On 2/16/2014 9:02 PM, Mike Marlow wrote:
> Bill wrote:
>> Mike Marlow wrote:
>>> woodchucker wrote:
>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>
>>>> It's all in the engineering.
>>>
>>> Jeff - cannot hear you well enough to understand you.
>>
>> No problem here. Maybe your speakers?
>
> No - my speakers are just fine. Maybe my ears...
>
> You have to admit - Jeff's volume is very low.
>
Yep, it is.
the camera is facing the TS and I am talking away to the outfeed.. so
it's not picking it up as if I were facing it.
I used my regular camera. My video camera is a pain to convert images.
Not worried, I won't be like Brian... just had to give some of these
people that build workbenches I see on LJ something to think about.
Too many weak benches... some very nice ones too.
--
Jeff
On 2/16/2014 11:51 PM, Dan Coby wrote:
> On 2/16/2014 7:52 PM, woodchucker wrote:
>> On 2/16/2014 9:52 PM, Dan Coby wrote:
>>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>
>>>> It's all in the engineering.
>>>
>>> You correctly point out that using a wide stretcher will make for
>>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>>> then its contribution to the stiffness of the bench is proportional
>>> to the square of its height. So doubling the height of the stretcher
>>> will quadruple its effect on the bench's stiffness. However other
>>> things like the size of the upper apron, legs, top, and the rigidity
>>> of the joints also affect stiffness. Diagonal braces can also have
>>> a major impact.
>>>
>>> However there are a few problems with your analysis when it comes
>>> to the location of the stretcher.
>>>
>>> If I am interpreting your video correctly, the magnet represents the
>>> stretcher and the bar of the magnetic base represents the leg of the
>>> bench. The joint between the stretcher and leg is free to pivot.
>> Well not exactly the yellow grip tite is the stretcher. But to
>> represent the lever principle simply, they are not connected. The
>> point is that even w/o locking them together
>> solidly, even if you had loose bolts the middle would offer less
>> leverage and the bottom, would be too much leverage.
>>>
>>> Real benches are not normally built with joints that pivot. The
>> You are taking this too literally, it's to show the benefit of a
>> middle stretcher vs a bottom stretcher.
>>> rigidity of many bench designs comes from the rigidity of the joints
>>> between the legs, aprons, top, and stretchers. If none of these joints
>>> were rigid then the bench would simply fall down due to gravity. You
>>> can build a bench with flexible joints but you need to have some form
>>> of diagonal bracing to convert some of the parallelograms into
>>> triangles.
>>>
>>>
>>> Lets do a simple analysis of a bench leg. To make things very simple,
>>> I am going to have a bench with only a single leg and without a top or
>>> an apron. Obviously this is not very representative of real benches.
>>> However this is somewhat equivalent to what you were showing in your
>>> video. I am also going to replace the stretcher with just a couple
>>> of forces. When the leg tries to rack (twist) it will apply a force
>>> at the top of the stretcher which is trying to push the stretcher to
>>> the right and a force at the bottom of the stretcher which is trying
>>> to pull the stretcher to the left. The stretcher pushes back on the
>>> leg with equal and opposite forces so the stretcher will push back to
>>> the left at the top and pull to the right at the bottom. With a rigid
>>> joint between the stretcher and leg, the top of the stretcher will be
>>> in compression and the bottom will be in tension as the stretcher tries
>>> to keep the bench from racking. (In a real joint the forces will be
>>> distributed across the joint and vary smoothly from compression at the
>>> top to tension at the bottom.)
>>>
>>>
>>> Fy ----> |---|
>>> | | |
>>> | | |
>>> | | |
>>> | | |
>>> | | |
>>> | |<--- Fsc |
>>> | | | |
>>> | | W H
>>> | |---> Fst | |
>>> | | | |
>>> | | | |
>>> | | | |
>>> | | S |
>>> | | | |
>>> | | | |
>>> |---| <---- Ff | |
>>>
>>> In this diagram:
>>> Fy is the force you are applying to bench while working
>>> Ff is the friction force at the bottom of the leg at the floor
>>> Fsc is the force due to trying to compress the top of the stretcher
>>> Fst is the force due to applying tension to the bottom of the
>>> stretcher
>>> S is the height of the bottom of the stretcher
>>> W is the width of the stretcher
>>> H is the height of the top of the bench
>>>
>>> If we apply Newton's second law to the stretcher we see:
>>> Fsc - Fst = 0
>>> This means that Fsc = Fst. I.e. there is as much tension force at the
>>> bottom of the stretcher as compression at the top. If these forces did
>>> not balance the the stretcher would start to accelerate.
>>>
>>> If we apply Newton's second law to the leg we see:
>>> Fy - Fsc + Fst - Ff = 0
>>> Since Fsc = Fst we get Fy - Ff = 0
>>> Which means Fy = Ff
>>> This is what we would expect. There needs to be enough friction at the
>>> floor to keep the bench from moving.
>>>
>>> Now lets look at the torques being applied to the leg. Please
>>> remember that a torque is determined by both the force being applied
>>> and the distance (moment arm) from the reference point. Lets use
>>> the floor as our reference point. This gives us:
>>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>>> Substituting Fst = Fsc we get:
>>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>>> or
>>> Fy*H - Fsc*W = 0
>>> or
>>> FY*H = Fsc*W
>>>
>>> This last equation tells us that the torque applied by Fy*H is equal
>>> to the counter torque being applied by the stretcher Fsc*W.
>>>
>>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>>> of the equation because the tension at the bottom of the stretcher is
>>> balanced by the compression at the top of the stretcher.
>> That really is not supported in reality. I can take a bench with the
>> same size stretcher and move it from the middle to the bottom and
>> cause the bench to rack. All things being equal.
