soluciÒn del quinto capÍtulo de anÀlisis estructural ii.docx

7/23/2019 SOLUCIÒN DEL QUINTO CAPÍTULO DE ANÀLISIS ESTRUCTURAL II.docx

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UNIVERSIDAD NACIONAL DE SAN CRISTÓBAL DE HUAMANGA

FACULTAD DE INGENIERÍA DE MINAS GEOLOGÍA Y CIVIL

ESCUELA DE FORMACIÓN PROFESIONAL DE INGENIERÍA CIVIL

ANÀLISIS ESTRUCTURAL II (IC-444)

DOCENTE : Ms. RUBÉN AMÉRICO YACHAPACONDEÑA.

ALUMNO : YUCRA RODAS, Rómulo

AYACUCHO – PERÚ

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#SOLUCI$N DE E%ERCICIOS PROPUESTOS DEL CAPITULO V&

EJERCICIO N° 8Elaborar un programa de computación para obtener el vector de cagas

generalizadas Q en que se da como dato el vector de empotramiento en

coordenadas locales para elementos cargados.

EJERCICIO N° 8Elaborar un programa de computación para encontrar el vector de cargas

generalizadas Q para un pórtico plano con elementos ortogonales, si sobre

los elementos horizontales actúan cargas triangulares y trapezoidales. El

programa deberá calcular las acciones de empotramiento perfecto.

SOLUCIÓNL solu!"ó# $mos %!&' (' los )os ('o*l&ms "m(l&m&#+#)ou# ('o'm &#&'l, )& +l -o'm #o lm&#+& (' &#!o#+'' &l$&!+o' / , +m(o!o #o solo (' o*+&#&' !!"o#&s )& &m(o+'m"&#+o(&'-&!+o, s"#o ('+& )& &#!o#+'' los $&!+o'&s m&#!"o#)os 0u&

#os mu&s+'& l m+'"1 )& '"")&1 +o+l )& l &s+'u!+u' &#!oo')&#)s lo*l&s 2 0u& &#!u&#+'& &l )&s(l1m"&#+o 3#l )& l&s+'u!+u' , '&sol$"&#)o )& &s+ m#&' &#!o#+'mos l solu!"ó# )&)"!% &s+'u!+u'.

'##########################################################################' '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$' %% % UNIVERSIDAD NACIONAL DE SAN CRISTÓBAL DE HUEMANGA %%% %% % ESCUELA DEFORMACIÓN PROFESIONAL "INGENIERÍA CIVIL"%%% %% % ASIGNATURA: ANÁLISIS ESTRUCTURAL II (IC-! %%% %% % DONCENTE : M RUBN AMRICO ACHAPA CONDE&A%%%

%% % ALUMNO : UCRA RODAS R)*+, %%% %% % ACUCHO - PER %%% %% % ./00%%% %% % PROGRAMA PARA RESOLVER UNA ESTRUCTURA DE TIPO "PÓTICO PLANO"%%% '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''##########################################################################'1,23415*6('71 N*)89, 28 1*2,:'!1193415*6('71 N*)89, 28 1*2, 986941;42,:'!1;+3/CG3,18(1,2<!

=,9 430:119

1*2983 415*6 ('71 N*)89, 28+ 1*2, 986941;42,:'!>0 3 415*6 ('71 D85+?@?)4816, 81 > 4(! , 1,(1!:'''!

4= >033'1' CG(40!3/8+8812 0 3 415*6 ('71 D85+?@?)4816, 81 4(! , 1,(1!:'''!4= 033'1' CG(4.!3/8+8812 R0 3 415*6 ('71 R,6?4,1 4(! , 1,(1!:'''!4= R033'1' CG(4<!3/8+8812

812

=,9 430:1,2

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444) 1




=,9 30:<4= CG(4!3/

1;+31;+0CG(4!31;+

8+8812 812

812 CG

)93415*6('71 N*)89, 28 )48)9,:' !=,9 430:)9

=59416= ('71 M48)9, %2:'4!414(4!3415*6 ('71 N*)89, 1*2, 4144?+:'!=41(4!3415*6 ('71 N*)89, 1*2, =41?+:'!

812 414=41

=,9 430:)9=,9 30:<

VC(4!3 CG(414(4! !VC(4<! 3 CG(=41(4!!

