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Load intensity given max deflection for strut subjected to uniformly distributed load Calculator

Load Intensity Formula:

\[ q_f = \frac{C}{\left(1 \times \left(\frac{\varepsilon_{column} \times I}{P_{axial}^2}\right) \times \left(\sec\left(\frac{l_{column}}{2} \times \sqrt{\frac{P_{axial}}{\varepsilon_{column} \times I}}\right)-1\right)\right) - \left(\frac{1 \times l_{column}^2}{8 \times P_{axial}}\right)} \]

m
Pa
m⁴
N
m
%

1. What is Load Intensity for a Strut?

Definition: This calculator determines the load intensity (force per unit area) that causes a specified maximum deflection in a strut subjected to uniformly distributed load.

Purpose: It helps structural engineers analyze the load-bearing capacity of columns and struts under distributed loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ q_f = \frac{C}{\left(1 \times \left(\frac{\varepsilon_{column} \times I}{P_{axial}^2}\right) \times \left(\sec\left(\frac{l_{column}}{2} \times \sqrt{\frac{P_{axial}}{\varepsilon_{column} \times I}}\right)-1\right)\right) - \left(\frac{1 \times l_{column}^2}{8 \times P_{axial}}\right)} \]

Where:

  • \( q_f \) — Load Intensity (Pa)
  • \( C \) — Maximum initial deflection (m)
  • \( \varepsilon_{column} \) — Modulus of Elasticity Column (Pa)
  • \( I \) — Moment of Inertia Column (m⁴)
  • \( P_{axial} \) — Axial Thrust (N)
  • \( l_{column} \) — Column Length (m)

3. Importance of Load Intensity Calculation

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

4. Using the Calculator

Tips: Enter all required parameters. The tolerance field (default ±5%) shows acceptable variation range.

5. Frequently Asked Questions (FAQ)

Q1: What is maximum initial deflection?
A: The greatest displacement of the strut from its original position under load.

Q2: How do I determine the modulus of elasticity?
A: This is a material property - for steel it's typically around 200 GPa, for concrete about 20-30 GPa.

Q3: What affects moment of inertia?
A: The cross-sectional shape and dimensions of the column.

Q4: Why include a tolerance range?
A: To account for material variations, construction tolerances, and safety factors.

Q5: When would this calculation be used?
A: In designing columns, struts, and other compression members in buildings, bridges, and mechanical systems.

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