I was recently reminded of an Excel User Defined Function (UDF) that works in a similar way, written by Eng-Tips regular “electricpete”.  The original version of the UDF appeared here: http://www.eng-tips.com/viewthread.cfm?qid=281108

This is both a useful function in it’s own right and a good illustration of the use of the VBA ParamArray function argument.  The code is shown below, and is also included in a sample spreadsheet that may be downloaded from SwitchPY. The spreadsheet includes several examples of the UDF used to generate soil PY curves for use in the analysis of piles under lateral loads.

Function SW(ParamArray invar()) As Variant

' Original function posted by "electricpete" on Eng-Tips forum: http://www.eng-tips.com/viewthread.cfm?qid=281108 12 Sep 2010
' Minor modifications by Doug Jenkins 27 Jan 2012

' implement logic similar to switch
' example call
'  =switch(boolean1, value1, boolean2, value2, boolean3, value3....)
'    returns the value corresponding to the first true boolean

' at least one of the boolean expressions must be true
' requires an even number of arguments
' the syntax is pretty much identical to vba switch, except that there is no explicit allowance for else value
' if you want an else clause, enter true for the next to last argument, followed by the associated value

' Note that indexing of invar starts at 0, regardless of Option Base statement

' Check to confirm even number of arguments (as required)

    Dim ctr As Long        ' loop counter
Dim tempswitch As Variant        ' variable which will hold the output value

If UBound(invar) Mod 2 <> 1 Then
        SW = "Error: Need even number of arguments for sw"
        Exit Function
    End If

    ctr = 0        ' initialize counter
    Do While True        ' loop until broken by exit command
        ' Check for boolean input
If VarType(invar(ctr)) <> vbBoolean Then
            SW = "Error 1st 3rd 5th etc arguments of sw must be boolean"
            Exit Function
        End If

If invar(ctr) Then        ' in this case have found a true value, assign function and exit
tempswitch = invar(ctr + 1)
SW = tempswitch
            Exit Do
        Else        ' Else have not found true yet, update counter and continue loop
ctr = ctr + 2
        End If

' Check for reaching end of invar without having found true
If ctr + 1 > UBound(invar) Then
            SW = "Error: sw needs at least one true boolean argument"
            Exit Function
        End If
    Loop

End Function

An example of the use of the UDF is shown in the screenshot below:

Switch Function used to generate PY curves

In Column D the UDF is used to select between two values, which has no real advantage over the use of a single IF function:

Simple use of the Sw UDF

A more complex example is shown below:

Complex Sw() UDF example

In this example the first expression checks if the depth of the section (D12) is below a calculated transition level (D16), and if so it returns the adjacent value in Column D:

•  =sw($D$12>$D$16,D26,

The second statement checks if the pile deflection, B26, is less than 3 x the Y50 value (D15), and if so returns the adjacent value in Column D:

• B26<=3*$D$15,D26,

The third statement checks if the pile deflection, is greater than 15 x the Y50 value (D15), and if so returns a calculated value:

• B26>15*$D$15,$D$13*0.72*$D$12/$D$16,

Finally any remaining values are evaluated with a different formula:

•  TRUE,$D$13*0.72*(1-(1-$D$12/$D$16)*(B26-$D$15*3)/(12*$D$15)))

The UDF includes error checking to check that there are an even number of inputs, the first input in each pair evaluates as a boolean (i.e. TRUE or FALSE), and that at least one of the boolean expressions is TRUE.  The only change I have made is to the message return method if an error is found.  The original function used a message box, which I have changed to the function returning a text error message (to avoid getting a million message boxes if a function with an error was copied to a million cells).

See LatPilePY 1.02 for more details of the spreadsheet content and background.

Hawkesbury River Bridge from the North-West

The bridge over the Hawkesbury River near North Richmond, North-West of Sydney, is one of the first reinforced concrete structures in Australia.  At the time of its construction it was the largest reinforced concrete bridge in the country, and it remained so for 25 years.

Hawkesbury River Bridge location

The bridge is one of a few examples of the Monier arch system in New South Wales.  The system was developed by Joseph Monier and licenced in Australia to the firm Carter Gummow and Co. and later to the firm Monash and Anderson.  Most of the structures built in Australia are in Victoria, including the Anderson Street Bridge in Melbourne.  The history of the structures in Victoria has been well documented, and can be found at Monash & Anderson’s Monier Arch Bridges.

The North Richmond Bridge is documented by the NSW Government Office of Environment and Heritage.

