Inner Depth Of Hollow Rectangular Shape Calculator

Formula Used:

\[ D_i = \left( \frac{(6 \times Z \times D_o) + (B_o \times D_o^3)}{B_i} \right)^{1/3} \]

Section Modulus (Z):

m³

Outer Depth (Dₒ):

Outer Breadth (Bₒ):

Inner Breadth (Bᵢ):

Inner Depth (Dᵢ):

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1. What is the Inner Depth of Hollow Rectangular Section?

The Inner Depth of Hollow Rectangular Section refers to the interior vertical dimension of a hollow rectangular cross-section. It is a critical parameter in structural engineering for calculating section properties and analyzing beam behavior under various loading conditions.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ D_i = \left( \frac{(6 \times Z \times D_o) + (B_o \times D_o^3)}{B_i} \right)^{1/3} \]

Where:

\( D_i \) — Inner Depth of the hollow rectangular section (m)
\( Z \) — Section Modulus (m³)
\( D_o \) — Outer Depth of the hollow rectangular section (m)
\( B_o \) — Outer Breadth of the hollow rectangular section (m)
\( B_i \) — Inner Breadth of the hollow rectangular section (m)

Explanation: This formula calculates the inner depth based on the known section modulus and other geometric properties of the hollow rectangular section.

3. Importance of Inner Depth Calculation

Details: Accurate calculation of inner depth is essential for determining the moment of inertia, section modulus, and other geometric properties that affect the structural performance of beams and columns with hollow rectangular sections.

4. Using the Calculator

Tips: Enter all values in meters. Section modulus should be in cubic meters. All input values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Section Modulus?
A: Section Modulus is a geometric property that represents a section's resistance to bending. It is used in structural engineering to determine the stress in beams under bending moments.

Q2: Why is the hollow rectangular section used in construction?
A: Hollow rectangular sections provide excellent strength-to-weight ratio, making them efficient for structural applications where weight reduction is important while maintaining structural integrity.

Q3: What are the typical applications of hollow rectangular sections?
A: They are commonly used in building frames, bridges, crane booms, vehicle frames, and various structural components where both bending and torsional resistance are required.

Q4: How does inner depth affect the section properties?
A: The inner depth, along with other dimensions, determines the distribution of material and affects the moment of inertia, section modulus, and overall stiffness of the structural member.

Q5: Can this formula be used for other cross-sectional shapes?
A: No, this specific formula is derived for hollow rectangular sections only. Other cross-sectional shapes (I-beams, circular tubes, etc.) have different formulas for calculating their geometric properties.