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Maximum deflection for strut subjected to compressive axial and uniformly distributed load Calculator

Maximum Deflection Formula:

\[ C = \frac{q_f \cdot (\epsilon_{column} \cdot I / P_{axial}^2) \cdot (\sec(\frac{l_{column}}{2} \cdot \sqrt{\frac{P_{axial}}{\epsilon_{column} \cdot I}}) - 1) - q_f \cdot l_{column}^2}{8 \cdot P_{axial}} \]

1. What is Maximum Deflection for Strut Calculator?

Definition: This calculator determines the maximum initial deflection of a strut subjected to both compressive axial load and uniformly distributed load.

Purpose: It helps structural engineers analyze the deformation behavior of columns or struts under combined loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = \frac{q_f \cdot (\epsilon_{column} \cdot I / P_{axial}^2) \cdot (\sec(\frac{l_{column}}{2} \cdot \sqrt{\frac{P_{axial}}{\epsilon_{column} \cdot I}}) - 1) - q_f \cdot l_{column}^2}{8 \cdot P_{axial}} \]

Where:

  • \( C \) — Maximum initial deflection (meters)
  • \( q_f \) — Load intensity (Pascal)
  • \( \epsilon_{column} \) — Modulus of elasticity (Pascal)
  • \( I \) — Moment of inertia (m⁴)
  • \( P_{axial} \) — Axial thrust (Newton)
  • \( l_{column} \) — Column length (meters)

Explanation: The formula accounts for both the compressive axial load and uniformly distributed load effects on the strut's deflection.

3. Importance of Maximum Deflection Calculation

Details: Calculating maximum deflection is crucial for ensuring structural stability, preventing excessive deformation, and meeting design code requirements.

4. Using the Calculator

Tips: Enter all required parameters with their ±5% tolerance. All values must be positive numbers. The calculator will compute the maximum initial deflection.

5. Frequently Asked Questions (FAQ)

Q1: What is a strut in structural engineering?
A: A strut is a structural component designed to resist longitudinal compression, similar to a column but often used in different contexts.

Q2: Why does the formula use secant function?
A: The secant function appears in the solution of the differential equation governing the strut's deflection under combined loading.

Q3: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, concrete: ~20-30 GPa, wood: ~8-12 GPa (along grain).

Q4: How does axial load affect deflection?
A: Increased axial compression generally increases lateral deflection under transverse loading.

Q5: When is this calculation most important?
A: For slender columns/struts where deflection effects are significant in the design.

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