Part (a)
For 1 plank
$I_1 = \dfrac{100(20^3)}{12}$
$I_1 = \frac{200\,000}{3} \, \text{mm}^4$
For the whole beam
$I = 6I_1 = 6(200\,000/3)$
$I = 400\,000 \, \text{mm}^4$
$\dfrac{M}{EI} = \dfrac{M_1}{E_1 I_1}$ where E1 = E
$\dfrac{M}{E(400\,000)} = \dfrac{M_1}{E(\frac{200\,000}{3})}$
$\dfrac{M_1}{M} = \dfrac{1}{6}$ answer
Part (b)
For 1 plank
$I_1 = \dfrac{100(10^3)}{12}$
$I_1 = \frac{25\,000}{3} \, \text{mm}^4$
For the whole beam
$I = 12I_1 = 12(25\,000/3)$
$I = 100\,000 \, \text{mm}^4$
$\dfrac{M}{EI} = \dfrac{M_1}{E_1 I_1}$ where E1 = E
$\dfrac{M}{E(100\,000)} = \dfrac{M_1}{E(\frac{200\,000}{3})}$
$\dfrac{M_1}{M} = \dfrac{1}{12}$ ) answer
