Beam Theory

#Physics

$\displaystyle E_{\text{bend}}=\frac{1}{2}K_{\text{eff}}\int_{0}^{L} \left\lvert \frac{\mathrm{d}\vec{t} }{ \mathrm{d}s} \right\rvert^{2} , \mathrm{d}s$

• Energy to bend a beam
• $\displaystyle K_{\text{eff}}=EI$
• $\displaystyle \vec{t}$ is the unit tangent
• $\displaystyle L$ is the length of the beam
• $\displaystyle \xi_{p}$ is the persistence length

$\displaystyle f\xi_{p}=\frac{z}{L}+\frac{1}{4\left( 1-\frac{z}{L} \right)^{2}}-\frac{1}{4}$

• $\displaystyle f$ is the force applied to the beam divided by $\displaystyle k_{B}T$
• $\displaystyle z$ is the extension length of the object
• $\displaystyle L$ is the length of the beam