To calculate the reaction forces at Points A and B, we need to apply the principles of static equilibrium, specifically the sum of forces and moments.

Given information:

• The length of the beam is 16.8 meters.
• The total applied load is 2.9 kN.
• The applied load is 9.4 meters from point A.
• The force at Point A is divided into horizontal (Ax) and vertical (Ay) components.
• The force at Point B is vertical (By), since there is no horizontal force given at B.

Step-by-Step Solution:

1. Sum of Forces in the Vertical Direction (ΣFy = 0): $\text{Ay} + \text{By} = 2.9 \, \text{kN}$ This is because the beam is in equilibrium and the total vertical forces must sum to zero. The applied load (2.9 kN) is vertical.

2. Sum of Moments about Point A (ΣMA = 0): To find Ay and By, we can use the sum of moments about Point A. The moment arm for Ay is 0 meters (since it acts at point A), and the moment arm for By is the full length of the beam (16.8 meters). The applied load creates a moment around point A at a distance of 9.4 meters.

   The moment equilibrium equation is: $2.9 \times 9.4 = \text{By} \times 16.8$ $\text{By} = \frac{2.9 \times 9.4}{16.8} = 1.62 \, \text{kN}$ So, the reaction at B is 1.62 kN upwards.

3. Substitute the Value of By into the Force Equation: Now, substitute By = 1.62 kN into the vertical force equilibrium equation: $\text{Ay} + 1.62 = 2.9$ $\text{Ay} = 2.9 - 1.62 = 1.28 \, \text{kN}$ So, the reaction at A in the vertical direction is 1.28 kN downward.

Summary of Reaction Forces:

• Ax = 0 kN (no horizontal forces).
• Ay = 1.28 kN (downward).
• By = 1.62 kN (upward).

Answer Box:

• Ax = 0 kN (no direction).
• Ay = 1.28 kN (down).
• By = 1.62 kN (up).

Would you like me to walk you through any further details of this solution? Also, here are 5 related questions:

1. How would the reaction forces change if the applied load was placed at a different distance along the beam?
2. What would happen if Point B was fixed instead of a roller?
3. How can we calculate the moment at Point A for different load types (point loads vs distributed loads)?
4. How do you handle horizontal forces in static equilibrium when Ax is non-zero?
5. What are the conditions for a beam to be in static equilibrium?

Tip: Always ensure that your moment arms are correctly identified based on the chosen pivot point when calculating moments in static equilibrium.