerted by table to apple.

Otherwise table would break Unit Sytem (Time for Caffeine. We need extra care!) SI System of Units Length: meters, m

Mass: kilograms, kg

Time: Second, s Three arbitrarily defined base units: Derived Unit: Force: 1 kg x 1 m/s2 = 1 N Pay Attention To Dimensional Homogeneity Both sides of an equation must have same units. All operands in the equation must have consistent units. Dimensional Homogeneity Both sides of an equation must have same units.

All operands in an equation must have compatible units. Some quantities are unitless:

Angle (radians) or strain In your calculations... Significant Figures Accuracy of the calculation depends on many parameters. 2-3 significant figures are sufficient for the results. (e.g. 23.456 N or 23.46 N) You can use more significant figures in your intermediate calculations. You are expected not to make simple calculation errors! Try to obtain a scientific calculator Idealizations Real mechanical systems are complex.

Idealizations help us to analyze complex systems within the principles of mechanics. can be modelled as... Point Force assumption Support Idealization Problem Solving Technique Define the Problem: Have a clear problem definiton in mind and identify clearly what is requested. Collect Information: Write down all available data. Make clear and neat sketches that describe the problem. Plan of Attack: Study the problem and determine which theories are required for solution. ? Apply Appropriate Principles

and Equations: Write down equations in symbol form. Make substitutions after you are confident. Solve: Use your mathematical background to implement the solution and use consistent units.

Don't make any calculation errors! Verify Your Solution: Check calculations and try to answer the question "Does the result make sense?" Middle East Technical University Department of Architecture Joseph Kubin, Civil Engineer, M.Sc.

Mustafa Tümer TAN, Civil Engineer, M.Sc. Instructors Have a Good Semester!

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# Architectural Engineering I: Statics and Strength

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