2-Concepts-in-Statics-Summary

2-Concepts-in-Statics-Summary - Review of Basic Concepts in...

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Review of Basic Concepts in Statics 1. Preliminaries Ordered set (coordinate) representation where the unit vector directions implied Position Vector: r xi yj zk   ,, x y z r i j k Dot Product: Given Cartesian vectors written as the dot product is defined as     1 2 3 1 2 3 , , and , , F F F F u u u u  W = W = cos F u F u  Cross Product:   sin yx M r F r F n M F x F y k   x y F r F y F x (2-D) Often the direction of rotation is known, a priori and vectors are implied, but not shown; i.e. , M F x F y  Couple - The moment of the planar force system { F , - F } about ‘O’: F -F r a O   PP M r F r a F M a F C      Couples are free vectors that can be translated onto any point on a body without changing direction. Right hand rule

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2. Force Components (y-z Plane) 3. Resultant of a System of Co-Planar Forces cos y F F j F sin z F F k F 22 yz FF  F 1 tan z y F F   , y z y z y z F F j F k F F F F F j k F Bold implies vector Resolution of Concurrent Forces 12 R F F R F F Bold implies vector
Equivalent Force System at (i) Resultant Force System at (i) 6. Generalized Equivalent Force System: Conditions for Equilibrium 2D: resultant force vanishes 0; 0 ii FC 

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7. Resultant Force for Triangular Load – Point Load Equivalent 8. Free Body Diagrams Simplification of actual structure or part of structure including: Essential geometric components External loading Reactions/Internal forces
9. Trusses – Equilibrium 10. Equilibrium at a Point in Member Solution Techniques: Method of Joints and Method of Sections A B Implicit Approach: Sum of the internal member forces at a point equals sum of the external forces ( F ) at that point. P A – P B = F F P A P A P B P B Explicit Approach: P B + F – P A = 0 (Joint Equilibrium) FBD A FBD B

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11. Sign Conventions and Internal Forces 12. Differential Form for Equilibrium of Beam M + D M V + D V D x V M p ( x ) x y +
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2-Concepts-in-Statics-Summary - Review of Basic Concepts in...

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