INSTITUTO TECNOLÓGICO DE OAXACA SUBDIRECCIÓN ACADEMICA DEPARTAMENTO DE METAL-MECÁNICA
PROYECTO “BRAZO HIDRÁULICO DIDACTICO”
ALUMNOS: CRUZ GARCIA GILBERTO CRUZ PACHECO JONATHAN JALIL LÓPEZ LÓPEZ VICENTE JOEL MELCHOR CERVANTES GERARDO JOSE
CATEDRATICO: M.C. Gryse P!"e#$e N%&'es Gr()%: MA
H%r': 10-11 Hrs.
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INTRODUCCIÓN……………………………………………………………………….…………..4 1. OBJETIVO OBJETIVO GENERAL…………… GENERAL…………………………… ……………………………… ……………………………. …………….………… ………… !. OBJETIVO OBJETIVO ESPEC"# ESPEC"#ICO…… ICO…………………… ………………………………… …………………………….… ………….……... …........ ......... ..... . $. JUSTI#IC JUSTI#ICACIÓN ACIÓN……………… ………………………………… ………………………………… ………………………………… ……………………….. …….. 4. HIPOTE HIPOTESIS SIS………… ………………… ……………… ……………… ……………… ………………… ………………… ……………… ……………… …………… …… . MARCO MARCO TEORICO…… TEORICO……………………… ………………………………… ………………………………… ……………………………… ……………..% ..% .1 RESISTENCIA DE MATERIALES…………………………………………………..& MATERIALES…………………………………………………..& .! PRINCIPIO DE PASCAL……………………………………………………………10 PASCAL……………………………………………………………10 .!.1 .!.1 MATR MATRIZ IZ DE PASCAL ASCAL……… ……………… ……………… ……………… ………………… ………………… ……………1 ……11 1 .!.! .!.! VENTA VENTAJA JA MECANI MECANICA… CA…………… ………………… ……………… ……………… ……………… ………………. ………..1$ .1$ .$ HIDRAULICA………………………………………………………………………..14 .$.1 .$.1 SISTEM SISTEMAS AS HIDRAU HIDRAULIC LICOS… OS………… ………………… ………………… ……………… ……………… ………….. …..1 1 .$.! VENTAJ VENTAJAS AS Y DESVENTA DESVENTAJAS JAS DE DE UN SISTEMA SISTEMA HIDRAULIC HIDRAULICO……..1 O……..1 .$.$ .$.$ CARACT CARACTERI ERISTI STICAS CAS DE LOS SISTEMA SISTEMAS S HIDRAU HIDRAULIC LICOS… OS………… …………1% …1% .$.4 .$.4 CAMPO CAMPO DE APLI APLICAC CACIÓN IÓN……… ………………… ………………… ……………… ……………… ……………… ………1' 1' .4 TRABAJO…………………………………………………………………………….1( . MECANICA DE #LUIDOS…………………………………………………………..!0 #LUIDOS…………………………………………………………..!0 ..1 ..1 PROPIE PROPIEDAD DADES ES DE LOS LOS #LUIDO #LUIDOS…… S…………… ……………… ……………… ………………… …………!0 !0 .% PRENSA HIDRAULICA……………………………………………………………..!! .%.1 APLICACION APLICACIONES ES DE LAS PALANCA PALANCAS S HIDRAULIC HIDRAULICAS………… AS…………………!4 ………!4 .%.! .%.! MOVIMI MOVIMIENT ENTOS OS DEL BRAZO BRAZO HIDRAUL HIDRAULICO ICO………… ………………… ……………… ………….! ….! .' GRADOS DE LIBERTA LIBERTAD D )MOVILIDAD* )GDL*………………………………….!% .'.1 GRADOS GRADOS DE DE LIBERT LIBERTAD AD EN MECANISMOS MECANISMOS ESPECIALES……… ESPECIALES………….!( ….!( .'.! .'.! MECANI MECANISMO SMOS S Y ESTRU ESTRUCTU CTURAS RAS……… ………………… ………………… ……………… ……………. …….$0 $0
%. DESARROLLO DESARROLLO DEL PROTOTIP PROTOTIPO……………… O……………………………… ………………………………… ……………………..$! …..$! %.1 MATERIALES……………………………………………………………………..…$! MATERIALES……………………………………………………………………..…$! %.! PROCEDIMIENTO…………………………………………………………………..$$ '. CALCULOS……… CALCULOS………………..… ………..………………… ………………………………… ………………………………… ……………………….. ………...$& .$& '.1 ES#UERZOS Y DE#ORMACIONES ……………………………………………..$& '.! PRINCIPIO DE PASCAL……………………………………………………………$( PASCAL……………………………………………………………$( '.$ GRADOS DE DE LIBERTA LIBERTAD…………………………………………………………...40 D…………………………………………………………...40 &. CONCLU CONCLUSIÓ SIÓN…… N…………… ……………… ……………… ……………… ………………… ………………… ……………… ……………… ……………4 ……41 1 (. ANE+OS ANE+OS……… ……………… ………………… ………………… ……………… ……………… ……………… ………………… ………………… ……………. ……..4! .4!
