SkewLoads_NonSymXSect

SkewLoads_NonSymXSect - Skew L d and N S Sk Loads d...

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Skew Loads and Non-Symmetric Cross Sections (Notes Only) MAE 316 – Strength of Mechanical Components C. Heeter Tran Skew Loads & Non-Symmetric XSections 1
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troduction Introduction ` Will perform advanced stress and deflection analysis of eams with skew loads and non- mmetric cross beams with skew loads and non symmetric cross sections. P P α Skew load x z P ` Challenge: Need to calculate y y z on ymmetric moments of inertia – I yy , I zz , and I yz – and principal moments of inertia. y Non-Symmetric Skew Loads & Non-Symmetric XSections 2
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oments of Inertia Moments of Inertia ` For any cross-section shape = = = A yz A zz A yy dA yz I dA y I dA z I , , 2 2 z C dA y Skew Loads & Non-Symmetric XSections 3
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oments of Inertia Moments of Inertia ` The moments of inertia can be transformed to y 1 -z 1 ordinates by coordinates by θ 2 sin 2 cos z zz yy zz yy I I I I I I + + = 2 sin 2 cos 2 2 1 1 1 1 yz zz yy zz yy z z y y y I I I I I I + + = z 2 cos 2 sin 2 2 1 1 yz zz yy z y I I I I + = ` Does this look familiar?? z C 1 θ dA 2 Skew Loads & Non-Symmetric XSections 4 y y 1
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oments of Inertia Moments of Inertia ` Similar to transformation of stress, principal angle (angle the principal axes of inertia) can be found from to the principal axes of inertia) can be found from yz I 2 n ` Where θ P is the angle at which I yz is zero. zz yy P I I 2 tan θ z C y 1 z 1 θ dA Skew Loads & Non-Symmetric XSections 5 y
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xample Example ` Find I yy and I zz for a rectangle b h z C dA = dydz y Skew Loads & Non-Symmetric XSections 6
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xample Example ` Find I yy and I zz for a Z-section (non-symmetric about y-z) et b = 7 in, t = 1 in, and h = 16 in Let b 7 in, t 1 in, and h 16 in.
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This note was uploaded on 07/07/2011 for the course MAE 315 taught by Professor Wu during the Spring '08 term at N.C. State.

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SkewLoads_NonSymXSect - Skew L d and N S Sk Loads d...

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