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I'm making metal frame to support a wooden deck.

The yellow object is the concrete base where there is a 2" trough where my metal frame needs to support a 300-500lbs deck load.

The span between the unsupported trough is 15'. The length of the cross brace is 22"

The red frame is 2" welded steel tubing. Wall thickness 1/8".

I understand 2" will have huge deflection at 15' unsupported span but will adding cross beam like this reduce this deflection to be acceptable to support a ground-level deck?

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user2727691
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2 Answers2

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No, it won't work. It won't even support it's own weight at that span. regardless of lateral support or cross bracing.

It is easy to calculate what size steel tubing you neef. I estimate it needs to be at least 10 by 3 inches.

kamran
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For HSS $2"$ x $2"$ x $1/8"$, $E = 29000 ksi, Ix = 0.486 in^4$

Assume uniformly distributed load. Let $w = 500 lbs/15 ft = 33.33 plf$, round up to $40 plf$ to include misc. weight.

$\Delta = 5*w*L^4/384*E*I = (5*40*15^4*12^3)/(2*384*29*10^6*0.486) = 1.616"$

$\Delta \approx L/111, NG(*)$

(*) Range of usual deflection limits:

  • Live Load: $L/180 - L/360$

  • Total Load: $L/120 - L/240$

As noted above, depending on the nature of the given load, the deflection limit varies. Since the deflection of your beam has exceeded the lowest limit, you need to determine a deflection limit according to the type of load, and that is suitable for your application.

(Note: Adding the cross bar does not add beam stiffness. You need a stronger beam)

As an example, assume $L/180$ governs, let's see what size of beam will satisfy it:

$I_{new} = I_{old}*(L/111)/(L/180) = 0.486*(180/111) = 0.788 in^4$

  • HSS $2"$ x $2"$ x $5/16", I = 0.815in^4, OK$

However, as the new tube is almost twice as heavy as the original tube, you need to re-check the deflection with the modified load.

Also, don't forget to check the flexural stress: $f_b = M/S <= 0.66fy$,

where $M = w*L^2/8$.

r13
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  • I of HSS 2x2x1/8 is 0.303 inch^4. – kamran May 02 '21 at 06:53
  • Double-check the moment of inertia. Depending on the radius of the corner and variation in the exact wall thickness, some producers may have a different value than that list on the AISC table. I got it from the AISC web table. – r13 May 02 '21 at 07:12
  • Note, if you are using cold-formed steel (which is not suggested), the properties will be very much different. – r13 May 02 '21 at 07:14
  • Thank you. Do you know where I can find a similar table for I beam to find the I value? – user2727691 May 02 '21 at 13:12
  • Based on this calculation, would it be better if I use a rectangular tube of 3" x 1" x 1/8" which weighs similar to 2x2 1/8 but has strong I value 0.817? On similar token, using I-beam/H-beam will even yield better weight to strength ratio, correct? Do you know where I can find similar chart for I beam? – user2727691 May 02 '21 at 13:20
  • Is supporting same load I-beam will be lighter than Rectangular tube?

    4x2x1/8 tube, 4.75lbs/ft, X-X axis I = 2.65 S3 x 5.7, 5.7lbs/ft, X-X axis I = 2.52

    Why is 4x2x1/8 tube better than s3x5.7 ibeam when it weighs less?

    Source: http://www.cim.mcgill.ca/~paul/HollowStruct.pdf https://amesweb.info/Profiles/Standard-Steel-I-Beam-Sizes-Chart.aspx

     – user2727691 May 02 '21 at 13:53
  • @user2727691 The link to the electronic steel shape table is attached at the end. For deeper beams, the S shape can be advantageous, but for so many crossbeams, the connections could be prohibitively costly. https://www.engineersedge.com/materials/aisc_structural_shapes/aisc_structural_shapes_viewer.htm – r13 May 02 '21 at 15:00
  • @user2727691 For your question about the advantages of tube vs S, I'll do comparisons on - (Wt/Ws) 4.75#/5.7# = 0.83; (It/Is) 2.65/2.52 = 1.052 ----> the tube weights less and is 5% stiffer than the S. Note stiffer means stronger and will deflect less, as I is in equations for both. – r13 May 02 '21 at 15:19
  • @r13, thank you! I'm also looking at 4"x2"x1/8" aluminum rec. tubing. Based on this db, I of alum. is 2.9762. Is this correct/possible that it is stiffer than same size steel. This looks wrong but I couldn't find aluminum I value to compare...

    source: https://mechanicalc.com/calculators/cross-sections/

     – user2727691 May 02 '21 at 19:21
  • @user 2727691 I couldn't find the information on aluminum rectangular tubing either. Just to note, the common alloys for structural use are 6061-T6 and 6063-T6, the yield strengths are 40 ksi and 31 ksi respectively (a little stronger or comparable with A36 structural steel), but the approximate E is 10.3x10^6 ksi is much less than that of steel, E = 29x10^6 ksi. So for the same span and loading, you will need a much deeper beam, as the resulting deflection will be much larger. Other than its lightweight, I don't see the advantages of aluminum over steel. – r13 May 02 '21 at 20:00
  • Actually, you shall compare the aluminum with the structural tube which is A500 steel grade B and C, the yield strengths are 46 ksi & 50 ksi respectively. E stays the same as before. – r13 May 02 '21 at 20:35
  • thank you @r13. You gave me a lot of great knowledge and formula to find the correct size for my project! I learned a lot. – user2727691 May 02 '21 at 21:13
  • You are welcome. Good luck and wish you do well. – r13 May 02 '21 at 22:26