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ComprehensiveReviewSheet - Concepts from Exam 1 Dimensional...

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Concepts from Exam 1: Dimensional Analysis: Dimensional analysis is the process of making sure that the dimensions on one side of the equation match the dimensions of the other side of the equation. Note that all terms of an expression should have the same units. If not, there is a problem! This is useful in double checking if your answers make sense and are correct on a very superficial level. Some useful units to know: Vectors: Vectors are characterized by two properties 1. Magnitude 2. Direction Methods of addition: 1. Parallelogram Method 2. (Tail – to – Tip) Triangle Method
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Unit vectors and direction cosines: Dot Product , , Note that θ is the angle between A and B. Cross Product , ,
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Note that C is perpendicular to both A and B and θ is the angle between A and B. Moments: About a point About a line Couples:
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Equilibrium: A free body diagram shows all the external forces that act on a chosen body (this includes loads, gravitational, and reaction forces) Equilibrium equations: 1. ∑ F = 0 → ∑ F x = 0, ∑ F y = 0, ∑ F z = 0 2. ∑ M = 0 → ∑ M x = 0, ∑ M y = 0, ∑ M z = 0 Connections (p160-162 in text):
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Equipollent Systems: Force/Couple Resultants (Screwdriver Problems): In general: Special cases that have force alone resultants Screwdriver problems:
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Distributed Loads:
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Concepts for Exam 2: Interacting Body Concepts : Truss Concepts : Static Determinacy: Let the number of pins = p and the number of truss members = m. There exist three distinct cases: 1.
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