alim almoite malang - matrix

20 KN/M

Length: Area: E:L1= 5000 mm A1= 3000 mm^2 E1= 200000L2= 5000 mm A2= 2500 mm^2 E2= 200000L3= 5000 mm A3= 3000 mm^2 E3= 200000

Angle radian cosine sineΘ1 = 90 degree 1.5707963267949 0.00 1Θ2 = 0 degree 0 1.00 0Θ3 = 270 degree 4.71238898038469 0.00 -1

Equivalent Nodal Loads for Each member:Member 1: W= 15 N/mm

0 0 1wL/2 37500 N 2

FM1= wL^2/12 31250000 N.mm 30 0 4

wL/2 37500 N 5wL^2/12 31250000 N.mm 6

Member 2: W= 20 N/mm0 0 4

- wL/2 -50000 N 5FM2= - wL^2/12 -41666666.6666667 N.mm 6

0 0 7 - wL/2 -50000 N 8

wL^2/12 41666666.6666667 N.mm 9

Member 3: W= 0 N/mm0 0 7

wL/2 0 N 8FM3= wL^2/12 0 N.mm 9

0 0 10wL/2 0 N 11

15KN

/M

wL^2/12 0 N.mm 12

REACTIONS:LEFT: VERTICAL 7.76E+03 N

HORIZONTAL -2.49E+04 NMOMENT -5.94E+07 N*mm

RIGHT: VERTICAL -7.76E+03 NHORIZONTAL 4.99E+04 NMOMENT -2.61E+06 N*mm

I:MPA I1: 225000000 mm^4MPA I2: 520833.333 mm^4MPA I3: 225000000 mm^4

member1:0.00 1.00 0.00 0.00

-1.00 0.00 0.00 0.00B1= 0.00 0.00 1.00 0.00

0.00 0.00 0.00 0.000.00 0.00 0.00 -1.000.00 0.00 0.00 0.00

AE/L= 120000 A= 4320B= 10800000

120000 0 0 -1200000 4320 10800000 0

K1= 0 10800000 36000000000 0-120000 0 0 120000

0 -4320 -10800000 00 10800000 18000000000 0

member2:1.00 0.00 0.00 0.000.00 1.00 0.00 0.00

B2= 0.00 0.00 1.00 0.000.00 0.00 0.00 1.000.00 0.00 0.00 0.000.00 0.00 0.00 0.00

AE/L= 100000A= 10B= 25000

100000 0 0 -1000000 10 25000 00 25000 83333333 0

K2= -100000 0 0 1000000 -10 -25000 00 25000 41666667 0

member3:0.00 -1.00 0.00 0.001.00 0.00 0.00 0.000.00 0.00 1.00 0.00

B3= 0.00 0.00 0.00 0.000.00 0.00 0.00 1.000.00 0.00 0.00 0.00

AE/l 120000 A= 4320B= 10800000

120000 0 0 -1200000 4320 10800000 00 10800000 36000000000 0

K3= -120000 0 0 1200000 -4320 -10800000 00 10800000 18000000000 0

Ft=Bt*FM

F1 = #VALUE! F1F2 = #VALUE! F2F3 = #VALUE! F3F4 = #VALUE! F4F5 = #VALUE! F5F6 = #VALUE! Fr^-1= F6

F7F4 = 0 F8F5 = -50000 F9F6 = -41666666.666667 F10F7 = 0 F11F8 = -50000 F12F9 = 41666666.666667

F7 = 0F8 = 0F9 = 0

F10 = 0F11 = 0

F12 = 0

20 KN/M

26612.4648N

50342.40947N

-121819060 N.mm

-10416666.67 N*mm

15KN

/M

-37500 N

-50000 N N

LEFT JOINT: -2.55E-110.00E+000.00E+00

RIGHT JOINT: 6.55E-110.00E+000.00E+00

0.00 0.000.00 0.000.00 0.00 B1t=1.00 0.000.00 0.000.00 1.00

C= 36000000000D= 18000000000

0 0-4320 10800000

-10800000 18000000000 Bt*K=0 0

4320 -10800000-10800000 36000000000

0.00 0.000.00 0.000.00 0.00 B2t=0.00 0.001.00 0.000.00 1.00

C= 83333333D= 41666667

0 0-10 25000

