To determine the shear force and bending moment along the beam, we will use the previously calculated reactions: Reaction at A ($R_A$) = 5 units (upward) Reaction at B ($R_B$) = 5 units (upward) Point load ($P$) = 10 units (downward) at $x=3$ from A. Total beam length = 6 units. We will analyze the beam in two sections: 1. From A to the point load (0 < x < 3) 2. From the point load to B (3 < x < 6) Shear Force Calculation Shear force ($V(x)$) is the algebraic sum of the vertical forces to the left of the section. Upward forces are positive, downward forces are negative. Step 1: Shear force for the section $0 \le x < 3$ (from A to the point load). Considering a section at a distance $x$ from A: $$ V(x) = R_A $$ $$ V(x) = 5 $$ The shear force is constant in this section. Step 2: Shear force for the section $3 < x \le 6$ (from the point load to B). Considering a section at a distance $x$ from A: $$ V(x) = R_A - P $$ $$ V(x) = 5 - 10 $$ $$ V(x) = -5 $$ The shear force is constant in this section. Bending Moment Calculation Bending moment ($M(x)$) is the algebraic sum of the moments of all forces to the left of the section about that section. Counter-clockwise moments are positive, clockwise moments are negative. Step 3: Bending moment for the section $0 \le x < 3$ (from A to the point load). Considering a section at a distance $x$ from A: $$ M(x) = R_A \times x $$ $$ M(x) = 5x $$ At $x=0$ (support A), $M(0) = 5 \times 0 = 0$. At $x=3$ (at the point load), $M(3) = 5 \times 3 = 15$. Step 4: Bending moment for the section $3 < x \le 6$ (from the point load to B). Considering a section at a distance $x$ from A: $$ M(x) = R_A \times x - P \times (x - 3) $$ $$ M(x) = 5x - 10(x - 3) $$ $$ M(x) = 5x - 10x + 30 $$ $$ M(x) = -5x + 30 $$ At $x=3$ (at the point load), $M(3) = -5 \times 3 + 30 = -15 + 30 = 15$. At $x=6$ (support B), $M(6) = -5 \times 6 + 30 = -30 + 30 = 0$. Summary of Shear Force and Bending Moment Functions The shear force and bending moment functions for the beam are: Shear Force ($V(x)$): $$ V(x) = \begin{cases} 5 & \text{for } 0 \le x < 3 \\ -5 & \text{for } 3 < x \le 6 \end{cases} $$ Bending Moment ($M(x)$): $$ M(x) = \begin{cases} 5x & \text{for } 0 \le x < 3 \\ -5x + 30 & \text{for } 3 < x \le 6 \end{cases} $$ The maximum bending moment occurs at the point load ($x=3$), with a value of 15 units. The final answer is $\boxed{\text{Shear Force: } V(x) = \begin{cases} 5 & \text{for } 0 \le x < 3 \\ -5 & \text{for } 3 < x \le 6 \end{cases}, \text{Bending Moment: } M(x) = \begin{cases} 5x & \text{for } 0 \le x < 3 \\ -5x + 30 & \text{for } 3 < x \le 6 \end{cases}}$.