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Continuous Beam Analysis
Analysis of a continuous beams or a continuous frame subject to distribut
Length 20.00 30.00 20.00
Theta 90.00 0.00 -90.00
Area 1.00 2.00 2.00
I 8.333E-02 1.667E-01 1.667E-01
E 20000000 20000000 20000000
Applied Loads
For distributed loads specify position of the start or the load, the load intensity at the start
For Point loads and moments specify the position and magnitude
Positions and load lengths are measured along the beam axis
Distributed and point load direction is either "X" (horizontal) or "Y" (vertical)
Beam No
Start Load/m start Load/m end Load Length
1 1 0 -20 -20 20
2 2 0 -30 -30 30
3 3 0 -30 -30 20
4 3
5 3
6
7
8
9
10
11
12
Enter 1 under End Fixity for restrained freedoms. End Actions and End Freedom numbe
Support No FX FY M FX
1 1 1 1 0
2 1
3 4
4 1 1 1 0
1 2 3
k_1 EA/L 1000000 1333333.333 2000000
k_2 12EI/L^3 2500 1481.481481 5000
End Fixity
Distributed Loads
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k_3 EI/L 83333.3333 111111.1111 166666.6667
k_4 6EI/L^2 25000 22222.22222 50000
c Cos() =(X2-X1)/L 0.0000 1.0000 0.0000
s Sin() =(Y2-Y1)/L 1.0000 0 -1
Stiffness matrix coefficients; Beam No
1 2 3 4 5
c2.k_1 + s
2.k_2 s.c.(k_1 - k_2) -s.k_4 -(c
2.k_1 + s
2.k_2) s.c.(-k_1 + k_2)
2 s2.k_1 + c
2.k_2 c.k_4 s.c.(-k_1 + k_2) -(s
2.k_1 + c
2.k_2)
3 4k_3 s.k_4 -c.k_4
4 Symmetrical c2.k_1 + s
2.k_2 s.c.(k_1 - k_2)
5 s2.k_1 + c
2.k_2
6
Beam Stiffness matrix; Beam No: 3
1 2 3 4 5
1 5.00E+03 -1.22E-10 5.00E+04 -5.00E+03 1.22E-10
2 -1.22E-10 2.00E+06 3.06E-12 1.22E-10 -2.00E+06
3 5.00E+04 3.06E-12 6.67E+05 -5.00E+04 -3.06E-12
4 -5.00E+03 1.22E-10 -5.00E+04 5.00E+03 -1.22E-10
5 1.22E-10 -2.00E+06 -3.06E-12 -1.22E-10 2.00E+06
6 5.00E+04 3.06E-12 3.33E+05 -5.00E+04 -3.06E-12
Deflection
Applied
Force Nett Force Reaction
FX1 0.0000000 -200.0 360.5 560.5
FY1 0.0000000 0.0 563.5 563.5
M1 0.0000000 666.7 -3484.0 -4150.6
FX2 -0.1296693 -200.0 -200.0 0.0
FY2 -0.0005635 -450.0 -450.0 0.0
M2 -0.0014534 -2916.7 -2916.7 0.0
FX3 -0.1297897 -480.0 -480.0 0.0
FY3 -0.0001682 -450.0 -450.0 0.0
M3 0.0065891 500.0 500.0 0.0
FX4 0.0000000 -480.0 319.5 799.5
FY4 0.0000000 0.0 336.5 336.5
M4 0.0000000 1750.0 -4293.1 -6043.1
FX5
FY5
M5
FX6
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FY6
M6
FX7
FY7
M7
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d loads, point loads and moments
Numbeams
m 3
degrees Angle of beam to X axis
m2 Cross Sectional Area
m4 2nd Moment of Area
kPa Young's Modulus
and end, and the load length
Direction X/Y Position Load Direction X/Y Position Moment FX1
X -200.00
Y 0.00
X 5 -120 X -480.00
10 -120 X 0.00
15 -120 X 0.00
0.00
s are calculated by the spreadsheet
FY M
0 0
2 3
5 6
0 0
4 5 6 Current Beam
2000000
5000
Moments
End Freedoms
Point
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166666.6667
50000
6.12574E-17
-1
6
-s.k_4
c.k_4
2k_3
s.k_4
-c.k_4
4k_3
6
5.00E+04
3.06E-12
3.33E+05
-5.00E+04
-3.06E-12
6.67E+05
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FY1 M1 FX2 FY2 M2
0.00 666.67 -200.00 0.00 -666.67
-450.00 -2250.00 0.00 -450.00 2250.00
