How to determine side load for 4x4 metal pole?

[bobca1]

I need to be able to support a variable side load up to a maximum of about 250lbs at 10' high. I am planning on using a 14' 4x4 steel pole that will be anchored 4ft in the ground (with concrete).
Question I have will 4x4 square pole be good for this application, and would 1/4" thickness would be sufficient? Thicker sidewalls like 3/8 and 1/2" also available but that significantly increases cost and weight. Not really concerned about deflection, but I would not want it to be so much as to cause fatigue over time.
Is this straight forward to calculate based on the information above, or anyone aware of rule-of-thumb table somewhere online I can consult for poles?

 

[jack action]

You can model this as a cantilever beam with a single load at one end. There is a calculator here. In the calculator, you have to input the following:

E = 30 000 000 psi (for steel)
I = Area moment of inertia section properties (see other calculator below)
W = 250 lb (your load)
l = 120 in (distance between ground and load)
x = 0 in (distance from ground where the stress is the highest, which is at the ground)
neutral axis distance = Extreme point (see other calculator below)

For I and the neutral axis distance you can use this calculator. In the calculator, you have to input the following (select "Inch (in.)"):

a = 4 in (outside width)
b = outside width - 2 * thickness

The value of interest will be «Stress at specific point». This value is in psi. For a ¼" thick tube (b=3.5 in),the stress is 6818 psi. The yield strength of steel (i.e. the necessary stress to permanently deform the tube) is 53 700 psi for 1018 steel and 36 300 psi for A36 steel (1018 finish is smooth and shiny, A36 finish is rough).

Dividing the yield strength by the calculated stress will give you the safety factor. In this case, with 1018 you have a safety factor of 7.88 and with A36 you have 5.32.

Here, you have a source for common safety factors. Normally a safety factor of 4-6 should be good («Structural steelwork in buildings»). But the model and data I used are a crude approximation, your load will be varying (it is worst if it is an impact force), so I wouldn't feel comfortable recommending a minimum safety factor of 7. If life or costly equipment might be at risk, 10 would be even better.

This is as close as a rule of thumb you can have, but in the end, this is at your own risk.

 

[berkeman]

I need to be able to support a variable side load up to a maximum of about 250lbs at 10' high. I am planning on using a 14' 4x4 steel pole that will be anchored 4ft in the ground (with concrete).
Question I have will 4x4 square pole be good for this application, and would 1/4" thickness would be sufficient? Thicker sidewalls like 3/8 and 1/2" also available but that significantly increases cost and weight. Not really concerned about deflection, but I would not want it to be so much as to cause fatigue over time.
Is this straight forward to calculate based on the information above, or anyone aware of rule-of-thumb table somewhere online I can consult for poles?

Welcome to the PF.

What is the application? What is the source of the side load? There is a big difference between supporting a sign, and supporting a person...

 

[bobca1]

Thank you jack for the explanation and the calculators! At a local metal supplier I see a product listed as "hot rolled square tube ERW ASTM-A500 Grade B" and its available in both 1/4" thickness as well as 3/8". To compare products I plugged in 3/8" (b = 3.25"), I get a stress of 5,000 and a safety factor of 7.26. I assume that A500 is the tube equivalent of A36... that reasonable?

 

[jack action]

I assume that A500 is the tube equivalent of A36... that reasonable?

Why assume when you can check?

 

[bobca1]

According to Wikipedia definitive source for everything says grade B A500 shaped is 315 MPa.
(I converted to 45,687 psi).

 

[SteamKing]

I assume that A500 is the tube equivalent of A36... that reasonable?

No, it's not reasonable. That's why the material is identified as A500 instead of A36. Standards have different identifiers for a reason.