-25000 41666667 Bt*K=0 0

10 -25000-25000 83333333

0.00 0.000.00 0.000.00 0.00

-1.00 0.00 B3t=0.00 0.000.00 1.00

C= 36000000000D= 18000000000

0 0-4320 10800000

-10800000 18000000000 Bt*K=0 0

4320 -10800000-10800000 36000000000

= -37500= 2.297153353E-12 Ur=Kr^-1*Fr= 31250000= -37500 ?= -50000 ?= -10416666.666667 Ur ? == 0 ?= -50000 ?= 41666666.666667 ?= 0= 0 U4= 0 U5

U6 =U7U8U9

F=KU

F1F2F3F4F5F6 =F7

\ F8F9F10F11F12

=

20 KN/M

10887.5352 N

49657.59053 N

-95218892.69 N.mm

41666666.67 N*mm

20 KN/M

-4.66E-10 N

-50000 N

4:[email protected]

mailto:[email protected]

0.00 -1.00 0.00 0.00 0.001.00 0.00 0.00 0.00 0.00

0.00 1.00 0.00 0.000.00 0.00 0.00 -1.000.00 0.00 1.00 0.00

0.00 0.00 0.00 0.00 0.00

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

1.00 0.00 0.00 0.00 0.000.00 1.00 0.00 0.00 0.000.00 0.00 1.00 0.00 0.000.00 0.00 0.00 1.00 0.000.00 0.00 0.00 0.00 1.000.00 0.00 0.00 0.00 0.00

1.00E+05 0.00E+00 0.00E+00 -1.00E+05 0.00E+000.00E+00 1.00E+01 2.50E+04 0.00E+00 -1.00E+010.00E+00 2.50E+04 8.33E+07 0.00E+00 -2.50E+04

-1.00E+05 0.00E+00 0.00E+00 1.00E+05 0.00E+000.00E+00 -1.00E+01 -2.50E+04 0.00E+00 1.00E+010.00E+00 2.50E+04 4.17E+07 0.00E+00 -2.50E+04

0.00 1.00 0.00 0.00 0.00-1.00 0.00 0.00 0.00 0.000.00 0.00 1.00 0.00 0.000.00 0.00 0.00 0.00 1.000.00 0.00 0.00 -1.00 0.000.00 0.00 0.00 0.00 0.00

7.35E-12 4.32E+03 1.08E+07 -7.35E-12 -4.32E+03-1.20E+05 -7.94E-13 -1.98E-09 1.20E+05 7.94E-130.00E+00 1.08E+07 3.60E+10 0.00E+00 -1.08E+072.21E-11 -4.32E+03 -1.08E+07 -2.21E-11 4.32E+031.20E+05 7.94E-13 1.98E-09 -1.20E+05 -7.94E-130.00E+00 1.08E+07 1.80E+10 0.00E+00 -1.08E+07


#VALUE! mm#VALUE! mm#VALUE! mm#VALUE! mm#VALUE! mm#VALUE! mm

4.32E+03 7.09E-12 -1.08E+07 -4.32E+03 -7.09E-127.09E-12 1.20E+05 6.62E-10 -7.09E-12 -1.20E+05

-1.08E+07 6.62E-10 3.60E+10 1.08E+07 -6.62E-10-4.32E+03 -7.09E-12 1.08E+07 1.04E+05 7.09E-12-7.09E-12 -1.20E+05 -6.62E-10 7.09E-12 1.20E+05-1.08E+07 6.69E-10 1.80E+10 1.08E+07 2.50E+040.00E+00 0.00E+00 0.00E+00 -1.00E+05 0.00E+000.00E+00 0.00E+00 0.00E+00 0.00E+00 -1.00E+010.00E+00 0.00E+00 0.00E+00 0.00E+00 2.50E+040.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+000.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+000.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

#VALUE! N 1.00E+00#VALUE! N 2.00E+00#VALUE! N*mm 3.00E+00#VALUE! N 4.00E+00#VALUE! N 5.00E+00#VALUE! N*mm 6.00E+00#VALUE! N 7.00E+00#VALUE! N 8.00E+00#VALUE! N*mm 9.00E+00#VALUE! N 1.00E+01#VALUE! N 1.10E+01#VALUE! N*mm 1.20E+01

