This preview shows page 1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-119-120-121-122-123-124-125-126-127-128-129-130-131-132-133-134-135-238-239-240-241-242-243-244-245-246-247-248-249-250-251-252-253-254 out of 254 pages.
BeerMOM ISM_C09-P001-P076BeerMOM ISM_C09-P077-P168CCHHAAPPTTEERR 99PROPRIETARY 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. 1373 BAyLPx PROBLEM 9.1 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. SOLUTION 0: ( ) 0JMMPLx ()MPL x 22()dyEI P L x PL Pxdx 2112dyEI PLx Px Cdx 110, 0 : 0 0 0 0dyxCCdx 23121126EIy PLx Px C x C 22[ 0, 0]: 0 000 0 xy CC (a) Elastic curve. 2(3 )6PxyLxEI (2 )2dy PxLxdx EI (b) at .yx L 23(3 )63BPLPLyLLEI EI 33BPLyEI (c) at .dyxLdx 2(2 )22Bdy PL PLLLdx EI EI 22BPLEI 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. 1374 BAyLxM0 PROBLEM 9.2 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. SOLUTION 000: 0KMMMMM 2001dyEI M MdxdyEI M x Cdx 01 1 0,0:0 dyxLMLCCMLdx 201212EIy M x C x C 22 20022011[,0]022xLy ML ML C C ML (a) Elastic curve: 220(2 )2MyxLxLEI 20()2MyLxEI (b) at 0:yx 20(0)2AMyLEI 202AMLyEI (c) at 0:dyxdx 000() (0)dy M M M LLx Ldx EI EI EI 0AMLEI 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. 1375 BAywLxPROBLEM 9.3 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. SOLUTION 20: ( ) 0212JxMwxMMwx 222311216dyEI M wxdxdyEI wx Cdx 331111, 0 : 066 dyxLwLCCwLdx 331166dyEI wx wLdx 4321124 6EIy wx wL x C 44211[, 0]0 024 6xLy wL wL C 44211 324 6 24CwLwL (a) Elastic curve. 43 4(4 3)24wyxLxLEI (b) at 0.yx 44324 8AwL wLyEI EI 48AwLyEI (c) at 0.dyxdx 36Ady wLdx EI 36AwLEI 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. 1376 w0xBAyL PROBLEM 9.4 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. SOLUTION Use Free body AJ. 0:JM20023wx xML [,0],0xLydyxLdx 3016wxML 23016dy wxdx L 401124dy w xEICdx L 50121120wxEIy C x CL , 0 :dyxLdx3011024wL C 310124CwL [,0]xLy 44002110120 24 EIy wL wL C 420130CwL (a) Elastic curve. 54 50(5 4)120 wyxLxLEIL 440()24dy wxLdx EIL (b) @ 0:yx 4030AwLyEI 4030AwLyEI ◄ (c) @0:dyxdx 3024Ady w Ldx EI 3024AwLEI 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. 1377 yAwBCxP 523waa2a PROBLEM 9.5 For the cantilever beam and loading shown, determine (a) the equation of the elastic curve for portion AB of the beam, (b) the deflection at B, (c) the slope at B. SOLUTION Using ABC as a free body, 20: 2 034433yAAFRwawaRwawa 20: (2 )( ) (3 ) 03AAMMwaawaa 0AM Using AJ as a free body, 240: ()() 0321423JxMMwaxwxMwx wax 22232114231263dyEI wx waxdxdyEI wx wax Cdx 110, 0 : 0 0 0 0dyxCCdx 4321224 9EIy wx wax C 22[0, 0]: 0 0 0 0xyCC (a) Elastic curve over AB. 43(3 16 )72wyxaxEI 32(4)6dy wxaxdx EI (b) at 2 .yx a 4109BwayEI 4109BwayEI (c) at 2 .dyxadx 343Bdy wadx EI 343BwaEI FBD ABC: FBD AJ: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. 1378 yAwBLaCxMC 5wL26 PROBLEM 9.6 For the cantilever beam and loading shown, determine (a) the equation of the elastic curve for portion AB of the beam, (b) the deflection at B, (c) the slope at B. SOLUTION Using ABC as a free body, 0:yF 0AARwL R wL [0, 0]0, 0xydyxdx 0:AM22() 02613AALwLMwLMwL Using AJ as a free body (portion AB only), 0:JM() 02AAxMwx RxM 212 AAMwx R x M 221123wx wLx wL 22221123 dyEIwxwLxwLdx 32111 162 3 dyEIwxwLxwLxCdx 110, 0 : 0 0 0 0 0dyxCCdx 432211 124 6 6 yEIwxwLxwLxC 22[0, 0]: 0 0 0 0 0
View Full Document
Unlocking...