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.