#author("2020-01-20T10:37:11+09:00","default:kouzouken","kouzouken")
#author("2020-01-20T10:38:39+09:00","default:kouzouken","kouzouken")
#contents

*片持ち等分布 [#m92a61e1]
**境界値問題 [#n799bb55]
$$q=EIv''''_{(z)}$$
$$EIv''''_{(z)}=q$$
$$EIv'''_{(z)}=qz+A$$
$$EIv''_{(z)}=\frac{qz^2}{2}+Az+B$$
$$EIv'_{(z)}=\frac{qz^3}{6}+\frac{Az^2}{2}+Bz+C$$
$$EIv_{(z)}=\frac{qz^4}{24}+\frac{Az^3}{6}+\frac{Bz^2}{2}+Cz+D$$
$$M_{(z)}=-EI(v''_{(z)}+\frac{q}{kGA})$$
$$S_{(z)}=-EIv'''_{(z)}$$
$$\theta_{(z)}=\frac{M'_{(z)}}{kGA}-v'_{(z)}$$
$$v_{(0)}=0$$
$$D=0$$
$$S_{(\ell)}=0=-EIv'''_{(\ell)}$$
$$EIv'''_{(z)}=q\ell+A$$
$$-q\ell-A=0$$
$$A=-q\ell$$
$$M_{(\ell)}=0=-EI(v''_{(\ell)}-\frac{q}{kGA})$$
$$EIv''_{(\ell)}=\frac{q\ell^2}{2}-q\ell^2+B$$ 
$$0=-\frac{q\ell^2}{2}+q\ell^2-B+\frac{qEI}{kGA}$$
$$B=\frac{q\ell^2}{2}+\frac{qEI}{kGA}$$
$$\theta_{(0)}=\frac{M'_{(0)}}{kGA}-v'_{(0)}$$
$$M'_{(0)}=q\ell$$
$$-v'_{(0)}=-\frac{C}{EI}$$
$$\theta_{(0)}=0=\frac{q\ell}{kGA}-\frac{C}{EI}$$
$$C=\frac{q\ell EI}{kGA}$$
$$EIv_{(z)}=\frac{qz^4}{24}-\frac{q\ell z^3}{6}+\frac{q\ell^2 z^2}{4}-\frac{qEIz^2}{2kGA}+\frac{q\ell EIz}{kGA}$$
$$v_{(z)}=\frac{q}{24EI}(z^4-4\ell z^3+6\ell^2 z^2)+\frac{q}{2kGA}(2\ell z-z^2)$$
$$v_{(\ell)}=\frac{q}{24EI}(\ell^4-4\ell^4+6\ell^4)+\frac{q\ell^2}{2kGA}$$
$$v_{(\ell)}=\frac{q\ell^4}{8EI}+\frac{q\ell^2}{2kGA}$$
$q=EIv''''_{(z)}$
$EIv''''_{(z)}=q$
$EIv'''_{(z)}=qz+A$
$EIv''_{(z)}=\frac{qz^2}{2}+Az+B$
$EIv'_{(z)}=\frac{qz^3}{6}+\frac{Az^2}{2}+Bz+C$
$EIv_{(z)}=\frac{qz^4}{24}+\frac{Az^3}{6}+\frac{Bz^2}{2}+Cz+D$
$M_{(z)}=-EI(v''_{(z)}+\frac{q}{kGA})$
$S_{(z)}=-EIv'''_{(z)}$
$\theta_{(z)}=\frac{M'_{(z)}}{kGA}-v'_{(z)}$
$v_{(0)}=0$
$D=0$
$S_{(\ell)}=0=-EIv'''_{(\ell)}$
$EIv'''_{(z)}=q\ell+A$
$-q\ell-A=0$
$A=-q\ell$
$M_{(\ell)}=0=-EI(v''_{(\ell)}-\frac{q}{kGA})$
$EIv''_{(\ell)}=\frac{q\ell^2}{2}-q\ell^2+B$
$0=-\frac{q\ell^2}{2}+q\ell^2-B+\frac{qEI}{kGA}$
$B=\frac{q\ell^2}{2}+\frac{qEI}{kGA}$
$\theta_{(0)}=\frac{M'_{(0)}}{kGA}-v'_{(0)}$
$M'_{(0)}=q\ell$
$-v'_{(0)}=-\frac{C}{EI}$
$\theta_{(0)}=0=\frac{q\ell}{kGA}-\frac{C}{EI}$
$C=\frac{q\ell EI}{kGA}$
$EIv_{(z)}=\frac{qz^4}{24}-\frac{q\ell z^3}{6}+\frac{q\ell^2 z^2}{4}-\frac{qEIz^2}{2kGA}+\frac{q\ell EIz}{kGA}$
$v_{(z)}=\frac{q}{24EI}(z^4-4\ell z^3+6\ell^2 z^2)+\frac{q}{2kGA}(2\ell z-z^2)$
$v_{(\ell)}=\frac{q}{24EI}(\ell^4-4\ell^4+6\ell^4)+\frac{q\ell^2}{2kGA}$
$v_{(\ell)}=\frac{q\ell^4}{8EI}+\frac{q\ell^2}{2kGA}$

