Cal Poly Pomona ME 218 - Sample Problem 4.2 (13 pages)

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Sample Problem 4.2



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Sample Problem 4.2

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Pages:
13
School:
California State Polytechnic University, Pomona
Course:
Me 218 - Strength Of Materials I
Strength Of Materials I Documents

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Fourth MECHANICS OF MATERIALS Beer Johnston DeWolf Sample Problem 4 2 SOLUTION Based on the cross section geometry calculate the location of the section centroid and moment of inertia Y yA A I x I A d 2 Apply the elastic flexural formula to find the maximum tensile and compressive stresses m A cast iron machine part is acted upon by a 3 kN m couple Knowing E 165 GPa and neglecting the effects of fillets determine a the maximum tensile and compressive stresses b the radius of curvature Mc I Calculate the curvature 2006 The McGraw Hill Companies Inc All rights reserved 1 M EI 4 1 Fourth MECHANICS OF MATERIALS Beer Johnston DeWolf Sample Problem 4 2 SOLUTION Based on the cross section geometry calculate the location of the section centroid and moment of inertia Area mm 2 y mm yA mm3 1 20 90 1800 2 40 30 1200 A 3000 50 20 90 103 24 103 3 yA 114 10 3 yA 114 10 Y 38 mm 3000 A 121 bh3 A d 2 1 90 203 1800 122 1 30 403 1200 182 12 12 I x I A d 2 I 868 103 mm 4 868 10 9 m 4 2006 The McGraw Hill Companies Inc All rights reserved 4 2 Fourth MECHANICS OF MATERIALS Beer Johnston DeWolf Sample Problem 4 2 Apply the elastic flexural formula to find the maximum tensile and compressive stresses Mc I M c A 3 kN m 0 022 m A I 868 10 9 m 4 M cB 3 kN m 0 038 m B I 868 10 9 m 4 m A 76 0 MPa B 131 3 MPa Calculate the curvature 1 M EI 3 kN m 165 GPa 868 10 9 m 4 2006 The McGraw Hill Companies Inc All rights reserved 1 20 95 10 3 m 1 47 7 m 4 3 Fourth MECHANICS OF MATERIALS Beer Johnston DeWolf Bending of Members Made of Several Materials Consider a composite beam formed from two materials with E1 and E2 Normal strain varies linearly x y Piecewise linear normal stress variation 1 E1 x E1 y 2 E2 x E2 y Neutral axis does not pass through section centroid of composite section Elemental forces on the section are Ey E y dF1 1dA 1 dA dF2 2 dA 2 dA x My I 1 x Define a transformed section such that 2 n x dF2 2006 The McGraw Hill Companies Inc All rights reserved nE1 y dA E1 y n dA E n 2 E1 4 4



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