Quiz3 Solution - Useful equations: Angle of twist for a...

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MEEG 344 – Mechanics of Materials Quiz #3 The column shown is subjected to a torque T. It is known that: G 2 = 2G 1 and d 2 = 2d 1 . Determine the Length L 2 as a function of L 1 if the angle of twist at A is twice that at B. SOLUTION d 2 = 2c 2 = 2d 1 = 2(2c 1 ) OR c 2 = 2c 1 1 4 1 4 1 4 2 2 16 2 16 ) 2 ( 2 2 J c c c J = = = = π 1 1 2 1 1 2 2 2 2 32 ) 2 )( 16 ( G J TL G J TL G J TL B = = = φ = i i i i i A G J L T 1 1 2 1 1 1 2 2 2 1 1 1 32 G J TL G J TL G J TL G J TL + = + = Condition given: B A 2 = = + 1 1 2 1 1 2 1 1 1 32 2 32 G J TL G J TL G J TL 1 1 2 1 1 1 32 G J TL G J TL = 2 1 32 1 L L = OR 1 2 32 L L =
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Unformatted text preview: Useful equations: Angle of twist for a single column: JG TL = , and for a combined column: ∑ = i i i i i G J L T Polar moment of inertia for a solid section: 4 2 c J = Shear strain in a shaft: L ρφ γ = Shear stress in a shaft: J T L G G ρ τ = = = T L 1 L 2 d 1 d 2 A B...
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