812 812 VC

=59416= ('71 C,,9281?2? 28 +, 1*2,: 71'!=,9 430:1,2

=59416= ('71 N*2, %2: '4!(4! 3 415*6 ('71 C,,9281?2? 81 ):'!J(4! 3 415*6 ('71 C,,9281?2? 81 J ):'!

812 =,9 430:)9

D(4! 3 (=41(4!! - (414(4!!DJ(4! 3 J(=41(4!! - J(414(4!!L(4! 3 ((D(4!!K. (DJ(4!!K.!K/SENO(4! 3 DJ(4!L(4!COSENO(4! 3 D(4!L(4!

812LSENOCOSENO

=59416= ('71 C?9?689464? 28 +, )48)9, : '!

E+?3 415*6 ('71 M,2*+, 28 E+?6442?2 T). :'!G3/E+?B86?3 415*6 ('71 F?6,9 28 F,9)? :'!?*3@89,(1;+1;+!=,9 430 : )9

=59416= ('71 M48)9, %2:'4!B(4! 3 415*6('71 B?8 ):'!H(4! 3 415*6('71 A+6*9? ):'!A98?(4! 3 B(4!H(4!I1894?(4! 3 B(4!H(4!K<0.=4 3 (<E+?I1894?(4!B86?!(GA98?(4!L(4!K.!3((E+?I1894?(4!!L(4!!((0=4!(0=4!!53

?3((.E+?I1894?(4!!L(4!!((0-.=4!(0=4!!3((?!L(4!!53

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444)




63(5!L(4!93((E+?A98?(4!!L(4!!

.(400!39.(40.!3/.(40<!3/.(40!3-9.(40!3/.(40!3/

.(4.0!3/.(4..!36.(4.<!3.(4.!3/.(4.!3-

6.(4.!35.(4<0!3/.(4<.!3.(4<<!3.(4<!3/.(4<!3-.(4<!3?

.(40!3-9.(4.!3/.(4<!3/.(4!39.(4!3/.(4!3/

.(40!3/.(4.!3-6.(4<!3-.(4!3/.(4!36.(4!3-5

.(40!3/.(4.!35.(4<!3?.(4!3/.(4!3-5.(4!35

T.Q<(400!3COSENO(4!T.Q<(40.!3SENO(4!T.Q<(40<!3/T.Q<(40!3/T.Q<(40!3/T.Q<(40!3/

T.Q<(4.0!3-SENO(4!T.Q<(4..!3COSENO(4!T.Q<(4.<!3/T.Q<(4.!3/T.Q<(4.!3/T.Q<(4.!3/T.Q<(4<0!3/T.Q<(4<.!3/T.Q<(4<<!30T.Q<(4<!3/T.Q<(4<!3/T.Q<(4<!3/T.Q<(40!3/T.Q<(4.!3/T.Q<(4<!3/T.Q<(4!3COSENO(4!T.Q<(4!3SENO(4!T.Q<(4!3/T.Q<(40!3/T.Q<(4.!3/T.Q<(4<!3/T.Q<(4!3-SENO(4!T.Q<(4!3COSENO(4!T.Q<(4!3/T.Q<(40!3/T.Q<(4.!3/T.Q<(4<!3/T.Q<(4!3/T.Q<(4!3/T.Q<(4!30

=,9 )30:=,9 130:

.I()1!3.(4)1!812

812=,9 )30:=,9 130:

T.Q<I()1!3T.Q<(4)1!812

812 =59416= ('71 M?694@ 28 R4;428@ 81 C,,92 G+,?+8:'!<3T.Q<I'.IT.Q<I

)?6?*3<=,9 30 :4= VC(4!33/

)?6?*(:!3/)?6?*(:!3/

8+8812 812

3@89,(1;+1;+!=,9 ,16030:=,9 ,16.30:4= )?6?* (,160,16.!3/

*1,3VC(4,160!

2,3VC(4,16.!6983)?6?*(,160,16.!(*1,2,!3(*1,2,!698

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444) !