0.00 -1750.00 -480.00 0.00 1750.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
End Actions
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Element Actions
1 -96.74 -15.45 -240.00 96.74
2 0.00 20.00 33.33 0.00
3 96.74 175.45 72.71 -96.74
4 7.12 207.99 -9.50 -7.12
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5 31.77 26.10 9.84 -31.77
6 -8.51 125.67 14.19 8.51
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15.45 54.58
-20.00 6.67
-175.45 145.42
-207.99 -18.99
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-26.10 19.68
-125.67 28.38
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Strand7 res
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0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
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Beam 1
Complete stiffness matrix Beam 2
1 2 3 4 5 6
1 2500 6.11043E-11 -25000 -2500 -6.11043E-11 -25000
2 6.11043E-11 1000000 1.53144E-12 -6.11043E-11 -1000000 1.53144E-12
3 -25000 1.53144E-12 333333.3333 25000 -1.53144E-12 166666.6667
4 -2500 -6.11043E-11 25000 1335833.333 6.11043E-11 250005 -6.11043E-11 -1000000 -1.53144E-12 6.11043E-11 1001481.481 22222.22222
6 -25000 1.53144E-12 166666.6667 25000 22222.22222 777777.7778
7 0 0 0 -1333333.333 0 0
8 0 0 0 0 -1481.481481 -22222.22222
9 0 0 0 0 22222.22222 222222.2222
10 0 0 0 0 0 0
11 0 0 0 0 0 0
12 0 0 0 0 0 0
13
14
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16
17
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7 8 9 10 11 12 13
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
-1333333.333 0 0 0 0 00 -1481.481481 22222.22222 0 0 0
0 -22222.22222 222222.2222 0 0 0
1338333.333 -1.22209E-10 50000 -5000 1.22209E-10 50000
-1.22209E-10 2001481.481 -22222.22222 1.22209E-10 -2000000 3.06E-12
50000 -22222.22222 1111111.111 -50000 -3.06287E-12 333333.3
-5000 1.22209E-10 -50000 5000 -1.22209E-10 -50000
1.22209E-10 -2000000 -3.06287E-12 -1.22209E-10 2000000 -3.1E-12
50000 3.06287E-12 333333.3333 -50000 -3.06287E-12 666666.7
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Stiffness matrix for active freedoms
1 2 3 4 5 6 7 8 9
1 1.34E+06 6.11E-11 2.50E+04 -1.33E+06 0.00E+00 0.00E+00
2 6.11E-11 1.00E+06 2.22E+04 0.00E+00 -1.48E+03 2.22E+04
3 2.50E+04 2.22E+04 7.78E+05 0.00E+00 -2.22E+04 2.22E+05
4 -1.33E+06 0.00E+00 0.00E+00 1.34E+06 -1.22E-10 5.00E+04
5 0.00E+00 -1.48E+03 -2.22E+04 -1.22E-10 2.00E+06 -2.22E+046 0.00E+00 2.22E+04 2.22E+05 5.00E+04 -2.22E+04 1.11E+06
7
8
9
10
11
12
13
14
15
16
17
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Inverted stiffness matrix
1 2 3 4 5 6 7 8 9
1 2.03E-04 2.76E-07 -4.16E-06 0.000202 -1.38E-07 -8.3E-06
2 2.76E-07 1.00E-06 -2.99E-08 2.76E-07 0 -2.6E-08
3 -4.16E-06 -2.99E-08 1.45E-06 -4.1E-06 1.49E-08 -1E-07
4 0.000202 2.76E-07 -4.1E-06 0.000203 -1.38E-07 -8.3E-06
5 -1.4E-07 1.15E-10 1.49E-08 -1.4E-07 5E-07 1.32E-086 -8.3E-06 -2.6E-08 -1E-07 -8.3E-06 1.32E-08 1.29E-06
7
8
9
10
11
12
13
14
15
16
17
18
19
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Force Deflection
-200 -0.12967
-450 -0.00056
-2916.67 -0.00145
-480 -0.12979
-450 -0.00017
500 0.006589