Value Obtained from Secant Formula given Allowable Axial Compression Stress Calculator

Secant Formula:

\[ σ_c' = \frac{F_{yw}/f_s}{1 + 0.20 \times \left(\frac{EAR}{r_{least}} \times \sqrt{\frac{f_s \times P_{compressive}}{4 \times ε_{column}}}\right)} \]

Specified minimum yield stress for column (F_yw):

Factor of Safety (f_s):

Effective Interest Rate (EAR):

Least Radius of Gyration Column (r_least):

Column Compressive load (P_compressive):

Modulus of Elasticity Column (ε_column):

Value obtained from secant formula (σ_c'): %

1. What is Value Obtained from Secant Formula?

Definition: This calculator computes the allowable axial compression stress using the Secant Formula, which accounts for eccentric loading in columns.

Purpose: It helps structural engineers determine the safe load capacity of columns considering both axial and bending stresses.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ σ_c' = \frac{F_{yw}/f_s}{1 + 0.20 \times \left(\frac{EAR}{r_{least}} \times \sqrt{\frac{f_s \times P_{compressive}}{4 \times ε_{column}}}\right)} \]

Where:

\( σ_c' \) — Value obtained from secant formula (%)
\( F_{yw} \) — Specified minimum yield stress for column (%)
\( f_s \) — Factor of Safety (%)
\( EAR \) — Effective Interest Rate (%)
\( r_{least} \) — Least Radius of Gyration Column (%)
\( P_{compressive} \) — Column Compressive load (%)
\( ε_{column} \) — Modulus of Elasticity Column (%)

Explanation: The formula accounts for both direct compression and bending effects in columns.

3. Importance of Secant Formula Calculation

Details: Proper calculation ensures structural stability and prevents column failure under combined loading conditions.

4. Using the Calculator

Tips: Enter all required parameters as percentages. The calculator will compute the allowable stress considering all factors.

5. Frequently Asked Questions (FAQ)

Q1: Why use the Secant Formula?
A: It provides more accurate results for columns with eccentric loading compared to Euler's formula.

Q2: What's a typical Factor of Safety?
A: Typically ranges from 1.5% to 3% depending on material and application.

Q3: How is Effective Interest Rate related?
A: EAR accounts for the compounding effect in structural deformation calculations.

Q4: What if I get negative results?
A: Check your inputs - all values must be positive percentages.

Q5: How precise are the results?
A: Results are typically accurate to ±5% when proper inputs are provided.