>>
>>>
>>> A final note: The width of the stretcher does determine the magnitude
>>> of the tension/compression in the stretcher needed to balance the torque
>>> due to the forces being applied to the bench. Since I simplified the
>>> analysis to just two forces in the stretcher, the magnitude drops
>>> inversely with the width instead of the square of the width.
>>>
>>>
>>> Your bench is stiff due to your building it with wide stretchers and
>>> rigid joints and not due to the stretchers being higher above the floor.
>>>
>> Certainly it is. I agree that wide stretchers are necessary, but if I
>> put that wide stretcher at the bottom I have more leverage and
>> therefore that joint will fail eventually. It
>> will cause compression of the fibers and the socket will widen if I
>> were to put that stretcher at the very bottom like I have seen on
>> benches.
>>
>
> Another way to look at the leverage issue. There are forces from both the
> your efforts at the top of the bench and counter balancing reaction force
> from the floor being applied to the bottom of the leg. As you move the
> location of the stretcher up, you are shortening the lever arm between the
> top of the bench and the stretcher. However at the same time, you are
> lengthening the lever arm between the force reaction at the bottom of the
> leg and stretcher. The decrease in the top torque is balanced by an
> increase in the bottom torque. The result is the the torque applied to
> the stretcher/leg joint is constant.
>
>
> Dan
>
>
Ok, added another video. http://youtu.be/F1MlotN9ssY you try it.
--
Jeff
On 2/16/2014 10:52 PM, woodchucker wrote:
> On 2/16/2014 9:52 PM, Dan Coby wrote:
>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>
>>> It's all in the engineering.
>>
>> You correctly point out that using a wide stretcher will make for
>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>> then its contribution to the stiffness of the bench is proportional
>> to the square of its height. So doubling the height of the stretcher
>> will quadruple its effect on the bench's stiffness. However other
>> things like the size of the upper apron, legs, top, and the rigidity
>> of the joints also affect stiffness. Diagonal braces can also have
>> a major impact.
>>
>> However there are a few problems with your analysis when it comes
>> to the location of the stretcher.
>>
>> If I am interpreting your video correctly, the magnet represents the
>> stretcher and the bar of the magnetic base represents the leg of the
>> bench. The joint between the stretcher and leg is free to pivot.
> Well not exactly the yellow grip tite is the stretcher. But to represent
> the lever principle simply, they are not connected. The point is that
> even w/o locking them together solidly, even if you had loose bolts the
> middle would offer less leverage and the bottom, would be too much
> leverage.
>>
>> Real benches are not normally built with joints that pivot. The
> You are taking this too literally, it's to show the benefit of a middle
> stretcher vs a bottom stretcher.
>> rigidity of many bench designs comes from the rigidity of the joints
>> between the legs, aprons, top, and stretchers. If none of these joints
>> were rigid then the bench would simply fall down due to gravity. You
>> can build a bench with flexible joints but you need to have some form
>> of diagonal bracing to convert some of the parallelograms into triangles.
>>
>>
>> Lets do a simple analysis of a bench leg. To make things very simple,
>> I am going to have a bench with only a single leg and without a top or
>> an apron. Obviously this is not very representative of real benches.
>> However this is somewhat equivalent to what you were showing in your
>> video. I am also going to replace the stretcher with just a couple
>> of forces. When the leg tries to rack (twist) it will apply a force
>> at the top of the stretcher which is trying to push the stretcher to
>> the right and a force at the bottom of the stretcher which is trying
>> to pull the stretcher to the left. The stretcher pushes back on the
>> leg with equal and opposite forces so the stretcher will push back to
>> the left at the top and pull to the right at the bottom. With a rigid
>> joint between the stretcher and leg, the top of the stretcher will be
>> in compression and the bottom will be in tension as the stretcher tries
>> to keep the bench from racking. (In a real joint the forces will be
>> distributed across the joint and vary smoothly from compression at the
>> top to tension at the bottom.)
>>
>>
>> Fy ----> |---|
>> | | |
>> | | |
>> | | |
>> | | |
>> | | |
>> | |<--- Fsc |
>> | | | |
>> | | W H
>> | |---> Fst | |
>> | | | |
>> | | | |
>> | | | |
>> | | S |
>> | | | |
>> | | | |
>> |---| <---- Ff | |
>>
>> In this diagram:
>> Fy is the force you are applying to bench while working
>> Ff is the friction force at the bottom of the leg at the floor
>> Fsc is the force due to trying to compress the top of the stretcher
>> Fst is the force due to applying tension to the bottom of the
>> stretcher
>> S is the height of the bottom of the stretcher
>> W is the width of the stretcher
>> H is the height of the top of the bench
>>
>> If we apply Newton's second law to the stretcher we see:
>> Fsc - Fst = 0
>> This means that Fsc = Fst. I.e. there is as much tension force at the
>> bottom of the stretcher as compression at the top. If these forces did
>> not balance the the stretcher would start to accelerate.
>>
>> If we apply Newton's second law to the leg we see:
>> Fy - Fsc + Fst - Ff = 0
>> Since Fsc = Fst we get Fy - Ff = 0
>> Which means Fy = Ff
>> This is what we would expect. There needs to be enough friction at the
>> floor to keep the bench from moving.
>>
>> Now lets look at the torques being applied to the leg. Please
>> remember that a torque is determined by both the force being applied
>> and the distance (moment arm) from the reference point. Lets use
>> the floor as our reference point. This gives us:
>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>> Substituting Fst = Fsc we get:
>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>> or
>> Fy*H - Fsc*W = 0
>> or
>> FY*H = Fsc*W
>>
>> This last equation tells us that the torque applied by Fy*H is equal
>> to the counter torque being applied by the stretcher Fsc*W.
