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Maximum stress given elastic modulus for strut subjected to uniformly distributed load Calculator

Maximum Bending Stress Formula:

\[ \sigma_{bmax} = \frac{P_{axial}}{A_{sectional}} + \frac{M}{\varepsilon_{column}} \]

N
m²
Nm
Pa

1. What is Maximum Bending Stress?

Definition: Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

Purpose: It helps engineers determine the structural integrity of columns and struts under combined axial and bending loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{bmax} = \frac{P_{axial}}{A_{sectional}} + \frac{M}{\varepsilon_{column}} \]

Where:

  • \( \sigma_{bmax} \) — Maximum bending stress (Pascal)
  • \( P_{axial} \) — Axial thrust (Newtons)
  • \( A_{sectional} \) — Column cross sectional area (m²)
  • \( M \) — Maximum bending moment (Nm)
  • \( \varepsilon_{column} \) — Modulus of elasticity (Pa)

Explanation: The formula combines the direct stress from axial load and bending stress from moment.

3. Importance of Maximum Bending Stress Calculation

Details: Proper calculation ensures structural safety and prevents failure due to excessive stress.

4. Using the Calculator

Tips: Enter all required values with ±5% tolerance. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is axial thrust?
A: The resultant force of all axial forces acting on the column.

Q2: How to measure cross sectional area?
A: Measure the area of the column's cross-section perpendicular to its length.

Q3: What affects modulus of elasticity?
A: Material properties and temperature primarily affect the modulus.

Q4: When is this calculation most important?
A: For slender columns subjected to combined axial and lateral loads.

Q5: What safety factor should be applied?
A: Typically 1.5-2.0 depending on application and building codes.

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