Hi friends,
Today we’ll cover the last timber roof system of this series: The purlin roof.😎😎
The timber purlin roof consists of:
Rafters
Purlins
Columns or walls which support the purlins
Knee braces
Support system (ceiling joists or concrete slab)
A wind bracing system like steel rods or plywood boards
As for the other roof types, there are many different variants. Google a bit and you’ll discover different types of the purlin roof.
Before we’ll get into the design calculations, let’s have a quick look at the static system. 👇👇
The loads are first applied to the rafters and then the reaction forces of the rafter beams are applied as point loads to the purlin beams.
Alright, now we are ready. Here’s the step-by-step process we are following (it’s the same for all timber beam elements 😁😁):
Determine the characteristic loads (snow, wind, dead and live load)
Set up load combinations
Choose the timber material and geometry of the rafters and purlins (width and height)
Calculation of the internal forces (normal force, shear force, bending moment)
ULS bending verification
ULS shear verification
SLS deflection verification
These are the steps, we need to follow to design the rafters and purlin beams, but there is more to the roof structure such as connection design, wind bracing, and support verification.
#1 Characteristic loads
We’ve written detailed articles about loads on roof structures, which you can follow to understand how to calculate these loads:
#2 Load combinations
Load combinations combine the characteristic loads and add safety factors.
→ Detailed guide to load combinations ←
#3 Timber material and geometry of beams
You choose the timber material between structural wood and glulam. Glulam is usually stronger and can be delivered in almost any size, as it glues layers of timber together.
Just google a bit, and you’ll find the strength properties for both types of timber.
Before starting the calculation, we need to define the cross-sectional dimensions’ height h and width w of the beams to then calculate cross-section properties such as the moment of inertia.
Rafter dimensions:
#4 Internal force calculation
In uni, you learn to calculate the internal forces by hand, which is good to get an understanding for it. Later, as a structural engineer, you’ll mainly use software for it. Mainly because it’s a lot faster. Or, as in our case, it would be extremely difficult to calculate a statically indeterminate structure by hand. Programs like Autodesk Robot, Dlubal Rfem, Sofistik, etc. are used.
You apply the characteristic loads, and the programs generate automatically load combinations and the internal forces.
Here’s an example of the bending moment diagram due to the load combination from the picture above.
#5 ULS bending and compression verification
First, calculate the bending and compression stresses:
Then, the bending and compression resistance:
Now, check if the utilization ratio is < 100% (EN 1995-1-1 (6.19)) . ✅✅
To see the whole calculation with examples, check out our 👉 article 👈.
#6 ULS shear verification
As for bending, we’ll calculate the shear stress and shear resistance.
And then the utilization ratio.
#7 ULS buckling verification
Buckling can happen to all elements which act in compression. So the rafters have to be verified for buckling and the purlin beams if they take up the horizontal wind load and transfer it further to a wind bracing system like shear walls or bracing straps.
Slenderness ratio
Relative slenderness ratio
Instability factor
Buckling reduction coefficient (EN 1995-1-1 (6.25))
Utilization ratio (EN 1995-1-1 (6.23))
#8 SLS deflection verification
The deflection is also calculated with structural analysis programs and checked against limits from either Eurocode or the client.
It’s a bit more tricky, I recommend reading the article for more detailed explanations. 😎😎
#9 Next steps
Once you have verified the rafters, you continue with the purlins. You either model the whole roof in 3D in a structural analysis software or the purlins in 2D to extract the internal forces. The reaction forces of the rafters are applied to the purlin beams.
Now, you do the same verifications as in steps #5 - #8.
This was the 5th (and last 😜😜) timber roof system. Hope you also liked this series about roof systems.
I am excited to share some insights and data from our journey at Structural Basics.
So see you next week. ✌️✌️
Cheers,
Laurin.