>>
>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>> of the equation because the tension at the bottom of the stretcher is
>> balanced by the compression at the top of the stretcher.
> That really is not supported in reality. I can take a bench with the
> same size stretcher and move it from the middle to the bottom and cause
> the bench to rack. All things being equal.
>
>>
>> A final note: The width of the stretcher does determine the magnitude
>> of the tension/compression in the stretcher needed to balance the torque
>> due to the forces being applied to the bench. Since I simplified the
>> analysis to just two forces in the stretcher, the magnitude drops
>> inversely with the width instead of the square of the width.
>>
>>
>> Your bench is stiff due to your building it with wide stretchers and
>> rigid joints and not due to the stretchers being higher above the floor.
>>
> Certainly it is. I agree that wide stretchers are necessary, but if I
> put that wide stretcher at the bottom I have more leverage and therefore
> that joint will fail eventually. It will cause compression of the fibers
> and the socket will widen if I were to put that stretcher at the very
> bottom like I have seen on benches.
>>
>>
>> Dan
>
>
I'll build a small mortise and tenon setup (2) to show middle pressure
vs end pressure.
This is about leverage and lever arms. A longer lever has more ability
to break the joint down, that a shorter one.
--
Jeff
On 2/16/2014 7:52 PM, woodchucker wrote:
> On 2/16/2014 9:52 PM, Dan Coby wrote:
>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>
>>> It's all in the engineering.
>>
>> You correctly point out that using a wide stretcher will make for
>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>> then its contribution to the stiffness of the bench is proportional
>> to the square of its height. So doubling the height of the stretcher
>> will quadruple its effect on the bench's stiffness. However other
>> things like the size of the upper apron, legs, top, and the rigidity
>> of the joints also affect stiffness. Diagonal braces can also have
>> a major impact.
>>
>> However there are a few problems with your analysis when it comes
>> to the location of the stretcher.
>>
>> If I am interpreting your video correctly, the magnet represents the
>> stretcher and the bar of the magnetic base represents the leg of the
>> bench. The joint between the stretcher and leg is free to pivot.
> Well not exactly the yellow grip tite is the stretcher. But to represent the lever principle simply, they are not connected. The point is that even w/o locking them together
> solidly, even if you had loose bolts the middle would offer less leverage and the bottom, would be too much leverage.
>>
>> Real benches are not normally built with joints that pivot. The
> You are taking this too literally, it's to show the benefit of a middle stretcher vs a bottom stretcher.
>> rigidity of many bench designs comes from the rigidity of the joints
>> between the legs, aprons, top, and stretchers. If none of these joints
>> were rigid then the bench would simply fall down due to gravity. You
>> can build a bench with flexible joints but you need to have some form
>> of diagonal bracing to convert some of the parallelograms into triangles.
>>
>>
>> Lets do a simple analysis of a bench leg. To make things very simple,
>> I am going to have a bench with only a single leg and without a top or
>> an apron. Obviously this is not very representative of real benches.
>> However this is somewhat equivalent to what you were showing in your
>> video. I am also going to replace the stretcher with just a couple
>> of forces. When the leg tries to rack (twist) it will apply a force
>> at the top of the stretcher which is trying to push the stretcher to
>> the right and a force at the bottom of the stretcher which is trying
>> to pull the stretcher to the left. The stretcher pushes back on the
>> leg with equal and opposite forces so the stretcher will push back to
>> the left at the top and pull to the right at the bottom. With a rigid
>> joint between the stretcher and leg, the top of the stretcher will be
>> in compression and the bottom will be in tension as the stretcher tries
>> to keep the bench from racking. (In a real joint the forces will be
>> distributed across the joint and vary smoothly from compression at the
>> top to tension at the bottom.)
>>
>>
>> Fy ----> |---|
>> | | |
>> | | |
>> | | |
>> | | |
>> | | |
>> | |<--- Fsc |
>> | | | |
>> | | W H
>> | |---> Fst | |
>> | | | |
>> | | | |
>> | | | |
>> | | S |
>> | | | |
>> | | | |
>> |---| <---- Ff | |
>>
>> In this diagram:
>> Fy is the force you are applying to bench while working
>> Ff is the friction force at the bottom of the leg at the floor
>> Fsc is the force due to trying to compress the top of the stretcher
>> Fst is the force due to applying tension to the bottom of the
>> stretcher
>> S is the height of the bottom of the stretcher
>> W is the width of the stretcher
>> H is the height of the top of the bench
>>
>> If we apply Newton's second law to the stretcher we see:
>> Fsc - Fst = 0
>> This means that Fsc = Fst. I.e. there is as much tension force at the
>> bottom of the stretcher as compression at the top. If these forces did
>> not balance the the stretcher would start to accelerate.
>>
>> If we apply Newton's second law to the leg we see:
>> Fy - Fsc + Fst - Ff = 0
>> Since Fsc = Fst we get Fy - Ff = 0
>> Which means Fy = Ff
>> This is what we would expect. There needs to be enough friction at the
>> floor to keep the bench from moving.
>>
>> Now lets look at the torques being applied to the leg. Please
>> remember that a torque is determined by both the force being applied
>> and the distance (moment arm) from the reference point. Lets use
>> the floor as our reference point. This gives us:
>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>> Substituting Fst = Fsc we get:
>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>> or
>> Fy*H - Fsc*W = 0
>> or
>> FY*H = Fsc*W
>>
>> This last equation tells us that the torque applied by Fy*H is equal
>> to the counter torque being applied by the stretcher Fsc*W.
>>
>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>> of the equation because the tension at the bottom of the stretcher is
>> balanced by the compression at the top of the stretcher.
> That really is not supported in reality. I can take a bench with the same size stretcher and move it from the middle to the bottom and cause the bench to rack. All things being equal.
