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# Re: Multiple Yield Stresses

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Multiple Yield Stresses
• From: Daryl Richardson <h.d.richardson(--nospam--at)shaw.ca>
• Date: Tue, 24 Sep 2002 11:33:59 -0600

Zachary,

You can analyse this by assuming strain compatibility.  Sections that were "plane" before deformation remain "plane" after deformation.

What you do is set the strain at any two convenient points in the section (unless you want to consider bi-axial bending; then you must select three convenient points) then, using linear interpolation and extrapolation, you can determine the strain at all points in the section.  From E = stress/strain you can determine the stresses at all points and subsequently the axial force and bending moment for the section.  By repeating this a few times you can get a complete interaction diagram for your "new" column.

This is a very powerful analysis tool.  With it you can consider partial yielding of the section, limits on projecting elements in compression and a number of other complicating considerations.  It's also filled with a large number of relatively simple but time consuming calculations; you minimize calculations by being very careful in your selection of sections to analyse.  You can probably get it down to not more than five sections to analyse for bi-axial bending: zero bending; bending about each axis with zero axial load; and balance point about each axis.

This only considers strength of the section.  Stability, fatigue, and code considerations of any kind are not considered in my description of this analysis.

This answers your question, however, for your jib crane this may be more than you need.  I would suggest that you over design the crane column by at least 20% or 30%; it only wastes a small amount of material and it gives substantial protection against users overloading the thing.  I recently checked out a crane failure where a fab shop was using their 5 ton crane to lift dumpsters full of scrap steel; the cable broke and they dropped the load.  They decided to weigh the stuff and found that it weighed 11 tons!  They were lucky!  The supplier who sold them the crane had down rated something he had in stock at the time; all it cost them was some new wire rope, new wheels and bearings and some new components in their electric drive.

Regards,

H. Daryl Richardson

Zachary Goswick wrote:

Can anybody direct me to references on how to analyze steel members with multiple yield stresses?  For example, how to analyze a column that originally had 30 ksi steel, but was modified using 50 ksi steel?

Zachary Goswick, P.E.
Structural Engineer
Angus-Young Associates, Inc.
555 South River Street
Janesville, WI  53545-4827
Phone: (608)756-2326
Fax: (608)756-0464
Email: zachg(--nospam--at)angusyoung.com