tugas 2 anstruk
19
SOAL : 4t DATA : BATANG 1 A = 100 0.2 t/m I = 5000 L = 500 300 BATANG 2 A = 100 I = 5000 L = 300 E = 2100 36.87 90 400 BEBAN Beban merata = 0.2 Momen = 500 Beban Horizontal = 4 PENYELESAIAN : Equivalent Joint Loads : a = T.m = 41.67 T.cm 0.2 t/m b = T.m = 41.67 T.cm b α btg 1 = α btg 2 = 1/12 x 0.2 x 1/12 x 0.2 x 5 tt 2 1 3 1 2 β 0.5 ton 0.5 ton 5 m 41.67 t.cm 41.67 tcm 41.67 t.cm 41.67 t.cm 0.5 ton 0.5 ton 0.3 T 0.4T 0.3 T 0.4T LOCAL GLOBAL
-
Upload
viny-aprilia-utami -
Category
Documents
-
view
90 -
download
0
Transcript of tugas 2 anstruk
SOAL :
4t
DATA :
BATANG 1
A = 100 cm²
0.2 t/m I = 5000L = 500 cm
300 BATANG 2A = 100 cm²I = 5000L = 300 cm
E = 2100 t/cm²36.87 derajad
90 derajad400
BEBANBeban merata = 0.2 t/m
Momen = 500 tcmBeban Horizontal = 4 t
PENYELESAIAN :Equivalent Joint Loads :
a = T.m= 41.67 T.cm
0.2 t/m b = T.m= 41.67 T.cm
b
cm^4
cm4
α btg 1 =α btg 2 =
1/12 x 0.2 x 52
1/12 x 0.2 x 52
5 tm
2
13
1 2
β
0.5 ton
0.5 ton
5 m
41.67 t.cm
41.67 tcm
41.67 t.cm
41.67 t.cm
0.5 ton
0.5 ton
0.3 T
0.4T
0.3 T
0.4T
LOCAL
GLOBAL
000000000
0
0
00
0
0
0
0
0
0
0
0
0
0
0000
0
0
MATRIK KEKAKUAN ELEMENBATANG 1 (ELEMEN 1) ; dipilih nodal i=1, j=2
=
= 0
-0.5
-41.67
0
-0.5
41.67
=
0.8 0.6 0 0 0 0-0.6 0.8 0 0 0 0
0 0 1 0 0 00 0 0 0.8 0.6 00 0 0 -0.6 0.8 00 0 0 0 0 1
0.8 -0.6 0 0 0 00.6 0.8 0 0 0 00 0 1 0 0 00 0 0 0.8 -0.6 00 0 0 0.6 0.8 00 0 0 0 0 1
=
420 0 0 -420 0 00 1.008 252 0 -1.008 2520 252 84000 0 -252 42000
-420 0 0 420 0 00 -1.008 -252 0 1.008 -2520 252 42000 0 -252 84000
=
=
0.8 -0.6 0 0 0 0 420 0 0 -420 0 00.6 0.8 0 0 0 0 0 1.008 252 0 -1.008 2520 0 1 0 0 0 0 252 84000 0 -252 420000 0 0 0.8 -0.6 0 -420 0 0 420 0 0
0 0 0 0.6 0.8 0 0 -1.008 -252 0 1.008 -252
0 0 0 0 0 1 0 252 42000 0 -252 84000
0.8 0.6 0 0 0 0
-0.6 0.8 0 0 0 0
0 0 1 0 0 0
0 0 0 0.8 0.6 0
0 0 0 -0.6 0.8 0
0 0 0 0 0 1
=
336 -0.6048 -151.2 -336 0.6048 -151.2 0.8 0.6 0 0 0 0
252 0.8064 201.6 -252 -0.8064 201.6 -0.6 0.8 0 0 0 0
0 252 84000 0 -252 42000 0 0 1 0 0 0
-336 0.6048 151.2 336 -0.6048 151.2 0 0 0 0.8 0.6 0
-252 -0.8064 -201.6 252 0.8064 -201.6 0 0 0 -0.6 0.8 0
0 252 42000 0 -252 84000 0 0 0 0 0 1
{f}(1)*
f1
g1
m1
f2
g2
m2
[T](1)
[T](1)T
[kl](1)
[kg](1) [T](1)T[kl](1)[T](1)
* *
1 2 3 4 5 6
=
269.16 201.12 -151.2 -269.16 -201.12 -151.2 1
201.12 151.85 201.6 -201.12 -151.85 201.6 2
-151.2 201.6 84000 151.2 -201.6 42000 3
-269.16 -201.12 151.2 269.16 201.12 151.2 4
-201.12 -151.85 -201.6 201.12 151.85 -201.6 5
-151.2 201.6 42000 151.2 -201.6 84000 6
=
=
0.8 -0.6 0 0 0 0 00.6 0.8 0 0 0 0 -0.50 0 1 0 0 0 -41.670 0 0 0.8 -0.6 0 00 0 0 0.6 0.8 0 -0.50 0 0 0 0 1 41.67
= =
0.3-0.4
-41.670.3-0.4
41.67
