Maximum Bending Moment for Strut Calculator

Maximum Bending Moment for Strut Subjected to Compressive Axial and Uniformly Distributed Load Calculator

Maximum Bending Moment Formula:

\[ M = -q_f \times \left(\frac{\epsilon_{column} \times I}{P_{axial}}\right) \times \left(\sec\left(\frac{l_{column}}{2} \times \sqrt{\frac{P_{axial}}{\epsilon_{column} \times I}}\right) - 1\right) \]

Load Intensity (q_f):

Modulus of Elasticity (ε):

Moment of Inertia (I):

m⁴

Axial Thrust (P_axial):

Column Length (l):

Tolerance:

Maximum Bending Moment (M):

1. What is Maximum Bending Moment for Strut?

Definition: This calculator determines the maximum bending moment in a strut (column) subjected to both compressive axial load and uniformly distributed lateral load.

Purpose: It helps structural engineers analyze and design columns under combined loading conditions to prevent buckling and excessive deflection.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = -q_f \times \left(\frac{\epsilon \times I}{P}\right) \times \left(\sec\left(\frac{l}{2} \times \sqrt{\frac{P}{\epsilon \times I}}\right) - 1\right) \]

Where:

\( M \) — Maximum bending moment (N·m)
\( q_f \) — Load intensity (Pa)
\( \epsilon \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)
\( P \) — Axial thrust (N)
\( l \) — Column length (m)
sec — Secant trigonometric function

3. Importance of This Calculation

Details: Accurate calculation of maximum bending moment is crucial for:

Determining required column strength
Preventing structural failure
Ensuring safety factors are met
Optimizing material usage

4. Using the Calculator

Tips:

Enter all values in consistent SI units
Default values are provided for common steel columns
Tolerance (±5% by default) accounts for material variations
All values must be positive numbers

5. Frequently Asked Questions (FAQ)

Q1: What is the secant function in this formula?
A: The secant (sec) accounts for the non-linear relationship between axial load and bending in slender columns.

Q2: How does axial load affect bending moment?
A: Higher axial loads increase the bending moment through the P-Δ (P-delta) effect.

Q3: What's a typical modulus of elasticity for steel?
A: About 200 GPa (2.0×10¹¹ Pa) for structural steel.

Q4: When would I adjust the tolerance?
A: Increase tolerance for less precise materials or decrease for critical applications.

Q5: What if my column has different end conditions?
A: This formula assumes pinned ends. For other conditions, use an effective length factor.