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HW 11 - Homework set 11 Solutions

Homework set 11 Solutions

Course

Mechanics of Materials (CE 3110)

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University of Connecticut

Academic year: 2017/2018

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Paige Angol

University of Connecticut

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80 mm PROBLEM 4 80 mm P P P C 1 2 3 As many as three axial loads, each of magnitude P  50 kN, can be applied to the end of a W200 × 31 rolled-steel shape. Determine the stress at point A (a) for the loading shown, (b) if loads are applied at points 1 and 2 only. A SOLUTION For W200  31 rolled-steel shape. A  3970 mm 2  4  103 m 2 c 1 1 d  (210)  105 mm  0 m 2 2 I  31  106 mm 4  31  106 m 4 (a) Centric load: 3P  50  50  50  150 kN  150  103 N   (b) Ececentric loading: 3P 150  103   37  106 Pa  37 MPa 3 A 3  10  e  80 mm  0 m 2 P  50  50  100 kN  100  103 N M  Pe  (50  103 )(0)  4  103 N  m A   2P Mc 100  103 (4  103 )(0)     38  106 Pa  38 MPa A I 3  103 31  106  PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 553 PROBLEM 4 P Three steel plates, each of 25  150-mm cross section, are welded together to form a short H-shaped column. Later, for architectural reasons, a 25-mm strip is removed from each side of one of the flanges. Knowing that the load remains centric with respect to the original cross section, and that the allowable stress is 100 MPa, determine the largest force P (a) that could be applied to the original column, (b) that can be applied to the modified column. 50 mm 50 mm SOLUTION (a) Centric loading:   P A A  (3)(150)(25)  11  103 mm 2  11  103 m 2 P   A  (100  106 )(11  103 )  1  106 N (b) P  1125 kN  Eccentric loading (reduced cross section): A, 103 mm 2 y , mm A y (103 mm3 )  3 87 328 76  3 0 0 10  2 87 218 98  10 d , mm 109 Y  A y 109  103   10 mm A 10  103 PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 571 y M ⫽ 300 N · m A z PROBLEM 4 ␤ ⫽ 60⬚ B 16 mm The couple M is applied to a beam of the cross section shown in a plane forming an angle  with the vertical. Determine the stress at (a) point A, (b) point B, (c) point D. C 16 mm D 40 mm 40 mm SOLUTION 1 (80)(32)3  218  103 mm 4  218  109 m 4 12 1 I y  (32)(80)3  1  106 mm 4  1  106 m 4 12 y A  yB   yD  16 mm Iz  z A   z B   z D  40 mm M y  300cos 30  259 N  m (a) A   M z  300sin 30  150 N  m M z yA M y zA (150)(16  103 ) (259)(40  103 )    Iz Iy 218  109 1  106  A  3 MPa   3  106 Pa (b) B   M z yB M y z B (150)(16  103 ) (259)(40  103 )    Iz Iy 218  109 1  106  B  18 MPa   18  106 Pa (c) D   M z yD M y z D (150)(16  103 ) (259)(40  103 )    Iz Iy 218  109 1  106  D  3 MPa   3  106 Pa PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 583

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