Example Problems

Solution: The difficult part of this problem is in determining the location and magnitude of the internal forces. This is because of the varied loading on the span. Figure 8.8.4.1 shows the basic load diagram for the specified beam.

Figure 8.8.4.1
Beam Load Diagram

Each of the three uniform loads has a different tributary width, as shown in the tributary area diagram in the spreadsheet solution.

The structural analysis given in the spreadsheet is only one way to solve the problem. Use your structural analysis skills to verify the answer. The method shown is a modular method that uses superposition. The method has been developed and used by the author.

The controlling load cases are LRFD LC-2 and ASD LC-2 since the loading consists only of dead and live loads.

Once we have the shear, moment, and deflection data, we can proceed with selecting a section for each of the three cases. For all three parts to this problem a sorted property table list was used. In each case, the sections are sorted by weight or area. Starting with the lightest section, you then proceed up the list until you find the lightest section that works. You can experiment with this technique by selecting other sections in the pull down lists available in the grey shaded boxes. Try it!

Also found in the spreadsheet solution is a brute force solution to part (b) of the problem. In this case all the rectangular HSS sections are sorted in weight (or area) order, with the lightest section first. Moving down the list, the first section that satisfies the flexure criteria is the HSS14x14x3/16.

Note that this table only looks at the applicable flexure limit states. Deflection and shear should be checked as well, however, it will be found that for this particular problem that flexure is the controlling limit state. The main solution to the problem checks all the limit states.

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