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e211test3 - φ k = µ k MOMENTS OF INERTIA Moment of...

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TEST 3 STATICS FORMULAS Page 1 CABLE FORMULAS Uniformly loaded cable (parabolic cable): L y x 2 x 1 y 2 y 1 w x H = internal horizontal force in the cable from statics, 1 1 2 1 + = y y L x for y 2 > y 1 , and 1 2 1 2 y wx H = Additional formulas from Cheng text (in the reserve library): w Hy x 1 1 2 = , 1 2 1 2 y wx H = , and H wx y 2 2 = Note that in this last equation that (x,y) is any point along the curve of the cable. From our textbook, + + = ... 5 2 3 2 1 4 2 x y x y x s , where s = distance along cable curve from the point of lowest sag to (x, y), and (x, y) = any point on the cable curve with the origin at the point of lowest sag.
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TEST 3 STATICS FORMULAS Page 2 FRICTION Coefficient of static friction N F s s max = µ Coefficient of kinetic friction N F k k max = µ where N = the normal force applied to the object from the contact surface F s , F k are friction forces parallel to the surface the angle of static friction, φ s , where tan φ s = µ s the angle of kinetic friction, φ k , where tan
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Unformatted text preview: φ k = µ k MOMENTS OF INERTIA Moment of Inertia 2D = Second Moment of an Area ∫ = dA y I x 2 where Ix, Iy are the axes about which the second moment of inertia is to be taken ∫ = dA x I y 2 y = distance from the x-axis x = distance from the y-axis Polar Moment of Inertia ( ) ∫ ∫ + = + = = y x o I I dA y x dA r J 2 2 2 Moments of Inertia by Integration x 2 x 1 f 1 (x) x dx y x f 2 (x) tall thin strips ( ) ( ) [ ] ∫ − = 2 1 1 2 2 x x y dx x f x f x I ( ) ( ) [ ] ∫ − = 2 1 3 3 1 3 2 x x x dx x f x f I Radius of Gyration A I k x x = A I k y y = Parallel Axis Theorem for Moments of Inertia of Composite Areas (n discrete shapes) ∑ ∑ = = + = n i i i n i x x d A I I i 1 2 1 ' where ' x I = moment of inertia of shape i about its own centroid A i i = area of shape i d i = distance between centroidal axis of i and reference axis....
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