Purlins and Girts for Structural Support in Buildings

Purlins and girts are structural members in roofs and walls that support loads from sheathing and cladding and are themselves supported by rafters,  trusses, or building walls. Purlins and girts can be made from timber or steel. As a rule of thumb,  purlins are frequently proportioned for a depth-to-length ratio of  1/32. Dead, live, snow, and wind loads should be calculated by the designer and checked against the bending, shear, torsion, buckling, and deflection capacity of the girt or purlin by relevant design codes.

Since Purlin and Girts are a very common building element, this article will be walking through on how to design them with the main key questions regarding Purlin & Girts as shown below : 

• What is Purlin in Constructions?
• What is a Girt?
• What are purlins used for?

This article will give you the most simplified data possible regarding Purlin and Girts to understand their usage in Structural Supports in buildings.

\( \textbf{1.1}\) Purlins & Girts

Purlins are horizontal structural members used in roof construction, they span across the roof trusses or frames and provide support for the roof sheeting or decking. They are used to support roof cladding and transfer roof loads to the primary structural elements like rafters or frames. Meanwhile, Girts are horizontal structural members that are used in wall construction, they support wall panels and transfer loads to primary structural fram with its purpose to provide lateral support for wall sheeting or cladding and transfer loads to vertical frames or columns.

Purlins has a few types but Steel purlin sections are namely C or Z sections. Steels are typically hot or cold-rolled. Hot rolling involves rolling steel at high temperatures to allow easy shaping and forming. Compared with hot-rolled sections of the same thickness, cold-rolled purlins tend to be lighter, stronger, and easier to assemble.

\( \textbf{1.1.1}\space\)Purlin Essentials

In the Table below, several terminology and application of Purlin and Girt are explained to understand the design considerations.

\( \textbf{1.1.2}\) Steps to Roof Purlin Design

Determine Spacing and Span direction

The following factors should be considered when determining roof purlin spacing:  

• The general rule of thumb: The maximum distance between steel purlins should be about 1200 mm. In residential buildings, the typical distance is about 600 to 800 mm.
• The maximum load from roof sheathing: as a rough guide, the maximum distance between purlins should be no more than 1200 mm with a 7 mm thick sheathing, and the maximum distance between purlins should be no more than 1000 mm with a 5 mm thick sheathing.
• Types of weather conditions: under low snow loads, spacing is typically 0.6 m.
• Spans of the purlins: Normally, the spacing of the purlins will be smaller than the span of the purlins to create a smaller uniformly distributed load along the length of the purlins, and the truss will endure a larger distributed load. Commonly, the span direction should be against the slope of the roof.
• Architectural considerations: Openings for windows, doors, and skylights should be considered when establishing purlin and girt spacing. Tertiary members can be added to frame openings if needed, but ideally, the primary purlin and girt members can also act as trimming members at openings.

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Assume the depth and width of the cross-section

• Apply the rule of thumb to estimate the depth of the purlins (the number could be rounded up) by depth = span/32
• Choose the available cross-section from the manufacturer's specifications with a suitable depth and design purpose
• C - section purlins are used in simple, non-continuous spans.
• Z - section purlins are used in continuous lines of purlins for lapping at internal supports.
• The manufacturer’s products should specify material properties like material density and other information essential for design checks.

💡 Note: the orientation of purlins should provide a shorter distance from the shear center to the loading vector to minimize torsional impacts.

Determine wind load and other load acting on purlins

Wind load is directly normal to the roof, which is on the y-axis of the local coordinate, so there is no need to convert it. Different design codes specify different approaches to calculating wind load on roofs. Wind load depends heavily on the region the structure is located in, the type of structure, and topographic factors.

The Design Codes that guide the wind load calculation are:

• Philippines Standard: NSCP Section 207
• European Standard: Eurocode 1 Part 1 - 4
• Australian Standard: AS1170.2
• US Standard: ASCE 7 - 10

The result will propose different wind load magnitudes (in kPa) on different locations on the roof, engineers usually choose the most significant wind load to design all purlins.

Calculate the uniformly distributed live load in kN/m along the purlin length by taking wind load on the effective area x spacing of purlins. The same steps could be repeated if there are any other environmental loads. Calculating wind loads on pitched roofs is a detailed affair, so we’ve written a separate article here that details the process.

Calculate all load combinations

Each Design Code will propose a different methodology to calculate the load combinations with different design factors. Due to the design factor, more loads on the structure don’t mean it will be the critical condition, so all load combinations should be checked and the most critical condition chosen. Here are some common combinations:

• Dead Load only
• Dead Load + Live Load
• Dead Load + Wind Load
• Dead Load + Wind Load + Live Load

Design Codes for load combinations:

• Australian Standard: AS1170.0
• European Standard: Eurocode 2
• US Code: ASCE 7 - 16

Choose the most critical scenario among those combinations to model and analyze the purlins. If the purlin system is simple enough, hand calculations can be performed.

Verify the member for bending.

Usually, bending is the deciding design factor for purlins; that is why it is commonly checked first.

• For each loading combination chosen from Step 5, determine bending forces for bending along the X and Y axes. For bending along the X-axis, evaluate bending moment using normal loads (Wn), and for bending along the Y-axis, evaluate using tangential loads (Wt).
• For a simply supported beam, the bending moment is calculated as M = wL2/8. Figure 7 illustrates some common beam configurations and the corresponding bending moment formula. Verify that bending moments are less than allowable or resistance stress limits.

Verify the beam for a combination of bending and axial load

The bending and axial loading combination is the second deciding factor for purlins. This occurs when a beam is subjected to loading that causes bending in both the major and minor axes. To verify combined loading refer to appropriate sections within steel or timber design Codes -

• AS4100-Clause 5 - Steel & AS1720-Clause 2  - Timber (Australian Code)
• AISC360-10 - Steel & ASCE7-22 - Timber (US Code)
• BS5950- Steel & BS5268 - Timber (UK Code)

❗If not verified, increase the width or height of the beam and recalculate.