10. BIBLIOGRA#IA…………………………………………………………………………...4% 2
INTRODUCCIÓN……………………………………………………………………….…………..4 1. OBJETIVO OBJETIVO GENERAL…………… GENERAL…………………………… ……………………………… ……………………………. …………….………… ………… !. OBJETIVO OBJETIVO ESPEC"# ESPEC"#ICO…… ICO…………………… ………………………………… …………………………….… ………….……... …........ ......... ..... . $. JUSTI#IC JUSTI#ICACIÓN ACIÓN……………… ………………………………… ………………………………… ………………………………… ……………………….. …….. 4. HIPOTE HIPOTESIS SIS………… ………………… ……………… ……………… ……………… ………………… ………………… ……………… ……………… …………… …… . MARCO MARCO TEORICO…… TEORICO……………………… ………………………………… ………………………………… ……………………………… ……………..% ..% .1 RESISTENCIA DE MATERIALES…………………………………………………..& MATERIALES…………………………………………………..& .! PRINCIPIO DE PASCAL……………………………………………………………10 PASCAL……………………………………………………………10 .!.1 .!.1 MATR MATRIZ IZ DE PASCAL ASCAL……… ……………… ……………… ……………… ………………… ………………… ……………1 ……11 1 .!.! .!.! VENTA VENTAJA JA MECANI MECANICA… CA…………… ………………… ……………… ……………… ……………… ………………. ………..1$ .1$ .$ HIDRAULICA………………………………………………………………………..14 .$.1 .$.1 SISTEM SISTEMAS AS HIDRAU HIDRAULIC LICOS… OS………… ………………… ………………… ……………… ……………… ………….. …..1 1 .$.! VENTAJ VENTAJAS AS Y DESVENTA DESVENTAJAS JAS DE DE UN SISTEMA SISTEMA HIDRAULIC HIDRAULICO……..1 O……..1 .$.$ .$.$ CARACT CARACTERI ERISTI STICAS CAS DE LOS SISTEMA SISTEMAS S HIDRAU HIDRAULIC LICOS… OS………… …………1% …1% .$.4 .$.4 CAMPO CAMPO DE APLI APLICAC CACIÓN IÓN……… ………………… ………………… ……………… ……………… ……………… ………1' 1' .4 TRABAJO…………………………………………………………………………….1( . MECANICA DE #LUIDOS…………………………………………………………..!0 #LUIDOS…………………………………………………………..!0 ..1 ..1 PROPIE PROPIEDAD DADES ES DE LOS LOS #LUIDO #LUIDOS…… S…………… ……………… ……………… ………………… …………!0 !0 .% PRENSA HIDRAULICA……………………………………………………………..!! .%.1 APLICACION APLICACIONES ES DE LAS PALANCA PALANCAS S HIDRAULIC HIDRAULICAS………… AS…………………!4 ………!4 .%.! .%.! MOVIMI MOVIMIENT ENTOS OS DEL BRAZO BRAZO HIDRAUL HIDRAULICO ICO………… ………………… ……………… ………….! ….! .' GRADOS DE LIBERTA LIBERTAD D )MOVILIDAD* )GDL*………………………………….!% .'.1 GRADOS GRADOS DE DE LIBERT LIBERTAD AD EN MECANISMOS MECANISMOS ESPECIALES……… ESPECIALES………….!( ….!( .'.! .'.! MECANI MECANISMO SMOS S Y ESTRU ESTRUCTU CTURAS RAS……… ………………… ………………… ……………… ……………. …….$0 $0
%. DESARROLLO DESARROLLO DEL PROTOTIP PROTOTIPO……………… O……………………………… ………………………………… ……………………..$! …..$! %.1 MATERIALES……………………………………………………………………..…$! MATERIALES……………………………………………………………………..…$! %.! PROCEDIMIENTO…………………………………………………………………..$$ '. CALCULOS……… CALCULOS………………..… ………..………………… ………………………………… ………………………………… ……………………….. ………...$& .$& '.1 ES#UERZOS Y DE#ORMACIONES ……………………………………………..$& '.! PRINCIPIO DE PASCAL……………………………………………………………$( PASCAL……………………………………………………………$( '.$ GRADOS DE DE LIBERTA LIBERTAD…………………………………………………………...40 D…………………………………………………………...40 &. CONCLU CONCLUSIÓ SIÓN…… N…………… ……………… ……………… ……………… ………………… ………………… ……………… ……………… ……………4 ……41 1 (. ANE+OS ANE+OS……… ……………… ………………… ………………… ……………… ……………… ……………… ………………… ………………… ……………. ……..4! .4!
10. BIBLIOGRA#IA…………………………………………………………………………...4% 2
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10
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L, 2rF8327, 5s 3, r,/, 5 3, s27, 985 5s?82, 53 7/:r?,/25? 5 3s 382s 5 872; 5 s8s :r:25,5s 5s:5727,s. Es 572r> 5s?82, 3,s :r:25,5s /57F27,s 5 3s 3982s 5:525 5 3,s 85r,s , 3,s 985 s s/5?2s. T 5s? 5:55 5 3,s 85r,s 985 s5 2?5r:5 7 3, /,s, , 3,s 72725s , 3,s 985 5s?6 s/5?2 53 382> r53,72,,s 7 3, 2s7s2, 5 5s?5. L, :,3, , s8 5> 255 5 [?8< 5 ,8,\> :,3,
ὕ]eϱ )[,8,\* ^ὐ`cd )[?8<\* 5 63 s5 5r2, 985 3, 2rF8327, 5s E3 8s 5
3s 3982s :,r, r5,32,r 8 ?r,<,=. A5/Fs 5 s5r 8, r,/, 5 3, /57F27, 5 382s ,/:32,/5?5 :r5s5?5 5 3, 2525r, 985 s5 57,r, 53 5s?82 5 3,s :r:25,5s /57F27,s 5 3s 3982s. T 5s? 5:55 5 3,s 85r,s 985 s5 2?5r:5 7 3, /,s, , 3,s 72725s , 985 s5 5s?F s/5?2 53 382> r53,72,,s 7 3, 2s7s2, 5 5s?5 5 3, 78,3 s5 ,:327, 3s s2825?5s 775:?s
•
#85r, Es 3, 7,8s, 985 :r875 8 7,/<2 5 2r5772; 5 5372,.
•
Pr5s2; Es 3, 85r, 5=5r72, 5 8 Fr5, 5?5r/2,,.
•
Tr,<,= Es 3, 85r, 575s,r2, :,r, 5s:3,,r 8 535/5? 5 8, 2s?,72, 5?5r/2,,.
•
#38= Es 53 /2/25? 53 3982.
•
C,8,3 Es 53 38/5 5s:3,, 5 8, 82, 5 ?25/:.
•
Xr5, Es 3, s8:5r2725 3,r :r ,7.
8.6.*. S!s$e"'s ?!,r(!%s Ls s2s?5/,s 2rF8327s s 8 7=8? 5 7/:5?5s 985 8?232, 3,s :r:25,5s 5 3s 382s 3982s :5r/2?5 5s,rr33,r 8, 85r, r,5 , :,r?2r 5 8, :5985,.
8.6./. 4e#$'>'s y ,es@e#$'>'s ,e (# s!s$e"' ?!,r(!%. Ls s2s?5/,s 2rF8327s ?255 /87,s 7,r,7?5rs?27,s :s2?2,s. S2 5/<,r> ?,/<26 :s55 ,38,s 5s5?,=,s 5 r53,72; , ?r,s r/,s 5 7s582r 55r,> s2 5/<,r 6s?,s s s8:5r,,s :r 3,s 5?,=,s> 3 985 ,75 5 3s s2s?5/,s 2rF8327s 3s /52s /Fs 57;/27s 5 ?r,s/2s2; 5 :?572,.
4e#$'>'s 15
•
P5r/2?5 ?r,<,=,r 7 535,s 2535s 5 85r, //5?s 5 2r
•
E3 ,752?5 5/:35, 5 53 s2s?5/, 5s F723/5?5 r578:5r,<35.
•
V5372, 5 ,7?8,72; F723/5?5 7?r3,<35.
•
Is?,3,725s 7/:,7?,s.
•
Pr?5772; s2/:35 7?r, s
•
C,/<2s rF:2s 5 s5?2
Des@e#$'>'s •
E3 382 2rF8327 s8s 7/:5?5s s 5 535, 7s?.
•
P6r2,s 5 :r5s2; 5 7,s 5 8,s.
•
R5985r2/25? 5 :5rs,3 5s:572,32, :,r, 3, /,?572;.
