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Constant Depending on Material of Column According to Johnson's Parabolic Formula Calculator

Johnson's Formula:

\[ r = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{\left(\frac{L_{eff}}{r_{least}}\right)} \]

1. What is Johnson's Parabolic Formula?

Definition: Johnson's formula calculates the critical load for intermediate columns that fail by inelastic buckling.

Purpose: It helps engineers determine the safe load capacity of columns that are too long to be treated as short columns but too short to fail by elastic buckling.

2. How Does the Calculator Work?

The calculator uses Johnson's formula:

\[ r = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{\left(\frac{L_{eff}}{r_{least}}\right)} \]

Where:

  • \( r \) — Johnson's formula constant
  • \( \sigma_c \) — Compressive yield stress
  • \( P \) — Critical load on column
  • \( A_{sectional} \) — Column cross-sectional area
  • \( L_{eff} \) — Effective column length
  • \( r_{least} \) — Least radius of gyration

Explanation: The formula calculates the material constant based on stress, load, geometric properties, and slenderness ratio.

3. Importance of Johnson's Constant

Details: This constant helps determine the transition point between short and long column behavior, crucial for structural design.

4. Using the Calculator

Tips: Enter all required values (all must be > 0). The ±5% indicates typical tolerance ranges for these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What does the ±5% tolerance mean?
A: It indicates the typical uncertainty range for each parameter in practical applications.

Q2: When is Johnson's formula applicable?
A: For intermediate columns where the slenderness ratio is between the limits for Euler and simple compression formulas.

Q3: How do I determine the effective column length?
A: It depends on end conditions - use length factors (K) based on column end constraints.

Q4: What's a typical value for Johnson's constant?
A: It varies by material but often ranges between 1-10 for common structural materials.

Q5: Does this include safety factors?
A: No, the calculated constant should be used with appropriate safety factors in design.

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