HW7 - ƨ 6Æ a ŽŽ r ¨ 0Gaxä‰ d60d60¢Vd6ÔÔ €k...

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Unformatted text preview: ƨ 6Æ a ŽŽ r ¨ 0Gaxä‰ d60d60¢Vd6ÔÔ €k ¨ g †U Ñ Å X k Ž Ž Ô Ž iŽ `Ô %&› ŽdŽd g ‰ ³ ag Õ › k g t‚ f e wg g| ’gy ± Ž ¨ „‚ ƒ| ‡ g u ‡| t w ‡e e w vu6I(`sV…ssq6| ¦dŽ d¨ …e6v‚V€Ge6…G°`ˆqhx“’ r …Õ‹‰ Æ ¨ ê » › Æ ‰ ×  r ¨ µk Æ g ¨Æ ‰ ­  ‰ «ŽŽÔ ‰ edd¿aÁµk Æ ê » gqd˜X‰ š  kŽŽ g «ŽŽÔ ‰ kŽŽ g [email protected] Æ g a¨ ‰ ­  ’ ‡ ¯|g e wg – t qve`6i`i¨`Gus’ Y » sg Æ ds˜p`6‚ ‚ r‚ „ eu ƒx6| Æ ‚s¦Ž~6s˜p„(`d‚€’6|¿”6|¦–`Gut`ƒ6G‚—Wئsvu~6€Ih`is`vƒ4G°f2dv‚sxvwd‚ v u g r‚ e u ep | ‡ ‚  g ‚ g t r | e ¯ e w gq e t t c x u t g ‡ Y u t r q po ¨ ÞÕxX %sshiSn F 400 N/m 0 3 7 x Y ue t– ƒ| ‡ e wg p „ reg ’ eyp „ g u ‡| t w ‡e e wg eg ‡ w ‡| 2€db°de6G‚(`i'd˜‚~qi”’ ® €s6˜‚Vqve6…G°x4q(`i"s…•|x€vy…'ç ¨ ÏÕ`X Y [email protected] D # A 7531 X Æ ¨ Õ r Õ Å a k Ž Ž Ž a g Æ Æ Ž ‘› k Ž Ž g k …Ž Ç d‰ dd0½€k 6dÆ Å 6Ǝ 68a 2d6Õ €dÏÕÅ ¨ g µU ‰ ³ g g| – tgy ± ŽŽÕ …¦`vusq6| ¨d60a pd‚†ŽdŽd¿aÁ›Ž66¦6‰qi€”€sx€seBH6¿eqsd˜‚—qix`G¯ss”v’x¸v’`sesd˜‚hs€x“’ Ž ŽÕ ’| ƒeg ue’ep fep e ¯ u|y eyp „ ƒeg w tpg t ƒ t wg ep „epe w r 6dÆ Å Æ µdÕ g ¨Æ ‰ š  ±ŽŽŽa ‰ kŽŽ gk 6dd0‚µd˜X€dÕ g a¨ ‰ š  ÆÆ ‰ k r ‰ k …ÏÕÅ ¨ ´6Õ g a¨ ‰ ­  ± Ž Ž Õ ‰ r Ü ±k Ž Žag rk g d66‹…fid0½†½dÕ ¬‰ ­  š gGgS6²dsmd"ved`…•|ss`ie`6| ­ lGed`6iq€”(`i2G‡6'µ2dv‚sxvwd‚ v  t „‚ f ‚g u ‚ ‡ – u tpg e wg ƒ u  ‡ – u|gyep e wg ‡| ç x u tg ‡ Y u t r q po Æ ÞÕxX %sshiSn 0 100 N/m 500 N/m 5 Y u tg| ‡ f f| „‚ g t‚ f ’ t ƒ u| ƒ| ‡ gu ‡| t w‡e e wg eg w f r‚ &dG‚i…€vyvtx`6œ6€vudB“ibg `…²6v‚V€Ge6…G°`ˆqhxifi„`¡6lç Æ ÏÕ`X Y Õ Æ ¨ ue w ’ Y ‡– u tp €x“œ6Ged`6v|ssg – t t| rep e wg eg‚ ue  g ‡ ƒ u| „† u ‚g