Program Correctness
Or, a known good…

How do we know the program is correct and produces a buildable working joist?

First of all, having created two joist programs already I’ve seen a lot of what can go wrong and right in a joist program. In writing the two previous programs I’ve learnt a great deal about what makes a good joist. I’ve also got all my original notes on how to design a joist, plus notes from a number of Engineers.

But that still isn’t enough.

One technique employed now, that didn’t exist years ago, is unit testing. For this program there are many unit tests. They get run whenever there are changes in the joist design. They quickly find issues with the code. Also ran are tests that can create 1000 or more different designs to check for errors.

Still lacking?

Well the definitive joist and analysis can be found in a great book for joist designers published by the Canadian Institute of Steel Construction called Steel Joist Facts… Recommended Practice Second Edition, published in 1990. Yes, out of date but still very useful. Amongst all the factual information in the Red Book they present a completely analyzed joist. Fortunately, the book covers Limit States Design, and despite all the changes in the building code the factorization for a joist with just a dead load and live load hasn’t changed. So here is their joist:

15000 mm design length
750 mm deep
10.8 kN/m dead load
6 kN/m live load

Below are the three main pages that describe the joist’s analysis:

Below is Briwood’s analysis of the exact same joist:

Right away you’ll notice some differences:

• Steel Joist Facts… presents their analysis vertically, Briwood presents it horizontally. So one has to map Briwood’s results to the results given in Steel Joist Facts… Presenting the analysis in a horizontal format, Briwood’s way, makes it quicker and easier to establish which panels have problems

• Steel Joist Facts… doesn’t use standard materials, they use metric sized angles and HSS that are unavailable in Canada for the most part

• Steel Joist Facts… didn’t state the thickness of the HSS sections they are using, hence Briwood’s program selected sections from the modern catalog

Let’s dig into this joist and see how Briwood’s analysis compares to Steel Joist Facts… We will start with the end panel of this Pratt Joist.

End Panel

The first diagram shows the forces on the joist. In the first panel a compressive force of 328 kN exists in the top chord, on Briwood’s analysis the equivalent information the section marked Top Chord Analysis, under the subheading Cf and Briwood indicates this force is 328.24 kN.

Force in the first panel’s tension rod indicates a tension of 362 kN, and the compression web member indicates 152 kN. Briwood analysis shows, in the section headed Web Analysis, subheading Vn (Vertical Normal shear) of 151.88 kN. To get the shear in the tension side of the panel we have to take the angle of the tension material into consideration, hence:

Panel Length: 1500 mm
Offset Length: 0 mm
Effective Depth: 693.82 mm
Vn: 151.88 kN

Length of Tension Member:

Angle of Tension Member:

Force in Tension Member:

The tension force matches the book value.

Moving on to the Steel Joist Facts top chord analysis. These values are given in kN•mm in the book and from Briwood’s analysis.

You’ll notice that the values differ a bit, but the pattern is identical. A number of reasons for this are:

• They could have done the moment distribution by hand, leading to lower accuracy as they only did a few passes

• They could have done it with an early program/calculator of some sort which had limited accuracy

• They cut off the internal two panels that are less than 610 mm long, thus altering the distribution

• Briwood’s code uses the moment distribution method

At the end panel the difference between SJF and Briwood is 0.55, which is pretty good.

Next in Steel Joist Facts they present the web analysis. They present all the values from the uniform distributed load analysis and the imaginary panel loads. According to the book’s calculations the shear force in the end panel is 151 kN, while Briwood gives 151.88 kN, hence they agree.

Next presented is the panel analysis of the top chord. Steel Joist Facts presents the values in a table that one must add the numbers up to see the results and if any point in the joist is overworked.

For the mid panel the Book gives the analysis results as:

Cf: 328
Cr: 839
Mf: 4040
Mr: 31300

Hence:

Briwood’s Analysis reports, in the section labeled Top Chord Analysis Cf/Cr, Mf/Mr and MP Tot for first panel at the mid panel point:

Which is fairly close to SJF analysis.

For the first panel’s panel point the book has:

Briwood’s analysis reports:

A difference of 0.1, with Briwood’s analysis being more conservative.

For the Mid Point analysis for panel 4 in SJF shows:

Briwood’s analysis indicates:

These two are identical.

The last thing we can compare is the tension force in the bottom chord, which the Red Book reports as being 912 kN and Briwood reports as being 912.07 kN.

This section of SJF also analyzes the web of the joist, which we can only do a partial comparision because we lack the exact dimensions of the HSS section used.

Since Briwood uses the Vn in analysis the conversion to Vn must be used:

Panel Length: 1000 mm

All other dimensions the same as the end panel.

Length of Tension Member:

Vn = 95.91 kN

Angle of Tension Member:

Force in Tension Member:

SJF indicates this force is 180 kN.

The selected HSS by Briwood in this panel is a 50.8 x 50.8 x 3.175 mm section which is likely to be larger then the one provided in the book.

For the compression side the same angle of SJF was used. This angle was a 55 x 35 x 4 mm, 300 MPa angle.

The angles capacity given by the Red Book is 113 kN, while Briwood reports 132.02 kN.

The difference between the book value and the value given by Briwood likely comes from Briwood calculating the angle’s properties, which the SJF likely used book values provided by the Handbook for Steel Construction or the angle manufacture’s specification sheets.