Ejercicios Torsión Resueltos 2

 

Mjmrikikfs rmsumatfs tfrskùl ? (gcurb) b) ifl nkâemtrf nkâemtrf n 5 94 ee ckrb akormemltm sform 9 ]l mjm sfaknf nm bimrf  BOINM (gcur ifjklmtms ml afs pultfs  B y M . Ma mjm ms kepuasbnf pfr ul mlcrblm ml I qum bpakib ul pbr nm tfrskùl ^ ? 5 >=4 L∛e ml ma smlnf qum sm eumstrb ml ab gcurb. Afs mlcrblms O y N sfl kepuasbnfs pfr ma mjm y mlml pbrms nm tfrskùl rmskstmltms ^ 2 5 ?3= L∛e y ^ 9 5 23= L∛e, rmspmivbemltm, qum bitúbl bitúbl ml ma smlnf fpumstf ba pbr nm tfrskùl ^ ?. Afs smcemltfs OI  y IN mlml aflcktunms aflcktunms ifrtbltm ms C 5 04 CTb.

AOI   5

=44 ee y =44

AIN  5

>44 ee, rmspmivbemltm, y ma eùnuaf nm

Nmtmreklm ma msumrzf ifrtbltm eâxkef ml ibnb pbrtm nma mjm y ma âlcuaf nm tfrskùl mltrm afs mlcrblms O y N. Yfauikùl Iumrpf akorm OI Ω ^ 5 4 5 ^IN ’ ^? + ^2 5 4   ^IN 5 ^? - ^2 5 >=4 ’ ?3= ?3= 5 23= Le Iumrpf akorm OI

Ω ^ 5 4 5 ^OI + ^2 5 4

^OI 5 - ^2 5 -?3= Le  5 27 ^ OI  / τ n9 5 27*?3=/ τ*4,49 9 5 =2,039 ETb

ώOI

 5 27 ^ IN / τ n9 5 27*23=/ τ*4,499 5 99 ETb

ώIN

Kp 5 τ*n> / 9? 5 τ*4,49 >/9?53,;= 24-0  e> ΰ 5 ^*A / C*K p 5 ΰON 5 ΰOI + ΰIN 5 ΰIN 5 ^IN*AIN / C*Kp 5 23=*4,>/04 24; 3,;= 24-0 5 4,422 rbn

4,79´

ΰOI 5 ^OI*AOI / C*Kp 5 -?3=*4,=/ 04 24 ; 3,;= 24-0 5 -4.4?27 rbn

2,?>´

ΰON 5 ΰOI + ΰIN 5 -2,?> + 4,79 5 -4,72´

 

> ]l eftfr qum kepuasb ul mjm sfaknf ikriuabr nm bimrf trblsektm >4 `p ba mlcrblm ml O (gcurb). Ma msumrzf ifrtbltm pmrekskoam ml ma bimrf ms 7444 psk.

b. ¶Iuâ ¶Iuâaa ms ms ma ma nkâ nkâem emtr trf f n rmqumrknf pbrb ma mjm sk fpmrb b ulb vmafiknbn nm =44 rpe6 o. ¶Iuâ ¶Iuâaa m mss ma ma n nkâ kâem emtr trf f n rmqumrknf pbrb ma mjm sk fpmrb b ulb vmafiknbn nm 944 rpe6 YFA]IKFL T 5 ?τ*l*^ / 99444

^ 5 99444 *T/ ?τ*l 5 99444*>4 /?τ*=44 5 >?4,? ao-pkm

n9 5 27 ^ / τ ώpmre 5 27*>?4,?*2?/ τ*7444 5 T 5 ?τ*l*^ / 99444

n5 2,7? kl

^ 5 99444 *T/ ?τ*l 5 99444*>4 /?τ*944 5 344,9 ao-pkm

n9 5 27 ^ / τ ώpmre 5 27*344,9*2?/ τ*7444 5

n5 2,;? kl

= ]l mjm sùaknf nm bimrf BOI ifl =4 ee nm nkâemtrf (gcurb 9.92b) ms kepuasbnb ml  B pfr ul eftfr qum trblsektm =4 hS ba mjm b 24 @z. Afs mlcrblms ml O y I kepuasbl ebquklbrkb qum rmqukmrm pftmlikb kcuba b 9= hS y 2= hS, rmspmivbemltm.

Ibaiuam ma msumrzf ifrtbltm eâxkef tebx ml ma mjm y ma âlcuaf nm tfrskùl ΰ BI  mltrm ma eftfr ml  B y ma mlcrblm ml I . (]akim C 5 04 CTb). YFA]IKFL

 

T 5 ?τ*l*^ / 74

^ 5 74*T / ?τ*l

T 5 ?τ*g*^

^ 5 T / ?τ*g  

^B 5 =4444 / ?τ*24 5 3;7 Le ^O 5 9=444 / ?τ*24 5 ==3 Le ^I 5 2=444 / ?τ*24 5 ?9; Le

Iumrpf akorm OI Ω ^ 5 4 5 ^OI+ ^O - ^B 5 4 ^OI 5 ^B ’ ^O 5 3;7 ’ ==3 5 ?9; Le

Iumrpf akorm BO

Ω ^ 5 4 5 ^BO - ^B 5 4

^BO 5 ^B 5 3;7 Le  5 27 ^ OI / τ n9 5 27*?9;/ τ*4,4=9 5 ;,3 ETb

ώOI

 5 27 ^BO / τ n 9 5 27*3;7/ τ*4,4=9 5 9?,> ETb

ώBO

Kp 5 τ*n> / 9? 5 τ*4,4= > / 9? 5 7,2> 24 -3 ΰBO 5 ^BO*ABO / C*Kp 5 3;7 3;7* *2 / 04 24; 24; 7,2 7,2> > 2424-3 3 5 4.4 4.427 rb rbn n ΰOI 5 ^OI*AOI / C*K p 5 ?9 ?9;*2,? / 04 04 24; 7,2> 24-3 5 4.44=0| rbn ΰBI 5 ΰBO + ΰOI 54,;9 + 4,99 5 2,?7´

4,;9 4,;9´´ 4,99´