>
>>
>> A final note: The width of the stretcher does determine the magnitude
>> of the tension/compression in the stretcher needed to balance the torque
>> due to the forces being applied to the bench. Since I simplified the
>> analysis to just two forces in the stretcher, the magnitude drops
>> inversely with the width instead of the square of the width.
>>
>>
>> Your bench is stiff due to your building it with wide stretchers and
>> rigid joints and not due to the stretchers being higher above the floor.
>>
> Certainly it is. I agree that wide stretchers are necessary, but if I put that wide stretcher at the bottom I have more leverage and therefore that joint will fail eventually. It
> will cause compression of the fibers and the socket will widen if I were to put that stretcher at the very bottom like I have seen on benches.
>
Another way to look at the leverage issue. There are forces from both the
your efforts at the top of the bench and counter balancing reaction force
from the floor being applied to the bottom of the leg. As you move the
location of the stretcher up, you are shortening the lever arm between the
top of the bench and the stretcher. However at the same time, you are
lengthening the lever arm between the force reaction at the bottom of the
leg and stretcher. The decrease in the top torque is balanced by an
increase in the bottom torque. The result is the the torque applied to
the stretcher/leg joint is constant.
Dan
On 2/16/2014 3:57 PM, Mike Marlow wrote:
> woodchucker wrote:
>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>
>> It's all in the engineering.
>
>
> Jeff - cannot hear you well enough to understand you.
>
Ah, probably better off that way.
I don't have a good camera where I can have a mic off the camera.
Not looking to make videos, but seeing some very bad benches where the
stretchers were at the bottom, I needed to explain why it's not a good
idea...
Thanks for letting me know.
--
Jeff
On 2/17/2014 9:44 PM, woodchucker wrote:
> On 2/18/2014 12:15 AM, Dan Coby wrote:
>> On 2/17/2014 7:46 PM, woodchucker wrote:
>>> On 2/16/2014 11:51 PM, Dan Coby wrote:
>>>> On 2/16/2014 7:52 PM, woodchucker wrote:
>>>>> On 2/16/2014 9:52 PM, Dan Coby wrote:
>>>>>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>>>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>>>>
>>>>>>> It's all in the engineering.
>>>>>>
>>>>>> You correctly point out that using a wide stretcher will make for
>>>>>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>>>>>> then its contribution to the stiffness of the bench is proportional
>>>>>> to the square of its height. So doubling the height of the stretcher
>>>>>> will quadruple its effect on the bench's stiffness. However other
>>>>>> things like the size of the upper apron, legs, top, and the rigidity
>>>>>> of the joints also affect stiffness. Diagonal braces can also have
>>>>>> a major impact.
>>>>>>
>>>>>> However there are a few problems with your analysis when it comes
>>>>>> to the location of the stretcher.
>>>>>>
>>>>>> If I am interpreting your video correctly, the magnet represents the
>>>>>> stretcher and the bar of the magnetic base represents the leg of the
>>>>>> bench. The joint between the stretcher and leg is free to pivot.
>>>>> Well not exactly the yellow grip tite is the stretcher. But to
>>>>> represent the lever principle simply, they are not connected. The
>>>>> point is that even w/o locking them together
>>>>> solidly, even if you had loose bolts the middle would offer less
>>>>> leverage and the bottom, would be too much leverage.
>>>>>>
>>>>>> Real benches are not normally built with joints that pivot. The
>>>>> You are taking this too literally, it's to show the benefit of a
>>>>> middle stretcher vs a bottom stretcher.
>>>>>> rigidity of many bench designs comes from the rigidity of the joints
>>>>>> between the legs, aprons, top, and stretchers. If none of these
>>>>>> joints
>>>>>> were rigid then the bench would simply fall down due to gravity. You
>>>>>> can build a bench with flexible joints but you need to have some form
>>>>>> of diagonal bracing to convert some of the parallelograms into
>>>>>> triangles.
>>>>>>
>>>>>>
>>>>>> Lets do a simple analysis of a bench leg. To make things very simple,
>>>>>> I am going to have a bench with only a single leg and without a top or
>>>>>> an apron. Obviously this is not very representative of real benches.
>>>>>> However this is somewhat equivalent to what you were showing in your
>>>>>> video. I am also going to replace the stretcher with just a couple
>>>>>> of forces. When the leg tries to rack (twist) it will apply a force
>>>>>> at the top of the stretcher which is trying to push the stretcher to
>>>>>> the right and a force at the bottom of the stretcher which is trying
>>>>>> to pull the stretcher to the left. The stretcher pushes back on the
>>>>>> leg with equal and opposite forces so the stretcher will push back to
>>>>>> the left at the top and pull to the right at the bottom. With a rigid
>>>>>> joint between the stretcher and leg, the top of the stretcher will be
>>>>>> in compression and the bottom will be in tension as the stretcher
>>>>>> tries
>>>>>> to keep the bench from racking. (In a real joint the forces will be
>>>>>> distributed across the joint and vary smoothly from compression at the
>>>>>> top to tension at the bottom.)
