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### 15_39

Course: MECHANICAL EM217, Spring 2011
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Word Count: 435

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A 15.39 short rectangular post supports compressive loads of P = 175 kN and Q = 90 kN as shown in Fig. P15.39a. A top view of the post showing the locations where loads P and Q are applied to the top of the post is shown in Fig. P15.39b. Determine the vertical normal stresses at corners a, b, c, and d of the post. Fig. P15.39a Fig. P15.39b Top view of post Solution Section properties: A = (120 mm)(160 mm) = 19,...

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A 15.39 short rectangular post supports compressive loads of P = 175 kN and Q = 90 kN as shown in Fig. P15.39a. A top view of the post showing the locations where loads P and Q are applied to the top of the post is shown in Fig. P15.39b. Determine the vertical normal stresses at corners a, b, c, and d of the post. Fig. P15.39a Fig. P15.39b Top view of post Solution Section properties: A = (120 mm)(160 mm) = 19, 200 mm 2 (120 mm)(160 mm)3 = 40.960 106 mm 4 12 (160 mm)(120 mm)3 Iz = = 23.040 106 mm 4 12 Ix = Equivalent forces at base of post: F = 175 kN + 90 kN = 265 kN = 265,000 N M x = (175 kN)(60 mm) (90 kN)(40 mm) = 6,900 kN-mm = 6.900 106 N-mm M z = (175 kN)(40 mm) = 7,000 kN-mm = 7.000 106 N-mm Axial stress due to F: 265,000 N axial = = 13.802 MPa (C) 19, 200 mm 2 Bending stress due to Mx: M x z (6.900 106 N-mm)( 80 mm) bend x = = = 13.477 MPa Ix 40.960 106 mm 4 Bending stress due to Mz: M z x (7.000 106 N-mm)( 60 mm) bend z = = = 18.229 MPa Iz 23.040 106 mm 4 Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission the of copyright owner is unlawful. Normal stresses at corners a, b, c, and d: The normal stresses acting at each of the four corners of the post can be determined by superimposing the results obtained above. In all instances, the normal stresses act in the vertical direction; that is, the y direction. The sense of the stress, either tension or compression, can be determined by inspection. Corner a: a = 13.802 MPa (C) + 13.477 MPa (T) + 18.229 MPa (C) = 13.802 MPa + 13.477 MPa 18.229 MPa = 18.555 MPa = 18.56 MPa (C) Ans. Corner b: b = 13.802 MPa (C) + 13.477 MPa (T) + 18.229 MPa (T) = 13.802 MPa + 13.477 MPa + 18.229 MPa = 17.904 MPa = 17.90 MPa (T) Ans. Corner c: c = 13.802 MPa (C) + 13.477 MPa (C) + 18.229 MPa (T) = 13.802 MPa 13.477 MPa + 18.229 MPa = 9.049 MPa = 9.05 MPa (C) Ans. Corner d: d = 13.802 MPa (C) + 13.477 MPa (C) + 18.229 MPa (C) = 13.802 MPa 13.477 MPa 18.229 MPa = 45.508 MPa = 45.5 MPa (C) Ans. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
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Naval Academy - MECHANICAL - EM217
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Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
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Naval Academy - MECHANICAL - EM217
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Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
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Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319