BATANG 2 (ELEMEN 2) ; dipilih nodal i=3, j=2
= =
0
dan =
00 00 00 00 00 0
=
0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1
=
0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
=
700 0 0 -700 0 00 4.6667 700 0 -4.6667 7000 700 140000 0 -700 70000
-700 0 0 700 0 00 -4.6667 -700 0 4.6667 -7000 700 70000 0 -700 140000
=
=
0 -1 0 0 0 0 700 0 0 -700 0 01 0 0 0 0 0 0 4.66667 700 0 -4.6667 7000 0 1 0 0 0 0 700 140000 0 -700 700000 0 0 0 -1 0 -700 0 0 700 0 00 0 0 1 0 0 0 -4.6667 -700 0 4.66667 -7000 0 0 0 0 1 0 700 70000 0 -700 140000
{F}(1)* [T(1)]T {f}(1)*
{F}(1)*
{F}(1)*
F1
G1
M1
F2
G2
M2
{f}(2)*
f3
{F}(2)*
g3
m3
f2
g2
m2
[T](2)
[T](2)T
[kl](2)
[kg](2) [T](2)T[kl](2)[T](2)
*
*
* * *
0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1
=
0 -4.6667 -700 0 4.6667 -700 0 1 0 0 0 0700 0 0 -700 0 0 -1 0 0 0 0 0
0 700 140000 0 -700 70000 0 0 1 0 0 00 4.6667 700 0 -4.6667 700 0 0 0 0 1 0
-700 0 0 700 0 0 0 0 0 -1 0 00 700 70000 0 -700 140000 0 0 0 0 0 17 8 9 4 5 6
=
4.6667 0 -700 -4.6667 0 -700 7
0 700 0 0 -700 0 8
-700 0 140000 700 0 70000 9
-4.6667 0 700 4.6667 0 700 4
0 -700 0 0 700 0 5
-700 0 70000 700 0 140000 6
Overall Stiffness Matriks
+ {F} = [K]{U}
1 2 3 4 5 6 7 8 9
+ =
269.163 201.12 -151.2 -269.16 -201.12 -151.2 0 0 0
201.116 151.85 201.6 -201.12 -151.85 201.6 0 0 0
-151.2 201.6 84000 151.2 -201.6 42000 0 0 0
-269.16 -201.12 151.2 273.83 201.12 851.20 -4.6667 0 700
-201.12 -151.85 -201.6 201.12 851.85 -201.60 0 -700 0
-151.2 201.6 42000 851.20 -201.60 224000 -700 0 70000
0 0 0 -4.6667 0 -700 4.66667 0 -700
0 0 0 0 -700 0 0 700 0
0 0 0 700 0 70000 -700 0 140000
0.3
+ =
269.163 201.12 -151.2 -269.16 -201.12 -151.2 0 0 0 0
-0.4 201.116 151.85 201.6 -201.12 -151.85 201.6 0 0 0 0
-41.67 -151.2 201.6 84000 151.2 -201.6 42000 0 0 0 0
0.3 -4 -269.16 -201.12 151.2 273.83 201.116 851.2 -4.667 0 700
-0.4 0 -201.12 -151.85 -201.6 201.116 851.845 -201.6 0 -700 0
41.67 500 -151.2 201.6 42000 851.2 -201.6 224000 -700 0 70000
0 0 0 0 -4.6667 0 -700 4.66667 0 -700 0
0 0 0 0 0 -700 0 0 700 0 0
0 0 0 0 700 0 70000 -700 0 140000 0
=
269.163 201.12 -151.2 -269.16 -201.12 -151.2 0 0 0 0
201.116 151.85 201.6 -201.12 -151.85 201.6 0 0 0 0
-151.2 201.6 84000 151.2 -201.6 42000 0 0 0 0-3.7 -269.16 -201.12 151.2 273.83 201.116 851.2 -4.6667 0 700 U2-0.4 -201.12 -151.85 -201.6 201.116 851.845 -201.6 0 -700 0 V2
541.67 -151.2 201.6 42000 851.2 -201.6 224000 -700 0 70000 θ2
0 0 0 -4.6667 0 -700 4.66667 0 -700 0
0 0 0 0 -700 0 0 700 0 0
0 0 0 700 0 70000 -700 0 140000 0
{F}*
F1 F1 U1
G1 G1 V1
M1 M1 θ1
F2 F2 U2
G2 G2 V2
M2 M2 θ2
F3 F3 U3
G3 G3 V3
M3 M3 θ3
F1
G1
M1
U2
V2
θ2
F3
G3
M3
F1+0.3
