2 cents from a carpenter. Preventing roof loads from pushing the walls outward is solved by using collar ties closer to the sill plates...typically joists serve this function. Collar ties are placed in the lower third of the rafter span. If a "cathedral" ceiling is desired then a structural ridge beam is used which transfers loading to the gable ends. Increasing the depth of rafters will not prevent outward thrust on the walls. The root of the problem is hinging at the rafter's intersection at the peak.
This. Andres rafters have deflection, the latter has no observable deflection. So this is a lesson on deflection effects rather than simply about load.
The way I have always done this with rafters when building a structure is to first use thick, at least 1/4” steel gusset plates at the peak that extend downward at least 12 to 18 inches. Next I put diagonal bracing between the rafters that are anchored to the walls. Then, when you add the decking to the rafters, this adds additional strength by acting as additional diagonal bracing. Although the decking adds weight, it adds much more in structural integrity. All of this, of course, will depend on the span of the rafters. If you have no load bearing walls and a long span, you will need more support, such as the cross beam.
The more the trusses bend under load, the more horizontal the forces becomes. If the trusses have minimal deflection under load, the outward forces will be less.
The first thing I noticed is that the set up has the left side in a locked position with the right side being metered. What you need is a meter on both sides to measure them independently because your set up is basically doubling the amount of force on the right hand side being that the left-hand side can’t move. Basically you’re forcing all of the movement in One Direction when in reality it would be going in both directions equally
What Andre never talked about is the effect of tension in the beam. If one of the supports is free to move just a little, tension will increase in the beam until it's carrying all the horizontal thrust, and the thrust at the supports will be zero. As Andre mentioned, it's indeterminate -- there is a relationship between tension in the beam and thrust at the supports, but neither is completely determined. I think builders can rely on the beam to reduce the thrust. It's easy to design the structure so that there is no thrust at all -- just assume it's zero, calculate how much tension is required in the beam to achieve that, and size it accordingly.
In old traditional houses in the Uk built over 200 years ago, A frame construction was used, but as in the last experiment the beams were oversized and rigid. This offset the problematic spreading loads. As the walls were built of cob which is a mud and straw mixture this was important.
The fact of the matter is that although the cross beam could help maintain the shape of the rafter slope by developing tension, no structural member can resist load unless it is allowed to deform - in this case stretch. As erected, your structure does not allow for movement outwards of the two rafters so that the tension could not arise in the horizontal tie. Your analysis thereafter is correct and the results predictable. In order for the tie to take effect one side of the foundation should be allowed to slide freely outwards until equilibrium is reached. At the point the horizontal beam would be in tension and would contribute to the stability without imposing a lateral force. If the structure was then further loaded by tiles or snow, the outward movement would still be necessary to avoid pressure on the walls. Some bridges take advantage of sliding joints both to account for thermal expansion and varying loads. This is not really a paradox it is simply a problem created by design.
The two experiments have the 'beam' working in different ways. With very flexible truss, the 'beam' is in compression as it tries to hold the midpoint of each rafter apart. But in the second, the rafters are more rigid and the 'beam' is in tension, trying to prevent the rafters from spreading outward. Trusses that I've seen almost always include a stringer from wall to wall that is in tension. This absorbs all the 'spreading' forces and the walls only provide vertical support. If the rafters are long and flexing is a concern, shorter diagonal 'beams' between the rafter and bottom stringer can be used.
As a rule of thumb, if the tie is at ceiling level we use the rafter size from the tables, if it is in the bottom third we increase the rafter by one size, if it is at the top third we go up two sizes, so the beam bending stiffness contains the spreading force . Great experiment though, i will actually be more careful in future, especially on long rafters.
Most traditional roofs in the UK have the tie at the wall plate, which should reduce the lateral load to near zero while the connection between the tie (ceiling joist) and the rafter holds.
The roof rafters are statically indeterminate since they see three supports. The end reactions depend on how much the rafters deflect, and how much lateral movement there is at the end supports. For a statically determinate arrangement, as in the roof rafters without the brace, the reactions will be the same no matter what the flexibility of members or end condition. In the second, indeterminate arrangement, the flexibility will change the resulting reactions.
