Column_Design

Column_Design - Column Design (6.1-6.3, 6.6) MAE 316...

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Column Design (6.1-6.3, 6.6) MAE 316 – Strength of Mechanical Components C. Heeter Tran Column Design 1
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troduction Introduction ` “Long” columns fail structurally (buckling failure) “ hort” columns fail materially (yielding failure) ` Short columns fail materially (yielding failure) ` We will examine buckling failure first, and then transition yielding failure. P to yielding failure. “Long” P 2 2 L EI P cr π = “Short” A P cr cr σ = P Column Design 2 P
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uckling of Columns .2) Buckling of Columns (6.2) ` For a simply supported beam (pin-pin) ) ( ) ( 2 = x Pv x M y, v y, v v(x) 0 ) ( 2 2 2 = + = = Pv x v d EI Pv x M dx v d EI F.B.D Æ dx The solution to the above O.D.E is: x x EI P B x EI P A x v cos sin ) ( + = Column Design 3
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uckling of Columns .2) Buckling of Columns (6.2) pply boundary conditions: v(0)=0 & v(L)=0 x EI P B x EI P A x v cos sin ) ( + = ` Apply boundary conditions: v(0) 0 & v(L) 0 0 sin & 0 = = L EI P A B ` Either A = 0 (trivial solution, no displacement) or P P n here n = 1 2 ` The critical load is then π n L EI L EI = = 0 sin where n = 1, 2, … 2 ) ( EI n P = `
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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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Column_Design - Column Design (6.1-6.3, 6.6) MAE 316...

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