The original structure consists of 13 arch spans, monolithic with heavy concrete piers, consisting of twin concrete caissons founded on rock, joined by a deep headstock with curved soffit.

Arch spans monolithic with concrete piers

Caissons with curved soffit headstock

The northern end of the bridge can be accessed from Hanna Park, immediately to the north, which has an access path under the bridge, the path providing excellent views of the bridge and along the Hawkesbury River in both directions.

Access track under the northern span.

Hawkesbury River, looking West towards Blue Mountains

In 1926 the bridge was widened with the addittion of an additional pier and two steel girders, supported on steel rocker bearings, to provide a rail line, which has since been removed and replaced with an additional road lane.

Additional steel girder supports for rail line

Steel girder bearings

Steel girder addition viewed from the South-East

The south end of the bridge is not so easily accessible, the banks being heavily overgrown with weeds.

View from South West bank

Historic Bridges plaque

View from North-West

The main change, as discussed in the Eng-Tips thread, is to the way in which the initial soil stiffness is calculated.  The soil stiffness is defined by a factor Ki which has units of Force/Length^3.  The previous version of the spreadsheet converted this factor to units of Force/unit deflection/unit length of pile by multiplying the Ki factor by the pile diameter (resulting in a factor independent of depth), whereas in COM624 the Ki factor is multiplied by the depth of the soil layer (resulting in a factor independent of pile diameter).  Both approaches clearly involve gross approximations, but to allow users to get a reasonable comparison with COM624 results I have now introduced an option to allow either method to be applied, with the COM624 method being the default (see screenshot below):

LatPile input; click for full sized view

Other significant changes are:
The calculation of the effective depth of layered soils has been amended to follow the COM624 method more closely.  Soil layers with varying strength and density affect the stiffness of lower layers in 3 ways:

1. Where the ultimate soil resistance is controlled by wedge failure the failure load is affected by all the layers through which the wedge passes.
2. Where the initial stiffness of a soil is related to the vertical pressure, this is affected by the density of the overlying soils.
3. For deeper layers, where the ultimate resistance is controlled by soil flow around the pile, the failure stress of granular soils is related to the vertical pressure.

For this reason two separate effective depths are calculated at the top of each layer:

1. The depth of soil, with the same properties as the layer, that would have the same ultimate resistance to wedge failure as the actual upper layers.
2. The depth of soil, with the same density as the layer, that would have the same vertical pressure as the actual upper layers.

These two effective depths are calculated by the program, but provision has also been made to specify override values in the Soil Properties Tables; see screenshot below:

Soil property input, including new optional effective depth rows

The other major change is that additional columns may (optionally) be added to the output array, providing details of the calculated effective depths, ultimate soil resistance, and calculated soil force/unit length of pile.

LatPile output options

LatPile output with Output Option 3 (11 columns)

The spreadsheet results have been compared with 3 examples from the COM624 manual (full details are included in the download file). The first example is for a single layer soil, and shows very good agreement in all respects:

COM624 Example 1

COM624 Example 1

The second example is for a layered soil with varying soil types and densities.  When user defined effective depths have been used reasonably good agreement was found:

COM624 Example 2; User defined effective depths

COM624 Example 2; User defined effective depths

Where the effective depth has been calculated by the spreadsheet the agreement was less good, but maximum bending moments and shear forces are within about 10%.  The reason for the difference seems to be that the spreadsheet calculates an effective depth based on density, whereas COM 624 uses the actual depth in these cases.

COM624 Example 2; spreadsheet calculated effective depths

COM624 Example 2; spreadsheet calculated effective depths

The Example 2 file  also compares the PY Curves generated by the spreadsheet with those given in the COM624 manual, finding excellent agreement:

PY curves for COM624 Manual Example 2

The final example is Example 4 from the COM624 manual, which uses 7 user input PY curves. In this case the COM624 program interpolates stiffness values between the curves above and below for each point down the pile, whereas the spreadsheet uses the values from the specified curve to apply to each layer. The spreadsheet input for this example is shown below:

Input for COM624 Example 4

In spite of the different method of application of the stiffness from the PY curves, the spreadsheet shows good agreement with the COM624 results:

Results for COM624 Manual Example 4

Results for COM624 Manual Example 4

(Click on Vimeo to visit site, or click play, then full screen button:

Family Tree by The Former Love from Kerinne Jenkins on Vimeo.

The result was three new User Defined Functions (UDFs), EqualT(), LTEqualT(), and GTEqualT().  The input and criteria for the new functions are shown in the screenshot below:

Floating Point comparison UDFs, click for full size view

The basis of the function is to find the value abs(a/b -1), where b is the lesser of the two values, and a is the greater.  Is this value is less than the specified tolerance then the two values are treted as being equal.  If the tolerance is not specified it defaults to 1E-14.

