An example of a 3 span Beam / Column Subframe analysis using matrix stiffness method.
Source of example given in the sm and pdf files.
A basic approach used in this exercise.
Sufficient explanatory notes added as far as possible.
Vectorize operator very helpful in arranging the results.

Cheers.

Worked_Ex_EC2_STIFFNESS_Method_FINAL.pdf (781 KiB) downloaded 255 time(s).
Worked_Ex_EC2_STIFFNESS_Method_FINAL.sm (653 KiB) downloaded 148 time(s).

Subframe Analysis by Stiffness method revisited.

The program in my previous post was based on the manual calculation of the Stiffness Matrix.
However, this method becomes tedious with changes on the number of spans, heights of upper columns not being same as that of lower columns. In some cases, columns from foundation to the first floor have different heights (Internal columns heights different to external columns).

With all these limitations, intention was to develop a set of common programs that will automatically:
1. Calculate the Stiffness Matrix.
2. For defined loading cases, calculate support moments, span moments, shear forces, column moments etc.
3. Also Draw BMD, SFD and Column moments for such loading cases.

With several attempts it was possible to achieve this goal, subject to final verification.
All the common programs (43 definitions) are in an external SMath file which could be accessed in any separate example file using SMath include() function. I think this is an easier approach.

This method was tested successfully on several examples involving 2 span and 3 span Substitute Frames.

The attached four (4) sm files (with sufficient explanatory notes) refer to a design example on following. I have done my best to minimize the file sizes. PDF files also included.

1. First floor (All lower columns pinned at foundation, with option to change to fixed condition). Also, heights of lower columns can be changed suitably.
2. Second and Third floors (All joints fixed).
3. Roof floor (All joints fixed).
4. Common definition file (43 definitions).

All above sm files must be in the same folder

Ref: Designed and detailed (BS 8110: 1997) by J.B. Higgins and B.R. Rogers, published by British Cement Association.

Include_Programs-R10.sm (118 KiB) downloaded 53 time(s).
Designed_Detailed_BS8110_Ex-R10-Roof-Simple.sm (525 KiB) downloaded 56 time(s).
Designed_Detailed_BS8110_Ex-R10-1st Floor-Simple.sm (550 KiB) downloaded 64 time(s).
Designed_Detailed_BS8110_Ex-R10-2nd+3rd Floor-Simple.sm (580 KiB) downloaded 57 time(s).

Include_Programs-R10.pdf (403 KiB) downloaded 55 time(s).
Designed_Detailed_BS8110_Ex-R10-1st Floor-Simple.pdf (699 KiB) downloaded 61 time(s).
Designed_Detailed_BS8110_Ex-R10-2nd+3rd Floor-Simple.pdf (734 KiB) downloaded 60 time(s).
Designed_Detailed_BS8110_Ex-R10-Roof-Simple.pdf (718 KiB) downloaded 63 time(s).