FEM solution. We did "method of sections "and " virtual work" in structural engineering. Before FEM computers . In statics the one support is often a hinged rollor support or it becomes static indeterminate problem. Excellent channel 👍
Beers and Johnson book on statics has a section on trusses. I remember transposing the forces at each point of contact in vector form and cutting the truss into sections to solve
If the rafters are flexible, they will absorb some of the force as they bend downward. If the rafters are rigid, all the force goes to the walls in lateral thrust?
In the first experiment the diagonal roof members were too thin to take bending moment. This structure is not a truss were no members take have bending. These diagonal members have a bending load. When thin as in experiment 1 they deflect transferring compression into the rafter that buckles under this compessive load. In the 2nd experiment the diagonal roof members are stiff and resist the bending load in the center of them at the load point. They hinge outward with the hinge at the peak. This defelection causes a tension in the horizontal rafter instead of a compression. This tension takes away some of the thrust at the wall joint. In the 2nd experiment you do not need the lateral rectation braces at the wall, i.e. the vertical blocks. Take them away and the rafter will take all of the thrust as tension, so long as the diagonal roof members do not bend under the downward loads at their centers.
The trusses with the beam in the last experiment, or in real life, creates a force that push down on the walls more than out? Reducing the outward thrust forces?
I subscribed to this channel to learn with my kids, but if they don't eventually provide the answers, I don't see the point in it. If you guys are reading this.... you'll get more views if you actually give the answer instead of telling us that you know it.
Well you could just ask a structural engineer. In the first scenario with no tie beam the 2 beams along try to push on the walls. The walls hav to resist the entire force. In a lot of houses the walls won't be able to do this, they will just fall over. In an old building with very heavy exterior masonry walls maybe they can resist. In the second scenario with the tie beam, the 3 pieces connected together are stable, they do not have to rely on forces on the walls to remain in place. This is a better solution because it works with any type of wall construction. What would happen in reality is in the first scenario the walls will always have to resist the forces from the 2 beams. If the walls cannot then they will move and the beams will collapse. In the second scenario the walls would likely not be completely stiff so they would move a little bit and as they move they would relieve the horizontal forces so after moving a small amount they no longer have to carry any horizontal force.
🧱 _The claim that the beam increases horizontal force on the walls can be very easily refuted experimentally: In a pin-jointed rigid truss without the beam, and without walls, the truss can't even hold its own shape, amd it would fall and flatten out... it needs the walls to constrain it from falling flat._ _But if you add the connecting beam, the same truss without walls can support not only its own weight, but much more load as well._ _This clearly shows that the beam carries a lot of horizontal load._ _Using flexible trusses like Andre used, allows the joinys to move, this changing the geometry and makes the truss roof angle more horizontal... which naturally increases the horizontal force needed to support a vetical load._ _Mathematically, when a flexible truss withiut a beam "flattens out", then the beam tension or compression force are given by N × sin(theta/2), where theta is the roof angle between the two trusses. A bigger theta means higher truss member forces, which in turn need bigger forces from the wall to counteract their horizontal component. (I hope I didnt get my sin and cos mixed up, as I did this quick analysis without drawing)._😅
Where’s the paradox. This is a pretty simple bit of design work. So long as the timbers are strong enough, then the horizontal beam holds the tension load and the loading on the walls is purely a downward force. Just the weight. In reality, there will be a small amount of flex and stretch of these timbers. Providing that is small, then usually there’s no problem, no paradox to worry about.
If you have a structural engineer design it they would use the truss system in some form or fashion. If you have a guy with a saw and hammer build it he might very well rely on the birdnest principle. The bird didn't go to college, he didn't study physics, he puts sticks together until they stay in position. And this generally works, until it doesn't and you find the next laying on the ground. Generally people who own buildings don't want to find parts of their building laying on the ground.
Thank goodness for the last minute and a half, as nothing was making sense to me (as a real world construct) up to that point. The theory was sound and interesting, but the application and functionality made no sense.
? It becomes a ratiometric matter of where the beam mounts. If the beam is at the walls then it takes ALL the outward force in tension so ALL of the roof load is downward.
On the contrary- without the horizontal tie the walls have to always resist the horizontal force. In normal building construction the walls won't be able to do this and the roof will be close to collapse. With the tie in place the walls no longer have to resist the horizontal forces, they can move outwards a little bit along with the movement of the ends of the beams until an equilibrium is reached where there is no more force pushing on the walls.
@@billj5645 You are claiming that cathedral ceilings without cross bars don't exist as part of "normal building construction", which is clearly not true. How do you resist the outward pressure? Shear walls and wider top plates. In areas without snow load but with high winds or seismic activity, the wind load or seismic load is going to be greater than outward component of the roof load.
