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Chapter 1: Fundamental Concepts and Principles Mechanics:  Branch of physical science that deals with the state of rest or motion of bodies under the action of forces  Mechanics’ principles are used in almost all technical analysis and design  Divided into three branches: o Statics  equilibrium of bodies under the action of balanced forces o Dynamics  motion of bodies under the action of unbalanced forces o Strength of materials  relationship among external forces applied to the body: resulting stresses and deformations. Assumes rigidity Makes math easier Approximate answer very quickly with Strength of Materials, math gets hard quickly -> FEA What is Statics - Brain Waves.avi

Chapter 1: Fundamental Concepts and Principles 1.12 Brief Review of MATH: See examples in class

Chapter 1: Fundamental Concepts and Principles Assumption:  All bodies are considered to be perfect rigid ( the distance between any two points in the body remains unchanged. o Note: this is an idealization – deformations do occur, BUT they are considered negligible The Nature of Force:  Any influence that may change the state of rest (or motion) of a body;  Applied by: o direct, physical contact between the bodies ( Ex: force between a beam and its supports, water and hull of a boat, air and airplane body & wings, etc.), and o by remote action (Ex: gravitational force, magnetic forces, electrical forces, etc.).

Chapter 1: Fundamental Concepts and Principles Characteristics of a force:  Magnitude  a number with a proper unit  Direction  line of action  Point of application  the point where the force is exerted  Scalar  a quantity described by a magnitude (Ex: L, A, V, m, t)  Vector  a quantity described by magnitude, direction, and point of action (Ex: F, v, a) A

Chapter 1: Fundamental Concepts and Principles 1.4 Types of forces:  Distributed  applied over a line, area, or through a volume  Concentrated  applied to a point (this is an idealization !)  External  done a body on another body  Internal Types of force system:  Concurrent coplanar  Non concurrent coplanar  Concurrent spatial  Non concurrent spatial See examples in class

Chapter 1: Fundamental Concepts and Principles 1.6. Newton’s Laws:

Chapter 1: Fundamental Concepts and Principles 1.7 Principle of transmissibility:  The point of application of a force acting on a rigid body may be placed anywhere along its line of action without altering the conditions of equilibrium or motion of the body o Note: Not valid for internal effects 50N A B

Chapter 1: Fundamental Concepts and Principles 1.8 System of units:  International System of Units Length: meter (m) Mass: kilogram (kg) Force: Newton (N) Time: second (s) See examples in class  US Customary Units: Length: foot (ft) Force: pound (lb) Mass: slug ( 1 slug = lb m ) Time: second (s) o Note: All mechanical quantities can be expressed in terms of these units

Chapter 1: Fundamental Concepts and Principles 1.9 Unit Conversion: See examples in class Length: 1ft = m Mass: 1slug = 14.59kg Force: 1lb = N

Chapter 1: Fundamental Concepts and Principles 1.10 Consistency of Units:  Every quantity is measured with respect to a unit  when substituting into an equation, make sure that the final result have the correct unit See examples in class

Chapter 1: Fundamental Concepts and Principles 1.11 Rules for numerical computations:  Approximate numbers: o obtained through some kind of measurement (vs. those numbers derived from counting or by definition – “exact numbers”) o usually written with a decimal and may include zeros that serves as placeholders  Significant digits: all the digits in an approximate number except the zeroes used as placeholders See examples in class

Chapter 1: Fundamental Concepts and Principles Rules for numerical computations:  Accuracy: refers to the number of significant digits  Precision: refers to the decimal position of the last significant digit  Rules: o When approximate numbers that are multiplied or divided, the result is expressed with the same accuracy as the least accurate number o When approximate numbers that are added or subtracted, the result is expressed with the same precision as the least precise number See examples in class

Chapter 1: Fundamental Concepts and Principles

Process for Solving Statics Problems - Brian Waves.avi Recipe: 1- Identify givens and finds 2- Draw a picture 3- Draw Free Body Diagram 4- Write equations of equilibrium 5- Solve equations GFSA (Given, Find, Solve, Answer)