Math Problem Statement

How do I analyze the beam with a distributed load (200 lb/ft) and point loads of 1.8 kip at both ends, supported by pin and roller supports?

Solution

This is a static beam diagram that involves multiple loads, including:

  • A uniformly distributed load of w=200lb/ftw = 200 \, \text{lb/ft} over a certain span.
  • Two point loads of 1.8kip1.8 \, \text{kip} each located at both ends of the beam.
  • Two supports: one triangular and one circular, indicating pin and roller supports, respectively.

The distances between points along the beam are also provided: 6 ft, 1 ft, 7 ft, and 4 ft, giving a total beam length of 18 feet.

To analyze this beam, I would need to:

  1. Calculate the reactions at the supports using static equilibrium equations (sum of forces and moments).
  2. Break down the uniformly distributed load (UDL) into its resultant force.
  3. Determine internal forces (shear force and bending moments) along the beam to construct shear force and bending moment diagrams if necessary.

Would you like me to proceed with a step-by-step analysis of the reactions at the supports and internal forces, or do you want help with a specific aspect of this problem?

Let me know! Here are 5 possible questions to help you think further:

  1. How do we find the resultant of a distributed load?
  2. How do we calculate the reactions for a statically determinate beam?
  3. How would the shear force diagram look for this beam?
  4. What is the significance of calculating bending moments?
  5. How does the location of supports affect the load distribution?

Tip: To simplify the analysis of distributed loads, you can replace them with equivalent point loads at their centroids!

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Math Problem Analysis

Mathematical Concepts

Statics
Structural Analysis
Equilibrium

Formulas

Sum of forces: ΣF = 0
Sum of moments: ΣM = 0
Resultant force of distributed load: F = w * L (where w is load per unit length and L is the length of the load)

Theorems

Equilibrium conditions
Method of sections

Suitable Grade Level

College-level engineering (Statics)