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Ma Triks

This document contains information about matrix calculations. It includes the definition of matrices A, S, and K, where K is defined as the transpose of A multiplied by S multiplied by A. It then shows the calculation of the inverse of K multiplied by a force vector Q to determine displacement vector D. It also shows the calculation of the moment M using S multiplied by A multiplied by D, and compares the calculated moments to the input primer moments.

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Ainy
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29 views1 page

Ma Triks

This document contains information about matrix calculations. It includes the definition of matrices A, S, and K, where K is defined as the transpose of A multiplied by S multiplied by A. It then shows the calculation of the inverse of K multiplied by a force vector Q to determine displacement vector D. It also shows the calculation of the moment M using S multiplied by A multiplied by D, and compares the calculated moments to the input primer moments.

Uploaded by

Ainy
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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4 t 

1 t/m  1 t/m 
P .a .b 2 .q . L 2
M  M AB 
EI EI EI
AB
L2 12

6 m  6 m  6 m 

Matrik [A] Matrik [S] Matrik [S].[A]


d1 0 0 0 0.667 0.333 0 0 0 0 0.333 0.000 0.000 0.333 0.000 0.000
d2 1 0 0 0.333 0.667 0 0 0 0 0.667 0.000 0.000 0.667 0.000 0.000
d3 1 0 0 EI 0 0 0.667 0.333 0 0 0.667 0.333 0.000 0.667 0.333 0.000
d4 0 1 0 0 0 0.333 0.667 0 0 0.333 0.667 0.000 0.333 0.667 0.000
d5 0 1 0 0 0 0 0 0.667 0.333 0.000 0.667 0.333 0.000 0.667 0.333
d6 0 0 1 0 0 0 0 0.333 0.667 0.000 0.333 0.667 0.000 0.333 0.667
D1 D2 D3
Matrik [A]T Matrik [K] = [A]T . [S] . [A]  
0 1 1 0 0 0 1.333 0.333 0.000
0 0 0 1 1 0 0.333 1.333 0.333
0 0 0 0 0 1 0.000 0.333 0.667
D
K‐1 Q D=K‐1.Q
0.808 ‐0.231 0.115 0 0.3462

1 t/m 
D1 4 t  D2 1 t/m 
D3 ‐0.231 0.923 ‐0.462 . 0 = ‐1.385 1/EI
0.115 ‐0.462 1.731 3 5.1923

H=S.A.D Mprimer Makhir VER % Beda % Tepat


0.115 3 3.115 3.112 0.11 99.89
0.231 ‐3 ‐2.769 ‐2.774 ‐0.17 99.83
‐0.231 + 3 = 2.769 2.774 ‐0.17 99.83
M.Primer 3 ‐3 3 ‐3 3 ‐3 ‐0.808 ‐3 ‐3.808 ‐3.799 0.23 99.77
0.808 3 3.808 3.799 0.23 99.77
Q 0 0 3 3.000 ‐3 0.000 0 0 100.00
STAAD

3.112 MTon-m 2.774 MTon-m 3.799 MTon-m


0 MTon-m
-2.713 MTon-m

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