Cantilever beam deflection

• 05-24-2016, 05:53 PM
PS2112
Cantilever beam deflection
I need to calculate the maximum beam deflection on a horizontal beam fixed at one end.

My beam is a round carbon fibre tube 80mm outside diameter and 74mm inside diameter. The tube is 2 metres long. At the free end is a weight of 5kg.

Please show me how to do this.
• 05-24-2016, 06:49 PM
Kelly Bramble
See: [B][URL="https://www.engineersedge.com/beam_calc_menu.shtml"]Beam Stress and Deflection Equations and Calculators[/URL][/B]
• 05-25-2016, 03:36 AM
Cake of Doom
As long as you know the E and I values (It can be worked out arithmetically), it's pretty straight forward from there.
• 05-25-2016, 10:32 AM
PS2112
Thanks, I have found the correct calculator and have requested the E value from the manufacturer. Sorry but I don't know how to arrive at an I value. I'm assuming it is related to the cross sectional area but confused by the unit mm^4. Please help.
• 05-25-2016, 11:11 AM
Kelly Bramble
See [B][URL="https://www.engineersedge.com/calculators/section_square_case_12.htm"]section properties round tube[/URL][/B]..

or
Section properties calculators and equations[/URL][/B]
• 05-25-2016, 11:52 AM
PS2112
Thank you, I'm beginning to see that Engineers Edge is very comprehensive and seems to have every possible resource :)

Right, I've got the I value sorted thanks. No email back from the manufacturer about the modulus of elasticity, and as it is past 5pm now, I won't get that till tomorrow. I'm eager to play with these figures tonight and hoping someone can provide me with a ball park figure to use for E on each size of tube. Then I can at least get some provisional deflections tonight. I'm hoping for a deflection well under a millimetre, but if it is a lot more will have to seriously reconsider my design and materials.

Thanks for all your help, as I have not found the need to work with such calculations since my college days nearly 40 years ago.
• 05-25-2016, 05:27 PM
PS2112
I have now found an E value on a different manufacturers website for a similar carbon fibre tube that allows me to use the calculator to make a reasonable estimate.

If my beam was pointing at a different angle from horizontal, say 45 degrees up, would I be correct in thinking that the deflection could be multiplied by the sine of the angle? So at 45 degrees the deflection would be...
sine (45) = 0.707 x (horizontal deflection)
• 05-25-2016, 06:54 PM
Kelly Bramble
[QUOTE=PS2112;12367]I have now found an E value on a different manufacturers website for a similar carbon fibre tube that allows me to use the calculator to make a reasonable estimate.

If my beam was pointing at a different angle from horizontal, say 45 degrees up, would I be correct in thinking that the deflection could be multiplied by the sine of the angle? So at 45 degrees the deflection would be...
sine (45) = 0.707 x (horizontal deflection)[/QUOTE]

No... See: [URL]https://www.engineersedge.com/beam_bending/combined-stress-1.htm[/URL]

or just scroll down and see all options...

• 05-26-2016, 02:58 AM
Cake of Doom
As Kelly points out: No. Members under loading act differently once angles become a factor.
• 05-26-2016, 08:24 AM
PS2112
Thanks, but I have looked through all the options and can't find a calculator that allows me to change the angle of the beam. Could you give me a link straight to it please.
• 05-26-2016, 08:54 AM
Kelly Bramble
[QUOTE=PS2112;12371]Thanks, but I have looked through all the options and can't find a calculator that allows me to change the angle of the beam. Could you give me a link straight to it please.[/QUOTE]

I think this is the one you're looking for...

[URL]https://www.engineersedge.com/beam_bending/combined-stress-1.htm[/URL]

[U][B]** Tilt your Head*** to the right....[/B][/U]
• 05-26-2016, 04:59 PM
PS2112
Thanks, but I'm not sure that is the one. My cantilevered beam will move from horizontal to vertical with the weight on the free end, and will be used at all angles in between. Will a simple trigonometric calculation not modify the deflection from that calculated in the horizontal position? When the beam is vertical, I would assume that there would be zero (measurable) deflection since the beam would be in compression not bending. When the beam is horizontal the deflection should be at its maximum.