Simple beam strength analysis

[sfought]

I'd like to evaluate three supports to see what sort of load they can handle. Basically they are all 48" long with 4 bolts, one at each end and one 5" from each end, with a load hanging in the center. I'm not worried about the bolts as I can make them plenty strong enough, but I'd like to create a model of the 3 beam types and see what loads they would support on the 38" span between the two interior bolts. Here's a simple picture.

B---B-------------------|------------------B---B

B's are bolts and the vertical line represents the load.

Here are the support specifications:
1. 1.75" OD x .125" wall mild steel round tubing
2. 2" x 2" x .125" 6061-T6 Aluminum square tubing
3. 2" x 2" x .25" 6061-T6 Aluminum square tubing

Is there a simple program out there that will help me model this and determine the maximum load for each support type?

Thanks,
Shane

 

[MrStohler]

Please describe the connection of the member to the supporting elements. This connection could have a greater effect on capacity than the beam span.

If (and this is a big if) the connection is sufficient, your could consider each end to be a fixed connection. Under this assuption, the maximum bending moment(Mb) in the tube is: Mb=P*L/8, where P= applied load (what you intend to find) and L=38". To solve for P, set the allowable bending stress for each material to be equal to Mb/S (S=section modulus of tube under consideration)

Fb=(P*L/8)/S

You should find section moduli and allowable stresses in reference texts.

 

[sfought]

Thank you for the quick response. Assuming the ends are fixed do these calculations look correct?

---------------------------------
1.75" x 1/8" mild steel round tubing
Yield strength = 36,000psi
Section modulus = .24172 in^3

36000psi = (P * 38in / 8) / .24172 in^3
P = 1831.98lbs

-----------------------------------
2" x 2" x 1/8" 6061-T6 aluminum square tubing
Yield Strength = 40,000psi
Section modulus = .55176 in^3

40000psi = (P * 38in / 8) / .55176 in^3
P= 4646.4lbs

------------------------------------
2" x 2" x 1/4" 6061-T6 aluminum square tubing
Yield Strength = 40,000psi
Section modulus = .91146 in^3

40000psi = (P * 38in / 8) / .91146 in^3
P= 7675.45lbs

Thanks,
Shane

 

[desertfox]

Hi sfought

Stohler as given you the correct formula so there's no point
in saying anymore on that.I checked your calculation for the first tube and your spot on with your number crunching, but are you going to consider deflections of these tubes before deciding section and material and last but not least
what safety factor are you going to use for the final design?

 

[sfought]

There are existing systems using the 1.75" x 1/8" mild steel tubing. I wanted to make it out of aluminum in an effort to save weight and avoid corrosion, but I wasn't sure what size aluminum support would be up to the task. Thanks for all your help! It looks like the 2x2x1/8" aluminum will work well.

Thanks,
Shane

 

[MrStohler]

Please be aware that the values you calculated for P result in the maximum bending stress being equal to the yield stress. Allowble stresses are lower. But since you appear to be using the calculations to make a comparison between options the approach is reasonable (do not assume these tubes can safely carry the loads calculated).

As noted in my previous post. The connection of the tube to its support has a significant effect on the accuracy of these calculations. A "worst case senario" would result in a nearly simple span, resulting in a 50% loss in capacity.