Downloads update

A list of files available for free download can be found under the Downloads link at the top of the page:

The list has now been updated and there are now 189 files available for download, most with open source VBA and/or Python code.

The list is in Excel worksheet format, and can be displayed in full-screen view by clicking on the icon in the bottom-right corner:

The list can be sorted by any of the columns, and has hyperlinks to download the file (Column A) and to the latest blog post featuring the file (Column B):

Note that the linked blog posts also have download links, but those from early 2019 or before will often be in http: format (rather than https:), which will not work with modern browsers. In that case just return to the download list, where all the links should work.

Posted in Computing - general, Excel | Tagged , , , , , , | Leave a comment

A not so easy problem

A seemingly simple problem was posted in my Quora feed:

or to put it more mathematically, what three positive integers satisfy the equation:

It turns out the answer is not so simple. A full and detailed derivation can be found at:

Alon Amit

Checking the results is not so simple either. The values have up to 80 digits, which is way beyond the standard precision available in Excel, but using the Python mpmath library, with the EvalU spreadsheet, it can be done. Enter the three values as text (or copy and paste!), enter the formula, set the number of significant figures to 85 or more, and use the mp_Eval function:

Changing the last digit of one of the values confirms that the evaluation is working to the required precision:

The spreadsheet can be downloaded from:

For more details see: Pint MPmath and implied units

Posted in Excel, Link to Python, Maths, Newton, PyXLL, UDFs | Tagged , , , , | Leave a comment

Displaying You-tube transcripts

This is probably widely known, but I only found out this week.

I find You-tube informative videos frustrating because you have to sit through 10-20 minutes of video to get maybe 1-2 minutes worth of information. If only you could display a transcript of the spoken words!

Well it turns out you can:

Click on the three dots below the bottom right corner of the video, and select “show transcript”

… and the transcript is displayed to the right. You can then click on the three vertical dots to the top-right of the transcript and select toggle time-stamp.

You can then read the transcript on-line, or select and copy to a word-processor or text editor.

Here is the video featured above:

Posted in Bach, Newton | Tagged , | Leave a comment

ULS Design Functions 2.16

The ULS Design Spreadsheet has now been updated to Version 2.16, which can be downloaded from:

ULS Design Functions

The main new feature is the option to design for prestress loads applied to circular tanks. Due to axi-symmetric effects, when circumferential prestress is applied to a circular tank structure this generates a uniform axial stress across the cross section, in spite of the eccentric position of the prestress cables. This is handled by applying a virtual reaction moment, equal and opposite to the moment due to the eccentricity of the prestress. Use of this feature is illustrated in the screenshots below (click any image for full-size view):

If the “Adjust for circular tank loading” is set to “False”, or left blank, the section capacity is calculated in the usual way, allowing for the eccentricity of the prestress force:

If the option is set to True, the virtual moment is applied to the section, reducing the section capacity:

The correction for the circular tank effect is shown in the function output:

Posted in Beam Bending, Concrete, Excel, Newton, UDFs, VBA | Tagged , , , , , , , , | Leave a comment

Secondary moments in prestressed beams with FEA-2

Following the first post in this series, this post compares friction losses in prestressing cables as defined in the Australian Concrete Structures Code (AS 3600), compared with a cable modelled with contact elements in Strand7. The example used is based on the same three span beam used in the previous post (taken from the book Concrete Structures by Warner, Rangan, Hall and Faulkes), but the cable profile has been modified over the internal supports to provide a more realistic profile:

In the Strand7 analyses the prestress was applied by applying a strain preload to additional elements at each end of the cable, representing the stressing jacks. The strain was adjusted to generate a force of 1500 kN at each end of the cable.

Friction in AS 3600 is defined by:

As in the previous post, the friction curvature coefficient was taken as 0.2, and the wobble factor as 0.016.

In Strand7 the frictional behaviour of the contact elements is controlled by two factors:

  • The friction coefficient
  • The “sticking friction stiffness”: For Zero Gap and Normal Gap elements with non-zero coefficients of friction, the Sticking Friction Stiffness provides the lateral elastic connection between nodes until the point where the element slips in the lateral (frictional) direction; while the frictional force is below the current frictional capacity the lateral elastic stiffness is added.

There is little guidance on how the Strand7 sticking friction stiffness should be determined, and as far as I know, no guidance on how it relates to the AS 3600 “wobble factor”. A range of values have therefore been used, and the results of the Strand7 FEA and the AS 3600 formula compared.

The friction factor was initially varied between 0.2 and 0.3, with a constant sticking friction stiffness of 10,000 kN/m. The resulting tendon forces from one end to mid-length are shown below:

Over the first ten metres, where the cable profile had a low curvature, the AS 3600 formula gave slightly higher friction losses than the FEA with 0.3 friction factor, but over the remainder of the length all FEA results had higher friction losses and the friction factor of 0.2 was the best overall fit.

The analysis was then run with a friction factor of 0.2, and sticking friction stiffness values of 10,000 kN/m, 1000 kN/m, and 100 kN/m. The AS 3600 formula was checked with a wobble factor of 0.016 (Code 1) and 0.0 (Code 2):

All three of the FEA results are very close, up to 11.0 metres, where the 100 kN/m diverges to meet the Code 2 line. The other two lines remain very close over the full length, and are a good match with the Code 1 line from 14 metres onwards.

The above analyses were continued by reducing the strain in the jack elements by 5%, resulting in approximately 8 mm shortening of the elements, representing the loss of jack force due to lock off of the strands. In the graph below line 4a is the 10,000 kN/m line without the reduction in prestress:

Now all three runs with different sticking friction values have significantly different results over the full length. The effect of these differences on the bending moments in the beam will be examined in the next post in this series.

Posted in Beam Bending, Excel, Finite Element Analysis, Frame Analysis, Newton, Strand7 | Tagged , , , , , , | 1 Comment