Accounting of eccentricity on pinned support?

[drile007]

I’m wondering how to correctly take into account the eccentricity in steel-beam and wood-column joint, which is modeled as pinned support. I’m sure that some eccentricity is present since the steel beam is “heavily” rotated at the ends. So, my question is basically: how to account beam rotation on supporting force eccentricity. How to obtain it?

Thanx for any reply

 

[ferrarialberto]

The beam rotation at the support is ql^3/(24EJ). The eccentricity of reaction and the distribution of stress in the column depend of support detailing.

Hi.

ing. FERRARI Alberto -

http://www.ferrarialberto.it

 

[dhengr]

That’s an interesting question and problem to be aware of, but probably not one to lose much sleep over, in most cases. That’s a good sketch (FBD) to help understand the potential problem. Imagine the possibilities: the carpenter used a square to draw the cut line, but the one blade was on a little knot, so the line is off by .5° and then he makes the cut freehand so now he’s off by .25 or .75°, and the darn bed on the saw was also leaning by .33°; the beam is cambered a bit so your sketch is bass-acwards; the column flexes (not buckles though) a bit under load, so its top conforms with the slope of the beam; in the immediate bearing area (your triangular brg. area) the column crushes a bit and then conforms; the column is made up of 4-2x6's all slightly different in length, darn carpenters.... Only you can resolve these kinds of questions for yourself, so do some calcs. to get an order of magnitude feel for the problem, and report back to us. What is the rotational angle and slope at the end of a properly designed stl. beam and how does that compare with the carpenter’s accuracy? Given that beam slope at the bearing, how much crushing (elastic shortening parallel to the grain) must (will) take place to pick up the reaction, so now what is “e”? Consider, that some of this kind of action is accounted for in our codes and design approach and formulas, adjustment factors and mat’l. grading, due to history and experience. This kind of thinking and exercise will help you develop a feel for when your concern is important. Certainly, there are conditions and details where “e” is obvious and important to consider.

 

[PicoStruc]

Why not using joint offset or length offset ? There are standard features in FEA Software !

 

[BAretired]

Probably the best assumption you could make would be to assume the top of column rotates to match the rotation of the simple span beam. So the column would be designed to resist the applied load plus the applied rotation, hence the applied moment at the top of column.

But as dhengr says, the framer could have cut the column out of square, so the safest assumption would be to assume an eccentricity of c/2 - b/2 where c is the column dimension and b is the width of bearing required to sustain the load.

Or, if you want to save a little time, assume the reaction occurs at the face of the column, giving an eccentricity of c/2. That would be conservative and good design practice in my humble opinion. You should never design wood columns too tight as the material properties are not very well known.

BA