•
#382 /8 s5s2<35 , 3, 7?,/2,72;.
8.6.6. C'r'$ers$!'s ,e %s s!s$e"'s ?!,r(!%s. •
E2725?5s 72,<35s 5 7/:,r,72; 7 ?rs s2s?5/,s.
D5s7?, 3,s :6r2,s 985 :85, 78rr2r 5 s8s 783s /57F27s> :rF7?27,/5?5 ?, 3, 55r, ?r,s/2?2, , ?r,6s 5 8 s2s?5/, 2rF8327 5s r572<2, , 3, s,32,> 5 53 ?r,<,= 5s 335, , 7,< ,3 100f. E3 s2s?5/, 5367?r27> s8 7/:5?2r /Fs 75r7,> 5s 1 , $0f /5r 5 5272572,. Ls /5=r5s s2s?5/,s ??,3/5?5 /57F27s s 55r,3/5?5 $0 , '0f /5s 52725?5s 985 3s s2s?5/,s 2rF8327s 7/:,r,<35s> 5<2 , :6r2,s r2772;,35s 5 25r72, 535,, )3, 25r72, 5s 3, r5s2s?572, ,3 /2/25?> ,772; 7,/<2*.
•
S5s2<35s 5 7?r3,r. 16
E3 3982 72, 5 8 s2s?5/, 2rF8327 :5r, 7/ 8, <,rr, 5 ,75r ,3 ?r,s/2?2r 3, 85r,. S2 5/<,r> 3,s :,r?5s /;235s s 322,,s :855 s5r :85s?,s 5 /2/25? 5?52,s 7,s2 2s?,?F5,/5?5. L,s F383,s 5?r 53 s2s?5/, :855 557?8,r 7,/<2s 5 2r5772; s5?2 5 2r 7?r3,r 3,s r538725s 5372,5s 5 ?s 3s r,s 2?5r/52s 985 :5r/2?, 53 7/:5?5> :825 2272,r 5?55r 3, 72r783,72; 5 382s :r5s8r2,s 7,s2 5 r/, 2s?,?F5, r5985r2r 5 /8 :7 5s85r :,r, s5r /,2:83,,s.
#352<35s 5 2s?,3,r.
•
L,s 35,s 2rF8327,s r2,s 352<35s :855 s5r 737,,s 7,s2 5 78,39825r 38,r. A 25r572, 5 3s s2s?5/,s /57F27s 985 5<5 s582r r57rr2s r57?s> 3,s 35,s 5 8 s2s?5/, 2rF8327 :855 s5r 2r22,s ,3r55r 5 7 3, 575:72; 5 3,s </<,s 2/:83s,,s 37,32,,s 75r7, 5 3, 85?5 5 s8/22s?r 5 :?572,> :855 s5r 2s?,3,,s 5 8, ,r25, 5 38,r5s.
•
B,= :5s.
E3 s2s?5/, 2rF8327 :5s, r53,?2,/5?5 :7 5 7/:,r,72; 7 3, 7,?2, 5 ?r,<,= 985 ,75. U s2s?5/, /57F27 5367?r27 7,:, 5 ,75r 53 /2s/ ?r,<,= :5s, 7s25r,<35/5?5 /Fs. D, 985 53 :5s 5 3, 7,r, @?23 5s 8 ,7?r 2/:r?,?5 s 53 s2s?5/, 2rF8327 5s 25,3 :,r, 53 8s 5 ,2,72;.
•
A8? 38
L, /,r, 5 3,s :,r?5s 5 8 s2s?5/, 2rF8327 :5r, 5 8 <, 5 ,752?5. L 985 :5r/2?5 3, ,8? 38 53 5s,s?5 :r?525 7?r, 3, 7rrs2;. Ls r52s?rs 5 /,?52/25? s5,3, 985 3s ,=8s?5s 3,s r5:,r,725s 2/:r52s?,s 5 7/:5?5s s2s?5/,s s :7 :r<,<35s s2 s5 17
s285 3,s 2s?r87725s 5 3s ,
8.6.7. C'")%s ,e ')!'!# L,s ,:327,725s 5 3, 2rF8327, s /8 ,r2,,s> s5 5<5 :r272:,3/5?5 ,3 57 5 985 5s?, r, 55r, s5 :855 7?r3,r 7 8, 85r, /8 :5985,. O?r,s r,5s 5 s8 55r,32,, ,:327,72; s 53 2s5 , ,7/:,,s ,5/Fs 5 5s?82s /Fs ,7,<,s 5 3,s /,?5r2,s :r272:2s 985 r25 3, 2rF8327,. T 3 ,?5r2r s5 , 2s? r535=, 5 5982:s 985 :5r/2?5 ?r,<,=s 7,, 5 /Fs :r572ss 7 /,r5s 2535s 5 55r,> s2/:3272,.
A)!'!%#es M@!es E3 5/:35 5 3, 55r, :r:r72,, :r 8 382 3982 , :r5s2;> :855 ,:327,rs5 :,r, ?r,s:r?,r> 57,,r> 35,?,r> :5rr,r> /,2:83,r /,?5r2,35s> 7?r3,r 5 2/:83s,r 5783s /;235s ?,35s 7/ •
Tr,7?r5s
•
Gr@,s
•
R5?r57,,r,s
•
C,/25s r57357?r5s 5 <,s8r,
•
C,r,r5s r?,35s
•
#r5s s8s:5s25s 5 7,/25s
•
V5783s :,r, 3, 7s?r8772; /,?572; 5 7,rr5?5r,s
•
E?7.
A)!'!%#es I#,(s$r!'es E3 5/:35 5 3, 55r, :r:r72,, :r 8 382 3982 , :r5s2;> 5s 8?232,, ?,/<26 5 /,982,r2, 5s:572,32,, :,r, 7?r3,r> 2/:83s,r> :s272,r /57,2,r ?,35s 7/ 18
•
M,982,r2, :,r, 3, 28s?r2, :3Fs?27,
•
M,982,r2, :,r, 3, 53,<r,72; 5 ,32/5?s
•
E982:,/25? :,r, r<;?27, /,2:83,72; ,8?/,?2,,
•
E982: :,r, /?,=5 28s?r2,3
•
M,982,r2, :,r, 3, /25r,
•
M,982,r2, :,r, 3, 28s?r2, s25r@r27,
•
E?7.
O$r's ')!'!%#es L, 55r, 2rF8327, ?255 ?,/<26 ,:327,725s 5 ,r2,s 7,/:s> ?,35s 7/ •
A8?/?r2 s8s:5s2;> r5s> 2r5772;> r5r25r,72;> 5?7.
•
A5rF8?27, ?2/5s> ,35r5s> ?r55s 5 ,?5rr2,=5> r5s> s2/83,r5s> 5982:s 5 /,?52/25? ,5rF8?27> 5?7.
