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Cantilevered Beam Stress Calculation

11/12/2017 7:34 AM

Hi folks,

I'm wondering if you can help me with a calculation please, I'm a bit out of my comfort zone. I'm trying to use the first formula found here to calculate stress at any given point on a cantilever but I'm a bit confused as to what 'z' is.

It's stated as being the distance from neutral axis to fibre edge, is that the distance from the support to the end of the beam? If so isn't that what v is? Or is it from whatever distance I choose x to be to the end of the beam?

Thanks in advance,

Darren

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#1

Re: Cantilevered beam stress calculation

11/12/2017 7:49 AM

If the beam is symmetrical, z is the distance from the center of the beam to either the top or bottom.

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#2
In reply to #1

Re: Cantilevered beam stress calculation

11/12/2017 9:05 AM

You sir have just made my day.

Thank you kindly :)

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#3
In reply to #2

Re: Cantilevered beam stress calculation

11/12/2017 11:29 AM

Are you certain that user is male?

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#4
In reply to #3

Re: Cantilevered beam stress calculation

11/12/2017 11:44 AM

Have you ever heard of a woman named Eugene before?

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#6
In reply to #3

Re: Cantilevered beam stress calculation

11/12/2017 3:09 PM

I am certain Tornado is male. So what do you say about that? Nothing? I figured as much. I, Mr. Tornado, and Darren don't need to hide behind a cloak of anonymity. So be gone!

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#10
In reply to #6

Re: Cantilevered beam stress calculation

11/14/2017 11:15 AM

At least he is not named: NewGene Ledbetter from Mississippi.

Those folks can git'-R-dun'! But there are often hours of stories related to the fall-out of the task, and who needed relief from whatever poor critter was caught treed with one of them (John) that always insisted on giving the poor animal a "fightin'" chance!

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#11
In reply to #10

Re: Cantilevered beam stress calculation

11/14/2017 11:27 PM

Uh-oh; I been busted. Next up, they'll call me beerbelly or potbelly or worse.

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#5

Re: Cantilevered Beam Stress Calculation

11/12/2017 2:37 PM

The definitions are given in the table in your link, so not clear what your problem is. For standard beams section modulus Z is tabulated, so you don't need to calculate it from I and z. z isn't usually given, but for a symmetrical beam it's 1/2 the beam depth.

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#7
In reply to #5

Re: Cantilevered Beam Stress Calculation

11/13/2017 5:44 AM

I did see the definitions, as I said what the definition of z was in my original post. My problem was that I just did not understand what it meant, I've never used that formula before and am not a mechanical engineer. You've given me the answer though at the end which is great so thank you.

There seems to be a whole lot of pointless comments here lads so let's leave it at that, the first reply to my post answered my question so it's all good.

Thanks!

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#8
In reply to #7

Re: Cantilevered Beam Stress Calculation

11/13/2017 6:45 AM

To follow on from AP#1's post #3, how can you be certain we're all lads?

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#9
In reply to #7

Re: Cantilevered Beam Stress Calculation

11/13/2017 7:54 PM

A decent Statics, and/or Strength-of-Materials, and/or structural-analysis textbook should have a adequate explanatory diagram that shows how the key to the concept is that (little z) is the (usually vertical) lateral distance from the neutral axis of the beam, in the plane of bending, perpendicularly out to the extreme edge of the beam, all relative to the same point along the longitudinal axis of the beam...

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#12
In reply to #9

Re: Cantilevered Beam Stress Calculation

11/16/2017 7:53 PM

Alternatively, go to:

https://www.engineeringtoolbox.com/section-modulus-conversion-d_1332.html

and see that, for your cantilever beam, ''little z'', in your website, is the distance from the origin (i.e.: the intersection of the x- and y-axis), and is, in this included website, upwards to the beam's top edge for tensile stress above the x-axis (i.e.: plus a/2), and downwards to the bottom edge for compressive stress below the x-axis (i.e.: minus a/2).

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