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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
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Module Objectives:
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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:
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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