011409-Ch3

011409-Ch3 - 2 92-411 Machine Design Winter 2009 Department...

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1 92-411 Machine Design Winter 2009 Department of Mechanical, Automotive, and Materials Engineering 92-411: Machine Design I 2 Chapter 3: Load and Stress Analysis | Torsion: moment that is collinear with an axis of an element z Assumptions: Pure torque, considering sections far from point of application Parallel sections remain parallel after twisting Hooke’s Law applies 92-411: Machine Design I Figure 3-21 3 z Angle of twist, (solid, round bar) z Shear stress: Chapter 3: Load and Stress Analysis GJ Tl = θ J Tr J T = = max τ ρ 92-411: Machine Design I 4 z Torque/power relations Chapter 3: Load and Stress Analysis n H T T W H Units SI Tn FV hp H 55 . 9 ) ( : 63025 33000 ) ( = = = = ω
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2 92-411: Machine Design I Figure 3-25 5 Chapter 3: Load and Stress Analysis | Torsion of a thin-walled tube (t<<r) z Shear stress inversely proportional to the wall thickness 92-411: Machine Design I Figure 3-27 6 Chapter 3: Load and Stress Analysis | Torsion of open thin-walled sections z These members should be avoided in applications where there is torsion z Shear stress and angle of twist per unit length are inversely proportional to c 2 and c 3 , respectively 92-411: Machine Design I 7 Chapter 3: Load and Stress Analysis Stress Concentration | Irregularities in geometry cause increases in stress in the vicinity of the irregularity | Call them “stress raisers” and they are said to induce a “stress concentration” | Include holes, nicks in the material, grooves, threads 92-411: Machine Design I 8 Chapter 3: Load and Stress Analysis | Stress concentration factor, K t z Where the subscript “0” denotes nominal stress calculated using net cross sectional area (check source data notes) z K t is a value that is material independent and depends solely on the geometry of the stress concentration ( ) () 0 max 0 max , τ σ actual ts actual t K K = =
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3 92-411: Machine Design I 9 Chapter 3: Load and Stress Analysis z For an infinite plate with an elliptical hole: z For a circular hole, a = b , so K t 3 z Can also be used for cracks which can be approximated as an elliptical hole height - half hole width, - half hole , 2 1 a b a b K t + = 92-411: Machine Design I 10 Chapter 3: Load and Stress Analysis | Most stress concentration factors are determined experimentally z Strain gage measurements z Photoelasticity z Etc. | We will use table look-up methods for K t 92-411: Machine Design I Figure 3-29 11 Chapter 3: Load and Stress Analysis 92-411: Machine Design I Figure 3-30 12 Chapter 3: Load and Stress Analysis | Example 3-13 K t based on net area (w-d x t) vs. gross area (w x t), K t
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4 92-411: Machine Design I 13 Chapter 3: Load and Stress Analysis 2.45 2.6 2.8 3.2 3.7 4.6 5.4 7.4 K t 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 d/w | These stress concentration values are for the net area, A=(w-d)t t d w F K A F K K t t t ) ( max 0 max = = = σ 92-411: Machine Design I 14 Chapter 3: Load and Stress Analysis | What if we want to develop a stress concentration factor, K t ’, based on the gross area, A’= w x t () w d K d w w K t d w F K F wt F wt K wt F K t t t t t / 1 ) ( ) ( ' ' max
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011409-Ch3 - 2 92-411 Machine Design Winter 2009 Department...

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