Beam3 Portal

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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

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15

16

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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

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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

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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

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