The image shows a simply supported beam with a central point load of 600 kg applied at the center (C), with the distances from the supports (A and B) to the load being equal (4.5 m each).

To calculate the slope (or pendiente) at point A and the maximum deflection (or flecha máxima) of the beam, we use formulas derived from beam theory under bending. Since $EI$ (modulus of elasticity multiplied by the moment of inertia) is constant, we can apply these formulas for a beam with a central load.

Step 1: Convert the Load to Newtons

Given that the load is 600 kg, we convert it to Newtons: $W = 600 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 5886 \, \text{N}$

Step 2: Use Deflection and Slope Formulas for a Central Load

For a simply supported beam with a central load $P$, the slope at the ends (A or B) and the maximum deflection occur at the midpoint. The formulas for these are:

• Slope at A (or B): $\theta_A = \frac{PL^2}{16EI}$
• Maximum deflection (at C): $\delta_{\text{max}} = \frac{PL^3}{48EI}$ Where:
• $P$ is the central load (5886 N),
• $L$ is the length of the beam (9 m total, 4.5 m on each side),
• $EI$ is the flexural rigidity (constant).

Step