To calculate the reaction at \( R_{B1} \) (the reaction at the roller support \( B \) on the left span), we will again use the principles of static equilibrium, but we will focus specifically on the left span of the beam from \( A \) to \( B \).

### Step 1: Restate the problem and known values
- The beam is 9 meters long, with a hinge at \( A \), a roller at \( B \) (5 meters from \( A \)), and another roller at \( C \) (9 meters from \( A \)).
- A point load of 50 kN is located 7 meters from \( A \).

We already calculated the reaction at \( A \) as \( R_A = 20.1625 \, \text{kN} \).

### Step 2: Analyze the left span (from \( A \) to \( B \))
For the left span, we consider only the section from \( A \) to \( B \). This section is 5 meters long.

### Step 3: Sum of vertical forces for the left span (\(\sum F_y = 0\))
\[
R_A + R_{B1} = 0
\]

Since \( R_A = 20.1625 \, \text{kN} \) (upward), the equation simplifies to:

\[
R_{B1} = -20.1625 \, \text{kN}
\]

### Step 4: Interpretation
The negative sign indicates that the direction of the reaction \( R_{B1} \) is opposite to the assumed direction. Since we initially assume upward reactions, \( R_{B1} \) is actually \( 20.1625 \, \text{kN} \) downward.

### Answer:
The reaction at \( B \) on the left span (or \( R_{B1} \)) is **20.1625 kN downward**.

Would you like more details, or have any other questions?

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Here are five related questions to consider:

1. How would the reaction at \( B \) change if the load were applied directly at \( B \)?
2. What is the difference between analyzing a left span and the entire beam?
3. How would the reaction at \( C \) be affected by different load placements?
4. How can you confirm the downward direction of \( R_{B1} \)?
5. How would you calculate the shear force at any point between \( A \) and \( B \)?

**Tip:** When calculating reactions, always check your assumptions about the direction of the forces; a negative result indicates a direction opposite to what you initially assumed.

Learn how to calculate the reaction at B (Rb1) on the left span of a beam using principles of static equilibrium and beam analysis. Includes step-by-step solution with specific details on beam length, support types, and applied loads.

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