Bending Moment At Section For Strut Subjected To Compressive Axial And Uniformly Distributed Load Calculator

Bending Moment Formula:

\[ M_b = -(P_{axial} \times \delta) + (q_f \times \left( \frac{x^2}{2} - \frac{l_{column} \times x}{2} \right)) \]

Axial Thrust (P_axial):

Deflection at Section (δ):

Load Intensity (q_f):

Distance of Deflection from End A (x):

Column Length (l_column):

Bending Moment in Column (M_b):

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1. What is the Bending Moment Formula?

The bending moment formula calculates the internal moment in a structural column subjected to both compressive axial load and uniformly distributed load. This formula accounts for the combined effects of axial thrust and distributed loading on the structural member.

2. How Does the Calculator Work?

The calculator uses the bending moment formula:

\[ M_b = -(P_{axial} \times \delta) + (q_f \times \left( \frac{x^2}{2} - \frac{l_{column} \times x}{2} \right)) \]

Where:

\( M_b \) — Bending Moment in Column (N·m)
\( P_{axial} \) — Axial Thrust (N)
\( \delta \) — Deflection at Section (m)
\( q_f \) — Load Intensity (Pa)
\( x \) — Distance of deflection from end A (m)
\( l_{column} \) — Column Length (m)

Explanation: The formula calculates the bending moment by considering both the axial thrust component and the distributed load component at a specific section of the column.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for structural design and analysis, ensuring that columns and struts can safely withstand combined axial and bending loads without failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (Newtons for force, meters for distance, Pascals for load intensity). Ensure all values are positive and within reasonable engineering limits.

5. Frequently Asked Questions (FAQ)

Q1: What is axial thrust in structural analysis?
A: Axial thrust refers to the compressive force acting along the longitudinal axis of a structural member, such as a column or strut.

Q2: How does distributed load affect bending moment?
A: Distributed load creates a varying bending moment along the length of the member, with maximum moment typically occurring at points of maximum deflection or support.

Q3: What are typical units for bending moment?
A: Bending moment is typically measured in Newton-meters (N·m) or kilonewton-meters (kN·m) in the SI system.

Q4: When is this formula applicable?
A: This formula is specifically for struts or columns subjected to both compressive axial loads and uniformly distributed lateral loads.

Q5: What factors influence bending moment in columns?
A: Bending moment is influenced by the magnitude of axial load, distributed load intensity, column length, material properties, and support conditions.