Tanh-Sinh Quadrature V2.1

Posted on 27/10/2011 by dougaj4

Graeme Dennes has released another update to his Tanh-Sinh Quadrature spreadsheet, which can be downloaded from:  Tanh-Sinh Quadrature (including, as usual, full open source code).  Here is Graeme’s description of the changes:

In Version 2.0, the nodes and weights array data for the Tanh-Sinh, DE and DE_OSC programs are calculated every time for every integration calculation.  Also as noted above, for each program, the nodes and weights are fixed, being independent of the function being integrated and the integration limits. Therefore, the nodes and weights need only be generated once, stored in an array, and made available for use by the three programs as required.

This has been done in Version 2.1, where the nodes and weights for the three programs are automatically pre-generated via calls to the array generation code in the three program modules. The (one-time) calls to the array generators are located in the Workbook_Open() Sub in the ThisWorkbook object, which is activated on opening of the workbook by Excel.

This improves the efficiency of the three programs.

The new version is in Excel 2007 format only.  The previous version including a copy in 2003 format can be downloaded from: Tanh-Sinh 2.0

Previous post on Tahn-Sinh Quadrature.

Posted in Excel, Newton, Numerical integration, UDFs, VBA | Tagged , , , , | 2 Comments

Equivalent Stress Blocks

Posted on 19/10/2011 by dougaj4

Previous posts (e.g. Stress blocks in AS 3600) have presented Excel User Defined Functions (UDFs) that determine the ultimate bending strength of a reinforced concrete section with the use of a rectangular concrete stress block, with depth and stress factors adjusted so that the results are identical to those using a parabolic-rectangular block, such as that defined in Eurocode 2.  This post provides details of this procedure, including VBA code for a UDF to calculate the required factors for any specified concrete strength.

The figure below (from Eurocode 2) illustrates how a non-linear stress-strain curve may be approximated by a rectangular stress block, applied over part of the area in compression.

Eurocode 2 Rectangular Stress Block

If the stress block is being used with a rectangular cross section it is possible to calculate values for the depth and stress such that the area under the block, and the lever arm from the neutral axis, are exactly equal to that for any specified curvilinear stress-strain relationship.

Parabolic and Equivalent Rectangular Blocks

The procedure for calculating the rectangular stress block equivalent to the Eurocode 2 parabolic/rectangular block is shown below :

Equivalent Rectangular Stress Block Procedure

This procedure can be simply coded in a VBA function (to use the function in your own spreadsheet, copy and paste the code into any VBA module):

Update 15 Aug 2020:
Wordpress was corrupting the the posted code, so I have uploaded a spreadsheet with full open-source code to:
EquivSB.zip

And this is what the function looks like in use:

Equivsb() Function

The function arguments are:

  • Fc: the concrete strength grade
  • Out (optional): 0 or omit to return the full array of output values
    -1 to return an array of descriptions of each output value
    1 to 5 to return a specified value
  • Rfact (optional): reduction factor on concrete stress (default = 0.9)

Enter as an array function to return the full array (see here for details of using array functions).

Posted in Beam Bending, Concrete, Excel, Newton, UDFs | Tagged , , , , , , , | 4 Comments

A Very Relaxing Post

Posted on 19/10/2011 by dougaj4

Another Bach installment, with (possibly) a splash of Newton:

Scientists discover most relaxing tune ever

A British band and a group of scientists have made the most relaxing tune in the history of man, an Mp3 of which is at the bottom of this article.

Sound therapists and Manchester band Marconi Union compiled the song. Scientists played it to 40 women and found it to be more effective at helping them relax than songs by Enya, Mozart and Coldplay.

Weightless works by using specific rhythms, tones, frequencies and intervals to relax the listener. A continuous rhythm of 60 BPM causes the brainwaves and heart rate to synchronise with the rhythm: a process known as ‘entrainment’. Low underlying bass tones relax the listener and a low whooshing sound with a trance-like quality takes the listener into an even deeper state of calm.  …

The “weightless” piece can be downloaded at the link.  Personally, I don’t think it was that relaxing compared with something more rythmic such “Falling” by Kate Rusby (as featured on Wonders of the Universe) , or even more so, this song from Anne Briggs:

Just rediscovered this one.  A beautiful song from Sandy Denny with Dave Swarbrick on fiddle, accompanied by some stunning photographs:

 

What do you think?

What is your favourite relaxation music?

Posted in Bach | Tagged , , | 1 Comment

Bert Jansch

Posted on 09/10/2011 by dougaj4

Regulars here will know my liking for the music of Bert Jansch and his contemporaries.  Bert died after a long illness last Wednesday, but leaves behind a rich legacy of music usually categorised as “folk”, but really beyond categorisation.

The 1992 BBC series “Acoustic Routes” documents the early days when the likes of Paul Simon and Bob Dylan were playing in Soho Pubs for “30 bob”:

Here are a small selection of pieces from Youtube, some well known, some less so, finishing up with one of his final performances at the Glastonbury Festival this year (only a fleeting glimpse of Bert, but the music’s the thing).

Posted in Bach | Tagged , , , , , , | 2 Comments

Spreadsheet Solutions For Structural Engineering

Posted on 07/10/2011 by dougaj4

Another site where the tasks considered suitable for programming in Excel and VBA are anything but “boring and repetitive” is Yakpol’s Spreadsheet Solutions For Structural Engineering:

“This web site contains a collection of engineering spreadsheets for structural analysis and design of concrete and steel structures. The programs have been developed by practicing professional engineers with emphasis on productivity, dependability, and clarity. To insure quality of the spreadsheets we have comprehensively compared analysis results to leading commercial software products and found them to be accurate.”

Those of you not into structural engineering may like to have a look at a few non-engineering applications, including:

Yakpol's Travelling Salesman Spreadsheet

Posted in Beam Bending, Excel, Newton, VBA | Tagged , , , | 2 Comments