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

Formula Used:

\[ M_b = \frac{\sigma_b \times A_{sectional} \times (r_{least})^2}{c} \]

Bending Stress in Column:

Column Cross Sectional Area:

m²

Least Radius of Gyration Column:

Distance from Neutral Axis to Extreme Point:

Bending Moment in Column:

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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:

\[ M_b = \frac{\sigma_b \times A_{sectional} \times (r_{least})^2}{c} \]

Where:

\( M_b \) — Bending Moment in Column (N·m)
\( \sigma_b \) — Bending Stress in Column (Pa)
\( A_{sectional} \) — Column Cross Sectional Area (m²)
\( r_{least} \) — Least Radius of Gyration Column (m)
\( c \) — Distance from Neutral Axis to Extreme Point (m)

Explanation: This formula calculates the bending moment based on bending stress, cross-sectional properties, and geometric characteristics 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 other structural elements can safely resist applied loads without excessive deformation or failure.

4. Using the Calculator

Tips: Enter bending stress in Pascals, cross-sectional area in square meters, least radius of gyration in meters, and distance from neutral axis in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is bending stress?
A: Bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

Q2: What is the least radius of gyration?
A: The least radius of gyration is the smallest value of the radius of gyration used for structural calculations, representing the distribution of cross-sectional area.

Q3: What is the neutral axis?
A: The neutral axis is the line in a beam or column where there is no tension or compression during bending.

Q4: When is this formula applicable?
A: This formula is specifically for struts with axial and transverse point load at center, where bending stress is known.

Q5: What are typical units for bending moment?
A: Bending moment is typically measured in Newton-meters (N·m) or pound-feet (lb·ft) in engineering applications.