I am trying to compute the deflection of a hollow tube of mild steel, and my computation seems to give radically different results than a couple of online calculators. Apparently one is in error.

The tube is 1.5" nominal Schedule 40, 100" long, with a point load of 100lb at the center. The formula for maximum deflection of a simple supported beam with point load at center is P*L^/48EI. For mild steel, E = 2.9e7. The tube has 1.9" OD and 1.61" ID, which gives its area moment of inertia as 0.310 in^4. Thus the maximum deflection is 0.23".

However, both these calculators:



give similar and much higher results of about 3.5". They appear to be using a factor of 3, instead of 48, in the denominator in the formula. This is correct for a cantilever beam with a point load at the end. But neither site suggests it's for a cantilever beam, making me wonder if there's something special about round tube beams that I do not understand.

  • 1
    $\begingroup$ Does either website indicate how the beam is constrained or loaded? Without those details, the website is useless. $\endgroup$
    – JohnHoltz
    Jul 24, 2022 at 17:05
  • $\begingroup$ @blacksmith37 Gonna be a vertical pipe. And 100 inches, not 100 feet. $\endgroup$ Jul 24, 2022 at 19:40
  • $\begingroup$ @JohnHoltz Good point. $\endgroup$ Jul 24, 2022 at 19:41

1 Answer 1


Your suspicion is correct. The deflection formula was noted below the first cal page. The second should be similar.

enter image description here

Similarly, below the second calculator:


MI for Solid Round Beams = (pi * (OD^4 - ID^4))/64

Deflection = (length^3 * force)/(3 * E * MI)

Bending Stress = (force * length) * (0.5 * height)/MI

  • $\begingroup$ So they meant it to be for a cantilevered beam, even though they didn't say so ? Lame. But 3.5" deflection seem pretty obviously wrong, just intuitively. $\endgroup$ Jul 24, 2022 at 19:42
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    $\begingroup$ Any calculator should list the formula, units, and explanation all of the parameters in the formula, otherwise, switch to other calculators that are well documented. $\endgroup$
    – r13
    Jul 24, 2022 at 19:59
  • $\begingroup$ I actually prefer my own calculator. A little spreadsheet with three sets of entries. One set is modulus of elasticity of various materials, one set is the moment of inertia of various cross-sections, and one is 4 cases (point and distributed loads for simple-supported and cantilevered). In each set, I check one entry. And I enter the length of the beam, and the load. Works for almost everything I do around the house and shop. But I like to check it against another calculator from time to time, and was disturbed when I got an order of magnitude larger deflection. $\endgroup$ Jul 24, 2022 at 22:16
  • $\begingroup$ Yes, it is a wise choice. $\endgroup$
    – r13
    Jul 24, 2022 at 23:23
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    $\begingroup$ Good note. I guess they mean the pipe wall is solid rather than perforated. $\endgroup$
    – r13
    Jul 25, 2022 at 2:38

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