# Statics - Cantilever Beam

## Main Question or Discussion Point

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It's been a while since I've done a FBD, but I wanted to get someone's input here and tell me if my math/logic is correct. I want to install a cantilever steel beam with a 20 lb mass at the end of it. I'm using carbon steel ASTM A108 (cheapest steel on McMaster-carr). I plan on the cross section being 0.5" x 2". According to the math below, the beam should not fail correct? As long as the bending stress is lower than the yield stress we should be ok, correct? Is there something else I should take into consideration here?

Also, the mass on the end of the beam may be pull in direction coming out from the page. Would adding a truss feature help negate the stress in the beam, or is best option to use a thicker piece of material?

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PhanthomJay
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What's happening Form,
It's been a while since I've done a FBD, but I wanted to get someone's input here and tell me if my math/logic is correct. I want to install a cantilever steel beam with a 20 lb mass at the end of it. I'm using carbon steel ASTM A108 (cheapest steel on McMaster-carr). I plan on the cross section being 0.5" x 2". According to the math below, the beam should not fail correct? As long as the bending stress is lower than the yield stress we should be ok, correct? Is there something else I should take into consideration here?

Also, the mass on the end of the beam may be pull in direction coming out from the page. Would adding a truss feature help negate the stress in the beam, or is best option to use a thicker piece of material?

View attachment 196882
Don't forget to apply a safety factor when checking the actual stress against the yield stress, but your stress is very low according to your calculation which is correct, so the beam is theoretically more than adequate. In the other direction which is much weaker, the bending stress ,and deflection into the plane of the page, depends on what force into the plane of the page at the free end is applied. You don't give that info and calculation.

Don't forget to apply a safety factor when checking the actual stress against the yield stress, but your stress is very low according to your calculation which is correct, so the beam is theoretically more than adequate. In the other direction which is much weaker, the bending stress ,and deflection into the plane of the page, depends on what force into the plane of the page at the free end is applied. You don't give that info and calculation.
Thanks for your reply. As far as the force that will be applied (coming out of the page) I can't really provide too much info here. In reality I will be bolting a 20 Lb mass on the h side of this beam (at the end), so I perhaps need to take twisting stress into consideration as well. The mass will have an arm that can be extended so the operator will pull the arm (out of the page). Is there a better set up that I can design for this?

PhanthomJay
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Gold Member
Thanks for your reply. As far as the force that will be applied (coming out of the page) I can't really provide too much info here. In reality I will be bolting a 20 Lb mass on the h side of this beam (at the end), so I perhaps need to take twisting stress into consideration as well. The mass will have an arm that can be extended so the operator will pull the arm (out of the page). Is there a better set up that I can design for this?
If this is an actual project, I hesitate to reply because there are other factors to consider like fixed end connection design, bolt design, steel plate details, possible twisting, unknown sidewards load, etc. The plate is considerably weaker under the 'out of page' load than it is under the mass weight load, and will likely control the design. You may want to consider bracing it to the wall in that direction, and/or using a beam shape other than a plate.

If this is an actual project, I hesitate to reply because there are other factors to consider like fixed end connection design, bolt design, steel plate details, possible twisting, unknown sidewards load, etc. The plate is considerably weaker under the 'out of page' load than it is under the mass weight load, and will likely control the design. You may want to consider bracing it to the wall in that direction, and/or using a beam shape other than a plate.
I agree. There is no wall around the installation. I was hoping to bolt the cantilever beam to a vertical building support column (20 inches to the left) but, what I may now do is install a vertical column directly below my device, and brace that to the support column.

PhanthomJay
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I agree. There is no wall around the installation. I was hoping to bolt the cantilever beam to a vertical building support column (20 inches to the left) but, what I may now do is install a vertical column directly below my device, and brace that to the support column.
but the beam should be braced the other way due to the 'out
of page' unspecified load,.you might want to consider a stronger shape, like a piece of steel tubing

but the beam should be braced the other way due to the 'out
of page' unspecified load,.you might want to consider a stronger shape, like a piece of steel tubing
Yes we would use some type of tubing for the vertical section, not the 1/2 x 2" piece of steel. If needed, we could install 45o braces at the bottom of the vertical tube.