Cross-sectional area given elastic modulus for strut subjected to uniformly distributed load Calculator

Formula:

\[ A = \frac{P}{\sigma_{max} - \left(\frac{M}{\varepsilon}\right)} \]

Axial Thrust (P):

Maximum bending stress (σ_max):

Maximum Bending Moment (M):

Modulus of Elasticity (ε):

Tolerance:

Cross-sectional Area (A):

1. What is Cross-sectional Area Calculator?

Definition: This calculator determines the required cross-sectional area of a strut based on axial thrust, maximum bending stress, bending moment, and modulus of elasticity.

Purpose: It helps engineers design struts and columns that can withstand combined axial and bending loads while considering material properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{P}{\sigma_{max} - \left(\frac{M}{\varepsilon}\right)} \]

Where:

\( A \) — Cross-sectional area (m²)
\( P \) — Axial thrust (N)
\( \sigma_{max} \) — Maximum bending stress (Pa)
\( M \) — Maximum bending moment (Nm)
\( \varepsilon \) — Modulus of elasticity (Pa)

Explanation: The formula calculates the required area to ensure the combined stresses (axial + bending) don't exceed the material's capacity.

3. Importance of Cross-sectional Area Calculation

Details: Proper area calculation ensures structural integrity, prevents buckling, and maintains safety factors under combined loading conditions.

4. Using the Calculator

Tips: Enter all required values in consistent units. The tolerance field (default ±5%) helps account for material variations and safety factors.

5. Frequently Asked Questions (FAQ)

Q1: What is axial thrust in this context?
A: It's the compressive force acting along the longitudinal axis of the strut.

Q2: How does bending moment affect the calculation?
A: Higher bending moments require larger cross-sections to prevent excessive bending stresses.

Q3: Why include modulus of elasticity?
A: It accounts for the material's stiffness and how it resists deformation under bending.

Q4: When should I adjust the tolerance?
A: Increase tolerance for higher safety factors or when material properties vary significantly.

Q5: What units should I use?
A: Use consistent SI units: Newtons (N), Pascals (Pa), Newton-meters (Nm), and square meters (m²).