Civ100-M1 - CIV100: Mechanics Lecture Notes Module 1: Force...

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1 CIV100: Mechanics Lecture Notes Module 1: Force & Moment in 2D By: Tamer El-Diraby, PhD, PEng. Associate Prof. & Director, I2C University of Toronto Acknowledgment: Hesham Osman, PhD and Jinyue Zhang, MASc., contributed to this module You Know What to Do!
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2 Module Objectives: By the end of this Module you should be able to: Be familiar with the units used in this course Know the requirements regarding significant figures in this course. Know how to resolve a force in any 2 axis. Know how to add 2 or more forces and find their resultant. Graphically Using Algebra Understand the concept of vector, their addition and products. Know how to develop free body diagram Understand the concept of moment in 2D Know how to transfer forces form one point to another in 2D Understand the concept of Equilibrium Make sure to test your knowledge of these objectives before moving to module 2. Module 2 will take these concepts to a higher level The Module in a Nutshell: Forces as Vectors The Nature of Force: A Force has a direction (line of action & sense) and a value. Forces are measured by N (not Kg) Forces are added as geometrical vectors not arithmetic (scalar) values: R = F1 + F2 + F3 …. . Fn Forces are added by the parallelogram law Forces are added by the triangle rule The Unit Vector is used to express the direction of force: •F = F x i + F y j + F z k Never Use Kg to measure Force. It is measured by N . A Figure to Remember: the Unit Vector The Unit Vector is just another way to express X, Y & Z
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3 Module in a Nutshell: Forces in 2D In 2D, a force can be resolved in any two dimensions. X & Y are the most common: F x = F Cos Θ , F y = F Sin Θ A Force can be represented as a Vector: •F = F x i + F y j Forces can be added using their components Forces can be added using their components •Rx = F1x + F2x + F3x …. . Fnx (no need for vectors, as X ( i ) is the direction) •Ry = F1y + F2y + F3y …. . Fny (no need for vectors, as Y ( j ) is the direction) •R = Rx 2 + Ry 2 ; tan Θ = R y / Rx A Figure to Remember Graphical Addition/Resolution of Forces F A Figure to Remember: Best Way to Add Forces 1. We are adding vectors not values 2. F X and F Y are the most used Fx= F Cos Θ Fy= F Sin Θ Always add forces using their X & Y components. This easier and safer! R= Rx2 + Ry2 ; tan Θ = Ry / Rx Module in a Nutshell: Moment as Vector The Nature of a Moment A Force could have a moment around an axis and, in 3D, around a point. A Figure to Remember: Moments d x Fy Fx d y F M 2 =d y x F x The moment sense M 1 =d x x F y The moment sense is from dx to Fy d F M = d x F r is from dy to Fx Note: M1 is positive and M2 is negative; M=dx Fy – dy Fx M is a vector coming out of the paper (+ve) or going into the paper (-ve) The General rule is that Moment is a vector product of d and F (in this order). It so happens that in magnitude (only), that the value of the Moment is equal to r.F
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4 Quantities, units & significant figures Quantities: Length: Meters (m) & Millimeters (mm) .
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Civ100-M1 - CIV100: Mechanics Lecture Notes Module 1: Force...

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