Deflection Analysis of Beam-Column Joint

[JohnRalston]

I'm having a bit of an issue with the deflection of a beam column. I've attached an image to show the problem. Please note the following:

- Assume the beams and column are both circular hollow sections of diameter 76.1mm. Wall thickness 5mm.

- The joint of the beam and column can be assumed as translating moment i.e. it is not pinned.

- F1 and F2 are applied separately, not simultaneously. The aim of the problem is to establish the horizontal deflection under F2, and the tip deflection under F1.

My initial attempt at solving this assumed that the horizontal deflection is basically tip deflection of a cantilever beam i.e. no contribution from the beam. And that the tip deflection at F1 is essentially tip deflection of a cantilever fixed where the joint between the 2 is. This is clearly wrong, as I haven't accounted for the possible movement of the joint i.e. it is not entirely fixed in reality.

Any help would be greatly appreciated, I can't seem to find anything relevant in my textbooks.

John

 

[nvn]

JohnRalston: Could you label the points on your diagram (such as A, B, C, ...), so we know which point(s) you are referring to in your discussion in post 1? You can hit the Edit button, if you wish. Is this school work? Is it an exam question? I notice you deleted the homework template. No relevant equations are listed, and no solution attempt is shown. You must list relevant equations, and show a valid attempt; and then someone might check your math. Are you interested in buckling, or only tip deflection? And which tip(s), and which deflection(s)? Deflection of problems like this is covered in any Mechanics of Materials or Strength of Materials textbook. Are you sure you could not find it in these books, under beam deflection? Perhaps look for the word "superposition" in the index.

(1) By the way, always leave a space between a numeric value and its following unit symbol. E.g., 100 kN, not 100kN. See the international standard for writing units (ISO 31-0).