Moment of Inertia Calculator Hollow Rectangle

Hollow Rectangle Moment of Inertia Formula:

\[ I = \frac{b h^3}{12} - \frac{b_{inner} h_{inner}^3}{12} \]

Outer Width (b):

length units

Outer Height (h):

length units

Inner Width (b_inner):

length units

Inner Height (h_inner):

length units

Moment of Inertia (I):

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1. What is Moment of Inertia for Hollow Rectangle?

The moment of inertia (second moment of area) for a hollow rectangle is a geometric property that quantifies its resistance to bending about a particular axis. It's calculated by subtracting the inner rectangle's moment of inertia from the outer rectangle's moment of inertia.

2. How Does the Calculator Work?

The calculator uses the hollow rectangle formula:

\[ I = \frac{b h^3}{12} - \frac{b_{inner} h_{inner}^3}{12} \]

Where:

\( b \) — Outer width of the rectangle
\( h \) — Outer height of the rectangle
\( b_{inner} \) — Inner width of the hollow section
\( h_{inner} \) — Inner height of the hollow section
\( I \) — Moment of inertia (result)

Explanation: The formula calculates the difference between the moments of inertia of the outer and inner rectangles about their centroidal axis.

3. Importance of Moment of Inertia Calculation

Details: Moment of inertia is crucial in structural engineering for determining beam deflection, stress distribution, and buckling resistance in hollow rectangular sections.

4. Using the Calculator

Tips: Enter all dimensions in consistent length units. Inner dimensions must be smaller than outer dimensions. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical units for moment of inertia?
A: Common units are mm⁴, cm⁴, or in⁴ depending on the input units. The calculator uses generic "length⁴" units based on your input.

Q2: How does hollow section affect moment of inertia?
A: Hollow sections provide higher stiffness-to-weight ratio compared to solid sections, making them efficient for many structural applications.

Q3: What if my inner dimensions are zero?
A: If inner dimensions are zero, the calculator will compute the moment of inertia for a solid rectangle.

Q4: Can this be used for any axis?
A: This formula calculates moment of inertia about the centroidal axis. For other axes, parallel axis theorem must be applied.

Q5: What materials is this valid for?
A: The calculation is purely geometric and valid for any homogeneous material as long as the section maintains its shape under load.