ILD: shear at C, propped cantilever 14 m

Sign convention: sagging moment (+), hogging moment (-); shear positive when the left part tends to go up; reaction positive upward. Ordinates are for a unit load moving along the beam.

Method

Propped cantilever AB, $L = 14$ m, A fixed, B roller, C at 6 m from B (8 m from A). Redundant: $R_B$. With support B removed, the cantilever deflection at B due to a unit load at $x$ from A is $\delta_{Bx} = \dfrac{x^2(3L-x)}{6EI}$, and due to a unit load at B it is $f_{BB} = \dfrac{L^3}{3EI}$. Compatibility (zero deflection at B) gives

$$R_B = \frac{\delta_{Bx}}{f_{BB}} = \frac{x^2(3L-x)}{2L^3}$$

Shear at C (left part): load left of C: $V_C = -R_B$; load right of C: $V_C = 1 - R_B$.

Sample: $x = 10$: $R_B = \dfrac{100\times32}{2\times2744} = 0.583$, so $V_C = 0.417$. At C: $R_B(8) = \dfrac{64\times34}{5488} = 0.397$, giving $-0.397$ (just left) and $+0.603$ (just right).

Ordinates (2 m interval)

ILD shape

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The ordinates are 0 at A and B; the jump at C is 1.0 (from $-0.397$ to $+0.603$).