STATICS FORMULA SHEET
Distributed Loads
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Resultant: R = ∫ w(x) dx
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Location: xbar = (∫ x w(x) dx) / (∫ w(x) dx)
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Uniform: R = wL at center
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Triangle: R = (1/2)wL at 1/3 from larger side
Centroids
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Discrete: xbar = Σ(xiAi)/ΣA, ybar = Σ(yiAi)/ΣA
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Continuous: xbar = (1/A)∫x dA, ybar = (1/A)∫y dA
First Moment of Area
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Qx = ∫ y dA
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Qy = ∫ x dA
Moment of Inertia
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Ix = ∫ y² dA
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Iy = ∫ x² dA
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Parallel Axis: I = centroid + Ad²
Friction
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F ≤ µN
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Tan(theta)= µ
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Phi is the angle of friction, a bigger µ means a bigger phi
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When theta=phi, then this is the exact angle where something just slides
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Impending motion: F = µ
A hinge is also called a pin