A Purlin Size Calculator is a tool used to determine the optimal size, spacing, and number of purlins required for a roof structure. Purlins are horizontal structural members that support roofing sheets or cladding and are essential in maintaining the roof’s structural integrity. Accurate purlin calculations ensure the roof can withstand various loads, such as wind, snow, and dead loads while complying with local building codes.

Using a purlin-size calculator simplifies the design process for engineers, architects, and builders, ensuring structural efficiency, safety, and cost-effectiveness. The calculator can compute the total number, length, and size of purlins required for a roof structure based on span, roof pitch, load requirements, and materials used.

Key Concepts and Terminology

• Purlin: Horizontal beams that support roofing sheets and transfer loads to rafters or trusses.
• Beam: A horizontal structural member that resists bending under load.
• Span: The distance between two supports, such as rafters, trusses, or girders.
• Rafter: Inclined beams supporting the roof structure, often carrying purlins.
• Purlin Spacing: The distance between two adjacent purlins.
• Dead Load: The static weight of the structure, such as roofing sheets and cladding.
• Live Load: Temporary loads on the roof, such as snow or maintenance workers.
• Deflection: The degree to which a structural element bends under load.
• Girt: Horizontal structural members used in wall framing, similar to purlins in roof construction.
• AISI: American Iron and Steel Institute, which provides standards for cold-formed steel design.

Calculation Methods for Purlin Size

Several variables and formulas must be considered when calculating the size and number of purlins. Here are the steps:

Step 1: Identify Key Inputs

• Roof Span (L): Measure the distance from one side of the roof to the other.
• Roof Pitch: Determine the slope of the roof.
• Dead Load (DL): The weight of the roofing material, cladding, sheathing, and permanent fixtures.
• Live Load (LL): Temporary loads like snow or maintenance personnel.
• Wind Load (WL): Pressure applied to the roof due to wind.

Step 2: Calculate Maximum Bending Moment (M)

The bending moment can be calculated using the following formula for a simply supported beam:

[ M = \frac{(w \cdot L^2)}{8} ]

Where:

• ( w ) = Total load per unit length (Dead Load + Live Load + Wind Load) (kN/m)
• ( L ) = Span of the purlin (m)

Step 3: Calculate Required Section Modulus (S)

The section modulus determines the cross-sectional shape and size of the purlin. It is calculated as:

[ S = \frac{M}{\sigma} ]

Where:

• ( M ) = Maximum bending moment (km)
• ( \sigma ) = Allowable stress (MPa) from the material’s structural capacity

Step 4: Select Purlin Size Calculator

Use span tables or software to select an appropriate purlin size that satisfies the calculated section modulus. Timber, steel, or cold-formed steel can be used, depending on local building regulations.

Step 5: Calculate Purlin Spacing

Purlin spacing is influenced by the roofing material and load conditions. It is calculated as:

[ Purlin \ Spacing = \frac{L}{n} ]

Where:

• ( L ) = Total span of the roof (m)
• ( n ) = Number of purlins required

Detailed Calculation Example

Problem: Calculate the size and number of purlins for a roof with the following specifications:

• Roof span (L) = 6m
• Dead load (DL) = 0.5 kN/m²
• Live load (LL) = 0.75 kN/m²
• Wind load (WL) = 0.25 kN/m²
• Allowable stress (( \sigma )) = 150 MPa

Step 1: Calculate total load per unit length (w) [ w = DL + LL + WL ] [ w = 0.5 + 0.75 + 0.25 = 1.5 \ kN/m^2 ]

Step 2: Calculate maximum bending moment (M) [ M = \frac{(1.5 \cdot 6^2)}{8} ] [ M = \frac{54}{8} = 6.75 \ kNm ]

Step 3: Calculate required section modulus (S) [ S = \frac{6.75}{150} ] [ S = 0.045 \ m^3 = 45,000 \ mm^3 ]

Step 4: Select purlin size based on the required section modulus from span tables.

Step 5: Calculate purlin spacing. Assuming 4 purlins are required: [ Purlin \ Spacing = \frac{6}{4} ] [ Purlin \ Spacing = 1.5 \ m ]

Alternative Approaches

• Manual Calculation: Manually calculate load, bending moment, and section modulus using the steps above.
• Software Tools: Use specialized structural design software like STAAD.Pro or SkyCiv to automate purlin size calculations.

How to Use a Purlin Size Calculator

1. Input Dimensions: Enter roof span, pitch, and height.
2. Specify Loads: Input dead load, live load, and wind load.
3. Select Material: Choose between timber, cold-formed steel, or other materials.
4. View Results: The calculator will compute the size, number, and spacing of purlins.

Practical Tips for Using a Purlin Size Calculator

• Ensure local building codes are considered.
• Account for environmental loads like snow and wind.
• Verify materials’ stress limits and deflection limits.
• Use software for more complex structures.

Frequently Asked Questions

Conclusion

A Purlin Size Calculator is an essential tool for structural design, ensuring safe, efficient, and code-compliant roof structures. By following the calculation methods outlined in this guide, you can confidently determine the size, number, and spacing of purlins. For more complex projects, software tools and professional advice should be sought to ensure structural integrity.