Y Ž g w te w „‚ `Gu`vu6¡€” xiei6x€`ƒ × nqGe¥`…¦g …1dsmbax¡dv–q`"…¡ „g Ç ig Õ d”˜p„ ‚ r‚ vedx6•h€sl`ils6`q`ƒ š e€g V(s"Á6s˜ps€s6“xils6`€xƒ ­ Yhe º 2dv‚sxvwd‚ v ‡– u|gyep e wg eg‚ ue j „ Õ ‚g Ž r‚ „ |ep| e wg eg‚ ue  g x u tg ‡ X Y u t r q po …ÞÕxX %sshiSn 0.2 ton/ft 0.1 ton/ft g …¿Ga`£‰ s ‚ „Ž Å X ³‚ g ‚ a …| ’`udsg¸ÏÔÅd‰   xÆ C€‹‰‚ × ‚  Ý ÜX › Õ ‚ k Ågk X [email protected] a¨ ‰ ×  Ý 8Ga½€ˆ˜X¬‰ k Ågk g  ¨ ¨ ‰³ ¬µU Ý ÜX › Õ „¨ C€‹‰ š  „¨ 6‹‰ ­  Ý ÜÕ š  Ý k ¨ i€6Õ ‰ ­  Ågk g Y u tg| ‡ f f| „‚ g t‚ f ’ t ƒ u| ƒ| &dG‚i…€vyGt``6†6“vudB“ibg x6²6G‚‡ g u ‡| t w ‡e e wg eg w f r‚ ç Y ƒe ¯ žy wpg | – u ‡| ƒeg w tpg t ƒ t ƒ u|’ „‚ ƒ| €ve…6b°`ˆ€´`ii„`¡6lµ&qI(•`”i“sxdv‚6¢€sx`G¯siiv’`G’`6s`6h6G‚‡ Í …ÏÕ`X X Y 0 5 ft 4 ft ¿ c ( ƒ ¦B š m4oWl B n1 ¾ ’ e¸³ · k •ƒ ™y ™y ¹ ³ ½ Cƒ n  ‘ƒ `‡1 »mfjjgyš 2g •  “ djg™ ¹ ƒ ‰ jdgˆy ‘‚n  … fjj2gyš g •  “ djg™ º¤ ³ £ e ™ ¼ n’ k ƒ  k ¤ e¸¶µ·´fd— £ ‰`jg y ˆ ™ q ™y {¤ q ™y q ˆ Ww  dƒ ‚n  … dyjg ™ s g “rWw  { djg ™ s g “  phWw £ g djg ™ s “ ¡ˆ « w s ˜’0|w ‚%Ppag ) ( t r q ih 150 y x g ˆ “ ¡ˆ « ˆ “ ¡ˆ « ) ) 5@ ­ ² ± We1|( u ™GW©¤eED F¦|°§9VGFEG™W|A®GC¨0`h`T ¡ˆ %bC`ªG9©`¨cb¦W¦¨GWbAC§G9GFE¦CA986vœ’0( D ¯T 57T D d@ Q QR 5 H7 7 ­Q ¬ ˆ « [email protected] 5 H7 YQ 7 E5 B Q B d E QR5¦ 5 H7 5 D [email protected] 3 ) 80 y dx 120  ‰ x† „ ‚€ x ‘ˆ‡…ƒy  W ( i jg “ ‘¤ ⠁ Ó ¿ £  ä g “ i jg k { ä  p¤ âã¼ Ó £ g “ocw À %Ð t i B — 1 ¾ ¢ n 1 — ¿— » n l 1 — jg —™— «4WQ¤ƒ æ  p¤ B Õm¼n 4Ó ojgi l g ž ¿ ¼ œ’W1 ҍ  Ô “ ½ n “  p— W¤ « V‡¼’ p£ pS«  ¤ `“ ‡f£ ™— g « @ pâ £ ٗ Ñ ä æ D Q D × [email protected] 5 H7 @ QY 5@ QY 5@ 5 yFdWAFåG`C9GC®WˆCWˆ8Cb0H “ Û k SmÔ •ÒÚ •  ™ sxo{c´GqWw i q Ü ™ — SUÔ “ w á ÛÚ à Ý CÞ ™ Û Ú s “ ’ q s ™Ù— — ß — k bo• s SUÔ ”€–w i tx“ W« 3e5WGE`FTC9GHC®WQˆt7cb5Ø`p¨U™`¢G9C0G¦Wb‚S85 Ö I ² [email protected] 5 7 @ Y E BQ B [email protected] 5 H7 57 ­ × B QR 7 ¯ ¶Ò  ÔÕrWw 8i q v”€–w i tx“ ™S« “ q Ó Ò ™ s “ ’ q s — ї À 3 Ð Ï Î I² ET7R5@ 5 H7 BQ o®%F5W0`¡8bCPGCÍW™@ g t r q ih ¿ )0(|w ‚%Ppag Ë Ê É Ì Á ŠàĩÁ È Ç Æ À E D7 IQ yWFQC0F­WSw ) ) 5@ ­ ² ± We1|( u ™GW©¤eED F¦|°ª9V©eEGC`|A®G9¨0W`T ™— %U™`GC©`acApW¦~GWAbCªG9GFE¦CA9863 ¿ 0( D ¯T 57T D [email protected] QR 5 H7 7 ­ Q ¬ — « [email protected] 5 H7 YQ 7 E5 B Q B d E QR5¦ 5 H7 5 D [email protected] ) l( õ ƒ ˆ ¤ gƒ õ ¼ ƒ™ j£ ò “ ¡ˆ « ™ i › i ƒ ƒ ñw D ò™ ò •i  údi ùøF÷öx¼ ñ g z ·³ Ñ Ú ³ó Ñ “¢SVñ i FE™¦ •i s ·³ Ñ Ú ó³ Ñ “ ·Ñ‰ ƒ ƒ ò õ ñ–™¤ gƒ õ ¼ ƒ™ ƒ£ ñ i FED™¦ g •i ™ ”¢ñSw óSÑ ³ VPñ i eEC¦ •i ™ ”“ w s “ ô… D ò s › ‰ ñ w Sw ð `ñ i eEDC¦  ð SÑ Ñ C… ò•i ™ s€¢ñ–w  ð w ð i `ñ FEC¦¨j£ · SÑ Ñ s •i ™ x“ ¡ˆ « “ ¤ D ð ó ò s ˆ ó· s ð ™W–w ðj£ “”cw U™`T…I`97–ApAF5A¢0H “ w¤ ñ ’ T5@ T E5 B I5 5 ˆ ’ cw i { s “ ¡ˆ « î ( r q ih  )0|w t‚%Ppag í Äë ï Fêé ê è  ‰ x† „ ‚€ x ‘ˆ‡…ƒy ) u t r q ih  |( vss¢p¨g Ri x ì Cë )  |( u CGWe²D g FEçE } 0C~GFE™PG9®WˆY ¡ˆ 6GFE¦CA9863  0( ) 5@ ­ D Q H¦ ² D@ 5 H7 @ Q ˆ « 5 D [email protected] ) Ro y ’l Wc( ƒ ¦B  U1 ~n ˜ 1  “ ™ « B n ¾ — « ˆ ƒ ¦B  m1 ¾ ¤ n   ¿ tV’ ¿ £ “ ™—  ¡ˆ « “ ™ « B n  n 5@ QY 5@ 5 CWˆ8Cb0H “ ƒ pB  mº¦n   ¿ ¨¤ Wn i ˜ p£ ¤ `Ä£ ¤ `‡f£ B n1 ¾ “ n 1 n’ n’1 i  n ’ k ™jgi › n ’ n ’ 1 n’ n’1 n n ’ 1 n ’ jg “ ™i `v ‹ fdjeg• ¤ `ƒ£ ¤ `mp£ “ ¤ VÄ£ ¤ `‡p£ i `’   ¤ `‡p£ ¤ `ƒ£ g “ ’w n’ ’ –‚s i `v –w i™ q 7 x”cw i ¤ `’  ™ q £ 7 x“ ™— « s “ ’ n s — ƒ ¦B  U1 ~`’ ¿ a¤ Wn ˜ f£ ¤ VÄ©m1 “  Wm” dj™i™ g ƒ › ¤ `Ä©V‡1 “ n ’£ n ’ B n ¾ n “ n 1 n ’£ n nn1 i ˆ n’ n’1 n1 n ’ n ’ 1 jg “ n ’ 1 n ’ n 1 q w { ™ ™ ™ ™ ¤ VÄ£ ¤ `‡p£ i m”  ¤ `Ä£ ¤ `‡f£ g ´¤ V‡p£ ¤ `Ä£ i m” W|–w i { jg jg Ú s dšdš Ú s “ ¡ˆ « n €’ E|WhV¨T 9pbGeEaVt–Ap`p‚™™©G96AGFESw “ D 7 ­ Q ¬T [email protected] D YQ 7 E5 B Q B 7¦@ ± 5 H7 5R D ’w n1 ’ c‚s i m” cw i™ { ˆ 7 s n “ cw 7 s i m1  cw ™ { 7 G¤ mpG’  cw i™ { 7 s “ cw i ¤ m1  ™ { £ 7 s “ ¡ˆ « ’ ’ s n1£ ’ ’ n íB 1We1)|0w ‚%Ppag ( t r q ih î íBì í eíC í B íè íA  ‰ x† „ ‚€ x ‘ˆ‡…ƒy 1 ) u t r q ih We1|( vss¢p¨g 20 mm 80 mm 120 mm 0 x íB ) 1 ) 5@ ­ ² ± D n 7 D Q × 7 ­ Q ¬ T [email protected] W`e10( u C0W©¤FE~tcFE`ht0`h`¨FT9pbGeED YQ 7 E5 B Q B @ I Q × 5 H7 d ET [email protected] 5 H7 YQ ¦7 E5 B Q B d E QR5¦ 5 H7 5 D [email protected] 3 1 ) V$cApW¦6`FTWpGCºGVçbC`pG9§`P9cb¦W¦4GWAb™pGCoGFE¦CA9864W210( y l˜( i  jg  €Ó g Ô ¼ i`… Ô ‰ i Ó £ … i  ¼  ¥¤ U € › i ‰ i Ó jg  Ó jg š Ó “  g §1  m g “ ‹ Ô U   m g “ i — « Ó “ i w6’  ™— « “ — 0æ  U gX “ ˆ « i Ó jg  ˆ U g z ƒ ÓU   U jgi g “ i w%’  ¡ˆ « “ ˆ « Ó À ’ 0`hsÎ 7­Q¬ i  jg —  €Ó i g “ ™— « Ó jg ˆ  U g “ ¡ˆ « ) ( t r q ih ¿ ˜’|0w ‚%Ppag  ‡Á p p ‡Á ( p ‡Á É Á Ë Ç p p  ‰ x† „ ‚€ x ‘ˆ‡…ƒy ) u t r q ih ¿ ˜’|( vss¢p¨g h /3 A B h/3 o ) m dE XnG`T 7 T D D @ Q H ¦ 5 ¯ d E 7 ­ Q ¬ T T 5 @ ’ °rFEWe²CWr927D } A|°T { G`T q 0W`~UCVT 5 H7 YQ 7 E5 B Q d EQR5¦ 5 H7 5 D [email protected] d Q [email protected] H7 D ¯T I [email protected] × 5 H 5 G9¥`%cb¦WpB G`bb™¨G9¢GFE¦CA98G†97 bC`bGC®F¦|°fl¤be5FI`C`©¨GC7 C¦ q ¿ œ’0( ) ˜ W˜ ( i jg i Ó i jg  £   €Ó % “ i ¤  £ ¤ U x  €Ó i g “ — « Ó jg  U % “ ˆ « ‰ mgš §1 Óm gi i i jg ‰Vi i Ó jg “  ÓU g   ÓU g “ i Ô … ÓU   U g “ ˆ « …  À Ï 7­Q¬ %‚0`hsÎ  æ  €Ó gX “ — « ’ž( ‰ ð© ³ ôi