Bending Moment At Section For Strut With Axial And Transverse Point Load At Center Calculator

Formula Used:

\[ M_b = -(P_{compressive} \times \delta) - \left(\frac{W_p \times x}{2}\right) \]

Column Compressive Load (P_compressive):

Deflection at Section (δ):

Greatest Safe Load (W_p):

Distance of Deflection from End A (x):

Bending Moment in Column (M_b):

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1. What is Bending Moment in Column?

Bending Moment in Column is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. It represents the internal moment that resists bending deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_b = -(P_{compressive} \times \delta) - \left(\frac{W_p \times x}{2}\right) \]

Where:

\( M_b \) — Bending Moment in Column (N·m)
\( P_{compressive} \) — Column Compressive load (N)
\( \delta \) — Deflection at Section (m)
\( W_p \) — Greatest Safe Load (N)
\( x \) — Distance of deflection from end A (m)

Explanation: This formula calculates the bending moment at a specific section of a strut subjected to both axial compressive load and transverse point load at the center.

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 transverse loading conditions without failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (Newtons for loads, meters for distances). Ensure all input values are positive and within reasonable engineering ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the negative sign in the formula?
A: The negative sign indicates that the bending moment acts in the opposite direction to the applied loads, representing the internal resisting moment.

Q2: When is this formula typically used?
A: This formula is used for structural analysis of columns and struts subjected to combined axial compressive loads and transverse point loads at the center.

Q3: What are the limitations of this formula?
A: This formula assumes linear elastic behavior and may not account for large deformations, material nonlinearities, or complex boundary conditions.

Q4: How does deflection affect bending moment?
A: Increased deflection typically increases the bending moment due to the P-δ effect (moment amplification from axial load acting through deflection).

Q5: Can this formula be used for dynamic loading conditions?
A: This formula is primarily for static analysis. Dynamic loading conditions require additional considerations for inertia and damping effects.