Critical Stress for Carbon Steel by Chicago code Calculator

Critical Stress Formula:

\[ S_w = 16000 - 70 \times \left(\frac{L}{r_{gyration}}\right) \]

Critical Stress (Pa):

1. What is Critical Stress for Carbon Steel by Chicago Code?

Definition: This calculator determines the critical stress for carbon steel columns according to the Chicago building code formula.

Purpose: It helps structural engineers and designers verify the stability of carbon steel columns under compressive loads.

2. How Does the Calculator Work?

The calculator uses the Chicago code formula:

\[ S_w = 16000 - 70 \times \left(\frac{L}{r_{gyration}}\right) \]

Where:

\( S_w \) — Critical stress (Pa)
\( L \) — Effective length of column (m)
\( r_{gyration} \) — Radius of gyration of column (m)

Explanation: The formula calculates the maximum allowable stress before buckling occurs, considering the column's slenderness ratio.

3. Importance of Critical Stress Calculation

Details: Proper critical stress estimation ensures structural stability, prevents buckling failures, and complies with building codes.

4. Using the Calculator

Tips: Enter the effective length of column, radius of gyration, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the effective length of a column?
A: It's the length between points of zero moment (points of inflection), accounting for end support conditions.

Q2: How do I determine the radius of gyration?
A: It's calculated as \( r = \sqrt{I/A} \), where I is moment of inertia and A is cross-sectional area.

Q3: Why include a tolerance percentage?
A: The tolerance accounts for material variations, fabrication tolerances, and safety factors.

Q4: What units does this calculator use?
A: The calculator uses meters for length inputs and outputs stress in Pascals (Pa).

Q5: Is this formula specific to carbon steel?
A: Yes, this formula is specifically for carbon steel as per the Chicago building code.