2009+3-ForceSystemResultantsII

2009+3-ForceSystemResultantsII - 1 SJTU 上 海 交 通 大...

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Unformatted text preview: 1 SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • Right-handed coordinate system 2.5 Cartesian vectors Chapter 2 Force Vectors SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • Rectangular components of a vector 2.5 Cartesian vectors Chapter 2 Force Vectors y A y A x A z A’ A x z A = A x + A y + A z SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • Cartesian unit vectors 2.5 Cartesian vectors Chapter 2 Force Vectors u A = A / A a dimensionless vector SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 2.5 Cartesian vectors Chapter 2 Force Vectors • Cartesian vector representation A = A x i + A y j + A z k SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 2.5 Cartesian vectors Chapter 2 Force Vectors Magnitude of a Cartesian vector 2 2 2 z y x A A A A + + = A y A x A z A’ A x z SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • Directions of a Cartesian vector—direction cosines 2.5 Cartesian vectors Chapter 2 Force Vectors A A A A A A z y x = = = γ β α cos cos cos 1 cos cos cos 2 2 2 = + + γ β α 2 SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 2.6 Addition and subtraction of Cartesian vectors Chapter 2 Force Vectors Find the resultant of a concurrent force system F R = ∑ F = ∑ F x i + ∑ F y j + ∑ F z k SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 Any number of forces treated as a group constitute a force system. The force systems may be classified as follows: • Coplanar (forces in a plane 2D ) : concurrent, parallel, general case • Non-coplanar (forces in a space 3D ) : concurrent, parallel, general case • A force system is coplanar when all the forces lie in the same plane. • A force system is concurrent if the action lines of all the forces intersect in a common point. 2.6 Addition and subtraction of Cartesian vectors Chapter 2 Force Vectors SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • If the action lines of all the forces are parallel , this force system is called a parallel one, the senses of the forces are not necessarily the same. • If a force system applied to a body produces no external effect on the body, it is said to be an equilibrium force system. • Two force systems are said to be equivalent if they will produce the same external effect when applied in turn to a given body. 2.6 Addition and subtraction of Cartesian vectors Chapter 2 Force Vectors SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • x, y, z coordinates • Position vector 2.7 Position vectors Chapter 2 Force Vectors y j x i z k P (x ,y , z) x z y r r SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 Chapter 2 Force Vectors 2.8 Force vector directed along a line F = F u = F ( r/ r ) r Position vector SJTU 上 海 交 通 大 学 Introduction to Solid Mechanics -Vm211 • Definition: The dot product of vectors...
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This note was uploaded on 08/09/2011 for the course EE 211 taught by Professor Liuxila during the Summer '09 term at Shanghai Jiao Tong University.

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2009+3-ForceSystemResultantsII - 1 SJTU 上 海 交 通 大...

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