What are purlins?

Purlins are structural timbers that are used in the construction of traditional pitched roofs. They are installed horizontally within a roof assembly, on the underside of the rafters to provide support to the structure. Typically, purlins are installed at approximately halfway up the span of the common rafters. This was common in homes built within the last 150 years in the UK, as the thickness of the common rafters were typically much thinner (often 4”x2”) in comparison to modern rafters, despite their long span. By installing purlins within a roof assembly, the effective unsupported span of the rafters is halved, preventing sagging from occurring in the planes of the roof over time under the weight of the tiles.  

Purlins also feature a more prominent implementation in some varieties of post and beam framing, depending on the era and cultural location of construction.  

How are purlins implemented?

In gable end and terraced houses, purlins are built into the masonry that forms the internal partition of the roof - providing a load bearing structure for the purlin to bear down on. At common intervals along the length of the purlin, purlin struts are installed to distribute the load of the purlins onto internal load bearing walls. In hipped roofs that feature no masonry that can directly support the purlin ends, purlin braces provide the main stability to the purlins by distributing the load onto the internal load bearing walls. Where purlins meet at a hip or valley intersection, a special angle is cut for the two timbers to come together neatly. In traditional roofs, larger timbers were used as purlin timbers, such as deep 6”x3” beams.

In modern roof framing, purlins are less commonly implemented due to the increased structural capacity of the common rafters in accordance with modern structural calculations. That being said, the installation of purlins may be called upon depending on the circumstances and criteria of the roof assembly.  

How are the angles for purlins and struts calculated?

The following section explains how the angles of purlins and purlin struts/braces are calculated and cut. Some of the processes here are more advanced and will be explained again further on in this chapter when we look at the geometric layout of roofs.  

There are 2 main angles that are required for cutting a purlin accurately. These are known as the purlin edge bevel and the purlin side bevel. They may also be referred to as the purlin top bevel and purlin face bevel respectively.

The edge bevel is made on the edge of the purlin as it faces us from the outside of the roof on the underside of the rafters. This is the angle that the purlin meets the 45 degrees on plan hip or valley, as the jack edge cut would meet the hip or valley. Interestingly, or rather mathematically, the purlin edge cut is the opposite angle to the jack edge cut within a right-angle triangle. For a regular hip and valley roof, calculating the purlin edge cut by drawing it out is very straightforward. If we draw the run of the roof at 90 degrees to the true rafter length, the resulting connecting line is the true length of the hip. The angle intersection between this line and the run line is the angle of the purlin edge cut. The relationship to this angle and the jack edge cut angle can also be demonstrated here, as a perpendicular line anywhere off of the run line will display the jack edge cut where it intersects the hip line. These two angles add up to 90 degrees, and so are opposites of each other.  

Example - 5m span = 2.5m run. 2500/cos(35) = 3052. Draw 3052 and 25

The side bevel/face bevel is the “vertical angle” of the purlin and is made on the inside face of the purlin as it faces towards us inside the room. Imagine for a second that the roof structure was pushed down flat to a pitch of 0 degrees. As the purlin meets the side of the valley or hip rafter, the face cut angle is 90 degrees to the edge of the purlin. As the pitch is increased and the hip/valley rises away from the horizontal plane, the angle of the face cut begins to pull backwards to accommodate the change in presentation of the purlin. Visualising this angle can be difficult, as opposed to the easy explanation of the edge bevel angle. That being said, the method for calculating the angle is very straightforward. The common rafter true length is drawn on paper or the corner of a sheet of plywood, with the rise of the roof coming away from this at 90 degrees. With the two points connected to form a full right angled triangle, the angle between the rise and the new line is the face cut of the purlin. This partially demonstrates how the angle of the face cut is related to the pitch of the roof. 

With these two angles marked out and cut simultaneously to produce a compound angle, the face of the purlin should meet the edge of the hip or valley provided that the purlin is positioned perfectly horizontally across the underside of the rafters. In the event that the hip or valley is deeper in the roof than the thickness of the purlin, then a lip cut must be made to allow the two purlins to meet each other as well as the structural timber in its full capacity.  

The lip cut refers to a notch made on the end of the purlin to receive around the hip or valley. Marking out this cutout is very straightforward and is marked out after the main two angles are cut to form the compound angle on the end of the purlin. Firstly we must mark the point where the bottom edge of the hip or valley contacts the compound cut of the purlin. We can do this by holding the purlin or an offcut in place and marking against the rafter, or by measuring the vertical depth of the hip or valley from the underside of the common rafters. With the depth of the hip or valley marked down from the top edge of the purlin, we can pull this mark backwards down the length of the timber a few inches. From the front edge of the purlin, mark the diagonal thickness of the hip along the intersection line. Redraw the purlin face cut angle and edge angle from this point. Where the intersection line meets the face bevel, make a line at 90 degrees. We can now see our waste marked. When both purlins have this waste removed, they will fit around the hip or valley, housing the rafter in between them.  

Purlin Lip Cut Angle = arctan (tan Backing Angle × cos Jack Rafter Side Cut Angle)l

To fix purlins, nails were traditionally skewed through the sides of the rafters from above where they sit above the purlin. If the purlins were installed from inside the roof after the fact, they can sometimes be seen skew nailed through the top inside edges. In modern construction, structural coach screws are used to fasten the purlin to the rafters directly through the face of the purlin.

As the purlin bears the weight of the rafters and roof tiles, purlin struts/braces must be installed inside the roof to transfer this load onto internal load bearing beams or walls. Ordinarily, the purlin struts are installed perpendicular to the purlin, regardless of the pitch of the roof. This ensures that all load is directed at 90 degrees to the purlin for maximum strength in the struts. In scenarios where the exact location that the load is being transferred to is out of the perpendicular fall of the struts, adjustments in the angle of presentation can be made. Traditionally, the struts - sometimes dimensionally the same timber as the purlin, sometimes thinner - are halved on their ends the depth of the purlin to provide additional fixings and stability to the brace on the purlin. In some instances, the halved tenons are oriented on the face of the purlin - in others they are placed behind the purlin. Fixings are placed through the half lap to secure the brace to purlin. Where the purlin strut meets a load bearing surface, the appropriate bevel is cut on the end to allow the strut to be fully seated.

Note here that these angles are applicable to the installation of horizontal trimmers between hips or valleys, as the horizontal timbers are in the same orientation as purlins. This could apply to trimmers that form light openings between two hips or valleys.