ILD: shear at A, propped cantilever 7 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, span $L = 7$ m, fixed at the left end and on a roller at the right end B. Section A is 1 m from the right end, i.e. 6 m from the fixed end. Let $x$ be the position of the unit load measured from the fixed end. Redundant: $R_B$.

$$R_B = \frac{x^2(3L-x)}{2L^3} = \frac{x^2(21-x)}{686}$$

Shear at A (left part): load to the left of A ($x < 6$): $V_A = R_{fixed} - 1 = -R_B$; load to the right of A ($x > 6$): $V_A = R_{fixed} = 1 - R_B$.

Sample: $x = 3$: $R_B = \dfrac{9\times18}{686} = 0.236$, so $V_A = -0.236$. At the section ($x = 6$): $R_B = \dfrac{36\times15}{686} = 0.787$, so $V_A = -0.787$ (just left) and $+0.213$ (just right).

Ordinates (1 m interval)

ILD shape

                                         |***
*************----------------------------|---****
             ***********                 |
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                                ******   |
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^                                               ^

The ILD is negative from the fixed end up to the section, with a maximum of $-0.787$ just left of A. It jumps by +1 at the section to $+0.213$ and falls to zero at the roller.