>>>>>>
>>>>>>
>>>>>> Fy ----> |---|
>>>>>> | | |
>>>>>> | | |
>>>>>> | | |
>>>>>> | | |
>>>>>> | | |
>>>>>> | |<--- Fsc |
>>>>>> | | | |
>>>>>> | | W H
>>>>>> | |---> Fst | |
>>>>>> | | | |
>>>>>> | | | |
>>>>>> | | | |
>>>>>> | | S |
>>>>>> | | | |
>>>>>> | | | |
>>>>>> |---| <---- Ff | |
>>>>>>
>>>>>> In this diagram:
>>>>>> Fy is the force you are applying to bench while working
>>>>>> Ff is the friction force at the bottom of the leg at the floor
>>>>>> Fsc is the force due to trying to compress the top of the
>>>>>> stretcher
>>>>>> Fst is the force due to applying tension to the bottom of the
>>>>>> stretcher
>>>>>> S is the height of the bottom of the stretcher
>>>>>> W is the width of the stretcher
>>>>>> H is the height of the top of the bench
>>>>>>
>>>>>> If we apply Newton's second law to the stretcher we see:
>>>>>> Fsc - Fst = 0
>>>>>> This means that Fsc = Fst. I.e. there is as much tension force at the
>>>>>> bottom of the stretcher as compression at the top. If these forces
>>>>>> did
>>>>>> not balance the the stretcher would start to accelerate.
>>>>>>
>>>>>> If we apply Newton's second law to the leg we see:
>>>>>> Fy - Fsc + Fst - Ff = 0
>>>>>> Since Fsc = Fst we get Fy - Ff = 0
>>>>>> Which means Fy = Ff
>>>>>> This is what we would expect. There needs to be enough friction at
>>>>>> the
>>>>>> floor to keep the bench from moving.
>>>>>>
>>>>>> Now lets look at the torques being applied to the leg. Please
>>>>>> remember that a torque is determined by both the force being applied
>>>>>> and the distance (moment arm) from the reference point. Lets use
>>>>>> the floor as our reference point. This gives us:
>>>>>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>>>>>> Substituting Fst = Fsc we get:
>>>>>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>>>>>> or
>>>>>> Fy*H - Fsc*W = 0
>>>>>> or
>>>>>> FY*H = Fsc*W
>>>>>>
>>>>>> This last equation tells us that the torque applied by Fy*H is equal
>>>>>> to the counter torque being applied by the stretcher Fsc*W.
>>>>>>
>>>>>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>>>>>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>>>>>> of the equation because the tension at the bottom of the stretcher is
>>>>>> balanced by the compression at the top of the stretcher.
>>>>> That really is not supported in reality. I can take a bench with the
>>>>> same size stretcher and move it from the middle to the bottom and
>>>>> cause the bench to rack. All things being equal.
>>>>>
>>>>>>
>>>>>> A final note: The width of the stretcher does determine the magnitude
>>>>>> of the tension/compression in the stretcher needed to balance the
>>>>>> torque
>>>>>> due to the forces being applied to the bench. Since I simplified the
>>>>>> analysis to just two forces in the stretcher, the magnitude drops
>>>>>> inversely with the width instead of the square of the width.
>>>>>>
>>>>>>
>>>>>> Your bench is stiff due to your building it with wide stretchers and
>>>>>> rigid joints and not due to the stretchers being higher above the
>>>>>> floor.
>>>>>>
>>>>> Certainly it is. I agree that wide stretchers are necessary, but if I
>>>>> put that wide stretcher at the bottom I have more leverage and
>>>>> therefore that joint will fail eventually. It
>>>>> will cause compression of the fibers and the socket will widen if I
>>>>> were to put that stretcher at the very bottom like I have seen on
>>>>> benches.
>>>>>
>>>>
>>>> Another way to look at the leverage issue. There are forces from
>>>> both the
>>>> your efforts at the top of the bench and counter balancing reaction
>>>> force
>>>> from the floor being applied to the bottom of the leg. As you move the
>>>> location of the stretcher up, you are shortening the lever arm
>>>> between the
>>>> top of the bench and the stretcher. However at the same time, you are
>>>> lengthening the lever arm between the force reaction at the bottom of
>>>> the
>>>> leg and stretcher. The decrease in the top torque is balanced by an
>>>> increase in the bottom torque. The result is the the torque applied to
>>>> the stretcher/leg joint is constant.
>>>>
>>>>
>>>> Dan
>>>>
>>>>
>>> Ok, added another video. http://youtu.be/F1MlotN9ssY you try it.
>>
>> If the stretcher were attached to something fixed like a wall then I
>> would agree with what you have been showing. Indeed if you are fastening
>> your bench to a wall then you should fasten it near the top of the
>> bench.
>>
>> However the stretcher is not attached to a fixed object. It is simply
>> attached to another leg of the bench. That leg can also move and flex.
>>
>> Let me give you another example. Take your argument to the extreme and
>> move the stretcher all the way to the top of the bench. If I understand
>> your arguments then since this would produce a near zero lever arm then
>> the bench would be extremely rigid.
>>
>> However this is basically the same situation as most tables with an apron
>> around the top. (The stretcher in this case is the same as the apron.)
>> However to make a table rigid, table makers have to go to great lengths to
>> make the leg/apron joint very strong and rigid. The problem is that the
>> table leg makes a very long lever arm connected to the bottom of the
>> apron/stretcher. You have simply shortened one lever arm and lengthened
>> another when you move the stretcher.
>>
>>
>> Dan
>
> A table is not meant to overcome racking forces. A workbench is.
Both benches and table have to overcome racking forces. Take a look at
the joints between a table leg and table top and apron sometime. These
can be massive on a large heavy table. Check out any book on table
construction and you will see the emphasis that is placed on making this
joint correctly.
> The floor is now the top when you put the apron at the top. You are
> looking to minimize the leverage of the top or the floor. putting it
> closer to the middle does this.
To keep the bench from racking, you have to counteract the torque created
when you push on the top. This applied force also creates an equivalent
force at the floor. Both of those forces are trying to twist the joint
between the stretcher and the leg. You are not including this second
force in your demonstrations or in your arguments.
Moving the stretcher up or down simply increases the torque from one
force while decreasing the other.
When the stretcher is at the bottom then:
torque = F*L + F*0 = F*L
Where F is the force applied and L is the length of leg.
