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Matrices de rigidez de una estructura en mathcad
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Ee 1:= Ie 1:= Ke Ee Ie, xi, xf, ( ) L xf xi
K
12Ee Ie
L3
6Ee Ie
L2
12Ee Ie
L3
6Ee Ie
L2
6Ee Ie
L2
4Ee Ie
L
6Ee Ie
L2
2Ee Ie
L
12Ee Ie
L3
6Ee Ie
L2
12Ee Ie
L3
6Ee Ie
L2
6Ee Ie
L2
2Ee Ie
L
6Ee Ie
L2
4Ee Ie
L
:=
K1 Ke Ee Ie, 0, 18, ( )2.058 10 3
0.019
2.058 10 30.019
0.0190.222
0.0190.111
2.058 10 30.019
2.058 10 30.019
0.0190.111
0.0190.222
=:=
K2 Ke Ee Ie, 0, 18, ( )2.058 10 3
0.019
2.058 10 30.019
0.0190.222
0.0190.111
2.058 10 30.019
2.058 10 30.019
0.0190.111
0.0190.222
=:=
K3 Ke Ee Ie, 0, 18, ( )2.058 10 3
0.019
2.058 10 30.019
0.0190.222
0.0190.111
2.058 10 30.019
2.058 10 30.019
0.0190.111
0.0190.222
=:=
E1
1
234
:= E2
3456
:= E3
567
8
:=
n 1 4..:= p 1 4..:=
K3G 0 identity 8( ):= K2G 0 identity 8( ):=K1G 0 identity 8( ):=
K1GE1n
E1p,
K1n p,
:= K2GE2n
E2p,
K2n p,
:= K3GE3n
E3p,
K3n p,
:=
KG K1G K2G+ K3G+:=
KG
2.058 10 30.019
2.058 10 30.019
00
00
0.0190.222
0.0190.111
00
00
2.058 10 30.019
4.115 10 30
2.058 10 30.019
00
0.0190.111
00.444
0.0190.111
00
00
2.058 10 30.019
4.115 10 30
2.058 10 30.019
00
0.0190.111
00.444
0.0190.111
00
00
2.058 10 30.019
2.058 10 30.019
00
00
0.0190.111
0.0190.222
=
f stack augment submatrix KG 4, 4, 4, 4, ( ) submatrix KG 4, 4, 6, 6, ( ), ( ) augment submatrix KG 6, 6, 4, 4, ( ) submatrix KG 6, 6, 6, 6, ( ), ( ), ( ):= fem 8140.5
:=
f0.4440.111
0.1110.444
=
2
3
f 1 fem218.7145.8
=:=
v23m2
v32m3
K2
02
03
1.3532.41.358.1
=:=
v12
m1
v21m2
K1
0002
27812781
+
31.05105.322.95
32.4
=:=
v34m3v43m4
K3
0300
13.540.513.540.5
+
10.88.1
16.256.7
=:=