•
N,,3 ?2/;> /57,2s/s 5 ?r,s/2s2;> s2s?5/,s 5 /,s> s2s?5/,s 5s:572,32,s 5 5/<,r7,725s <8985s /232?,r5s
•
M5272, Is?r8/5?,3 982r@r27> /5s,s 5 :5r,725s> 7,/,s 5 s:2?,3> s233,s 5 2s?r8/5?,3 ?3;27> 5?7.
8.7.
•
T5,?r C?r35s 5s7627s
•
H,<2?,72,3 ,s75sr5s
Tr''>%
Es 8, /,2?8 s27, 5s7,3,r 985 s5 r5:r5s5?, 7 3, 35?r,
W
)53 236s
Work * 985 s5 5:r5s, 5 82,5s 5 55r,> 5s? 5s 5 =832s =835s )J*. E
/57F27, 73Fs27,> 53 ?r,<,= 985 r5,32, 8, 85r, s
19
C/ 25, 55r,3> ,<3,/s 5 ?r,<,= 78, 8, 85r, )5:r5s,, 5 5Q?* /855 8 785r: 32<5r, 3, 55r, :?572,3 5 5s?5 5s 572r> 8 / :,r, 35,?,r 8, 7,=, , 985 575r 8, r5s2s?572,> 53 :5s P 53 <=5?> , 3 3,r 5 8 7,/2> 3, ,3?8r, , 3, 985 s5 35,?, 3, 7,=,. E3 ?r,<,= T r5,32, 5s 53 :r87? 5 3, 85r, P :r 3, 2s?,72, r57rr2, d
.
T = F ∗d
Tr,<,= #85r, g D2s?,72,
A98 5<5/s ,75r 8, ,73,r,72;> 7/ 5/s> s5@ 3, ;r/83, :r5755?5> Tr,<,= 5s 53 :r87? )3, /83?2:327,72;* 5 3, 2s?,72, ) d * )53 5s:3,,/25?* r57rr2, :r 8 785r: :r 53 ,3r 5 3, 85r, ) F * ,:327,, 5 5s, 2s?,72, 5s 8, /,2?8 5s7,3,r> 985 ?,/<26 s5 5:r5s, 5 J835 )28,3 985 3, 55r,*. D5 / /Fs s2/:35 L, 82, 5 ?r,<,= )5 J835* s5
A:,r575 ,98 3, 5:r5s2;
2r5772; 5 3, 85r, 3, 78,3 :855 s5r r2?,3> <3278, 5r?27,3 r5s:57? , 3, 2r5772; 5 985 s5 /855 53 <=5? s 3, 2r5772; 5 3, 85r, 3, 2r5772; 53 /2/25? :855 r/,r 8 F83 ) r/,r3 s2 ,/<,s s :,r,353,s*. S2 r/, 8 F83 )
*>
5<5/s 27r:r,r 5s5 ,? 5 85s?r, ;r/83, :,r, 7,3783,r 53 ?r,<,=> :,r, 985,r ,s
20
T = F ∗cos α ∗d
L 78,3 s5 355 Tr,<,= #85r, :r 7s5 5 ,3, :r
2s?,72,
8.8.
Me#!' ,e 5(!,%s
Es 3, :,r?5 5 3, s27, 985 s5 78:, 5 3, ,772; 5 3s 382s 5 r5:s 5 /2/25?> ,s 7/ 5 3,s ,:327,725s /57,2s/s 5 2525r, 985 8?232, 382s. L, /57F27, 5 382s 5s 8,/5?,3 5 7,/:s ?, 25rss 7/ 3, ,5rF8?27,> 3, 2525r, 98/27,> 7223 5 28s?r2,3> 3, /5?5r3,> 3,s 7s?r87725s ,,35s 3, 75,r,,. L, /57F27, 5 382s :855 s8<222rs5 5 s 7,/:s :r272:,35s 3, 5s?F?27, 5 382s> 2rs?F?27,> 985 s5 78:, 5 3s 382s 5 r5:s> 3, 2F/27, 5 382s> 985 ?r,?, 5 3s 382s 5 /2/25?. E3 ?6r/2 5 2r2F/27, s5 ,:327, ,3 38= 5 3982s ,3 38= 5 3s ,s5s , <,=, 5372,> 5 53 985 :855 7s25r,rs5 985 53 ,s 5s 5s572,3/5?5 27/:r5s2<35. L, ,5r2F/27,> 2F/27, 5 ,s5s> s5 78:, 53 7/:r?,/25? 5 3s ,s5s 78, 3s 7,/<2s 5 5372, :r5s2; s 3 s82725?5/5?5 r,5s :,r, 985 s5, 575s,r2 27382r 3s 557?s 5 3, 7/:r5s2<232,. E?r5 3,s ,:327,725s 5 3, /57F27, 5 382s 5s?F 3, :r:83s2; , 7rr> 3,s ?8r<2,s> 3s 7/:r5sr5s 3,s </<,s. L, 2rF8327, 5s?82, 3, 8?232,72; 5 2525r, 5 3, :r5s2; 53 ,8, 53 ,752?5.
8.8.*. Pr%)!e,',es ,e %s 5(!,%s Ls 382s> 7/ ?s 3s /,?5r2,35s> ?255 :r:25,5s s27,s 985 :5r/2?5 7,r,7?5r2,r 78,?227,r s8 7/:r?,/25? ,s 7/ 2s?282r3s 5 ?rs. A38,s 5 5s?,s :r:25,5s s 5738s2,s 5 3s 382s ?r,s s ?:27,s 5 ?,s 3,s s8s?,72,s. C,r,7?5rs?27,s 7/ 3, 2s7s2,> ?5s2; s8:5r272,3 :r5s2; 5 ,:r s3 s5 :855 522r 5 3s 3982s ,s,s. S2 5/<,r 3,
21
/,s, 5s:5727,> 53 :5s 5s:5727 3, 5s2, s ,?r2<8?s 5 78,39825r /,?5r2,.
M's' es)e!'= )es% es)e!% y ,e#s!,', S5 5/2, /,s, 5s:5727, , 3, 7,?2, 5 /,?5r2, :r 82, 5 38/5 5 8, s8s?,72,. S5 5s2, :r P s5 525 P=
lim m
v V −¿ 0
E3 :5s 5s:5727 7rr5s:5 , 3, 85r, 7 985 3, ?25rr, ,?r,5 , 8, 82, 5 38/5. S5 5s2, :r ß . L, /,s, 53 :5s 5s:5727 5s?F r53,72,s :r ß = gP
D5 g r5:r5s5?, 3, 2?5s2, 53 7,/: r,2?,72,3. S5 5/2, 5s2, , 3, r53,72; 985 52s?, 5?r5 3, /,s, 5s:5727, 5 8, s8s?,72, 78,39825r, 8, s8s?,72, 5 r55r572,. P,r, 3s 3982s s5 8?232, 3, /,s, 5s:57227, 53 ,8, , 4hC 7/ r55r572,> 985 7rr5s:5 , 1
g 3
cm
:,r, 3s ,s5s s5 8?232, ,3 ,2r5 7 /,s, 5s:5727, , !0hC 1 1>01$ <,r 5 :r5s2; 5s 1>!04
kg 3
m
.