*単純梁等分布 [#uee05e31]
**境界値問題 [#g1dbe97d]
$$q=EIv''''_{(z)}$$
$$EIv''''_{(z)}=q$$
$$EIv'''_{(z)}=qz+A$$
$$EIv''_{(z)}=\frac{qz^2}{2}+Az+B$$
$$EIv'_{(z)}=\frac{qz^3}{6}+\frac{Az^2}{2}+Bz+C$$
$$EIv_{(z)}=\frac{qz^4}{24}+\frac{Az^3}{6}+\frac{Bz^2}{2}+Cz+D$$
$$M_{(z)}=-EI(v''_{(z)}+\frac{q}{kGA})$$
$$S_{(z)}=-EIv'''_{(z)}$$
$$\theta_{(z)}=\frac{M'_{(z)}}{kGA}-v'_{(z)}$$
$$v_{(0)}=0$$
$$D=0$$
$$M_{(0)}=0$$
$$EIv''_{(0)}=B$$
$$-EIv''_{(0)}=-B$$
$$M_{(0)}=-B-\frac{qEI}{kGA}$$
$$B=-\frac{qEI}{kGA}$$
$$S_{(\frac{\ell}{2})}=0$$
$$EIv'''_{(\frac{\ell}{2})}=\frac{q\ell}{2}+A$$
$$0=-\frac{q\ell}{2}-A$$
$$A=-\frac{q\ell}{2}$$
$$v_{(\ell)}=0$$
$$EIv_{(z)}=\frac{qz^4}{24}-\frac{q\ell z^3}{12}-\frac{qEIz^2}{2kGA}+\frac{q\ell^3 z}{24}+\frac{qEI\ell z}{2kGA}$$
$$v_{(z)}=\frac{q}{24EI}(z^4-2\ell z^3+q\ell^3 z)+\frac{q\ell^2}{2kGA}(-z^2+\ell z)$$
$$v_{(\frac{\ell}{2})}=\frac{q\ell^4}{24EI}(\frac{1}{16}-\frac{1}{4}+\frac{1}{2})+\frac{q\ell^2}{2kGA}(-\frac{1}{4}+\frac{1}{2})$$
$$v_{(\frac{\ell}{2})}=\frac{5q\ell^4}{384EI}+\frac{q\ell^2}{8kGA}$$
$q=EIv''''_{(z)}$
$EIv''''_{(z)}=q$
$EIv'''_{(z)}=qz+A$
$EIv''_{(z)}=\frac{qz^2}{2}+Az+B$
$EIv'_{(z)}=\frac{qz^3}{6}+\frac{Az^2}{2}+Bz+C$
$EIv_{(z)}=\frac{qz^4}{24}+\frac{Az^3}{6}+\frac{Bz^2}{2}+Cz+D$
$M_{(z)}=-EI(v''_{(z)}+\frac{q}{kGA})$
$S_{(z)}=-EIv'''_{(z)}$
$\theta_{(z)}=\frac{M'_{(z)}}{kGA}-v'_{(z)}$
$v_{(0)}=0$
$D=0$
$M_{(0)}=0$
$EIv''_{(0)}=B$
$-EIv''_{(0)}=-B$
$M_{(0)}=-B-\frac{qEI}{kGA}$
$B=-\frac{qEI}{kGA}$
$S_{(\frac{\ell}{2})}=0$
$EIv'''_{(\frac{\ell}{2})}=\frac{q\ell}{2}+A$
$0=-\frac{q\ell}{2}-A$
$A=-\frac{q\ell}{2}$
$v_{(\ell)}=0$
$EIv_{(z)}=\frac{qz^4}{24}-\frac{q\ell z^3}{12}-\frac{qEIz^2}{2kGA}+\frac{q\ell^3 z}{24}+\frac{qEI\ell z}{2kGA}$
$v_{(z)}=\frac{q}{24EI}(z^4-2\ell z^3+q\ell^3 z)+\frac{q\ell^2}{2kGA}(-z^2+\ell z)$
$v_{(\frac{\ell}{2})}=\frac{q\ell^4}{24EI}(\frac{1}{16}-\frac{1}{4}+\frac{1}{2})+\frac{q\ell^2}{2kGA}(-\frac{1}{4}+\frac{1}{2})$
$v_{(\frac{\ell}{2})}=\frac{5q\ell^4}{384EI}+\frac{q\ell^2}{8kGA}$



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