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Bending Feats

Vzearr

Vzearr

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Bending feats, I kick a pole and it bends, how would we calculate the energy behind this? Current calculations I see calculate it like this. It's not necessarily wrong, it's just unreliable because it assumes a constant force and ignores the nonlinearness of plastic bending. The old way uses a bending force calculator to estimate force, then multiplies that force by displacement to get work, i.e. Energy. Which is flawed, as explained above.

The goal of this thread is to install a method onto the calculations page.

This link will be important for the thread.
https://en.wikipedia.org/wiki/Section_modulus

Energy is given by:

{\displaystyle E=\int M,d\theta }

OR

The other formula I use. I used too many images.

Where the plastic moment for a hollow circular cylinder bar is:

{\displaystyle M_{p}=\sigma _{y}\cdot {\frac {D^{3}-d^{3}}{6}}}


Combining:

{\displaystyle E\approx \left(\sigma _{y}\cdot {\frac {D^{3}-d^{3}}{6}}\right)\theta }


This formula changes as per different shapes.

I suggest just adding it for cylindrical object cause like. What other feats bend... A rectangle.

The plastic moment for a non-hollow circular cylinder bar is:

From here since I can't use 20+ images.

Combining:

{\displaystyle E\approx \left(\sigma _{y}\cdot {\frac {d^{3}}{6}}\right)\theta }


Before yielding though, bending is elastic, so we've got to calculate that too. The energy stored in this region is given by:

{\displaystyle E_{\text{elastic}}=\int _{0}^{\theta _{y}}M,d\theta }


For elastic bending, the moment is equal to rotation in rad:

{\displaystyle M={\frac {EI}{L}}\theta }

Thus:

Removed an image.

{\displaystyle E_{\text{elastic}}={\frac {EI}{L}}\cdot {\frac {\theta _{y}^{2}}{2}}}

So:
{\displaystyle E_{\text{elastic}}={\frac {1}{2}}M_{y}\theta _{y}}


Where:

E = Young’s modulus


I = second moment of area

L = length of the bar

My = yield moment


The yield moment is given by:

{\displaystyle M_{y}=\sigma _{y}\cdot S}


Where:

S = elastic section modulus.

The plastic moment for a hollow circular cylinder bar is:

{\displaystyle S={\cfrac {\pi \left(r_{2}^{4}-r_{1}^{4}\right)}{4r_{2}}}={\cfrac {\pi (d_{2}^{4}-d_{1}^{4})}{32d_{2}}}}


Second moment of area:

{\displaystyle I={\frac {\pi (D^{4}-d^{4})}{64}}}



The elastic moment for a non-hollow circular cylinder bar is:
{\displaystyle S={\cfrac {\pi d^{3}}{32}}}

Second moment of area:

{\displaystyle I={\frac {\pi d^{4}}{64}}}

Rotation at yield is:
{\displaystyle \theta _{y}={\frac {M_{y}L}{EI}}}


Hollow final formula:
{\displaystyle E_{\text{elastic}}={\frac {\sigma _{y}^{2}\pi (D^{4}-d^{4})L}{32ED^{2}}}}

Solid final formula:
{\displaystyle E_{\text{elastic}}={\frac {\sigma _{y}^{2}\pi d^{2}L}{32E}}}

Final Formula:​

The total energy for a bending feat can be calculated as the sum of elastic and plastic contributions:

{\displaystyle E_{\text{total}}\approx {\frac {1}{2}}M_{y}\theta _{y}+M_{p}(\theta -\theta _{y})}


Where:

{\displaystyle E_{\text{total}}}
= Total energy

My = yield moment
0y = rotation at yield
Mp = fully plastic moment
0 = total rotation in radians


Solid Circular Bar​

{\displaystyle S={\frac {\pi d^{3}}{32}},\quad I={\frac {\pi d^{4}}{64}},\quad Z_{p}={\frac {d^{3}}{6}}}


Hollow Circular Bar​

{\displaystyle S={\frac {\pi (D^{4}-d^{4})}{32D}},\quad I={\frac {\pi (D^{4}-d^{4})}{64}},\quad Z_{p}={\frac {D^{3}-d^{3}}{6}}}


Holy dump?
 
24 hour bumps man
edit: you did this time but i mean prior
 
Before yielding though, bending is elastic, so we've got to calculate that too. The energy stored in this region is given by
Click to expand...
It's negligible compared to total work so calculating it is generaly not secessary. But the formulas you brought are correct nontheless
 
Ugarik said:
It's negligible compared to total work so calculating it is generaly not secessary. But the formulas you brought are correct nontheless
Click to expand...
OP has been permanently banned. Should i close the thread?
 
Sahlwrld said:
I think so, cause OP will never reply again.
Click to expand...
There have been cases where threads were concluded without the OP, depending on whether staff feel that something can be done here even in their absence.
 
Yeah, same here.

Bending or deformation feats in general have been bothering me, but I don't have the knowledge to say anything on this.

I've been very busy in real life, so I haven't had time to sit down and study.
 
Thank you very much for helping out. 🙏❤️
 
TheRustyOne said:
Bending or deformation feats in general have been bothering me, but I don't have the knowledge to say anything on this.
Click to expand...
yeah pretty much

More recently we've had guys using this and it's generally gotten more reasonable results than I've seen in the past and there was this one time I did this, though it felt less like a calc and more like an incoherent rant to go through (So imagine how pissed I was that there were better lifting strength feats to come...)
 
Last edited by a moderator:
A friendly reminder to be respectful and remain on topic.
Someone being banned does not give a free pass to demean them however you'd like.
(I had to edit something above if you're confused.)
 
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