弯矩分类

边界条件

铰接

固接

立柱隆起 $M_{\delta }$

$M_{\delta 跨中}=\frac{3EI\delta }{{l^{\prime }}^2}=\frac{1}{2}P{l}^{\prime }$

$M_{\delta 端部}=0$

$M_{\delta 跨中}=\frac{6EI\delta }{{l^{\prime }}^2}=\frac{1}{4}P{l}^{\prime }$

$M_{\delta 端部}=-\frac{6EI\delta }{{l^{\prime }}^2}=-\frac{1}{4}P{l}^{\prime }$

自重荷载

$M_{g跨中}=\frac{q{l^{\prime }}^2}{8}$

$M_{g端部}=M_{g跨中}=\frac{q{l^{\prime }}^2}{24}$

轴力 $M_N$

$M_{N跨中}=N\delta$

$M_{N跨中}=N\delta$

总弯矩M

$M_{跨中}=\frac{3EI\delta }{{l^{\prime }}^2}+\frac{q{l^{\prime }}^2}{8}+N\delta$

$M_{端部}=0$

$M_{跨中}=\frac{6EI\delta }{{l^{\prime }}^2}+\frac{q{l^{\prime }}^2}{24}+N\delta$

$M_{端部}=-\frac{6EI\delta }{{l^{\prime }}^2}+\frac{q{l^{\prime }}^2}{24}$

竖向作用力P

$P=\frac{6EI\delta }{{l^{\prime }}^3}+\frac{5q{l}^{\prime }}{4}=2M_{\delta }/l^{\prime }+\frac{5q{l}^{\prime }}{4}$

$P=\frac{24EI\delta }{{l^{\prime }}^3}+q{l}^{\prime }=4M_{\delta }/l^{\prime }+q{l}^{\prime }$