4!s%s!,',: 5s 8, :r:25, 2s?2?2, 5 3s 382s. Es?F 32,, , 3, r5s2s?572, 985 :5 8 382 , 5r/,rs5 7?28,/5?5 78, s5 35 s/5?5 , 8 22
5s85r 5 7r?5. Es?, :r:25, 5s 8?232,, :,r, 2s?282r 53 7/:r?,/25? 5?r5 382s s;32s. A5/Fs 3s 382s :855 s5r 5 55r,3 73,s227,s 5 ,785r , 3, r53,72; 985 52s?, 5?r5 53 5s85r 5 7r?5 ,:327, 3, 5372, 5 5r/,72;.
C%")res!!!,',: r5:r5s5?, 3, r53,72; 5?r5 3s 7,/<2s 5 38/5 3s 7,/<2s 5 :r5s2; , 985 5s?F s/5?2 8 382. L,s ,r2,725s 5 38/5 :855 r53,72,rs5 2r57?,/5?5 7 ,r2,725s 5 3, /,s, 5s:5727, s2 3, 7,?2, 5 /,s, :5r/,575 7s?,?5.
Pres!# ,e 4')%r: Ls 382s 5 ,s5 32982, ,s5s, 5:525 5 3,s 72725s 5 985 s5 5785?r5. L,s s8s?,72,s :8r,s :855 :,s,r :r 3,s 78,?r ,s5s> 5s5 s;32 , :3,s/,> s5@ 3,s 72725s 5 :r5s2; ?5/:5r,?8r, , 985 5s?6 s/5?2,s. S5 ,7s?8/ s5 275 985 ,37,, 3, :r5s2; 5 ,:r. Es?, :r5s2; 5:55 5 3, ?5/:5r,?8r,.
Te#s!# S()er!!': S5 , 7/ 5s 53 7,s 5 ?8<s 7,:23,r5s> <8r<8=,s> ?,s s2?8,725s s2/23,r5s.
8.1.
Pre#s' H!,r(!'
23
L, :r5s, 2rF8327, 5s 8, /F982, 7/:35=, 985 :5r/2?5 ,/:3227,r 3,s 85r,s 7s?2?85 53 8,/5? 5 535,r5s> :r5s,s 2rF8327,s> r5s /87s ?rs 2s:s2?2s 2rF8327s. L, :r5s, 2rF8327, 7s?2?85 3, ,:327,72; 8,/5?,3 53 :r272:2 5 P,s7,3 ?,/<26 8 2s:s2?2 985 :5r/2?5 5?55r /5=r s8 s2227,. Cs2s?5> 5 5s572,> 5 s 7232rs 5 25r5?5 s5772; 7/827,s 5?r5 s> 78 2?5r2r 5s?F 7/:35?,/5?5 335 5 8 3982 985 :855 s5r ,8, ,752?5. Ds 6/<3s 5 s57725s 25r5?5s s5 ,=8s?,> r5s:57?2,/5?5> 5 7,, 8 5 3s s 7232rs> 5 / 985 5s?6 5 7?,7? 7 53 3982. C8, s 5s 572r P1= P2
C 3 985 3,s 85r,s s5rF F 1= P 1 A1 < P1 A 2= P2 A 2= F 2
C A1 i A!. Pr ?,?> 3, r53,72; 5?r5 3, 85r, r5s83?,?5 5 53 6/<3 r,5 78, s5 ,:327, 8, 85r, /5r 5 53 6/<3 :5985 s5rF ?,? /,r 78,? /,r s5, 3, r53,72; 5?r5 3,s s57725s F 1= F 2
( ) A 1 A 2
24
#2. & A?28, Pr5s, H2rF8327,
8.1.*. A)!'!# ,e 's P''#'s ' Br'9% H!,r(!% E 3, 28r, s5 :855 ,:r572,r 985 3,s :,3,7,s 985 s5 8?232,r, 5 53 :r57? s5rF 5 ?5r75r ?2: 5 ?5r75r r, , 985 5 5s?5 ?2: 5 :,3,7,s 3, 85r, ,:327,, 5<5 s5r /,r , 3, 85r, , 35,?,r 5 53 ?r,<,= 5s 5 2?,3 2/:r?,72, :5r 35,?,r <=5?s. A5/Fs> s5 8?232,rF :,3,7,s /@3?2:35s , 985 5s 985 :5r/2?2rF
25
#2. ( A:327,72; 5 3,s P,3,7,s ,3 Br, H2rF8327
A)!'!# ,e P%$e#!' e# 3er!#&'s E3 3,r 7232r 5 3, 28r, :855 s5r 222 5 s 7232rs 2228,35s 53 /2s/ 2F/5?r 737,s , 2s?,72, 8 5 ?r 757?,s 5?r5 s :r 8, 7,5r,. E3 /2s/ :r272:2 5 ?r,s/2s2; 5 3, 85r, :855 s5r ,:327,> 3, 85r, 5s,rr33,, 5 53 :2s?; B , s5r 28,3 , 3, 85r, 5=5r72, :r 53 :2s?; A. E 53 s2825?5 rF27 :5/s ?r,s/2?2r 3,s 85r,s 5 r/, 2/52,?, , ?r,6s 5 2s?,72,s 7s25r,<35s 7 5s7,s,s :5r2,s. L,s ?r,s/2s25s :855 335,rs5 , 78,39825r :s272;. A8 <3, 5s982,s> :855 ?r,s/2?2rs5 , ?r,6s 5 ?8<5r,s r53,?2,/5?5 :5985,s 7 :5985,s :5r2,s 5 :?572,.
