Paul Kelly and Joni Mitchell

Leading Australian singer-songwriter Paul Kelly is about to release a powerful new single that tackles Australia’s lack of action on climate change and environmental destruction.

Entitled Sleep, Australia, Sleep, Kelly says the song is both “a lament in the form of a lullaby” and “a critique of the widespread attitude among humans that we are the most important life form on the planet”. (From The Sydney Morning Herald).

50 years ago, Joni Mitchell had a similar message:

… which seems to support this comment:

How sad – all these years have passed and it’s still relevant. For an intelligent animal, we’re awfully slow learners.

Lyrics to Sleep Australia Sleep:

Sleep, Australia, sleep
The night is on the creep
Shut out the noise all around
Sleep, Australia, sleep
And dream of counting sheep
Jumping in fields coloured brown
Who’ll rock the cradle and cry?
Who’ll rock the cradle and cry?
Sleep, Australia, sleep
As off the cliff the kingdoms leap
Count them as they say goodbye
Count down the little things
The insects and birds
Count down the bigger things
The flocks and the herds
Count down our rivers
Our pastures and trees
But there’s no need to hurry
Oh, sleep now, don’t worry
‘Coz it’s only a matter of degrees
Fog, Australia, fog
Just like the boiling frog
As we go we won’t feel a thing

Who’ll rock the cradle and cry?
Who’ll rock the cradle and cry?
Sleep, my country, sleep
As off the cliff the kingdoms leap
Count them as they pass on by
Our children might know them
But their children will not
We won’t know ’til it’s gone
All the glory we’ve got
But there are more wonders coming
All new kinds of shows
With acid seas rising
To kiss coastal mountains
And big cyclones pounding
And firestorms devouring
And we’ll lose track of counting
As the corpses keep mounting
But hey, that’s just the way this old world goes
Sleep, my country, sleep
As we sow so shall we reap
Who’ll rock the cradle and cry?

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

Asymmetric Catenary Function

Back in 2009, I posted a user defined function (UDF) to generate a catenary curve, that could be used together with the Excel Solver to generate a curve of a specified span and sag:

A catenary function

Following a discussion at Eng-Tips (Chain catenary vertical reaction help ) I have updated the spreadsheet to allow different levels at each end, and to plot the full catenary.

The revised spreadsheet can be downloaded from:

Catenary.zip

To use the spreadsheet enter the total horizontal span, the required sag at each end, and an estimate of the span from the left hand support to the low point (“XEnd1”).  Then press the “Adjust A and XEnd1” button.  The solver will adjust the catenary sag and the position of the low point to generate the required sag from each end.  If nothing happens:

  1. Try adjusting the XEnd1 value, then click the left hand button, followed by the right.
  2. Make sure Solver is enabled.
  3. See the previous post
Posted in Coordinate Geometry, Curve fitting, Excel, Maths, Newton, UDFs, xlwings | Tagged , , , , | 1 Comment

Using Excel Solver from VBA

Using the “record macro” icon in Excel to record the solver process, I had a couple of problems:

  • When I tried to run the recorded macro, I got the message “Compile Error – Sub or Function not defined”.
  • When that was fixed the solver worked, but stopped on the final solver screen, rather than returning to the spreadsheet.

The solutions to these problems and many more are given in a detailed article by John Peltier:

Using Solver in Excel VBA

The end result of my work, including open source code, will be covered in my next post.

Posted in Excel, VBA | Tagged , , , , | 1 Comment

Column buckling under multiple loads

Following another buckling discussion at Eng-tips I have modified my Frame4-buckle spreadsheet to allow input of multiple axial loads at any point along the column, along with any number of sections with different section properties.  Background on the method used in the spreadsheet, and installation of the Alglib solver (if desired) can be found at: Buckling of columns with varying cross section and Using Frame4Buckle with the Alglib solver and the new spreadsheet (Frame4buckle-multiload.xlsb) can be downloaded from:

Frame4Buckle.zip

Input and results for a column with a top load and one intermediate load are shown in the screen-shots below:

End conditions input and results:

Section properties and loads input:

Note that for multiple loads the input allowing varying section properties must be used.  The cell E24 in the Constant Section input (“Number of Segments”) must be blank.

Any consistent units may be used.  In the example above lengths are in inches and force in kips.

The calculated buckled shape may be plotted:

The example shown above was taken from a spreadsheet published by Alex Tomanovich, available from: StepCol

This spreadsheet uses a different analysis method, but gives very close results for the column effective lengths:
L1 = 19.25 ft = 231 in. (compared with 230.8 in.)
L2 = 29.08 ft = 349 in. (compared with 348.6 in.)

Posted in AlgLib, Beam Bending, Excel, Finite Element Analysis, Frame Analysis, Newton, UDFs, VBA | Tagged , , , , , , , , , | Leave a comment

Trinity Bridge and Bridge of the Month

Bill Harvey has been doing a monthly report on historical bridges for many years, but recent issues have the added interest of interactive 3D models of the selected bridges.

The Trinity Bridge at Crowland in South Lincolnshire is an excellent example, being a very old stone arch bridge of unique design.  See the 3D model below, or go to Bridge of the Month No. 108 for the full report.

Posted in Arch structures, Historic Bridges, Newton | Tagged , , , | 1 Comment