When the stretcher is at the top then:
torque = F*0 + F*L = F*L
When the stretcher is in the middle then:
torque = F*L/2 + F*L/2 = F*L
Please note that the result is the same in each case.
> I don't understand why you say if it is fixed to a wall.
> I'm at a loss to understand that.
I am trying to say that your analysis would be correct if the other end of
your stretcher were connected to a fixed object instead of another bench
leg.
Dan
On 2/16/2014 12:10 PM, woodchucker wrote:
> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>
> It's all in the engineering.
You correctly point out that using a wide stretcher will make for
a stiffer bench. If the stretcher is rigidly connected to the leg,
then its contribution to the stiffness of the bench is proportional
to the square of its height. So doubling the height of the stretcher
will quadruple its effect on the bench's stiffness. However other
things like the size of the upper apron, legs, top, and the rigidity
of the joints also affect stiffness. Diagonal braces can also have
a major impact.
However there are a few problems with your analysis when it comes
to the location of the stretcher.
If I am interpreting your video correctly, the magnet represents the
stretcher and the bar of the magnetic base represents the leg of the
bench. The joint between the stretcher and leg is free to pivot.
Real benches are not normally built with joints that pivot. The
rigidity of many bench designs comes from the rigidity of the joints
between the legs, aprons, top, and stretchers. If none of these joints
were rigid then the bench would simply fall down due to gravity. You
can build a bench with flexible joints but you need to have some form
of diagonal bracing to convert some of the parallelograms into triangles.
Lets do a simple analysis of a bench leg. To make things very simple,
I am going to have a bench with only a single leg and without a top or
an apron. Obviously this is not very representative of real benches.
However this is somewhat equivalent to what you were showing in your
video. I am also going to replace the stretcher with just a couple
of forces. When the leg tries to rack (twist) it will apply a force
at the top of the stretcher which is trying to push the stretcher to
the right and a force at the bottom of the stretcher which is trying
to pull the stretcher to the left. The stretcher pushes back on the
leg with equal and opposite forces so the stretcher will push back to
the left at the top and pull to the right at the bottom. With a rigid
joint between the stretcher and leg, the top of the stretcher will be
in compression and the bottom will be in tension as the stretcher tries
to keep the bench from racking. (In a real joint the forces will be
distributed across the joint and vary smoothly from compression at the
top to tension at the bottom.)
Fy ----> |---|
| | |
| | |
| | |
| | |
| | |
| |<--- Fsc |
| | | |
| | W H
| |---> Fst | |
| | | |
| | | |
| | | |
| | S |
| | | |
| | | |
|---| <---- Ff | |
In this diagram:
Fy is the force you are applying to bench while working
Ff is the friction force at the bottom of the leg at the floor
Fsc is the force due to trying to compress the top of the stretcher
Fst is the force due to applying tension to the bottom of the stretcher
S is the height of the bottom of the stretcher
W is the width of the stretcher
H is the height of the top of the bench
If we apply Newton's second law to the stretcher we see:
Fsc - Fst = 0
This means that Fsc = Fst. I.e. there is as much tension force at the
bottom of the stretcher as compression at the top. If these forces did
not balance the the stretcher would start to accelerate.
If we apply Newton's second law to the leg we see:
Fy - Fsc + Fst - Ff = 0
Since Fsc = Fst we get Fy - Ff = 0
Which means Fy = Ff
This is what we would expect. There needs to be enough friction at the
floor to keep the bench from moving.
Now lets look at the torques being applied to the leg. Please
remember that a torque is determined by both the force being applied
and the distance (moment arm) from the reference point. Lets use
the floor as our reference point. This gives us:
Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
Substituting Fst = Fsc we get:
Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
or
Fy*H - Fsc*W = 0
or
FY*H = Fsc*W
This last equation tells us that the torque applied by Fy*H is equal
to the counter torque being applied by the stretcher Fsc*W.
PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
of the equation because the tension at the bottom of the stretcher is
balanced by the compression at the top of the stretcher.
A final note: The width of the stretcher does determine the magnitude
of the tension/compression in the stretcher needed to balance the torque
due to the forces being applied to the bench. Since I simplified the
analysis to just two forces in the stretcher, the magnitude drops
inversely with the width instead of the square of the width.
Your bench is stiff due to your building it with wide stretchers and
rigid joints and not due to the stretchers being higher above the floor.
Dan
On 2/18/2014 12:15 AM, Dan Coby wrote:
> On 2/17/2014 7:46 PM, woodchucker wrote:
>> On 2/16/2014 11:51 PM, Dan Coby wrote:
>>> On 2/16/2014 7:52 PM, woodchucker wrote:
>>>> On 2/16/2014 9:52 PM, Dan Coby wrote:
>>>>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>>>
>>>>>> It's all in the engineering.
>>>>>
>>>>> You correctly point out that using a wide stretcher will make for
>>>>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>>>>> then its contribution to the stiffness of the bench is proportional
>>>>> to the square of its height. So doubling the height of the stretcher
>>>>> will quadruple its effect on the bench's stiffness. However other
>>>>> things like the size of the upper apron, legs, top, and the rigidity
>>>>> of the joints also affect stiffness. Diagonal braces can also have
>>>>> a major impact.
>>>>>
>>>>> However there are a few problems with your analysis when it comes
>>>>> to the location of the stretcher.
>>>>>
>>>>> If I am interpreting your video correctly, the magnet represents the
>>>>> stretcher and the bar of the magnetic base represents the leg of the
>>>>> bench. The joint between the stretcher and leg is free to pivot.
>>>> Well not exactly the yellow grip tite is the stretcher. But to
>>>> represent the lever principle simply, they are not connected. The
>>>> point is that even w/o locking them together
>>>> solidly, even if you had loose bolts the middle would offer less
>>>> leverage and the bottom, would be too much leverage.
