C. Põhivalemid

Esitame õhukeseseinalise tala painde ja takistatud väände ülekandevõrrandid maatrikskujul:

$$\mathbf{Z_{L}\left( x\right) } = \mathbf{U}\bm{\cdot}\mathbf{Z_{A}} + \mathbf{\stackrel{\rm\circ}{Z}}$$ (C.1)

kus $\mathbf{Z_{A}}$, $\mathbf{Z_{L}}$ on vastavalt varda alguses ja lõpus olevad siirded, paindenurgad, põikjõud, paindemomendid, väändenurgad ja väändemomendid.

$$\mathbf{Z_{A}} = \left[\begin{array}{c} w_{A} \\ \varphi_{A} \\ ... ...} \\ {T_{t}}_{L} \\ B_{\omega L} \\ T_{\omega {L}} \end{array}\right] \qquad$$ (C.2)

Ülekandemaatriks $\mathbf{U}$ teise märgikokkuleppe puhul on

$$\mathbf{U_{8\times 8}} = \left[\begin{array}{cc} \mathbf{U_{12\le... ...4\right)}} & 0 \\ 0 & \mathbf{U_{22\left(4\times 4\right)}} \end{array}\right]$$ (C.3)

kus alammaatriks $\mathbf{U_{12\left(4\times 4\right)}}$ kirjeldab tala painet (vt [Lah12Lah12, lk 688]^6.1):

$$\mathbf{U_{12\left(4\times 4\right)}} = \left[\begin{array}{cccc}... ...- \frac{x}{EI_{y}} \\ 0 & 0 & - 1 & 0 \\ 0 & 0 & - x & - 1 \end{array}\right]$$ (C.4)

ning alammaatriks $\mathbf{U_{22\left(4\times 4\right)}}$ õhukeseseinalise tala takistatud väänet:

$$\mathbf{U_{22\left(4\times 4\right)}} = \left[ \begin{array}{cccc... ...mathrm{sh}{{{\kappa x}}}} & -\mathrm{ch}{{{\kappa x}}} \end{array}\right] \quad$$ (C.5)

$\mathrm{\mathbf{\stackrel{\rm\circ}{Z}}}$ on tala koormusvektor, mis koosneb painde koormusvektorist $\mathrm{\mathbf{\overset{\rm\circ}{Z}_{11}}}$ ja takistatud väände koormusvektorist $\mathrm{\mathbf{\overset{\rm\circ}{Z}_{21}}}$:

$$\mathbf{\stackrel{\rm\circ}{Z}} = \left[\begin{array}{c} \mathbf{... ...{\rm\circ}{Z}_{11}} \\ \mathbf{\stackrel{\rm\circ}{Z}_{21}} \end{array}\right]$$ (C.6)

Painde koormusvektori $\mathrm{\mathbf{\overset{\rm\circ}{Z}_{11}}}$ (vt [Lah12, avaldis (1.66) ^6.2ja tabel G.1 ^6.3)] saab siirde $w_{e}$ erilahendite tuletistest:

$$\mathbf{\stackrel{\rm\circ}{Z_{11}}} = \left[\begin{array}{c} w_{... ...}_{+} - \sum {q}_{z}\frac{\left( x-a_{q}\right)^{2}_{+}}{2!} \end{array}\right]$$ (C.7)

Takistatud väände koormusvektori $\mathrm{\mathbf{\overset{\rm\circ}{Z}_{21}}}$ saab väändenurga $\theta_{e}$ erilahendite tuletistest:

$$\mathbf{\stackrel{\rm\circ}{Z_{21}}} = \left[\begin{array}{c} \th... ... \\ E\hspace*{1pt}I_{\omega}\theta^{\prime\prime\prime}_{e} \end{array}\right]$$ (C.8)

Koormusvektori $\mathrm{\mathbf{\stackrel{\rm\circ}{Z}}}$ valime tabelitest C.1 ja C.2.

Õhukeseseinalise tala painde ja takistatud väände ülekandevõrrandid võib kirjutada võrrandisüsteemina

$$\mathbf{U}\bm{\cdot}\mathbf{Z_{A}} -\mathbf{I_{8\times8}\bm{\cdot} Z_{L}} = \mathbf{ - \stackrel{\rm\circ}{Z}}$$ (C.9)

Lühemalt

$$\mathbf{\widehat{UI}}_{8\times16}\cdot\mathbf{\widehat{Z}} = \mathbf{-\stackrel{\rm\circ}{Z}}$$ (C.10)

kus

$$\mathbf{\widehat{Z}} = \left[\begin{array}{c} \mathbf{Z_{A}} \\ \mathbf{Z_{L}} \end{array}\right]$$ (C.11)

kus

$$\mathbf{Z_{A}} = \left[\begin{array}{c} w_{A} \\ \varphi_{A} \\ ... ...\right) \\ Z\left(15,1\right) \\ Z\left(16,1\right) \end{array}\right] \qquad$$ (C.12)

ning laiendatud ülekandemaatriks avaldub

$$\mathbf{\widehat{UI}}_{8\times 16} = \boldsymbol{\left( U_{8\times8}\mid -I_{8\times8}\right)}$$ (C.13)