# AENG260 - Problem set, chapter 3.docx - PERIDO JOHN PAULO M...

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PERIDO, JOHN PAULO M. AENG 260 -EXPERIMENTAL STRESS ANALYSIS MSAE – FPM PROBLEM SET IV 2018-68796 DR. DELFIN C. SUMINISTRADO 3.31. A steel (E = 207 GPa and v = 0.30) ring is shrunk onto another steel ring, as shown in the figure below. Determine the maximum interference possible without yielding one of the rings if the yield strength of both rings is 900 MPa and the dimensions of the rings are as follows: θ Case 1 Case 2 Case 3 Case 4 a i ,mm 100 100 100 0 b i ,mm 125 115 150 100 b o ,mm 150 200 175 150 Interference between two different materials δ = σ [ r E o ( r o 2 + r 2 r o 2 r 2 + v o ) + d E i ( r 2 + r i 2 r 2 r i 2 v i ) ] Where: δ - interference, mm σ - pressure generated with the designed connection or yield strength, MPa E o - Modulus of elasticity of the outer materials, GPa E i - Modulus of elasticity of the inner materials, GPa
r o - outer radius of the larger ring, mm r i - inner radius of the smaller ring, mm r - inner radius of the larger ring or outer radius of the smaller ring, mm v i - Poisson’s ratio of the inner ring v o - Poisson’s ratio of the outer ring Interference of same the material r ¿ ( ¿ o ¿¿ 2 r 2 )( r 2 r i 2 ) ¿ r o 2 r i 2 ¿ δ = 2 σ r 3 E ¿ Where: δ - interference, mm σ - pressure generated with the designed connection or yield strength, MPa E i -

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