Verify the beam for shear

The shear stress in the most critical section of the cross-section can be calculated using the maximum shear force.

Shear stress for beams can be calculated using:

$$ T = \frac{VQ}{It} $$

Where : 

\( T\hspace{2.5em}\) : shear stress (N/m2)
\( V\hspace{2.5em}\) : Total shear force at the point of location (N.m)
\( Q\hspace{2.5em}\) : First moment of area (mm3)
\( I\hspace{2.5em}\) : Moment of Inertia of entire cross section \( m^4\)
\( t\hspace{2.5em}\) : Material Thickness Perpendicular to shear (m)

Verify that shear stresses are less than the resistance/allowable stress of material cross-section by referring to the appropriate design codes for timber or steel member design‍

❗If not verified, increase the width or height of the beam and recalculate.

Verify the beam for instantaneous and final deflection criteria.

• Instantaneous deflection can be calculated with the load from the characteristic load combination in Section 2.1, where there are multiple Beam Deflection Formulas that can be seen below in Figure 5.

• Calculate the final deflection by adding instantaneous deflection and creep deflection
• Creep deflection depends on the stiffness value of materials, using the instantaneous deflection and the specification of Design Codes to calculate. The formula for creep deflection will depend on which local Design Code you consult.
• Check the deflection by ensuring the allowable deflection is larger than the final deflection. Both the x and y axes need to be checked.
• A secondary structural component like purlins will usually have the allowable deflection of L/180 (Eurocode). Different Design Codes might specify different allowable deflections

❗If not verified, increase the width or height of the beam and recalculate.

💡 Note: consider sag rods (or struts)  for purlins and girts.

While cold-formed sections (particularly Z purlins or girts) can provide substantial material and cost savings due to their higher strength-to-weight ratios, it gives rise to conditions that may see these members deform under many loading conditions and fail by yielding or local buckling as a result of induced stresses. Sag rods (struts) may be added as lateral supports to provide alignment and reduce their tendency to twist and bend and allow the transfer of the lateral loads. Typical sag rods are 10-12mm in diameter. Generally, manufacturer’s tables will provide details on the application and installation of a bridging system such as sag rods.

After all the steps are verified, a safe and suitable beam dimensions can be achieved.

\( \textbf{2.1}\) Calculation of Characteristic Loads

Generally, loads in buildings are concentrated or uniformly distributed over an area. When designing purlins and calculating characteristic loads (i.e dead and live load components), you would need to consider the latter, as purlins would pick up different portions of the total load acting over the surface depending on their arrangement. Figure 4 shows a typical roof arrangement in a building and the highlighted regions show the effective area, also known as a loading strip, transferring the loads acting on the strip to the support beams.

To determine the effective area of a span of the purlin, Effective area is taken as the product of tributary width and breadth. To simplify the design, Tributary width is simply taken as the distance between two adjacent members.

Determine the dead load on the effective area in kPa (along the loading strip). Dead loads include the self-weight of building elements (i.e. the purlins themselves) and superimposed dead loads (i.e., cladding, tanking, insulation, plaster, finishes, services, etc.). To obtain the line load, you require element dimensions and density obtained in Step 2. Area load (kPa or kN/m2) is calculated as:

$$ Thickness\ [m]\ \times \frac{density}{100} [\frac{kg}{m^3}] $$

• Calculate the uniformly distributed dead load in kN/m along the length of the purlin or the line load:

$$ dead\ load\ on\ the\ effective\ area\ [kPa]\ \times Tributary\ width\ (=spacing\ between\ purlins) [m] $$

• Calculate the uniformly distributed live load in kN/m along the length of the purlin:

$$live\ load\ on\ the\ effective\ area\ [kPa]\ \times Tributary\ width\ (=spacing\ of\ purlins) [m]$$

Purlins are typically inclined at an angle that follows the roof's slope. Therefore, there is a tangential and normal component to the applied dead and live loads. These loads can be transferred to the local member axis direction using the roof slope/pitch. Wind loads are always taken as normal to the rafter and should be added to the normal component of the applied characteristic loads without conversion.

The x-axis of the local coordinate is parallel to the rafter. The y-axis of the local coordinate is perpendicular to the rafter. The process of transferring loads to local coordinates is illustrated in Figure 8:

💡Note: Do not add dead load and live load together when projecting them on the x and y axis because the load factor in the load combination will change it.

\( \textbf{2.2}\) Effect of Uniform Loads

The Uniform loads of Purlin typically acts uniformly along the length of the Purlin and Sloped roofs are distributed between the loads as components act in both global and local coordinated. Wind loads can affect the loads on Purlin as they are directional and able to create uplift forces to change the expected load patterns on Purlin. In regions with high wind of exposure, suction forces may dominate which requires more robust anchorage. Uplift loads of the wind suction can reduce or reverse the dead and live load effects which can be seen in Figure 9 as it introduce to a potential instability, while non-uniform wind pressure on roofs leads to varying loads along the length of the Purlins.

Summary of Effects

• Localized Concentrations: Uneven loads or roof irregularities create stress concentrations.
• Higher Reactions at Supports: Due to combined loading and non-uniform pressure distributions.
• Deflection and Stability: Increased deflection or buckling risk under eccentric or uplift loads.
• Load Redistribution: For continuous spans, moments redistribute, affecting load paths and member design.

❗Addressing these effects involves using design tools like finite element analysis (FEA) and adhering to building codes to ensure safe and effective load distribution

❗ If the design check is not satisfied, the sections' area must be increased or decreased.