Allowable Axial Compression Stress For Slenderness Ratio Greater Than 160 Calculator

Formula Used:

\[ F_a = \sigma_c' \times \left(1.2 - \frac{L_{eff}}{800 \times r_{least}}\right) \]

Value obtained from Secant Formula (σc'):

Pascal

Effective Column Length (Leff):

Meter

Least Radius of Gyration Column (rleast):

Meter

Allowable Compression Stress (Fa):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Allowable Axial Compression Stress?

Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material. For slenderness ratio greater than 160, this formula provides the allowable axial compression stress calculation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_a = \sigma_c' \times \left(1.2 - \frac{L_{eff}}{800 \times r_{least}}\right) \]

Where:

\( F_a \) — Allowable compression stress (Pascal)
\( \sigma_c' \) — Value obtained from secant formula, stress value on the column of mild steel (Pascal)
\( L_{eff} \) — Effective column length, length of an equivalent pin-ended column (Meter)
\( r_{least} \) — Least radius of gyration column, smallest value used for structural calculations (Meter)

Explanation: This formula calculates the allowable compression stress for structural columns with slenderness ratio greater than 160, accounting for column length and radius of gyration.

3. Importance of Allowable Compression Stress Calculation

Details: Accurate calculation of allowable compression stress is crucial for structural design and safety, ensuring that columns can withstand applied loads without buckling or failure, particularly for slender columns with high slenderness ratios.

4. Using the Calculator

Tips: Enter value obtained from secant formula in Pascal, effective column length in meters, and least radius of gyration in meters. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is slenderness ratio in structural engineering?
A: Slenderness ratio is the ratio of the effective length of a column to its least radius of gyration, used to determine the column's susceptibility to buckling.

Q2: When should this formula be used?
A: This formula is specifically designed for columns with slenderness ratio greater than 160, where different buckling considerations apply.

Q3: What is the secant formula in column design?
A: The secant formula is used to calculate the maximum stress in an eccentrically loaded column, accounting for both direct compression and bending stresses.

Q4: How does radius of gyration affect column strength?
A: The radius of gyration measures the distribution of cross-sectional area about its centroidal axis. A larger radius of gyration generally indicates greater resistance to buckling.

Q5: What are typical applications for this calculation?
A: This calculation is used in the design of tall slender columns in buildings, bridges, towers, and other structural systems where buckling is a primary concern.