G1-0.4
M1-41.67
F3
G3
M3
*
Unknown Displacement
-3.7=
273.83 201.12 851.2 U2 U2=
273.83 201.12 851.2 -3.7-0.4 201.12 851.85 -201.6 V2 V2 201.116 851.85 -201.6 -0.4
541.67 851.2 -201.6 224000 θ2 θ2 851.2 -201.6 224000 541.67
U2=
0.00449 -0.001 0 -3.7V2 -0.0011 0.0014 0 -0.4θ2 0 0 0 541.67
U2=
-0.0259V2 0.00625θ2 0.00252
Unknown Reactions
=
-269.16 -201.12 -151.2
-201.12 -151.85 201.6 -0.0259
151.2 -201.6 42000 0.00625
-4.6667 0 -700 0.00252
0 -700 0
700 0 70000
+
0.3
=
5.34459
=
5.34459
-
0.3
-0.4 4.77708 4.77708 -0.4
-41.67 100.757 100.757 -41.67
0 -1.6446 -1.6446 0
0 -4.3771 -4.3771 0
0 158.405 158.405 0
=
5.044595.17708142.427-1.6446-4.3771158.405
Member ForceElemen I
+ =
+ =
0.8 0.6 0 0 0 0-0.6 0.8 0 0 0 0
0 0 1 0 0 0
0 0 0 0.8 0.6 0
0 0 0 -0.6 0.8 0
0 0 0 0 0 1
269.163 201.12 -151.2 -269.16 -201.12 -151.2
201.116 151.85 201.6 -201.12 -151.85 201.6
-151.2 201.6 84000 151.2 -201.6 42000
-269.16 -201.12 151.2 269.163 201.116 151.2
-201.12 -151.85 -201.6 201.116 151.845 -201.6
F1+0.3
G1-0.4
M1-41.67
F3
G3
M3
F1 F1
G1 G1
M1 M1
F3 F3
G3 G3
M3 M3
{f}(1)* {f}(1) [T](1) [kg](1) {U}(1)
f1 f1
g1 g1
m1 m1
f2 f2
g2 g2
m2 m2
U1
V1
θ1
U2
V2
-1
*
-151.2 201.6 42000 151.2 -201.6 84000
0
+ =
0.8 0.6 0 0 0 0
-0.5 -0.6 0.8 0 0 0 0
-41.67 0 0 1 0 0 0
0 0 0 0 0.8 0.6 0
-0.5 0 0 0 -0.6 0.8 0
41.67 0 0 0 0 0 1
269.163 201.12 -151.2 -269.16 -201.12 -151.2 0201.116 151.85 201.6 -201.12 -151.85 201.6 0
-151.2 201.6 84000 151.2 -201.6 42000 0-269.16 -201.12 151.2 269.163 201.116 151.2 -0.0259-201.12 -151.85 -201.6 201.116 151.845 -201.6 0.0063
-151.2 201.6 42000 151.2 -201.6 84000 0.0025
=
336 252 0 -336 -252 0 0-0.6048 0.8064 252 0.6048 -0.8064 252 0-151.2 201.6 84000 151.2 -201.6 42000 0-336 -252 0 336 252 0 -0.0259
0.6048 -0.8064 -252 -0.6048 0.8064 -252 0.00625-151.2 201.6 42000 151.2 -201.6 84000 0.00252
=
7.14192
-
0
=
7.14192
0.61491 -0.5 1.11491
100.757 -41.67 142.427
-7.1419 0 -7.1419
-0.6149 -0.5 -0.1149
206.697 41.67 165.027
Elemen 2
+ =
0
+ =
0 1 0 0 0 0
0 -1 0 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 0 1 0
0 0 0 0 -1 0 0
0 0 0 0 0 0 1
4.66667 0 -700 -4.6667 0 -700
0 700 0 0 -700 0
-700 0 140000 700 0 70000
-4.6667 0 700 4.66667 0 700
0 -700 0 0 700 0
-700 0 70000 700 0 140000
=
0 700 0 0 -700 0 -0.0259
-5 0 700 4.66667 0 700 0.00625
-700 0 140000 700 0 70000 0.00252
θ2
f1
g1
m1
f2
g2
m2
f1
g1
m1
f2
g2
m2
{f}(2)* {f}(2) [T](2) [kg](2) {U}(2)
f2
g2
m2
f3
g3
m3
U1
V1
θ1
U2
V2
θ2
f2
g2
m2
*
=0 -700 0 0 700 0 0
4.66667 0 -700 -4.6667 0 -700 0
-700 0 70000 700 0 140000 0
=
4.37708
1.88675
371.296
-4.3771
-1.8868
194.729
f3
g3
m3
f2
g2
m2
f3
g3
m3
###
###
###
###
###
###
###
###
###