@@richdobbs6595 The point is that the 2 beam roof requires constant resistance from the walls in order to be stable, the truss system does not. As long as the walls can provide this everything is ok. As I said if you have walls that are built with a lot of masonry they can resist the forces trying to push them over just from their weight. If you build a wall out of wood studs the walls don't have much resistance. Even large buildings with steel columns are not built that way. A short wall out of wood studs is braced by the corners at the ends of the wall such as if you build a garden shed. A longer wall would not have that resistance. In older buildings with long walls they found that this wasn't enough so frequently they would provide buttresses and counterforts on thee outsides of the walls to provide this resistance as in old cathedrals. Resistance to wind and seismic loads is an entirely different thing. It is difficult and extremely rare to find buildings that are designed to resist loads perpendicular to walls by making the wall cantilever up from the foundation to resist these loads.
The beam is compressed. With the weak material the trusses bend but the base is fixed so the horizontal force of the beam is passed to the base. With the rigid material the triangle structure minimises the outward movement of the base. With this setup, the horizontal force is measured through displacement.
2 cents from a carpenter.
Preventing roof loads from pushing the walls outward is solved by using collar ties closer to the sill plates...typically joists serve this function. Collar ties are placed in the lower third of the rafter span.
If a "cathedral" ceiling is desired then a structural ridge beam is used which transfers loading to the gable ends.
Increasing the depth of rafters will not prevent outward thrust on the walls.
The root of the problem is hinging at the rafter's intersection at the peak.
A good example of how large deflections in the members can invalidate assumptions about how the structure works.
This. Andres rafters have deflection, the latter has no observable deflection. So this is a lesson on deflection effects rather than simply about load.
Well stated.
The first experiment used flexible materials, the bend in the straws affected the force on the walls compared to the rigid materials in the later.
End of discussion :)
The flimsy truss allows the beams to bend, reducing the height h, so F*a/2h when h decreases increases F.
The way I have always done this with rafters when building a structure is to first use thick, at least 1/4” steel gusset plates at the peak that extend downward at least 12 to 18 inches. Next I put diagonal bracing between the rafters that are anchored to the walls. Then, when you add the decking to the rafters, this adds additional strength by acting as additional diagonal bracing. Although the decking adds weight, it adds much more in structural integrity. All of this, of course, will depend on the span of the rafters. If you have no load bearing walls and a long span, you will need more support, such as the cross beam.
The more the trusses bend under load, the more horizontal the forces becomes. If the trusses have minimal deflection under load, the outward forces will be less.
The first thing I noticed is that the set up has the left side in a locked position with the right side being metered. What you need is a meter on both sides to measure them independently because your set up is basically doubling the amount of force on the right hand side being that the left-hand side can’t move. Basically you’re forcing all of the movement in One Direction when in reality it would be going in both directions equally
Fascinating ! New subscriber !
What Andre never talked about is the effect of tension in the beam. If one of the supports is free to move just a little, tension will increase in the beam until it's carrying all the horizontal thrust, and the thrust at the supports will be zero. As Andre mentioned, it's indeterminate -- there is a relationship between tension in the beam and thrust at the supports, but neither is completely determined.
I think builders can rely on the beam to reduce the thrust. It's easy to design the structure so that there is no thrust at all -- just assume it's zero, calculate how much tension is required in the beam to achieve that, and size it accordingly.
In old traditional houses in the Uk built over 200 years ago, A frame construction was used, but as in the last experiment the beams were oversized and rigid.
This offset the problematic spreading loads.
As the walls were built of cob which is a mud and straw mixture this was important.
The fact of the matter is that although the cross beam could help maintain the shape of the rafter slope by developing tension, no structural member can resist load unless it is allowed to deform - in this case stretch. As erected, your structure does not allow for movement outwards of the two rafters so that the tension could not arise in the horizontal tie. Your analysis thereafter is correct and the results predictable. In order for the tie to take effect one side of the foundation should be allowed to slide freely outwards until equilibrium is reached. At the point the horizontal beam would be in tension and would contribute to the stability without imposing a lateral force. If the structure was then further loaded by tiles or snow, the outward movement would still be necessary to avoid pressure on the walls. Some bridges take advantage of sliding joints both to account for thermal expansion and varying loads.
