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1.- Geometría del problema
4 m
5 m
6 m
P = 40 KN/mα = 0
E = 210
G = 80
γ = 1.2
3 KN/m
0.2 0.4 m
0.25 0.5 m
0.3 0.6 m
2.- E!e" #oorde$ado"
%1=
%2=
%3=
105 KN/m2
105
K&= 103
'(1=
'(2=
'(3=
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3.- N)merar $)do" * barra"
4.- +oorde$ada" de lo" $)do"
Nudo X
1 0
2 4
3 ,
4 15
5.- $#(de$#(a de la" barra"
Barra Ni Nf
1 1 2
2 2 33 3 4
6.- e"plaam(e$to de la" barra"
Barra
1 0 0 0
2 0
3 0
.- +ara#terí"t(#a" eomtr(#a" * el"t(#a" de #ada barra
Barra
m m
1 4 4 1 0 8 1.1 1.2 0.032
2 5 5 1 0 12.5 2.6 1.2 0.031
3 6 6 1 0 18 5.4 1.2 0.032
8.- atr( de r((de de #ada barra
8.1.- Epre"(o$e" e$erale"
0 d1 0 d1
K1 =22.4 11.2
K1 =21.88 10.6,
11.2 22.4 10.68 21.8,
d1 d2 d3 d1 d2
K1 =43.5 13.125 21.85
K1 =42.6 12.3
13.13 5.25 13.125 12.3 5.0,21
V 1
θ1
V 2
θ2
d1
d1
d2
d3
d2
d3
d4
Δxi
Li
li
mi
Aix
Iix
γi
βi
10-3 m 2 10-3 m 4
Barra 1 β=0 Barra 1 β≠0
103 103
Barra 2 β=0 Barra 2 β≠0
103 103
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21.88 13.125 43.5 20.8, 12.3
d2 d3 d4 d2 d3
K1 = 6.3 -18., -18., K1 = 6.105 -18.31-18., 5.6 3.8 -18.3 3.842
-18., 3.8 5.6 -18.3 36.042
,.- atr( de r((de total
β=0 β≠0
d1 d2 d3 d4 d1
66.15 13.125 21.85 0 64.642
[K] =13.13 14.542 -5.5 -18.,
K =12.3
21.88 -5.5 11,.35 3.8 20.888
0 -18., 3.8 5.6 0
0.022 0.0 -0.004 -0.01 0.0222
-0.03 0.1 0.001 0.034 -0.028
0 0.0 0.010 -0.01 -0.004
-0.01 0.0 -0.005 0.024 -0.005
10.- atr( de #ara" eter(ore" P
10.1.- 7)era" * mome$to" de empotram(e$to pere#to
P
Para 9=0 * 9:
Barra 1 Barra 2
-53.33 p= 40 53.333 -83.33 p= 40
80 80 100
4 5
10.2.- ;e#tore" de #ara" P
30 36. -120
Barra 3 β=0 Barra 3 β≠0
103 103
103 103
[K]-1 = 103 [K]-1 = 103
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-220
30
P=-220
36.
-120
β=0 β≠0
d1 d2 d3 d4 d1 d2
.258 .258 .258 .258 .2, .2,2
[d]=-35.4 -35.4 -35.42 -35.42
[d]=-35. -35.4
0.68 0.68 0.68 0.68 0.633 0.6335
-10.8 -10.8 -10.8 -10.8 -10.8 -10.8
d1= .258 d1= .2,2
d2= -35.4 d2= -35.4
d3= 0.68 d3= 0.6335
d4= -10.8 d4= -10.8
12.- +l#)lo de )era" * mome$to" ($ale"
Para 9=0
1=
2
FUERZAS Y MOMENTOS
Frame Joint F F! F" M M! M"
KN KN KN KN-m KN-m KN-m
1 1 0 0 0 0 0 0
1 2 0 0 0 0 0 0
2 2 0 0 0 0 0 0
2 3 0 0 0 0 0 0
3 3 0 0 0 0 0 0
3 4 0 0 0 0 0 0
#ES$LAZAMIENTO #E LOS NU#OS
n%&o' U U! U" R R! R"
m m m Radianes adiane adianes
1 0 0 0 0 0 0
2 0 0 0 0 0 0
3 0 0 0 0 0 0
4 0 0 0 0 0 0
11.- &e"ol)#(@$ del "("tema de e#)a#(o$e" d=K-1P
10-3 10-3
10-3
10-3
10-3
10-3
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REA((IONES
n%&o' F F! F" M M! M"
KN KN KN KN-m KN-m KN-m
1 0 0 0 0 0 0
2 0 0 0 0 0 04 0 0 0 0 0 0
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m-KN m-KN
5.6 5.43
10.,35 10.61
18., 18.31
I II
d3
20.8884
12.3036
EI/Lx103 EIx103/L(1β!
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42.634
d4
-18.3136.04
3.84
d2 d3 d4
12.3036 20.8, 0
14.1, -5.58 -18.3
-5.58 116.61 36.04
-18.3 36.04 3.84
0.0 0.00 -0.01
0.1 0.00 0.03
0.0 0.01 -0.01
0.0 -0.01 0.02
0 por "er #ara "(mtr(#a
Barra 3
83.33333 -120 p= 40 120
100 120 120
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%3=
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d3 d4
.2,232 .2,2323856
-35.36, -35.36853662
0.633455 0.633455448
-10.,6 -10.,5880336
10-3
10-3
10-3
10-3
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