8+8812812

812 4= 4330

?*38+8 4= 430

?*3?*8+8812 812

812=59416= ('71 M?694@ 28 R4;428@ 28 +? E69*6*9?:'!M?6Q94;428@3?*PORTICOPLANOO'##########################################################################' '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$' %% % UNIVERSIDAD NACIONAL DE SAN CRISTÓBAL DE HUEMANGA %%% %% % ESCUELA DEFORMACIÓN PROFESIONAL "INGENIERÍA CIVIL"%%% %% % ASIGNATURA: ANÁLISIS ESTRUCTURAL II (IC-! %%%

%% % DONCENTE : M RUBN AMRICO ACHAPA CONDE&A%%% %% % ALUMNO : UCRA RODAS R)*+, %%% %% % ACUCHO - PER %%% %% % ./00%%% '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''##########################################################################'=59416= ('71 D8=41441 28 : 71'!3@89,(01;+!V03 415*6 ('71 E4681 ?9;? 81 +? *16? 4(! , 1,(1!:'''!4= V0 33 '' 1 3 415*6 ('71 N*)89, 28 *16? ?9;?2? : '!=,9 430 :1

NC 3 415*6 (' 71 N*2, ?9;?2, :'!0(0!3 415*6 ('71 F*89@? ,94@,16?+ : '!0(.!3 415*6 ('71 F*89@? 8964?+ : '!0(<!3 415*6 ('71 M,)816, : '!VC(4:!3CG(NC:!

=,9 ) 30 :<13VC(4)!

4= 0()!3/(1!30()!

8+8 812 812

812 QC3'8+8 QC3'812 3@89,(01;+!.Q?+)? ()9! 3 @89,V<3 415*6 ('71 E4681 ?9;? 81 +, )48)9, 4(! , 1,(1! : ''' !4= V<33'' 1)3 415*6 ('71 NW)89, 28 )48)9, ?9;?2, : '!=,9 ++30:1)

MC 3 415*6 ('71 M48)9, ?9;?2, :'!V3415*6('71 E+ 8+8)816, 8 28 841 68 J ,1 ?9;? *14=,9)8)8168

24694*42? 4(! , 1,(1!:' ''!4= V33'' ?93 415*6 ('71 C?9;? 24694*42?: '!.(0!3/ .(!3/

.(.!3 ?9L(MC!

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444) "




.(!3.(.!.(<!3 ?9(L(MC!K.!X.(!3-.(<!

8+8 V33 '1' .(0!3 415*6 ('71 F*89@? ?4?+ NI : '!

.(.!3 415*6 ('71 F*89@? ,96?168 NI : '!

.(<!3 415*6 ('71 M,)816, NI : '!.(!3 415*6 ('71 F*89@? ?4?+ NF : '!.(!3 415*6 ('71 F*89@? ,96?168 NF : '!.(!3 415*6 ('71 M,)816, NF : '!

812 .3.'=,9 )) 30:

.Q?+)?(MC))!3.())!'812

=,9 )30:=,9 130:

T.Q<I()1!3T.Q<(MC)1!812

812 T.Q<I+8?9 < < 3 (-0!T.Q<I'.'

=,9 ; 30 : 3 VC(MC;!

4= 3/(!3 <(;!(!

8+8 812 812

812 QCM 3'8+8 QCM 3'812

=59416=( '71 V86,9 28 C?9;? T,6?+8:'!QTOTAL 3 QC QCM

=59416=( '71 V86,9 28 D85+?@?)4816, G8189?+8:'!YQ28 3 M?6Q94;428@7QTOTAL

=,9 430:)9=59416=( '71 M48)9, %2 :'4!=59416=( '71 D8=,9)?4,18 28 )48)9,:'!+8?9 P0 +8?9 P.

+8?9 P +8?9 .Q?* =,9 30:4= VC (4!3/

P0(!3YQ28(VC(4!!8+8

P0(!3/812

812 P03P0'=,9 )30:=,9 130:

.I()1!3.(4)1!

812 812 =,9 )30:

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444) #




=,9 130:T.Q<I()1!3T.Q<(4)1!

812 812

<3T.Q<I'.IT.Q<I

=59416=( '71 A4,18 28 )48)9, 81 ,,9281?2? ;+,?+8:'!P.3<P0=59416=( '71 A4,18 28 )48)9, 81 ,,92 +,?+8 (P

C,)5+8)816?94,!:'!P3T.Q<IP.

=59416=( '71 A4,18 28 )48)9, 81 ,,92 +,?+8 (PP94)?94,!:'!=,9 30:

.Q?*(!3.Q?+)? (4!812

.Q?*3.Q?*'=59416=( '71 A4,18 =41?+8 (PPPC! :'!PQFINAL3.Q?*P

812

INGENIERÍA CIVIL-UNSCH ANÀLISIS ESTRUCTURAL II (IC-444) $

soluciÒn del quinto capÍtulo de anÀlisis estructural ii.docx

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