12.0 A 12 meter beam is simply supported at both ends and has an overhang of 2 meters. The beam carries a uniformly distributed load of 30 kN/m over the entire length. What is the reaction at the left support? 

a) 216 kN

(b) 180 kN

C) 144 kN 

(d) 240 KN

To determine the reaction at the left support, we need to analyze the beam using static equilibrium. The beam is 12 meters long and is simply supported with an overhang of 2 meters. It carries a uniformly distributed load (UDL) of 30 kN/m over the entire length.

### Step 1: Determine the total load on the beam
The total length of the beam is 12 meters, and the UDL is 30 kN/m. Thus, the total load (\( W_{\text{total}} \)) is:

\[
W_{\text{total}} = 30 \, \text{kN/m} \times 12 \, \text{m} = 360 \, \text{kN}
\]

### Step 2: Reaction forces at supports
Let \( R_A \) be the reaction at the left support and \( R_B \) be the reaction at the right support.

Since the beam is in static equilibrium, we apply the following equilibrium conditions:

- **Sum of vertical forces = 0:**
\[
R_A + R_B = 360 \, \text{kN}
\]

- **Sum of moments about one of the supports (we'll take moments about the left support \( A \)):**

Taking moments about point \( A \) eliminates \( R_A \) and helps solve for \( R_B \). The UDL acts at the center of the beam (6 meters from each end), but with an overhang, the total load is distributed over 12 meters, and the load acts on both the supported part and the overhang.

For this problem, the 360 kN load can be thought of as two parts: 

1. A load on the 10-meter portion (the supported span) contributing directly to the reactions.
2. A 2-meter overhang contributing additional load.

We need more detailed balance of moments to accurately assess

A 12 meter beam is simply supported at both ends and has an overhang of 2 meters. The beam carries a uniformly distributed load of 30 kN/m over the entire length. What is the reaction at the left support?

(a) 216 kN
(b) 180 kN
(c) 144 kN
(d) 240 kN

This problem involves calculating the reaction at the left support of a 12-meter beam with a 2-meter overhang, subjected to a 30 kN/m uniformly distributed load. Using static equilibrium principles and beam analysis techniques, this step-by-step solution helps solve for the reaction forces.

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