A couple of return links to sites that have been sending traffic my way, and are well worth a look:

AJP Excel Information (Andy Pope’s site):

“The intention of this site is to be a useful resource of alternative solutions to the problems and limitations user encounter when using Microsoft® Excel.”

The Math Less Traveled

“Math? Beautiful? Yeah, right.

No fair, that’s not a question. But anyway, if you can’t understand how anyone could use the words “math” and “beautiful” in the same sentence, then I dare you to stick around a bit and see if you don’t change your mind. Math is about much more than figuring out when two trains will meet or calculating compound interest. Mathematics — like the hard sciences, but even more so — seeks to discover and understand the deep, elegant structure built into the very fabric of the universe. And it’s no surprise, really, that the deep mathematical structure of a universe featuring such things as clouds, crystal lattices, rainbows, galaxies, and atoms turns out to be beautiful. Personally, I see mathematics — and all beautiful structure in the universe — as evidence of a Creator at its source, but of course you can still appreciate it without sharing that belief.”

And finally a link to what is undoubtedly the most useful and comprehensive collection of Excel resources on the entire Internet (including the site run by Microsoft):

Pearson Software Consulting

At the Mr Excel discussion forum the output of the worksheet function Linest(), compared with chart trend lines raised a question, where it is said that in Excel 2007 the trend line gives different (and incorrect) coefficients for a polynomial curve constrained to pass through the origin, and that the R^2 values reported by the two methods are different.

I haven’t been able to reproduce the problem of different output from the trend line and Linest for the regression coefficients, but it is true that if the regression line is constrained to pass through the origin then the R^2 value (The coefficient of determination) is different in the trend line results and Linest (see screen shot below).  This is true both for polynomial results, as reported in the Mr Excel post, and for linear regression.

Chart Trend Line and Linest Output, Click to view full size

The Excel help is unhelpful in explaining this difference. More detail is given at the MSDN developer center, where the basis of the calculation of the R^2 value in Linest is described, but there is no explanation as to why the chart trend line gives different results, and I could find no other relevent discussion on the matter.

The clearest explanation I found was at the Curvefit.com site, where they had this to say, in relation to their own software:

“Why Prism doesn’t report r2 in constrained linear regression

Prism does not report r2 when you force the line through the origin (or any other point), because the calculations would be ambiguous. There are two ways to compute r2 when the regression line is constrained. As you saw in the previous section, r2 is computed by comparing the sum-of-squares from the regression line with the sum-of-squares from a model defined by the null hypothesis. With constrained regression, there are two possible null hypotheses. One is a horizontal line through the mean of all Y values. But this line doesn’t follow the constraint — it does not go through the origin. The other null hypothesis would be a horizontal line through the origin, far from most of the data.

Because r2 is ambiguous in constrained linear regression, Prism doesn’t report it. If you really want to know a value for r2, use nonlinear regression to fit your data to the equation Y=slope*X. Prism will report r2 defined the first way (comparing regression sum-of-squares to the sum-of-squares from a horizontal line at the mean Y value).”

Now it seems that the Excel Linest() function uses the second hypothesis for a constrained regression line, resulting in a higher R^2 value, compared with the unconstrained line. The chart trend line function on the other hand seems to use the first hypothesis.

This is confirmed in the calculation below:

It would have been nice if Microsoft could have explained that.

The examples shown above can be downloaded from: Linest Check.zip

The simplified reinforced concrete section analysis spreadsheet presented here has been revised to allow the input of a pre-tension stress to either or both layers of reinforcement.  The spreadsheet (including full open source code) can be downloaded from RC Design Functions3.

Note 26 Oct 2009: The version of Estress originally uploaded gave incorrect output for total force and bending moment when the neutral axis depth was below the bottom reinforcement.  A corrected version has now been uploaded and is dated 26 Oct 2009.

Note that this spreadsheet is intended for the analysis of rectangular beams or slabs with two layers of reinforcement.  For more complex sections refer to Reinforced Concrete Section Analysis – 5; Ultimate Limit State and Reinforced Concrete Section Analysis – 3.

In addition to the provision for prestressed reinforcement the revision also provides additional output data on section curvature, including analysis of tension stiffening effects and shrinkage according to the Eurocode EC2, and analysis of shrinkage curvature using a fictitious pre-compression stress applied to the reinforcement.  More details on these revisions will be given in a later post.

Typical Input and Output:

Estress input, including pre-stress

EStress Output

If in Excel 2007 you copy a range to the clipboard and paste into Word as a picture you get the worksheet gridlines displayed, which may well not be what you want.

This issue was raised at Smurf on Spreadsheets and has a fairly simple solution.

In their efforts to make all the Excel functionality intuitive and easy to access, Microsoft have placed a “Copy as Picture” command three levels down under the “Paste” button on the Home Tab.  The “Copy as Picture” command brings up a dialog box, which has the options “as shown on screen” and “as shown whan printed”, and an image copied as “as shown when printed” does not have the grid-lines.

Home - Paste - As Picture - Copy as Picture !

If you want to save the image as a separate file the easiest way to get a high quality emf (extended meta-file) image, without loss of image quality, seems to be to paste it into Powerpoint, and save it to a file from there.

Does anyone know a better way?

24th Oct 09:   See comments below for a link to a “Classic Menu” addin, available for trial or purchase.

I just found the Bend-it blog, which looks like it should be worth a good look:

Note 13 Oct 09:  See comment below.  This blog is temporarily closed whilst being reorganised, but contact the authors if interested.

