Cross-Sectional Area Given Bending Stress For Strut With Axial And Transverse Point Load Calculator

Formula Used:

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

Bending Moment in Column (M_b):

N·m

Distance from Neutral Axis to Extreme Point (c):

Bending Stress in Column (σ_b):

Least Radius of Gyration Column (r_least):

Column Cross Sectional Area (A_sectional):

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1. What is Cross-Sectional Area Given Bending Stress?

The cross-sectional area given bending stress formula calculates the required cross-sectional area of a structural member (such as a strut or column) when subjected to both axial and transverse point loads, ensuring it can withstand the induced bending stress.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula determines the minimum cross-sectional area required to prevent failure due to bending stress in structural members under combined loading conditions.

3. Importance of Cross-Sectional Area Calculation

Details: Accurate calculation of cross-sectional area is crucial for structural design, ensuring safety, stability, and proper load-bearing capacity while preventing structural failure due to excessive bending stress.

4. Using the Calculator

Tips: Enter bending moment in N·m, distance in meters, bending stress in Pascals, and least radius of gyration in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is bending moment in structural analysis?
A: Bending moment is the internal moment that causes a structural element to bend. It's calculated as the sum of moments about the neutral axis of the section.

Q2: Why is the least radius of gyration important?
A: The least radius of gyration determines the column's buckling resistance. Smaller values indicate higher susceptibility to buckling under compressive loads.

Q3: What factors affect bending stress in columns?
A: Bending stress depends on the applied loads, column geometry, material properties, support conditions, and the distance from the neutral axis.

Q4: When is this formula typically used?
A: This formula is used in structural engineering for designing columns and struts subjected to combined axial and transverse loading conditions.

Q5: What are the limitations of this calculation?
A: This calculation assumes linear elastic material behavior, small deformations, and may not account for all complex loading scenarios or material nonlinearities.