#2. 10 A:327,72; 5 P?572, 5 3,s J5r2,s 26
8.1./. M%@!"!e#$%s ,e Br'9% H!,r(!% E3 /2/25? 5r?27,3 7s2s?5 5 5s:3,,r ,rr2<, ,<,= 53 75?r 5 /,s,s /52,?5 8, 5?5s2; 8, 352; 5 3,s ,r?2783,725s. E3 /2/25? r?,?r2 5s 53 985 s5 <,s, 5 8 5=5 5 2r r,2 7s?,?5 L, ?r,57?r2, s5rF 8, 72r785r572,. S2> ,5/Fs> 3, 5372, 5 2r 5s 7s?,?5> s5 :r875 53 /2/25? 72r783,r 82r/5> 985 5s 8 7,s :,r?2783,r 5 /2/25? 72r783,r> 7 r,2 2= 5372, ,83,r 7s?,?5. E 53 /2/25? 72r783,r , 985 ?55r 5 785?, ,38s 775:?s 5s:5727s :,r, 5s?5 ?2: 5 /2/25? -E=5 5 G2r Es 3, 35, ,3r55r 5 3, 78,3 s5 r5,32, 3, r?,72;> 5s?5 5=5 :855 :5r/,575r 2= ,r2,r 7 53 ?25/:> :5r :,r, 7,, 2s?,?5 5 ?25/:> 5s 53 5=5 5 3, r?,72;. -Ar7 P,r?25 5 8 5=5 5 2r> 5s 53 F83 ,r7 5 r,2 82?,r2 7 53 985 s5 /25 53 5s:3,,/25? ,83,r. S8 82, 5s 53 r,2F. -V5372, A83,r Es 3, ,r2,72; 5 5s:3,,/25? ,83,r :r 82, 5 ?25/:. -A7535r,72; A83,r Es 3, ,r2,72; 5 3, 5372, ,83,r :r 82, 5 ?25/:. E 2F/27, 53 /2/25? 2r,?r2 s5 ?255 5 785?,> ,5/Fs -M/5? 5 I5r72, Es 8, 78,32, 5 3s 785r:s 985 r5s83?, 5 /83?2:327,r 8, :r72; 5 /,s, :r 3, 2s?,72, 985 3, s5:,r, ,3 5=5 5 2r. -M/5? 5 #85r, O :,r /?r 5s 3, 85r, ,:327,, :r 3, 2s?,72, ,3 5=5 5 2r.
8..
Gr',% ,e !er$', "%@!!,',F e# "e'#!s"%s )'#%s GDLF
27
P,r, 5?5r/2,r 53 GDL 3<,3 5 78,39825r /57,2s/> s5 5<5 7s25r,r 53 @/5r 5 5s3,<5s ,s 7/ 5 3,s =8?,s 3,s 2?5r,7725s 5?r5 533s. E3 GDL 5 78,39825r 5s,/<35 5 5s3,<5s s5 :855 :rs?27,r 7 8, 25s?2,72; 5 3, 7272; 5 Gr85<35r. C8,39825r 5s3,<; 5 8 :3, ?255 ?r5s GDL. Pr 7s2825?5> 8 s2s?5/, 5 L 5s3,<5s 757?,s 5 53 /2s/ :3, ?5rF $L GDL> 7/ s5 /85s?r, 5 3, #28r, 11,.
#2. 11,. s 5s3,<5s 5s757?,s> GDL% D5 3s s 5s3,<5s 757?,s ?255 8 ??,3 5 s52s GDL. C8, 5s?s 5s3,<5s 5s?F 757?,s :r 8, =8?, 7/:35?, 5 3, 28r, 11<> ∆ y 2 s5 7/<2, 7/
∆x
∆y >
∆ x1
∆ x 2 s5 7/<2, 7/
5s? 532/2, s GDL 5=, 78,?r.
#2. 11<. 757?,s :r 8, =8?, 7/:35?,> GDL4 28
∆ y1
E 3, 28r, 117> 3, s5/2=8?, 532/2, s3 8 GDL 53 s2s?5/, ):r985 8, s5/2=8?, ?255 s GDL* 5=, 53 s2s?5/, 5 s 5s3,<5s 757?,s :r 8, s5/2=8?, 7 8 ??,3 5 727 GDL.
#2.117. 757?,s :r 8, =8?, 5s32,?5 r,?5 )s5/2=8?,*> GDL A5/Fs> 78, 78,39825r 5s3,<; 5s?, 757?, , ?25rr, 82 ,3 /,r7 5 r55r572,> s5 532/2, s8s ?r5s GDL. Es?5 r,,/25? 335, , 3, 578,72; 5 Gr85<35r M =3 L−2 J −3 G …………………………………………………………………….. )1*
D5 M r, 5 32<5r?, /232, L 8/5r 5 5s3,<5s J 8/5r 5 =8?,s G 8/5r 5 5s3,<5s 757?,s , ?25rr,. H, 985 53 557? 5? s5rF 7r5,r 8 5s3,<; 757?, , ?25rr, 5 /,r r5 /Fs r,5> , 985 s3 5<5 29
:855 ,<5r 8 :3, 5 ?25rr,. Pr 3 ?,?> G s25/:r5 5s 8 3, 578,72; 5 Gr85<35r s5 725r?5 5. M =3 ( L−1 )− 2 J ………………………………………………………………….. )!*
E3 ,3r 5 J 5 3,s 578,725s 1 ! 5<5 r535=,r 53 ,3r 5 ?,s 3,s =8?,s 5 53 /57,2s/. Es 572r> 3,s s5/2=8?,s 785?, 7/ j :r985 s3 532/2, 8 GDL. Es? 5s /5s 78s s2 s5 8?232, 3, /227,72; 5 k8?<,7 5 3, 578,72; 5 Gr85<35r 5 5s?, r/, M =3 ( L−1 )− 2 J 1− J 2 ……………………………………………………………)$*
D5 M r, 5 32<5r?, /232, L 8/5r 5 5s3,<5s J 1 8/5r 5 =8?,s 5 1 GDL )7/:35?,s* J 2 8/5r 5 =8?,s 5 ! GDL )s5/2*
E3 ,3r 5 J
1
J
2
5 5s?,s 578,725s 5<5 s5r 5?5r/2, 7 782,
:,r, 7s25r,r ?,s 3,s =8?,s 7/:35?,s> s5/2=8?,s /@3?2:35s 5 78,39825r 5s3,<,/25?. L,s =8?,s /@3?2:35s 785?, 7/ 985 53 8/5r 5 5s3,<5s 82s 5 27, =8?, s5 ,r5, , 3, 7,?5r, 7/:35?, ) J ¿ . E3 GDL 5 1
78,39825r /57,2s/ s5 :855 5?5r/2,r rF:2,/5?5 , :,r?2r 5 5s?, 5:r5s2; ,?5s 5 985 s5 225r?, ?25/: 5 8 2s5 /,s 5?,33,.
30
#2. 1!. Es3,<,/25?s 985 7?255 =8?,s 5 ,r2s ?2:s
8..*. Gr',% ,e !er$', "%@!!,',F e# "e'#!s"%s es)e!'es E3 /6? 8?232, :,r, 5?5r/2,r 3, /232, 5 8 /57,2s/ :3, s5 :855 ,/:32,r 7 ,7232, , ?r5s 2/5s25s. C,, 5s3,<; 757?, 5 ?r5s 5s:,72s ?255 s52s GDL> 8 5 3s s52s :,r5s 25r2r5s s5 :855 8?232,r :,r, 757?,r3s> ,3 28,3 985 3s :,r5s s8:5r2r5s 7 /Fs 32<5r?,. U, =8?, 5 8 r, 5 32<5r?, 532/2, GDL> 8 5 s r,s 5 32<5r?, 532/2, 4 GDL> 5?7. L, <,7,, 532/2, % GDL. Es? 7875 , 3, 578,72; 5 /232, 5 k8?<,7 :,r, 5s3,<,/25?s 5s:572,35s M =6 ( L−1 ) −5 J 1−4 J 2−3 J 3−2 J 4− J 5
D5 53 s8<275 s5 r525r5 ,3 @/5r 5 r,s 5 32<5r?, 5 3, =8?,.
