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The image shows a beam with a uniform distributed load of \( w = 200 \, \text{lb/ft} \) over a span of 6 feet and a concentrated point load of \( 1,500 \, \text{lb} \) located 8 feet from the left end of the beam. The beam is supported by a roller support at the 6 ft mark and a pin support at the far right end (10 ft from the roller support).

### Step-by-step analysis:

1. **Distributed Load (w = 200 lb/ft over 6 feet)**:
   The total distributed load can be calculated as:
   \[
   W_{\text{distributed}} = w \times L_{\text{distributed}} = 200 \, \text{lb/ft} \times 6 \, \text{ft} = 1200 \, \text{lb}
   \]
   This distributed load acts at the center of the 6 ft span, which is 3 ft from the left end.

2. **Concentrated Load**:
   The concentrated load is 1,500 lb located at 8 ft from the left end.

3. **Supports**:
   There are two supports: a roller support at 6 ft (from the left) and a pin support at 16 ft (from the left).

### Equilibrium Equations:

The system must satisfy the conditions of static equilibrium:
- Sum of vertical forces: \( \Sigma F_y = 0 \)
- Sum of moments about a point (usually one of the supports): \( \Sigma M = 0 \)

Would you like to proceed with solving for the support reactions and further analysis (e.g., shear force, bending moment diagrams)?

Here are five questions to expand on the topic:

1. How do we calculate the location of the resultant force of a distributed load?
2. What is the difference between a pin support and a roller support in beam analysis?
3. How do we determine the moment caused by a distributed load on a beam?
4. What are the common methods for analyzing statically determinate beams?
5. How does the position of the loads on the beam affect the support reactions?

### Tip:
In beam analysis, always start by calculating the reactions at the supports before proceeding to analyze internal shear forces and bending moments.

The unit load (w) is 200 lb/ft, and the concentrated load is 1,500 lb. Analyze the beam and determine support reactions and other properties.

This detailed solution analyzes a beam subjected to a 200 lb/ft distributed load and a concentrated load of 1,500 lb. Learn how to calculate support reactions using static equilibrium principles. Suitable for undergraduate engineering students.

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