This post is in response to recent discussions at Daily-Dose-of-Excel where many and various worksheet formulas have been suggested to carry out tasks that are (it seems to me) better done with a simple User Defined Function (UDF):

Adding Every Other Cell (also at the Microsoft Office Blog: Adding Every Other Cell in a Column )
and
Summing the Digits of a Number

My solutions to these, and also another at Eng-Tips: Transposing data from columns, can be dowloaded here: Sum Tab.xls

The spreadsheet includes full open source code as usual:

SumSkip Function

The SumSkip function will sum every n’th row or column of a range, starting from any specified cell.


Function SumSkip(SumRange As Variant, Optional NumSkip _As Long _
= 2, Optional StartCell As Long = 1, _
Optional DirSkip As String) As Double
Dim Numrows As Long, NumCols As Long, Sums As Double
Dim i As Long, j As Long, k As Long
If TypeName(SumRange) = "Range" Then SumRange = SumRange.Value2
Numrows = UBound(SumRange)
NumCols = UBound(SumRange, 2)
If DirSkip = "" Then
If Numrows > NumSkip Then
DirSkip = "V"
ElseIf NumCols > NumSkip Then
DirSkip = "H"
End If
End If
DirSkip = UCase(DirSkip)
Select Case DirSkip
Case Is = "V"
For i = StartCell To Numrows Step NumSkip
For j = 1 To NumCols
Sums = Sums + SumRange(i, j)
Next j
Next i
Case Is = "H"
For j = StartCell To NumCols Step NumSkip
For i = 1 To Numrows
Sums = Sums + SumRange(i, j)
Next i
Next j
End Select
SumSkip = Sums
End Function


SumDig Function

The SumDig function sums the digits of a value or string (either including or excluding values to the right of the decimal point).  I have incorporated the use of  a Byte array to extract the numeric characters without tripping over non-numeric characters, thanks to Charles Williams who provided a neat UDF in the DDoE thread using this technique.

Function SumDig(SumVal As String, _
Optional SumFract As Boolean = False) As Long
Dim NumDig As Long, i As Long, DPPos As Long, ByteA() As Byte
DPPos = InStr(1, SumVal, ".") * 2 - 1
ByteA = CStr(SumVal)
NumDig = Len(SumVal) * 2 - 1
If DPPos > 0 Then
For i = 0 To DPPos Step 2
SumDig = SumDig + Val(Chr(ByteA(i)))
Next i
If SumFract = True Then
For i = DPPos + 1 To NumDig Step 2
SumDig = SumDig + Val(Chr(ByteA(i)))
Next i
End If
Else
For i = 0 To NumDig Step 2
SumDig = SumDig + Val(Chr(ByteA(i)))
Next i
End If
End Function


Tabulate Function

The tabulate function creates a table based on row and column numbers and data listed in a 3 column range.  It was pointed out in the Eng-Tips thread that this could also be done with a pivot table, but the UDF solution seems simpler to me.

Does a straightforward UDF beat a convoluted worksheet function, or are UDFs best avoided?

What do you think?

I have (at long last) updated my list of publications (all downloadable). Click on the link below to visit the site, or download direct from the list here.

My Publications

Here is the current list:

I was recently sent a link to:

Geometric Tools Documentation

Which has a host of pdf files with detailed instructions on all manner of geometric calculations.  The focus of the site is animation for games programs, but there is plenty here of interest to engineers.

A small part of their listing is shown below (click for full size view):

This post presents an Excel User Defined Function (UDF) to carry out the analysis of vertical piles subject to horizontal loads, using the same approach as employed in the DOS program COM624. A spreadsheet including the UDF and an on-spreadsheet solution using the same method may be downloaded from LatPile.zip.  As usual the file contains full open source code for the UDF and associated routines.

Detailed background information on the method of analysis is given in the COM624 manual, which can be downloaded from the link given in the previous post.  An outline of the method, including all relevant equations used, is given below and in the download file, together with some simple examples.

The equations used in the analysis are shown in the screenshot below (click on any image for full size view):

LPile Finite Difference Equations

On the FinDiff sheet of the download file these equations have been entered into a 25×25 matrix, which with the MINVERSE() and MMULT() functions allows the equations to be solved and the deflections calculated for any pile with 20 segments:

Finite Difference Equations in Matrix Format

The same basic method of analysis has also been incorporated in a UDF, allowing the solution to be carried out much more conveniently and flexibly.  Input for the UDF is shown below:

LPile UDF

Example 1 is a 20 m long pile of uniform stiffness in a uniform soil:

UDF Input and Results; Example 1

Example 1 Bending Moments

Example 1 Shear Forces

Example 1 Deflections

Example 2 is a reinforced concrete pile with a cracking moment of 60 kNm in a soil with stiffness increasing with depth. The pile and soil stiffness values have been adjusted by hand in this case. Future versions of the program will allow input of non-linear soil and pile section stiffness.

Example 2 Input and Results

Example 2 Bending Moments

Example 2 Shear Forces

Example 2 Deflections

COM624 is a freeware DOS based program for the analysis of lateral loads on piles produced by the FHWA in the USA.  The program and documentation are available for free download, but are well hidden, so I’m posting links to the download sites here:

COM624 Program

COM624 Manual

In coming posts I will post an Excel based pile lateral load analysis program, based on the same principles as COM624.