8../. Me'#!s"%s y es$r($(r's E3 r, 5 32<5r?, 5 8 5s,/<35 5 5s3,<5s :r5275 :r 7/:35? s8 7,rF7?5r 52s?5 s3 ?r5s :s2<232,5s. S2 53 GDL 5s :s2?2> s5rF 8 /57,2s/> 3s 5s3,<5s ?5rF /2/25? r53,?2. S2 53 GDL 5s 5,?2> 5?75s s5 31
?5rF 8, 5s?r87?8r, :r57,r,,> 3 985 s2227, 985 s5rF :s2<35 2@ /2/25? 985 ,38s 5s85rs ?,/<26 :855 5s?,r :r5s5?5s 5 53 //5? 53 5s,/<35. L, 28r, 1$ /85s?r, 5=5/:3s 5 5s?s ?r5s 7,ss. U 5s3,<; 5s?, 2= 5 7,, 7,s. L, 28r, 1$,> /85s?r, 78,?r 5s3,<5s 82s :r 78,?r =8?,s 7/:35?,s> 3 78,3> s5@ 3, 578,72; 5 Gr85<35r> , 8 GDL. S5 /5rF> s3 s5 r59825r5 8, 5?r,, :,r, :r872r 3s r5s83?,s :r5572<35s. L, 28r, 1$<> /85s?r, ?r5s 5s3,<5s 82s :r ?r5s =8?,s 7/:35?,s. T255 75r GDL > :r 3 ?,?> 5s 8, 5s?r87?8r,. H, 985 3s ?r5s :,s,r5s s5 :855 2s5r?,r 5 s8s :,r5s 5 r2272s 5 3s 5s3,<5s r5s:57?2s )Ns* s2 5sr,r , 3, 5s?r87?8r,> , 985 s25/:r5 s5 :rF 57?r,r 8, :s272; 985 :5r/2?, 53 5s,/<35. Es?, s5 5/2, r5s?r2772; 5,7?,. L, 28r, 1$7> /85s?r, s 5s3,<5s 82s :r s =8?,s 7/:35?,s. T255 8 GDL 28,3 , /5s 8> :r 3 985 5s 8, es$r($(r' )re'r&','. C 53 2 5 2s5r?,r 3s s :,s,r5s s2 5sr,r , 3s 5s3,<5s> 3,s 2s?,72,s 5?r5 75?rs 5 r2272s 5?r5 ,/<s 5s3,<5s 5<5 s5r 5,7?,/5?5 3,s /2s/,s. E 3, :rF7?27,> 5s 2/:s2<35 , ,8985 s5, /8 :5985. Pr 3 ?,?> 982F ?5, 985 r,r 53 s58 :,s,r :,r, 2s5r?,r3> 3 985 7r5, ,3@ 5s85r 5 3s 5s3,<5s. E?75s 3, 5s?r87?8r, 5s?,rF :r57,r,,. Pr<,<35/5?5 ,, 8, s2?8,72; s2/23,r 5 8 78rs 5 /57F27, ,:327,, 5 3, r/, 5 8, 2, 25?5r/2,,> ,98533, 985 ?255 5/,s2,s ,:s r5s?r27725s :,r, 3,s 578,725s 2s:2<35s. U, 2, 25?5r/2,, ?,/<26 ?255 GDL 5,?2> /25?r,s 985 8, 2, s2/:35/5?5 ,:,, GDL 28,3 , 75r.
32
#2.1$ M57,2s/s> 5s?r87?8r,s Es?r87?8r,s :r57,r,,s E 53 7,/: 5 3, 2525r, 7/@/5?5 s5 5785?r, ?,? 3,s 5s?r87?8r,s 7/ 3,s 5s?r87?8r,s :r57,r,,s. D5 57> 3, 5s?r87?8r, 5r,5r, ?255 GDL 28,3 , 75r 5s r,r, 5 3, :rF7?27, 5 2525r,. L, /,r, 5 3s 52272s> :85?5s <,s?2r5s 5 /,982, s 5s?r87?8r,s :r57,r,,s> 5<2 ,3 8s 5 =8?,s s3,,s r5/,7,,s 5 38,r 5 =8?,s 5 :,s,r. I738s 5s?r87?8r,s s2/:35s 7/ 8, s233, , /58 5s?F :r57,r,,s. C/ 3 985 ,98 2?5r5s, s 3s /57,2s/s s5 775?r,r, 5 2s:s2?2s s3 7 GDL :s2?2.
1. DESARROLLO DEL PROTOTIPO
1.* .
M'$er!'es:
3er!#&'s: S5rF 8?232,,s :,r, ,75r 872,r 53
C!#?%s: S5rF 8?232,s :,r, 2=,r 3,s =5r2,s ,3
M'%se: Es 3 5s572,3 :,r, :5r 53,<r,r 53
M'#&(er's ,e S(er% S5 8?232,rF :,r, 82r 3,s =5r2,s ,r35 /2/25? ,3 ?,/<26 s5 8?232,rF :,r, 985 :,s5 53 3982 5 8, =5r2, , ?r,.
A&(': S5rF 8?232, :,r, 5/s?r,r 985 8 3982 7 :7, 5s2, 5s 575s,r2 ,:327,r /,r 85r,.
L!>'s: S5 8?232,rF :,r, 32=,r 53 /,7s53 982?,r 3,s ,s?233,s 985 5s?, ?5,. A'$e e#&('s: S5r2rF :,r, 2=,r 3, <,s5 s5r2r 5 ,: 5 3, /2s/,. Pe&'"e#$%: S5 8?232,r, :,r, 2=,r 3,s :,r?5s 2=,s 82r 3,s :,r?5s 985 3 r59825r,.
34
#2. 14 M,?5r2,35s
1./. •
Pr%e,!"!e#$%. S5 2<8=,r, 5 53 /,7s53 3,s :25,s 985 s5rF 53 785r: 53
•
U, 5 2<8=,,s 3,s :,r?5s s5 :r755rF , 7r?,r3,s.
#2. 1 P25,s Cr?,,s •
L85 s5 82rF 3,s :25,s :,r5s :,r, ,r35 r/, ,3 8263,s 7 3s :,32?s 5
•
S5 ?/,r, 3,s =5r2,s :,r, ,75r35s 8 r2272 , 7,, :,r, 2s5r?,r 8 :,3233 , 7,, 8,.
