Radius Of Gyration If Maximum Bending Moment Is Given For Strut With Axial And Point Load Calculator

Formula Used:

\[ r_{least} = \sqrt{\frac{M \times c}{A_{sectional} \times \sigma_{bmax}}} \]

Maximum Bending Moment In Column (M):

N·m

Distance from Neutral Axis to Extreme Point (c):

Column Cross Sectional Area (A_sectional):

m²

Maximum Bending Stress (σ_bmax):

Least Radius Of Gyration Column (r_least):

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1. What is the Least Radius of Gyration Formula?

The least radius of gyration formula calculates the smallest value of the radius of gyration used for structural calculations, particularly for columns and struts subjected to bending moments and axial loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{least} = \sqrt{\frac{M \times c}{A_{sectional} \times \sigma_{bmax}}} \]

Where:

\( r_{least} \) — Least radius of gyration (m)
\( M \) — Maximum bending moment in column (N·m)
\( c \) — Distance from neutral axis to extreme point (m)
\( A_{sectional} \) — Column cross sectional area (m²)
\( \sigma_{bmax} \) — Maximum bending stress (Pa)

Explanation: This formula determines the minimum radius of gyration based on the bending moment, cross-sectional properties, and material stress limits.

3. Importance of Radius of Gyration Calculation

Details: The radius of gyration is crucial for determining the slenderness ratio of structural members, which affects their buckling behavior and overall stability under compressive loads.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Maximum bending moment and distance should be positive values. Cross-sectional area and maximum bending stress must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of radius of gyration?
A: The radius of gyration represents the distance from the axis at which the entire area could be concentrated and still have the same moment of inertia.

Q2: Why is the least radius of gyration important?
A: The least radius of gyration determines the maximum slenderness ratio and is critical for buckling analysis in structural design.

Q3: How does bending moment affect the radius of gyration?
A: Higher bending moments generally require larger cross-sections or different material properties to maintain stability, which affects the radius of gyration calculation.

Q4: What units should be used for input values?
A: Use consistent SI units: Newtons and meters for force and length dimensions, Pascals for stress.

Q5: When is this calculation most applicable?
A: This calculation is particularly important for slender columns and struts subjected to combined axial and bending loads where buckling is a concern.