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RESISTENCIA DE MATERIALES II
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RESISTENCIA DE MATERIALES IIAo de la Promocin de la Industria
Responsable y Compromiso Climtico
PROBLEMAS RESUELTOS DE
EXAMEN DE TERCERA UNIDAD
RESISTENCIA DE MATERIALES II
DOCENTE:
Ing. VILLAVICENCIO GONZLES, Felipe.
AUTORES:
REQUE VALQUI, Jaive Jen!
VELSQUEZ ARELLANO, "illia#! Iv$n
CICLO:
SE%TO
2014
NUEVO CHIMBOTE PER
PROBLEMA 1
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RESISTENCIA DE MATERIALES IICal&'la l(! #(#en)(! *
ea&&i(ne!, l'eg( +i'-a l(! DFC * DF +e la !ig'ien)e
viga, '!an+( /a+* C(!! * vei0&a p( el Te(e#a +e l(! Te!
(#en)(!. 1De)e#inan+(* 'i&an+( l( p'n)(! &2)i&(!3.
43 Cal&'l( +e 5
K=I
L=I
6 K=7
42
I K=6
K=I
L=
I
7
35
I K=5
K=I
L=
I
5 K=7
63 Cal&'l( +e rij
7UNTO A
rAB=1
7UNTO 8
rBA=7
13=0.54
7UNTO C
rCB= 5
12=0.42
7UNTO D
rDC=1
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6#9T#
;Tn
DC8A
#6#
9T#4.
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RESISTENCIA DE MATERIALES II
MCD=MDC= 1
12q l
2= 1
1235
2=6.25
@.@@ 4.@@ @. @.;6 @..@@ .@
@B.@@ [email protected]
4B=.= >.6
.6< B@. @.>; @.
>.6
B@.@< @.4@ @.@
B@.@6 B@.@9
@.4>
MF >.@@
[email protected]; [email protected];
B.; .;
@.@@
;3 O)en&in +e Rea&&i(ne! De0ni)iva!
>.@@ .@@ .@@ @.6;
[email protected];
>.@@ .94 .> .99 >.4= .4
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RESISTENCIA DE MATERIALES IITa#( A8: La p(!i&in +el #(#en)(
#$Ki#(! 1&()e n'l(3 +e!+e el ap(*( A
e!:
Xa=RA
q=
8.31Tn
3Tn/m=2.77m
Mmx=8.31Tn 2.77m3Tn
m2.77 m 2.77m 0.56Tn.m
Mmx=5.5Tn.m
Ta#( 8C: Si la &aga p'n)'al e!)$ a la iH'ie+a +el &en)(
+e la l'H +e la viga,
&al&'la#(! la p(!i&in +e % +e!+e el ap(*( +ee&(
1 Xb 3 * vi&eve!a:
Xb=RBq= 6.17Tn1.5Tn/m=
4.11m
Mmx=6.17Tn4.11m1.5Tn
m4.11m4.11m0.58.48Tn.m
Mmx=4.18Tn.m
Ta#( CD:
Xc=RC
q=9.19Tn
3Tn/m=3.06m
Mmx=9.19Tn3.06m3Tn
m3.06m3.06m0.58.48Tn.m
Mmx=5.58Tn.m
En la 'nin +el )a#( CD &(l'#na 1ap(*( +ee&(3 en geneal
el #(#en)(nega)iv( e!:
M=q l2
20=3Tn
m 5m5m
20=3.75Tn.m
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RESISTENCIA DE MATERIALES IIDiaga#a +e C()e * (#en)(!
Fle&)(e!:
DFC:
DF:
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.4
;.44
6.==
.>
4=
.99
>.@@
.94
[email protected]> B>.@@
B9.=
> 6> = @ B9
4 @ @ @ B>@ 6> = @ B966.;@ = 6; < B6=9.
4 @ @ @ B>@ 4 =6> @ B4>4;=49@@@ = 6; < B6=9.@ 4
=6> @ B4>4;=49@@@ @ @=;;96 @ B4>4;=49@@@ @ 4 6>44<
B464;4;9=
4 @ @ @ B>@ 4 @ B=44< B4
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RESISTENCIA DE MATERIALES II
+e 6 9 0la! !'!)aiga#(! la ; l2nea, #'l)ipli&a+a
e!pe&)iva#en)e p( B=4444@ 4 @ @ B4
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RESISTENCIA DE MATERIALES II
SOLUCION
/a&e#(! 'n )a#( i#aginai( +e L@ *
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RESISTENCIA DE MATERIALES II4
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RESISTENCIA DE MATERIALES II
5
4M3+2M4(54 +0)=
5 (3 )5
(5232)
4+0
5
M3
+M4
(10
)=48
(iii)
/a&ien+(: 4x (1)+6x (2 ):
104M3+30M4=90(4)
L'eg(: 3x (3)+(4 ):
89M3=54 M
3=0.61Tn .m
Ree#plaHan+( en (4 )! (1 ) :
104 (0.61 )+30M4=90 M
4=5.1Tn .m
6M2+0.61=40.5 M
2=6.85Tn.m
CO7RO8ANDO 7OR /ARD CROSS
C$l&'l( +e igi+e&e!:
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RESISTENCIA DE MATERIALES II
KAB=3I
6=
I
2KAB=5(34 )=3.75
KBC=4I
4
=I
(10
I
) KBC=10
KCD=4I
5KCD=8
C$l&'l( +e l(! &(e0&ien)e! +e +i!)i'&in:
rAB=1
rBA= 3.75
10+3.75= 3
11
rBC= 10
10+3.75=
8
11
rCB= 10
10+8=5
9
rCD= 8
10+8=
4
9
rDC=0
C$l&'l( +e l(! #(#en)(! )an!#i)i+(!:
MAB= 5
192 (4 )(62 )=3.75
MBA=11192
(4 )(62)=8.25
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RESISTENCIA DE MATERIALES II
MBC=MCB=0
MCD=5(3) (22 )
52 =2.4
MDC=5 (32 )(2)
52 =3.6
4.@@ 944 44
B9.=< 6.6< > B4.999 B4.@>= @B4.=< B
@.>>=
9 @ B@. 4.< B4.>>= B4.999
@
[email protected] @.9 @ B@.>> @.> B@. @.9 @ [email protected]@.@= @.4 [email protected]=
B
@.49@
B@.@6
B@.@.> >.> @.
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RESISTENCIA DE MATERIALES II
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