0.000.000.000.000.001.00

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! k= Bt*K*B= #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

1

0.000.000.000.000.001.00

0.00E+00 1.00E+052.50E+04 0.00E+004.17E+07 k= Bt*K*B= 0.00E+000.00E+00 -1.00E+05

-2.50E+04 0.00E+008.33E+07 0.00E+00

4

0.000.000.000.000.001.00

1.08E+07 4.32E+03-1.98E-09 -8.14E-121.80E+10 k= Bt*K*B= 1.08E+07

-1.08E+07 -4.32E+031.98E-09 8.14E-123.60E+10 1.08E+07

7

#VALUE! -37500#VALUE! -50000#VALUE! X -10416666.67#VALUE! 0#VALUE! -50000#VALUE! 41666666.67

-1.08E+07 0.00E+00 0.00E+00 0.00E+00 0.00E+006.69E-10 0.00E+00 0.00E+00 0.00E+00 0.00E+001.80E+10 0.00E+00 0.00E+00 0.00E+00 0.00E+001.08E+07 -1.00E+05 0.00E+00 0.00E+00 0.00E+002.50E+04 0.00E+00 -1.00E+01 2.50E+04 0.00E+003.61E+10 0.00E+00 -2.50E+04 4.17E+07 0.00E+000.00E+00 1.04E+05 -8.14E-12 1.08E+07 -4.32E+03

-2.50E+04 -8.14E-12 1.20E+05 -2.50E+04 -2.13E-114.17E+07 1.08E+07 -2.50E+04 3.61E+10 -1.08E+070.00E+00 -4.32E+03 -2.13E-11 -1.08E+07 4.32E+030.00E+00 8.14E-12 -1.20E+05 1.98E-09 2.13E-110.00E+00 1.08E+07 -1.98E-09 1.80E+10 -1.08E+07


2 3 4 5 6

0.00E+00 0.00E+00 -1.00E+05 0.00E+00 0.00E+001.00E+01 2.50E+04 0.00E+00 -1.00E+01 2.50E+042.50E+04 8.33E+07 0.00E+00 -2.50E+04 4.17E+070.00E+00 0.00E+00 1.00E+05 0.00E+00 0.00E+00

-1.00E+01 -2.50E+04 0.00E+00 1.00E+01 -2.50E+042.50E+04 4.17E+07 0.00E+00 -2.50E+04 8.33E+07

5 6 7 8 9

-8.14E-12 1.08E+07 -4.32E+03 8.14E-12 1.08E+071.20E+05 -1.98E-09 -2.13E-11 -1.20E+05 -1.98E-09-1.98E-09 3.60E+10 -1.08E+07 1.98E-09 1.80E+10-2.13E-11 -1.08E+07 4.32E+03 2.13E-11 -1.08E+07-1.20E+05 1.98E-09 2.13E-11 1.20E+05 1.98E-09-1.98E-09 1.80E+10 -1.08E+07 1.98E-09 3.60E+10

8 9 10 11 12

0.00E+00 0.00E+00 0.00E+000.00E+00 0.00E+00 0.00E+000.00E+00 0.00E+00 0.00E+000.00E+00 0.00E+00 #VALUE!0.00E+00 0.00E+00 #VALUE!0.00E+00 0.00E+00 X #VALUE!8.14E-12 1.08E+07 #VALUE!

-1.20E+05 -1.98E-09 #VALUE!1.98E-09 1.80E+10 #VALUE!2.13E-11 -1.08E+07 0.00E+001.20E+05 1.98E-09 0.00E+001.98E-09 3.60E+10 0.00E+00

1 U1= 0 U4=2 U2= 0 U5=3 U3= 0 U6=45 F1= ? F4=6 F2= ? F5=

F3= ? F6=

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

kr= #VALUE! #VALUE! #VALUE!-1.00E+05 0.00E+00 0.00E+000.00E+00 -1.00E+01 -2.50E+040.00E+00 2.50E+04 4.17E+07

4 5 6

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!4 kr^-1= #VALUE! #VALUE! #VALUE!5 #VALUE! #VALUE! #VALUE!6 #VALUE! #VALUE! #VALUE!7 #VALUE! #VALUE! #VALUE!89 U=(kr^-1)*F

U4 #VALUE! #VALUE!U5 #VALUE! #VALUE!U6 = #VALUE! #VALUE!U7 #VALUE! #VALUE!U8 #VALUE! #VALUE!U9 #VALUE! #VALUE!

