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The second co...

Question

The second column of stiffness matrix with reference to co-ordinate system as shown in the beam is:

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0 4 E I / 6 - E I / 6 E I / 3 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0 2 E I / 3 - E I / 3 E I / 3 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 4 E I / 6 2 E I / 3 - E I / 6 0 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0 2 E I / 3 E I / 6 - 4 E I / 6 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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Solution

The correct option is A $⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0 4 E I / 6 - E I / 6 E I / 3 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$
Let us give unit displacement in co-ordinate direction (2) without giving any displacement in other co-ordinates

$K_{12} = 0$
$K_{22} = \frac{4 E I}{6}$
$K_{32} = \frac{- E I}{6}$
$K_{42} = \frac{2 E I}{6}$

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⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{1000}{3 E I} & \frac{2500}{3 E I} \frac{2500}{3 E I} & \frac{3000}{3 E I} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦

\frac{2 E I}{L}

[\begin{matrix} 2 & + 1 + 1 & 2 \end{matrix}]

O

u = 5 \sqrt{5} m/s

α = {tan}^{- 1} (0.5)

C

AB

37^{\circ}

C

O A = \frac{10}{3} m

L

E I

K

P

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