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&[DATE] &[TIME] - &[FILENAME]

https://structville.com/2017/10/analysis-of-sub-frames-using-stiffness-method.html

H1 3 : H2 4 : L1 3.825 : L2 2.80 : L3 3.325 : 51 line

L 3.825 2.8 3.325 31 mat :

W 26.148 25.487 27.345 31 mat :

FEM 112 / W L 2^* vectorize * : 31.8801 16.6515 25.193 31 mat

The moment from unit rotation at any near end is given by 4EI/L and at far end is 2EI/L.
eg. 4 x 3.4 EI = 13.6 EI/L .
Also for example, if the upper column has lesser stiffness, we can have something like 0.75 EI for upper column, and 3.4 EI for beams.
If the beam is a T-beam with with a flange width of 1500 mm, and the columns are just 230x230 mm, you should expect a significant difference in their flectural rigidity.

Stiffness of Beam is 3.4 times that of columns

4 3.4 * 13.6

Case 1

EI is common to all, hence let EI = 1

ASDFASDFASDFASDF

EI 1 :

Symbolic optimization K 11 el 4 EI * H1 / 4 EI * H2 / + 13.6 EI * L1 / + : 5.8889 11 mat

θ 4 EI * H1 / 4 EI * H2 / 13.6 EI * L1 / 31 mat :

K 21 el 6.8 EI * L1 / : 5.8889 1.7778 21 mat

K 31 el 0 :

K 41 el 0 :

ST θ vectorize θ sum / : 0.2264 0.1698 0.6038 31 mat

Case 2

θ sum 5.8889

K 12 el 6.8 EI * L1 / : 5.89 1.78 1.78 0000042 mat

H1 3

H2 4

K 22 el 4 EI * H1 / 4 EI * H2 / + 13.6 EI * L1 / + 13.6 EI * L2 / + : 5.8889 1.7778 1.7778 10.746 000042 mat

K 32 el 6.8 EI * L2 / : 5.89 1.78 1.78 10.75 0 2.43 0042 mat

K 42 el 0 : 5.89 1.78 1.78 10.75 0 2.43 0042 mat

K 23 el 6.8 L2 / ≡

K 13 el 0 :

Above K 23 is wrong

L2 2.8

K 23 el 6.8 L2 / : 5.8889 1.7778 0 1.7778 10.746 2.4286 0 2.4286 000043 mat

6.8 L2 / 2.4286

K 33 el 4 EI * H1 / 4 EI * H2 / + 13.6 EI * L2 / + 13.6 EI * L3 / + : 5.8889 1.7778 0 1.7778 10.746 2.4286 0 2.4286 11.2807 00043 mat

K 43 el 6.8 EI * L3 / : 5.8889 1.7778 0 1.7778 10.746 2.4286 0 2.4286 11.2807 00 2.0451 43 mat

K 14 el 0 : 5.8889 1.7778 00 1.7778 10.746 2.4286 00 2.4286 11.2807 000 2.0451 044 mat

K 24 el 0 : 5.8889 1.7778 00 1.7778 10.746 2.4286 00 2.4286 11.2807 000 2.0451 044 mat

K 34 el 6.8 EI * L3 / : 5.8889 1.7778 00 1.7778 10.746 2.4286 00 2.4286 11.2807 2.0451 00 2.0451 044 mat

K 44 el 4 EI * H1 / 4 EI * H2 / + 13.6 EI * L3 / + : 5.8889 1.7778 00 1.7778 10.746 2.4286 00 2.4286 11.2807 2.0451 00 2.0451 6.4236 44 mat

W 26.15 25.49 27.34 31 mat

FEM 31.88 16.65 25.19 31 mat

FEM 2 el FEM 1 el - abs 15.23

MM FEM 1 el FEM 1 el - FEM 2 el + FEM 2 el - FEM 3 el + FEM - 3 el 41 mat : 31.8801 15.2286 - 8.5415 25.193 - 41 mat

Z F K 11 el Z 1 el * K 21 el Z 2 el * + K 31 el Z 3 el * + K 41 el Z 4 el * + MM 1 el ≡ K 21 el Z 1 el * K 22 el Z 2 el * + K 23 el Z 3 el * + K 24 el Z 4 el * + MM 2 el ≡ K 31 el Z 1 el * K 32 el Z 2 el * + K 33 el Z 3 el * + K 34 el Z 4 el * + MM 3 el ≡ K 41 el Z 1 el * K 42 el Z 2 el * + K 43 el Z 3 el * + K 44 el Z 4 el * + MM 4 el ≡ 41 mat :

Z.guess 111141 mat :

Stiffness Matrix

Z F Unknowns Z 11 mat

K 5.8889 1.7778 00 1.7778 10.746 2.4286 00 2.4286 11.2807 2.0451 00 2.0451 6.4236 44 mat

Method 1: Using "FindRoot" - Guess Value needed

Z F Z.guess FindRoot 6.3091 2.9662 - 2.2358 4.6338 - 41 mat

Method 2: Better - No guess value

ZZ K 1 -^MM * : 6.3091 2.9662 - 2.2358 4.6338 - 41 mat

K ZZ * MM ≡

Bottom Column Moments

M ZZ 24 / * : 3.1545 1.4831 - 1.1179 2.3169 - 41 mat

The moment from unit rotation at any near end is given by 4EI/L and at far end is 2EI/L. eg. 4 x 3.4 EI = 13.6 EI/L .