From Solution 826
$M_2 = -1.6923 ~ \text{kN}\cdot\text{m} = -1692.3 ~ \text{N}\cdot\text{m}$
$M_3 = -3.2307 ~ \text{kN}\cdot\text{m} = -3230.7 ~ \text{N}\cdot\text{m}$
Simple beam reactions
$V_{1L} = 8000 / 4 = 2000 ~ \text{N}$ first span, left support ↓
$V_{1R} = 8000 / 4 = 2000 ~ \text{N}$ first span, right support ↑
$V_{2L} = \frac{1}{2}(2000 \times 4) = 4000 ~ \text{N}$ second span, left support ↑
$V_{2R} = \frac{1}{2}(2000 \times 4) = 4000 ~ \text{N}$ second span, right support ↑
$V_{3L} = 2(6000) / 3 = 4000 ~ \text{N}$ third span, left support ↑
$V_{3R} = 1(6000) / 3 = 2000 ~ \text{N}$ third span, right support ↑
Couple Reactions
${R_1}' = M_2 / L_1 = 1690 / 4$
${R_1}' = 422.5 ~ \text{N}$ first span, left support ↓, right support ↑
${R_2}' = (M_3 - M_2) / L_2 = (3230 - 1690) / 4$
${R_2}' = 385 ~ \text{N}$ second span, left support ↓, right support ↑
${R_3}' = M_3 / L_3 = 3230 / 3$
${R_3}' = 1076.67 ~ \text{N}$ third span, left support ↑, right support ↓
Support reactions
$R_1 = 2422.5 ~ \text{N}$ ↓ answer
$R_2 = 2422.5 + 3615 = 6037.5 ~ \text{N}$ ↑ answer
$R_3 = 4385 + 5076.7 = 9461.7 ~ \text{N}$ ↑ answer
$R_4 = 923.3 ~ \text{N}$ ↑ answer
Maximum positive moment
$\dfrac{x}{3615} = \dfrac{4}{3615 + 4385}$
$x = 1.8075 ~ \text{m}$
$M_A = -2422.5(2) + 8000 = 3155 ~ \text{N}\cdot\text{m}$
$M_B = M_2 + \frac{1}{2}x(3615) = -1690 + \frac{1}{2}(1.8075)(3615) = 1577.06 ~ \text{N}\cdot\text{m}$
$M_C = 2R_4 = 2(923.3) = 1846.6 ~ \text{N}\cdot\text{m}$
Thus,
$M_{max(+)} = 3155~ \text{N}\cdot\text{m}$ answer
