
$\Sigma M_{R2} = 0$
$3R_1 = 5(2) + 2$
$R_1 = 4 \, \text{ kN}$
$\Sigma M_{R2} = 0$
$3R_2 + 2 = 5(1)$
$R_2 = 1 \, \text{ kN}$
Based on bending stress (square b = d):
$f_b = \dfrac{6M}{bd^2}$
$8 = \dfrac{6(4)(1000^2)}{d^3}$
$d = 144.22 \, \text{ mm}$
Based on shear stress (square b = d):
$f_v = \dfrac{3V}{2bd}$
$1 = \dfrac{3(4)(1000)}{2d^2}$
$d = 77.46 \, \text{ mm}$
Use 145 mm × 145 mm square beam answer