>>>>>
>>>>> Real benches are not normally built with joints that pivot. The
>>>> You are taking this too literally, it's to show the benefit of a
>>>> middle stretcher vs a bottom stretcher.
>>>>> rigidity of many bench designs comes from the rigidity of the joints
>>>>> between the legs, aprons, top, and stretchers. If none of these
>>>>> joints
>>>>> were rigid then the bench would simply fall down due to gravity. You
>>>>> can build a bench with flexible joints but you need to have some form
>>>>> of diagonal bracing to convert some of the parallelograms into
>>>>> triangles.
>>>>>
>>>>>
>>>>> Lets do a simple analysis of a bench leg. To make things very simple,
>>>>> I am going to have a bench with only a single leg and without a top or
>>>>> an apron. Obviously this is not very representative of real benches.
>>>>> However this is somewhat equivalent to what you were showing in your
>>>>> video. I am also going to replace the stretcher with just a couple
>>>>> of forces. When the leg tries to rack (twist) it will apply a force
>>>>> at the top of the stretcher which is trying to push the stretcher to
>>>>> the right and a force at the bottom of the stretcher which is trying
>>>>> to pull the stretcher to the left. The stretcher pushes back on the
>>>>> leg with equal and opposite forces so the stretcher will push back to
>>>>> the left at the top and pull to the right at the bottom. With a rigid
>>>>> joint between the stretcher and leg, the top of the stretcher will be
>>>>> in compression and the bottom will be in tension as the stretcher
>>>>> tries
>>>>> to keep the bench from racking. (In a real joint the forces will be
>>>>> distributed across the joint and vary smoothly from compression at the
>>>>> top to tension at the bottom.)
>>>>>
>>>>>
>>>>> Fy ----> |---|
>>>>> | | |
>>>>> | | |
>>>>> | | |
>>>>> | | |
>>>>> | | |
>>>>> | |<--- Fsc |
>>>>> | | | |
>>>>> | | W H
>>>>> | |---> Fst | |
>>>>> | | | |
>>>>> | | | |
>>>>> | | | |
>>>>> | | S |
>>>>> | | | |
>>>>> | | | |
>>>>> |---| <---- Ff | |
>>>>>
>>>>> In this diagram:
>>>>> Fy is the force you are applying to bench while working
>>>>> Ff is the friction force at the bottom of the leg at the floor
>>>>> Fsc is the force due to trying to compress the top of the
>>>>> stretcher
>>>>> Fst is the force due to applying tension to the bottom of the
>>>>> stretcher
>>>>> S is the height of the bottom of the stretcher
>>>>> W is the width of the stretcher
>>>>> H is the height of the top of the bench
>>>>>
>>>>> If we apply Newton's second law to the stretcher we see:
>>>>> Fsc - Fst = 0
>>>>> This means that Fsc = Fst. I.e. there is as much tension force at the
>>>>> bottom of the stretcher as compression at the top. If these forces
>>>>> did
>>>>> not balance the the stretcher would start to accelerate.
>>>>>
>>>>> If we apply Newton's second law to the leg we see:
>>>>> Fy - Fsc + Fst - Ff = 0
>>>>> Since Fsc = Fst we get Fy - Ff = 0
>>>>> Which means Fy = Ff
>>>>> This is what we would expect. There needs to be enough friction at
>>>>> the
>>>>> floor to keep the bench from moving.
>>>>>
>>>>> Now lets look at the torques being applied to the leg. Please
>>>>> remember that a torque is determined by both the force being applied
>>>>> and the distance (moment arm) from the reference point. Lets use
>>>>> the floor as our reference point. This gives us:
>>>>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>>>>> Substituting Fst = Fsc we get:
>>>>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>>>>> or
>>>>> Fy*H - Fsc*W = 0
>>>>> or
>>>>> FY*H = Fsc*W
>>>>>
>>>>> This last equation tells us that the torque applied by Fy*H is equal
>>>>> to the counter torque being applied by the stretcher Fsc*W.
>>>>>
>>>>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>>>>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>>>>> of the equation because the tension at the bottom of the stretcher is
>>>>> balanced by the compression at the top of the stretcher.
>>>> That really is not supported in reality. I can take a bench with the
>>>> same size stretcher and move it from the middle to the bottom and
>>>> cause the bench to rack. All things being equal.
>>>>
>>>>>
>>>>> A final note: The width of the stretcher does determine the magnitude
>>>>> of the tension/compression in the stretcher needed to balance the
>>>>> torque
>>>>> due to the forces being applied to the bench. Since I simplified the
>>>>> analysis to just two forces in the stretcher, the magnitude drops
>>>>> inversely with the width instead of the square of the width.
>>>>>
>>>>>
>>>>> Your bench is stiff due to your building it with wide stretchers and
>>>>> rigid joints and not due to the stretchers being higher above the
>>>>> floor.
>>>>>
>>>> Certainly it is. I agree that wide stretchers are necessary, but if I
>>>> put that wide stretcher at the bottom I have more leverage and
>>>> therefore that joint will fail eventually. It
>>>> will cause compression of the fibers and the socket will widen if I
>>>> were to put that stretcher at the very bottom like I have seen on
>>>> benches.
>>>>
>>>
>>> Another way to look at the leverage issue. There are forces from
>>> both the
>>> your efforts at the top of the bench and counter balancing reaction
>>> force
>>> from the floor being applied to the bottom of the leg. As you move the
>>> location of the stretcher up, you are shortening the lever arm
>>> between the
>>> top of the bench and the stretcher. However at the same time, you are
>>> lengthening the lever arm between the force reaction at the bottom of
>>> the
>>> leg and stretcher. The decrease in the top torque is balanced by an
>>> increase in the bottom torque. The result is the the torque applied to
>>> the stretcher/leg joint is constant.