This is not really a paradox it is simply a problem created by design.
The two experiments have the 'beam' working in different ways. With very flexible truss, the 'beam' is in compression as it tries to hold the midpoint of each rafter apart. But in the second, the rafters are more rigid and the 'beam' is in tension, trying to prevent the rafters from spreading outward.
Trusses that I've seen almost always include a stringer from wall to wall that is in tension. This absorbs all the 'spreading' forces and the walls only provide vertical support. If the rafters are long and flexing is a concern, shorter diagonal 'beams' between the rafter and bottom stringer can be used.
Aeromodelling in balsa taught me about the strength of diagonals, when I was about 11 years old!
As a rule of thumb, if the tie is at ceiling level we use the rafter size from the tables, if it is in the bottom third we increase the rafter by one size, if it is at the top third we go up two sizes, so the beam bending stiffness contains the spreading force . Great experiment though, i will actually be more careful in future, especially on long rafters.
Most traditional roofs in the UK have the tie at the wall plate, which should reduce the lateral load to near zero while the connection between the tie (ceiling joist) and the rafter holds.
The roof rafters are statically indeterminate since they see three supports. The end reactions depend on how much the rafters deflect, and how much lateral movement there is at the end supports. For a statically determinate arrangement, as in the roof rafters without the brace, the reactions will be the same no matter what the flexibility of members or end condition. In the second, indeterminate arrangement, the flexibility will change the resulting reactions.
FEM solution.
We did "method of sections "and " virtual work" in structural engineering.
Before FEM computers .
In statics the one support is often a hinged rollor support or it becomes static indeterminate problem.
Excellent channel 👍
Beers and Johnson book on statics has a section on trusses. I remember transposing the forces at each point of contact in vector form and cutting the truss into sections to solve
Seems flawed because the weight we are referring to lays on top of the truss instead of hanging from the bottom of the truss.
Rigid rafter beams are good.
The difference is flex of the trusses.
If the rafters are flexible, they will absorb some of the force as they bend downward. If the rafters are rigid, all the force goes to the walls in lateral thrust?
In order to reduce horizontal force, the beams have to be rigid.
In the first experiment the diagonal roof members were too thin to take bending moment. This structure is not a truss were no members take have bending. These diagonal members have a bending load. When thin as in experiment 1 they deflect transferring compression into the rafter that buckles under this compessive load. In the 2nd experiment the diagonal roof members are stiff and resist the bending load in the center of them at the load point. They hinge outward with the hinge at the peak. This defelection causes a tension in the horizontal rafter instead of a compression. This tension takes away some of the thrust at the wall joint. In the 2nd experiment you do not need the lateral rectation braces at the wall, i.e. the vertical blocks. Take them away and the rafter will take all of the thrust as tension, so long as the diagonal roof members do not bend under the downward loads at their centers.
The trusses with the beam in the last experiment, or in real life, creates a force that push down on the walls more than out? Reducing the outward thrust forces?
Agree. Adding more beams will further enforce the trusses to carry load more vertically than outward.
Exactly Sir. You hit the nail on the head.
I subscribed to this channel to learn with my kids, but if they don't eventually provide the answers, I don't see the point in it. If you guys are reading this.... you'll get more views if you actually give the answer instead of telling us that you know it.
Well you could just ask a structural engineer.
In the first scenario with no tie beam the 2 beams along try to push on the walls. The walls hav to resist the entire force. In a lot of houses the walls won't be able to do this, they will just fall over. In an old building with very heavy exterior masonry walls maybe they can resist.
In the second scenario with the tie beam, the 3 pieces connected together are stable, they do not have to rely on forces on the walls to remain in place. This is a better solution because it works with any type of wall construction.
What would happen in reality is in the first scenario the walls will always have to resist the forces from the 2 beams. If the walls cannot then they will move and the beams will collapse. In the second scenario the walls would likely not be completely stiff so they would move a little bit and as they move they would relieve the horizontal forces so after moving a small amount they no longer have to carry any horizontal force.
