Cross-Sectional Area Given Maximum Stress Induced For Strut With Axial And Point Load Calculator

Formula Used:

\[ A_{sectional} = \frac{P_{compressive}}{\sigma_{bmax}} + \frac{W_p \cdot \left( \frac{\sqrt{\frac{I \cdot \varepsilon_{column}}{P_{compressive}}}}{2 \cdot P_{compressive}} \cdot \tan\left( \frac{l_{column}}{2} \cdot \sqrt{\frac{P_{compressive}}{\frac{I \cdot \varepsilon_{column}}{P_{compressive}}}} \right) \right) \cdot c}{\sigma_{bmax} \cdot r_{least}^2} \]

Column Compressive Load (P_compressive):

Maximum Bending Stress (σ_bmax):

Greatest Safe Load (W_p):

Moment of Inertia Column (I):

m⁴

Modulus of Elasticity Column (ε_column):

Column Length (l_column):

Distance from Neutral Axis to Extreme Point (c):

Least Radius of Gyration Column (r_least):

Column Cross Sectional Area:

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1. What is Cross-Sectional Area Given Maximum Stress Induced For Strut With Axial And Point Load?

This calculation determines the required cross-sectional area of a strut or column that is subjected to both axial compressive load and a point load, ensuring that the maximum stress induced does not exceed allowable limits.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( A_{sectional} \) — Column Cross Sectional Area (m²)
\( P_{compressive} \) — Column Compressive Load (N)
\( \sigma_{bmax} \) — Maximum Bending Stress (Pa)
\( W_p \) — Greatest Safe Load (N)
\( I \) — Moment of Inertia Column (m⁴)
\( \varepsilon_{column} \) — Modulus of Elasticity Column (Pa)
\( l_{column} \) — Column Length (m)
\( c \) — Distance from Neutral Axis to Extreme Point (m)
\( r_{least} \) — Least Radius of Gyration Column (m)

Explanation: The formula accounts for both axial compression and bending effects from the point load, considering the column's elastic properties and geometry.

3. Importance of Cross-Sectional Area Calculation

Details: Accurate calculation of cross-sectional area is crucial for structural design to ensure that columns and struts can safely support combined axial and bending loads without exceeding material stress limits.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure compressive load, stresses, and material properties are positive values. Column length and geometric properties must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of structural elements is this calculation suitable for?
A: This calculation is designed for columns and struts that experience both axial compressive loads and transverse point loads.

Q2: How does the point load affect the required cross-sectional area?
A: The point load creates bending moments that increase stress, requiring a larger cross-sectional area to maintain safe stress levels.

Q3: What is the significance of the radius of gyration in this calculation?
A: The least radius of gyration determines the column's susceptibility to buckling and affects the bending stress distribution.

Q4: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior and may have limitations for very slender columns or materials with non-linear behavior.

Q5: How should safety factors be applied to the results?
A: Appropriate safety factors should be applied to both the calculated cross-sectional area and material properties based on relevant design codes and standards.