Maximum bending moment given max stress for strut subjected to uniformly distributed load Calculator

Maximum Bending Moment Formula:

\[ M = \frac{(\sigma_{bmax} - \frac{P_{axial}}{A_{sectional}}) \times I}{c} \]

Maximum bending stress (σ_bmax):

Axial Thrust (P_axial):

Column Cross Sectional Area (A_sectional):

m²

Moment of Inertia (I):

m⁴

Distance from Neutral Axis (c):

Tolerance:

Maximum Bending Moment (M):

1. What is Maximum Bending Moment Calculator?

Definition: This calculator determines the maximum bending moment in a strut subjected to uniformly distributed load, considering maximum bending stress, axial thrust, and section properties.

Purpose: It helps structural engineers and designers verify the bending capacity of columns and struts under combined loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = \frac{(\sigma_{bmax} - \frac{P_{axial}}{A_{sectional}}) \times I}{c} \]

Where:

\( M \) — Maximum bending moment (N·m)
\( \sigma_{bmax} \) — Maximum bending stress (Pa)
\( P_{axial} \) — Axial thrust (N)
\( A_{sectional} \) — Cross-sectional area (m²)
\( I \) — Moment of inertia (m⁴)
\( c \) — Distance from neutral axis to extreme point (m)

3. Importance of Maximum Bending Moment Calculation

Details: Accurate calculation ensures structural safety by preventing overstressing of members under combined axial and bending loads.

4. Using the Calculator

Tips: Enter all required parameters including the optional tolerance percentage (default ±5%). All dimensional values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the tolerance value?
A: The tolerance accounts for material variations and safety factors, providing a range of acceptable values.

Q2: How do I determine the moment of inertia?
A: Use standard formulas for common shapes or CAD software for complex sections.

Q3: What if my axial thrust is zero?
A: The formula simplifies to \( M = \frac{\sigma_{bmax} \times I}{c} \) for pure bending cases.

Q4: What units should I use?
A: Consistent SI units are required (Pa, N, m, m², m⁴).

Q5: How does distributed load affect the calculation?
A: The distributed load is accounted for in the maximum bending stress input value.