🧱 _The claim that the beam increases horizontal force on the walls can be very easily refuted experimentally: In a pin-jointed rigid truss without the beam, and without walls, the truss can't even hold its own shape, amd it would fall and flatten out... it needs the walls to constrain it from falling flat._
_But if you add the connecting beam, the same truss without walls can support not only its own weight, but much more load as well._
_This clearly shows that the beam carries a lot of horizontal load._
_Using flexible trusses like Andre used, allows the joinys to move, this changing the geometry and makes the truss roof angle more horizontal... which naturally increases the horizontal force needed to support a vetical load._
_Mathematically, when a flexible truss withiut a beam "flattens out", then the beam tension or compression force are given by N × sin(theta/2), where theta is the roof angle between the two trusses. A bigger theta means higher truss member forces, which in turn need bigger forces from the wall to counteract their horizontal component. (I hope I didnt get my sin and cos mixed up, as I did this quick analysis without drawing)._😅
the humans in this video look like AI
They are not AI but their mouths and voices are. These guys are speaking Russian.
Don’t use rubber beams in the sloping members. Roof trusses are designed to be very rigid cross their span.
Crossbar and Rafter Paradox is apparently an English translation of Russian “ Let’s ignore some simple facts “
There are no paradoxes in physics, only feeble minds.
It's all to do with the flexibility of the rafters....the more flexible they are the greater the horisontal force becomes.
The beam was under tension instead of compression
Where’s the paradox. This is a pretty simple bit of design work. So long as the timbers are strong enough, then the horizontal beam holds the tension load and the loading on the walls is purely a downward force. Just the weight.
In reality, there will be a small amount of flex and stretch of these timbers. Providing that is small, then usually there’s no problem, no paradox to worry about.
So what was the correct answer? What principle do builders rely on?
We have the answer, but the point of the videos is to activate the viewer's mindset
If you have a structural engineer design it they would use the truss system in some form or fashion. If you have a guy with a saw and hammer build it he might very well rely on the birdnest principle. The bird didn't go to college, he didn't study physics, he puts sticks together until they stay in position. And this generally works, until it doesn't and you find the next laying on the ground. Generally people who own buildings don't want to find parts of their building laying on the ground.
Thank goodness for the last minute and a half, as nothing was making sense to me (as a real world construct) up to that point. The theory was sound and interesting, but the application and functionality made no sense.
More stress was distributed to the peak. I would rather have that stress pushed to the walls. ;)
I'm a low intellect individual who couldn't get past the fact that the audio was out of sync.
Then bluetooth audio must really burn your biscuits.
Picking up load in tension will always be your friend . Add rafter ties . Flat earth crew
In practice, the purpose of the cross bar is to make the roof more rigid, not to decrease the outward load on the walls.
? It becomes a ratiometric matter of where the beam mounts.
If the beam is at the walls then it takes ALL the outward force in tension so ALL of the roof load is downward.
@@sprky777 If its at the walls, it is called a joist, not a cross bar.
On the contrary- without the horizontal tie the walls have to always resist the horizontal force. In normal building construction the walls won't be able to do this and the roof will be close to collapse. With the tie in place the walls no longer have to resist the horizontal forces, they can move outwards a little bit along with the movement of the ends of the beams until an equilibrium is reached where there is no more force pushing on the walls.
@@billj5645 You are claiming that cathedral ceilings without cross bars don't exist as part of "normal building construction", which is clearly not true. How do you resist the outward pressure? Shear walls and wider top plates. In areas without snow load but with high winds or seismic activity, the wind load or seismic load is going to be greater than outward component of the roof load.
@@richdobbs6595 The point is that the 2 beam roof requires constant resistance from the walls in order to be stable, the truss system does not. As long as the walls can provide this everything is ok. As I said if you have walls that are built with a lot of masonry they can resist the forces trying to push them over just from their weight. If you build a wall out of wood studs the walls don't have much resistance. Even large buildings with steel columns are not built that way. A short wall out of wood studs is braced by the corners at the ends of the wall such as if you build a garden shed. A longer wall would not have that resistance. In older buildings with long walls they found that this wasn't enough so frequently they would provide buttresses and counterforts on thee outsides of the walls to provide this resistance as in old cathedrals. Resistance to wind and seismic loads is an entirely different thing. It is difficult and extremely rare to find buildings that are designed to resist loads perpendicular to walls by making the wall cantilever up from the foundation to resist these loads.
The beam is compressed. With the weak material the trusses bend but the base is fixed so the horizontal force of the beam is passed to the base.
With the rigid material the triangle structure minimises the outward movement of the base. With this setup, the horizontal force is measured through displacement.
You ready think that's the simplest way to explain?
The points of contact in reality will hold a moment and not be free to swivel