The use of a relative tolerance raises a problem if both numbers are very close to the minimum values allowed by the floating point number system.  For this reason the numbers are treated as being equal if the absolute value of the difference is less than a constant, MinReal, currently set to 1E-300.  The code for the EqualT function is shown below, anad all code is available in the download file: http://www.interactiveds.com.au/software/CombineArray.xls

Private Const MinReal As Double = 1E-300
Private Const DefaultTol As Double = 0.00000000000001
Function EqualT(Value1 As Variant, Value2 As Variant, Optional Tol As Double = DefaultTol) As Boolean
' Test if Value1 is equal to Value2 within Tol
    If Abs(Value1 - Value2)         EqualT = True
        Exit Function
    End If

    If DiffRatio(Value1, Value2) < Tol Then         EqualT = True     Else         EqualT = False     End If End Function Function DiffRatio(Value1 As Variant, Value2 As Variant) As Double Dim BVal As Double, TVal As Double     If Abs(Value1) > Abs(Value2) Then
        BVal = Value1
        TVal = Value2
    Else
        BVal = Value2
        TVal = Value1
    End If
    DiffRatio = Abs((TVal / BVal) - 1)

End Function

Finally, in a comment on the previous post Lori Miller provided an on-sheet solution that will combine multi-column arrays in the same way as the UDF, other than that the precision of the comparison is fixed. The formulas are included in the spreadsheet, and the output is shown, compared with the CombineArray function in the screenshot below:

CombineArray UDF and on-sheet functions

Note that the on sheet formulas return values a 5 from the first array, and just over 5 from the second, whereas for the UDF results the tolerance has been set high enough for these two values to be treated as equal.

Precious

In a dystopian future, two men meet in an underground tunnel for an exchange of stolen goods.

Liam lives in the stacks, making small black market deals and dreaming of getting out of the city walls. The natural world is a distant memory for those who live in the slums of the city and the passes out are restricted to those with money. Conrad is young, rich and brash and thinks he can buy anything he wants. To him the world is there for his taking and those who aren’t as well off as him are just lazy.

Conrad has promised Liam a way out of the city and a better status in life, middle class status. The upgrade will give him a clean room, a small pension and a cremation service. For this and the transport pass Liam manages to steal an item for Conrad that he has been coveting.

The exchange seems set to give both parties what they want until Liam realises that Conrad has only come through on part of his deal. Ignoring Liam’s desperation and actual needs leads to a heated situation and neither party will leave with what they came for.

Culling is at the AFTRS site.  You need to register (click on the AFTRS link to the left, then on the Register Now link at the AFTRS site), but this is free and gives you access to over 30 films.

Culling

Culling

*This film can only be viewed within Australia

In an irradiated subterranean future where the unproductive are marked for death, a young man faces a terrifying choice between his duty to his father and his feelings for the girl he is supposed to terminate.

I have now converted the function that performs the combination so that it can also be used as a User Defined Function (UDF) in a worksheet.  The result (including full open source code) may be downloaded from: http://www.interactiveds.com.au/software/CombineArray.xls

The function works with single column or multiple column arrays, exmples of which are shown in the screenshots below:

CombineArray documetation and input ranges

Output for single and twin column arrays

Note that CombineArray works as an array function, and must be entered with the correct procedure:

• Enter the function
• Select the entire output range, as shown shaded blue above
• Press F2 to enter Edit mode
• Press Ctrl-Shift-Enter to enter as an array function.

The revised spreadsheet (including full open source code) can be downloaded from:

Macaulay.zip

The screenshots below show an example (included in the download file) of a three span beam with spring supports and shear deflections included, compared with output from the Strand7 FEA program.  It can be seen that there is near exact agreement for both beam actions and deflections.

Conbeam function input, including shear stiffness

Part of Conbeam function output, compared with Strand7 (click for full size view)

Graphical output comparing ConBeam and Strand7 results

“It is a song, and a story, of a nation that dreams. Indigenous singer-songwriter Kev Carmody, who performed with the Australian Ballet Company, said it’s also about, “The beauty (and) ancientness of this majestic place … imagine what it was like 250 years ago, my friends, it would’ve been paradise”.
“It’s a coming together of cultures, people and disciplines.”

… and the original from Nick Cave:

For anyone interested in the lyrics and what they mean, skip the Youtube comments and have a look at:

http://www.songmeanings.net/songs/view/66401/