ME 338 Lecture 8

# ME 338 Lecture 8 - ME 338 Lecture#8 Beam Deflections...

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ME 338 Lecture #8 – Beam Deflections Continued

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Outline Group Assignments Survey Stepped Shafts Beam Deflections Energy Methods Castigliano’s Theorem In Class Exercise
Stepped Shafts Determine the deflection curve and the deflections at B and C. F L/2 L/2 2I I F FL M -FL M/I -FL/2I -FL/4I -FL/2I ? = ? ± −1 ² ?³ ± −2 ² ? ± ² ³ −1 ? = ? ± 0 ² ?³ ± −1 ² ? ± ² ³ 0 ? = ? ± 1 ² ?³ ± 0 ² ? ± ² ³ 1 = ?± ² ?³ Step drop in M/I accomplished by adding step term and additional ramp function at L/2 ? ´ = ? µ´ ± ² µ´ ² ± ² ³ µ 0 + ? µ´ ± ² ³ µ 1 B C

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Stepped Shafts Determine the deflection curve and the deflections at B and C. F L/2 L/2 2I I F FL ? ?? ?? = ? ? 2 ³± ? − ? − ² ³ 1 + ? ? − ² ³ 2 + ? ´ ?? = ? ´³± ? 3 ? 2 ? − ² ³ 2 + ? ´³± ? − ² ³ 3 + ? ´ ? + ? ³ µ ± = ? ³± ? − ³± ? − ² ³ 0 + ? ³± ? − ² ³ 1 dy/dx = 0 and y = 0 at x=0 so C 1 = 0 and C 2 = 0 so ? = ? ³4?± ³? 3 − 6²? 2 − ¶² ? − ² ³ 2 + ³ ? − ² ³ 3 B C
Stepped Shafts Determine the deflection curve and the deflections at B and C. F L/2 L/2 2I I F FL ? = ? 24?? 3 − 6²± ³ − ´² ± − ² 2 ³ + 2 ± − ² 2 3 At x=L/2 ? = ?

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ME 338 Lecture 8 - ME 338 Lecture#8 Beam Deflections...

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