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I am considering a part of a steel column. A horizontal force of 5 kN is acting on the top part of the column. The distance from top to bottom is 500 mm. The distance between the two bolts in the bottom is 100 mm. I wish to find the pull force on the bolts (please see attached picture).

The moment in the bottom is M = 5 kN × 500 mm = 2500 kNmm.

As the force acts on the column there appears a pull-force on the bolts (we call it T).

If I take moment in one of the bolts then I have:

M = T × 100 mm, 2500 kN = T × 100 mm, T = 2500 kNmm / 100 mm, T=25 kN.

I have the following questions:

  1. Is the calculated moment of 2500 kNmm correct and where does is "act" specifically? In the bottom of the column, in the bolts?
  2. Is it correct to say that the above moment acts in the bottom of the column and therefore there is a pull-force on the bolts of 25 kN?
  3. Is there a pull-force on the left bolt and pressure-force on the right bolt?
  4. Since I am interested in the pull-force I can take the moment around the right bolt. Right?

(All measure are in mm)

Appreciate the help.

enter image description here

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2 Answers 2

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The moment calculation is correct, but without knowing the size and thickness of the base plate, it is no way to know the force in the anchor bolts, as there is compressive stress at the toe side of the base plate, that resists the moment, and renders the bolt ineffective (bolt is effective to resist tension only). Note in diagrams below, the distance between the force couple (T & C) varies.

Stress Diagram:

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  • $\begingroup$ I don't agree. The right bolt is just keeping it in place for other forces, The baseplate pressing on the base provides the force labeled "C" in your diagram. For problems like this, since we were giving no data about the base, we can assume it is infinitely strong so that is an appropriate place to use as a pivot. If we had more information, we could say the pivot is not at the right bolt but the right edge of the baseplate. The distance between the bolts is 100 mm and we have torque of (500-30)MM * 5KN so the force on the left bolt is 23.5 KN. $\endgroup$
    – user1683793
    Commented Mar 19, 2021 at 21:53
  • $\begingroup$ @1683793 Without information on the baseplate, you can assume anything, but does it serve the purpose? This is a "design" question, not typical mechanics, that's how I see the problem, thus the response. $\endgroup$
    – r13
    Commented Mar 19, 2021 at 22:07
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    $\begingroup$ For practical design, I suggest to review methods provided by the AISC DG 1, if you are in the US. $\endgroup$
    – r13
    Commented Mar 19, 2021 at 22:11
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1- Yes. It is correct.

2- Yes the above moment acts on the bottom of the column, but it also acts all along the length of the column $ M=5kN*H \quad \text{H= height from the base.} \ $ And it even acts beyond the embedment of the bolts into the concrete.

3- yes the left bolts are in tension. the torque they make with the right edge of the base plate compressive reaction counters the column's overturning moment.

4- Yes if you take the moment about the right bolt you get the approximate uplift force on the left bolt (s). You would need to allow for the complex forces of the base plate to be counted to get the exact result.

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  • $\begingroup$ For the sake of calculation, we will say the pivot is around the right bolt and 30 mm above the base. The torque at the pivot is (500mm-30mm) * 5 kN = 2350 NM. Since the bolts are 0.1 M apart, this works out to 23.5 kN on the left bolt. $\endgroup$
    – user1683793
    Commented Mar 19, 2021 at 21:41

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