•
S5 737,r, 3,s =5r2,s 7/ :2s?5s s5 2=,r, , 5 53
35
#2. 1% Cs?r8772 53 Br,
•
S5 :r755rF , ,75r 3, :2, 7r?, 8 ,<,?5 358,s , 3, /2?, :5F3s r/, 8 F83 r57?.
•
S5 r/,r, 53 785r: 5 3, :2, , r/, s5 82rF 7 3,s :2,s , 53,<r,,s :5F3,s r52s, 985 ?5, /232,.
•
S5 737,r, ,3,/
#2. 1' P2,
36
•
S5 2=,r, 3, :2, ,3
#2. 1& Br, H2r,8327
•
S5 2<8=,> 7r?, s5 :5, 8, :8?, 5 7,, 5?r5/ 5 3, :2, :,r, /5=r ,,rr5 5 53
•
Ar, s5 :r755rF , ,75r 53 s:r?5 53
•
53 5=5 :r 53 78,3 2r,r, 53
•
U, 5 5s,/<3,, 3, :25, s5 7/:r<,r, 985 ?5, /232,> 985 7985 7 3, <,s5 53
•
Y, 57 3s :,ss ,?5r2r5s s5 5/:5,r, :r ,75r 3s 7?r35s 985 2r22rF ,3
•
S5 ,rF 8, 78<25r?, :,r, 3s 7?r35s 53
37
#2. 1( Pr??2: T5r/2, •
Ar, s5 82rF 3s 7?r35s 7 3,s /,85r,s 5 s85r s5 335,r, 7 ,8, 3 s82725?5 :,r, :5r /5rs5 ? 53
•
L, :r2/5r, =5r2, s5rF 3, 985 2r5 ? 53 3, s58, =5r2, /5rF 3, s58, ,r?2783,72;> L, ?5r75r, =5r2, /5rF 3, :r2/5r, ,r?2783,72; 3, 78,r?, =5r2, ,772,r, 3, :2, 985 ss?5rF <=5?s.
•
S5 ,rF 872,r :,r, :5r 5r 5rrr5s 5 53 /2s/ :5r 7rr52r3s> 8, 5 57 ? 5s? s5 7/:r<,r, 985 5s?5
#2. !0 Pr??2: 5 872,/25?
38
#2. !1 Pr??2: 5 Br, Ar?2783,
. CALCULOS .*.
Es(er9%s y ,e%r"'!%#es
+ M O = EF M O =−0.5 KN ( 13 cm )+ 0.5 KN ( 20 cm )+ 25 ( cos30 )= 0 M O =25.15 KN
Esfuerz
39
! =
! =
P A 500 N 175 x 10
−6
−6
! =2.85 x 10
"efrm#c$% e% c#d# &#r'e de()r#z ! E
1¿
ϵ =
2.85 x 10
−6
N
m ¿ − 6 N 60 x 10 2 m
2
¿ 0.0475
! E
2 ¿ ϵ =
2.85 * 10
−6
N 2
m ¿ −6 N 75 * 10 2 m
¿ 0.038
3¿
! E
ϵ =
40
2.85 * 10
−6
N 2
m ¿ −6 N 60 * 10 2 m
¿ 0.0475 "efrm#c$% T'#( "e( +$s'em#
( )( )( )
¿ PL + PL + PL AE
¿
(
AE
1
2
AE
(
500 N .13 m −6
175 x 10
(
3
) −6
5.5 x 10
m
)) (
(
500 N .25 m
+
N
2
−6
175 x 10
(
) −6
5.5 x 10
m
2
¿ 0.067 + 0.0129 + 0.0103
¿ 0.0902
./.
C(%s "e,!'#$e e Pr!#!)!% ,e P's'
"e =0.5 cm "s= 1.5 cm F e =10 gr#ms − fuerz# =0.10 N Pe = Ps F e A e
=
F s A s
41
N
)) ( +
(
500 N .29 m −6
175 x 10
(
) −6
5.5 x 10
m
2
N
)
)
∴ F s
A =
, 4
=
F e A s A e
( ) , 2 d 4
2
d ¿s
¿ , 4
2
d ¿e
¿
(0.10 N )¿ F s =¿ ,
2
( 1.5 cm ) ¿s 4 ¿ , ( 0.5 cm ) ¿e 4 ¿ ( 0.10 N ) ¿ F s=¿ 2
F s=0.9 N = 91.77 gr#ms −fuerz#
.6.
Gr',%s ,e !er$',
P,r, 53 7F3783 5 3s r,s 5 32<5r?, 53 /57,2s/ 3 ,r5/s 5 s :,r?5s. L, :r2/5r, :,r?5 T55/s 7/ ,?s L= Es(#)%es =3 J 1= Ju%'#s cm&(e'#s =2
42
J 2= sem$-u%'#s =1 . P,r, 5s?5 7,s s5 ?255 8, s5/2=8?, 5<2 , 985 3, <,s5
5s 2=,. #r/83, M =3 ( L−1 )− 2 J 1− J 2 M =3 ( 3−1 ) −2 ( 2 )−1
M =1
P,r, 3, s58, :,r?5 s5 ?255 3s s2825?5s ,?s L= Es(#)%es=3
J = Ju%'#s cm&(e'#s =3
#r/83, M =3 ( L−1 )− 2 J M =3 ( 3−1 ) −2 ( 3 ) M =0
+. CONCLUSIÓN C 3, 7s?r8772; 53 5 28,3 /,5r, 3s 5s85rs 5r/,725s :r5s5?5s> 7/ 3s r,s 5 32<5r?, 985 ?255 53 /57,2s/.
S5 ,s2/23 3, ,:327,72; 5 7F3783s /,?5/F?27s 725?27s ?,/<26 8?232,r /,?5r2,35s 57;/27s :,r, 3, 53,<r,72; 53 :r??2: 5 ,785r ,3,s 43
:r:25,5s 5 3s /,?5r2,35s> :,r, :s?5r2r/5?5 s8 r5:r8772; 5 55r,725s 8?8r,s 7 53 2 5 5/s?r,r 53 872,/25?
. ANEXOS
A5 1 #2. !! M52,s 5 3,s :25,s
44
A5 ! #2. !$ L7,32,72; 5 3s :8?s , :5rr,r
A5 $ #2. !4 M52, 5 3, <,s5
A5 4 #2. ! P8? 5 2=,72; 53
45
A5 #2. !%-!& P8?s :,r, 3, 2=,72; 5 3,s =5r2,s
A5 #2. !%
A5 #2. !'
A5 #2. !& 46
TABLA 1. MÓDULOS DE ELASTICIDAD DE ALGUNOS MATERIALES
TABLA !. PROPIEDADES MECANICAS DE LA MADERA
47
TABLA 6. PROPIEDADES 52SICAS PROMEDIO DE MATERIALES COMUNES
48
49
50
51
52
