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

Formula:

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

1. What is Deflection at Section?

Definition: Deflection at Section is the lateral displacement at the section of the column.

Purpose: It helps structural engineers determine how much a column will bend under specific loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

  • \( \delta \) — Deflection at Section (meters)
  • \( M_t \) — Moment of Section (Newton Meter)
  • \( H \) — Horizontal Reaction (Newton)
  • \( l \) — Column Length (meters)
  • \( x \) — Distance b/w Fixed End and Deflection Point (meters)
  • \( P \) — Column Crippling Load (Newton)

Explanation: The formula calculates deflection considering the moment, horizontal reaction, column geometry, and crippling load.

3. Importance of Deflection Calculation

Details: Proper deflection estimation ensures structural stability and prevents excessive bending that could lead to failure.

4. Using the Calculator

Tips: Enter all required values with ±5% tolerance. Column Crippling Load cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the significance of ±5%?
A: It represents the acceptable tolerance range for input values in engineering calculations.

Q2: When is this formula applicable?
A: For columns with one fixed end and one hinged end under combined loading.

Q3: What's a typical value for horizontal reaction?
A: It varies based on loading conditions but is typically 5-15% of vertical loads.

Q4: How does column length affect deflection?
A: Longer columns generally experience greater deflection under the same loads.

Q5: What if I get negative deflection?
A: Negative values indicate deflection in the opposite direction of the assumed positive direction.

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