# Maximum Bending Moment and Shear Force Analysis of Beam

What are the bending moment and shear force functions for the different segments of the beam shown below? Where does the maximum bending moment occur and what is its value?

## Bending Moment and Shear Force Functions

**Segment AB (0 ≤ x ≤ 6):**For this segment, the shear force function is V(x) = RA - wx, where w = 2 kN/m and RA = 16 kN. The bending moment function is M(x) = 16x - x².

**Segment BC (6 ≤ x ≤ 9):**In this segment, the shear force function is V(x) = 10 kN. The bending moment function is M(x) = 16x - 2(x-6)²/2 - 10(x-6).

**Segment CD (9 ≤ x ≤ 12):**For the last segment, the shear force function is V(x) = -2x + 40 kN. The bending moment function is M(x) = 16x - 2(x-6)²/2 - 10(x-6) - 12(x-9).