U4 #VALUE!U5 #VALUE!U6 = #VALUE!U7 #VALUE!

7 U8 #VALUE!8 U9 #VALUE!9

10 Therefore: PM=[k]{U}-[FM]11 #VALUE! #VALUE!12 #VALUE! #VALUE!

PM1 = #VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

#VALUE! N#VALUE! N

= #VALUE! N*mm#VALUE! N#VALUE! N#VALUE! N*mm

1.00E+05 0.00E+000.00E+00 1.00E+01

PM2 = 0.00E+00 2.50E+04-1.00E+05 0.00E+000.00E+00 -1.00E+010.00E+00 2.50E+04

#VALUE! N#VALUE! N

= #VALUE! N*mm#VALUE! N

#VALUE! N#VALUE! N*mm

4.32E+03 -8.14E-12-8.14E-12 1.20E+05

PM3 = 1.08E+07 -1.98E-09-4.32E+03 -2.13E-11

8.14E-12 -1.20E+0510800000 -1.9847405E-09

7.76E+03 N-4.99E+04 N

= 4.14E+07 N*mm-7.76E+03 N4.99E+04 N

-2.61E+06 N*mm

? U7= ? U10=? U8= ? U11=? U9= ? U12=

0 F7= 0 F10=-12500 F8= -50000 F11=

-1.04E+07 F9= 4.17E+07 F12=

-1.00E+05 0.00E+00 0.00E+00 40.00E+00 -1.00E+01 2.50E+04 50.00E+00 -2.50E+04 4.17E+07 61.04E+05 -8.14E-12 1.08E+07 7-8.14E-12 1.20E+05 -2.50E+04 81.08E+07 -2.50E+04 3.61E+10 9

7 8 9

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! 0.00E+00#VALUE! #VALUE! #VALUE! #VALUE! -1.25E+04#VALUE! #VALUE! #VALUE! #VALUE! X -1.04E+07#VALUE! #VALUE! #VALUE! #VALUE! 0.00E+00#VALUE! #VALUE! #VALUE! #VALUE! -5.00E+04#VALUE! #VALUE! #VALUE! #VALUE! 4.17E+07

#VALUE! #VALUE! #VALUE! #VALUE! 0#VALUE! #VALUE! #VALUE! #VALUE! 0

#VALUE! #VALUE! #VALUE! #VALUE! X 0.00#VALUE! #VALUE! #VALUE! #VALUE! -4.24#VALUE! #VALUE! #VALUE! #VALUE! -0.10#VALUE! #VALUE! #VALUE! #VALUE! 0.00

123456

0.00E+00 -1.00E+05 0.00E+00 0.00E+00 #VALUE!2.50E+04 0.00E+00 -1.00E+01 2.50E+04 #VALUE!8.33E+07 0.00E+00 -2.50E+04 4.17E+07 X #VALUE!0.00E+00 1.00E+05 0.00E+00 0.00E+00 #VALUE!

-2.50E+04 0.00E+00 1.00E+01 -2.50E+04 #VALUE!4.17E+07 0.00E+00 -2.50E+04 8.33E+07 #VALUE!

4567

89

1.08E+07 -4.32E+03 8.14478693E-12 10800000 -4.32-1.98E-09 -2.13E-11 -120000 -1.9847405E-09 -0.423.60E+10 -1.08E+07 1.9847405E-09 18000000000 X 0.00

-1.08E+07 4.32E+03 2.1258776E-11 -10800000 01.98E-09 2.13E-11 120000 1.9847405E-09 0

18000000000 -10800000 1.9847405E-09 36000000000 0

789

101112

000

???

037500

- 312500000

3750031250000

0-50000

- -41666666.666670

-5000041666666.66667

00

- 0000

alim almoite malang - matrix

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