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Moment at Section if One End of Column is Fixed and Other is Hinged Calculator

Moment Formula:

\[ M_t = -P \times \delta + H \times (l - x) \]

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1. What is Moment at Section Calculator?

Definition: This calculator determines the moment at a specific section of a column when one end is fixed and the other is hinged.

Purpose: It helps structural engineers analyze column behavior under combined axial and lateral loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_t = -P \times \delta + H \times (l - x) \]

Where:

  • \( M_t \) — Moment at section (N·m)
  • \( P \) — Column crippling load (N)
  • \( \delta \) — Deflection at section (m)
  • \( H \) — Horizontal reaction (N)
  • \( l \) — Column length (m)
  • \( x \) — Distance from fixed end to deflection point (m)

Explanation: The formula accounts for both the bending moment due to axial load and the moment from horizontal reaction.

3. Importance of Moment Calculation

Details: Accurate moment calculation is crucial for designing columns that can resist buckling and maintain structural integrity.

4. Using the Calculator

Tips: Enter all required values in consistent units (N for forces, m for lengths). The distance x must be ≤ column length.

5. Frequently Asked Questions (FAQ)

Q1: What is column crippling load?
A: It's the axial load at which a column tends to buckle rather than compress.

Q2: How is horizontal reaction determined?
A: It's calculated from equilibrium conditions considering all applied loads.

Q3: What if my deflection is zero?
A: The first term becomes zero, and moment depends only on horizontal reaction.

Q4: Can this be used for other support conditions?
A: No, this formula is specific for fixed-hinged columns.

Q5: What's the typical accuracy range?
A: Results are typically within ±5% of actual values for elastic range.

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