In this case, we still are not able to determine the dimensions unless additional information is given.  In the case of a rectangle, we might be told that the base of the height has a specific value, or perhaps that the height is some multiple of the base.  Then we can complete the design. 

 

Recognize that these determined dimensions are minimums, that is, something larger is okay but not smaller.  So if we are asked to round to a particular fractional size, we always round up.

 

If we want to design the beam using a standard manufactured section such as a Wide Flange cross section, then we select the appropriate size from a table of standard sizes.  Appendix B of the textbook contains sample tables.  You will note that one column of the tables contains the section modulus.

 

When choosing the appropriate cross section, we will note that several sections may have S larger than our S_req.  First of all, we should only consider the section modulus for the x axis of the cross section which is larger and assumes the cross section is oriented as an I as opposed to the H orientation.  Next, we want to choose the most economical section.  Since steel is typically sold by weight, the best section will be the lightest one with S > S_req. 

 

Once we have determined the cross section dimensions, we must make sure that the shear stress is acceptable.  Using the selected cross section, we can calculate t_max and compare to t_allow for the material.  Most of the time, it will be okay.  If not, we will need to choose a larger section based on shear.

 

Generally, we also ignore the beam’s weight when designing a beam.  The reason for this is that the beam’s weight is normally quite small compared to the applied loads.  If we want to include the weight in the design, we have a problem that is iterative.  First, we design the beam ignoring the weight, then we can calculate the weight and include as a distributed load.  Next, we redesign the beam including the weight, but this can change the weight meaning that we have to repeat the process.

 

This iterative process can be cut short by choosing a cross section that is slightly larger than required or by rounding up.  Another approach is to increase the maximum moment by 5-10% at the beginning of the process to allow for the weight’s contribution.

Lecture #28, page 2                 Back