ò “ ‹ ƒ ô i … ³ ô ƒ ò “ i miô … i …Œ ð© ³ ôƒ ò ƒ ñ w SQ ò s “ ñ w SQ –Vñ i TRI ‹ ô •i ™ x¢–`ñ i TRI ¤ ð ( ) ( t r q ih `˜’|0w ‚%Ppag Ì  † s 0 hÌ p s s ˆ ˆ ¡ˆ « “ i 6’  ¡ˆ « “ ¡y ˆ « ˆ w ™ ƒ i› ƒ “ ò ‰‡ •i  ú ‹Škˆ¼ ú ‹ ô “ ˆ ò s — w  ð ô ™ s £ •i ™ €“ p— « “ ¡ˆ « Ç  ‰ x† „ ‚€ x ‘ˆ‡…ƒy ( ) u t r q ih `˜’|( vss¢p¨g „ … $„ )[email protected]`‚bCcbbPGCWmhV~’ ~ rbCVUSFQy q e¦0‡"`‚|WhV¦bC`¢GC¨VQ IR DR 5 H7 YQ @57 E5R 5 H7 5þQ ¬T ð d57TR I D ¯T ET 7 ­Q ¬T [email protected] 5 H7 Y 7 E5 B Q B d E QR5¦ 5 H7 5 D [email protected] d æ ð ¦ D d T@ Y E Q DR5¦¤¦¦ [email protected] @ I ­R DR T @ ( ) cb¦W¦ü0WbACoGC$GeEp™bCAG|sGF­0`9`Q `9e7Ab™d™WCAsVT [email protected] g `œ’0( lž( ƒ dƒ gg — Ô ¶Ò dg “ · ™— « — jg —ƒ ‰ ‰ i —ƒ — — Ô Ò  Ó  ä g “ i ҏ … Ô Ò …  Ó  ä g “ iˆ %’  @ ™— « “ · ™— « w i jg  ƒÔ Ò “  Ó ä  ¥¤c ªf£  š Ô  Ò “ “  1 ‰ iX  š g  Ó  X Ò i   š  Ò ‰ ‰¨i š ˆ ˆ Ô “ i Ô  i … Ô Ò …   Ô  Ò “ i— w%’  @ ¡ˆ « “ · ¡ˆ « …  䀓 Ô B5 Q H D T I T T× ² D d [email protected]`C@`©~GEeC¦G­ GE`T¢1 ¿ 0( u W™@ g ) BQ  ‰ x† „ ‚€ x ‘ˆ‡…ƒy ) ) 5@ ­² ± D I² E D@ W1 ¿ 0( u CG`©†FE%e5WG`FTCC7 5 H7 YQ @5 E@ Q × Q7 5 H7 7T D D@ H 7 H D5 d ET 5¦T ¬ 5 H7 Q7 I [email protected] G96VXb0CWAR WCçGCpVeEWF²™WQ Ce7D } –`F²b0H G`"C`©çG9ü9ªAF5eI`9`G× ¦5 ¯T YQ DT × T 7 ­ Q ¬T I² E D@ 5 H7 YQ ¦7 E5 BQ d E QR5¦ 5 H7 5 D [email protected] 3 ) [email protected]`rF5`G`T ™97 G96VpC–Ap`pB 0WbAC"09†GFE¦CA986v’ ¿ 0( ...
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This note was uploaded on 07/25/2008 for the course ME 221 taught by Professor Buch during the Summer '08 term at Michigan State University.

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