f(a) 공식

기본

• 넓이 A : $f(0)=\int dA$
• 1차 모멘트 Q : $f(y)=\int ydA$
• 2차 모멘트 I : $f(y^2)=\int y^{2}dA$

Axixally loaded Members

• $M_x=\int \sigma ydA$, $M_y=\int \sigma xdA$
• $\delta ={\int }_0^{L}d\delta ={\int }_0^L\frac{P_x}{E{A}_x}dx$
• $U=W={\int }_0^{\delta }Pd\delta ={\int }_0^L\frac{P_x^2}{E{A}_x}dx$

Torsion

• $I_p=\int {\rho }^{2}dA$
• $\varphi ={\int }_0^{L}d\varphi ={\int }_0^L\frac{T_x}{G{I}_{px}}dx$

Normal Stresses in Beams

• $M=\int {\sigma }_{x}ydA=-\kappa E\int y^{2}dA$
• $\tau =\frac{V}{Ib}\int ydA$