>>>
>>>
>>> Dan
>>>
>>>
>> Ok, added another video. http://youtu.be/F1MlotN9ssY you try it.
>
> If the stretcher were attached to something fixed like a wall then I
> would agree with what you have been showing. Indeed if you are fastening
> your bench to a wall then you should fasten it near the top of the
> bench.
>
> However the stretcher is not attached to a fixed object. It is simply
> attached to another leg of the bench. That leg can also move and flex.
>
> Let me give you another example. Take your argument to the extreme and
> move the stretcher all the way to the top of the bench. If I understand
> your arguments then since this would produce a near zero lever arm then
> the bench would be extremely rigid.
>
> However this is basically the same situation as most tables with an apron
> around the top. (The stretcher in this case is the same as the apron.)
> However to make a table rigid, table makers have to go to great lengths to
> make the leg/apron joint very strong and rigid. The problem is that the
> table leg makes a very long lever arm connected to the bottom of the
> apron/stretcher. You have simply shortened one lever arm and lengthened
> another when you move the stretcher.
>
>
> Dan
A table is not meant to overcome racking forces. A workbench is. The
floor is now the top when you put the apron at the top. You are looking
to minimize the leverage of the top or the floor. putting it closer to
the middle does this.
I don't understand why you say if it is fixed to a wall.
I'm at a loss to understand that.
--
Jeff
On 2/17/2014 7:46 PM, woodchucker wrote:
> On 2/16/2014 11:51 PM, Dan Coby wrote:
>> On 2/16/2014 7:52 PM, woodchucker wrote:
>>> On 2/16/2014 9:52 PM, Dan Coby wrote:
>>>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>>
>>>>> It's all in the engineering.
>>>>
>>>> You correctly point out that using a wide stretcher will make for
>>>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>>>> then its contribution to the stiffness of the bench is proportional
>>>> to the square of its height. So doubling the height of the stretcher
>>>> will quadruple its effect on the bench's stiffness. However other
>>>> things like the size of the upper apron, legs, top, and the rigidity
>>>> of the joints also affect stiffness. Diagonal braces can also have
>>>> a major impact.
>>>>
>>>> However there are a few problems with your analysis when it comes
>>>> to the location of the stretcher.
>>>>
>>>> If I am interpreting your video correctly, the magnet represents the
>>>> stretcher and the bar of the magnetic base represents the leg of the
>>>> bench. The joint between the stretcher and leg is free to pivot.
>>> Well not exactly the yellow grip tite is the stretcher. But to
>>> represent the lever principle simply, they are not connected. The
>>> point is that even w/o locking them together
>>> solidly, even if you had loose bolts the middle would offer less
>>> leverage and the bottom, would be too much leverage.
>>>>
>>>> Real benches are not normally built with joints that pivot. The
>>> You are taking this too literally, it's to show the benefit of a
>>> middle stretcher vs a bottom stretcher.
>>>> rigidity of many bench designs comes from the rigidity of the joints
>>>> between the legs, aprons, top, and stretchers. If none of these joints
>>>> were rigid then the bench would simply fall down due to gravity. You
>>>> can build a bench with flexible joints but you need to have some form
>>>> of diagonal bracing to convert some of the parallelograms into
>>>> triangles.
>>>>
>>>>
>>>> Lets do a simple analysis of a bench leg. To make things very simple,
>>>> I am going to have a bench with only a single leg and without a top or
>>>> an apron. Obviously this is not very representative of real benches.
>>>> However this is somewhat equivalent to what you were showing in your
>>>> video. I am also going to replace the stretcher with just a couple
>>>> of forces. When the leg tries to rack (twist) it will apply a force
>>>> at the top of the stretcher which is trying to push the stretcher to
>>>> the right and a force at the bottom of the stretcher which is trying
>>>> to pull the stretcher to the left. The stretcher pushes back on the
>>>> leg with equal and opposite forces so the stretcher will push back to
>>>> the left at the top and pull to the right at the bottom. With a rigid
>>>> joint between the stretcher and leg, the top of the stretcher will be
>>>> in compression and the bottom will be in tension as the stretcher tries
>>>> to keep the bench from racking. (In a real joint the forces will be
>>>> distributed across the joint and vary smoothly from compression at the
>>>> top to tension at the bottom.)
>>>>
>>>>
>>>> Fy ----> |---|
>>>> | | |
>>>> | | |
>>>> | | |
>>>> | | |
>>>> | | |
>>>> | |<--- Fsc |
>>>> | | | |
>>>> | | W H
>>>> | |---> Fst | |
>>>> | | | |
>>>> | | | |
>>>> | | | |
>>>> | | S |
>>>> | | | |
>>>> | | | |
>>>> |---| <---- Ff | |
>>>>
>>>> In this diagram:
>>>> Fy is the force you are applying to bench while working
>>>> Ff is the friction force at the bottom of the leg at the floor
>>>> Fsc is the force due to trying to compress the top of the stretcher
>>>> Fst is the force due to applying tension to the bottom of the
>>>> stretcher
>>>> S is the height of the bottom of the stretcher
>>>> W is the width of the stretcher
>>>> H is the height of the top of the bench
>>>>
>>>> If we apply Newton's second law to the stretcher we see:
>>>> Fsc - Fst = 0
>>>> This means that Fsc = Fst. I.e. there is as much tension force at the
>>>> bottom of the stretcher as compression at the top. If these forces did
>>>> not balance the the stretcher would start to accelerate.
>>>>
>>>> If we apply Newton's second law to the leg we see:
>>>> Fy - Fsc + Fst - Ff = 0
>>>> Since Fsc = Fst we get Fy - Ff = 0
>>>> Which means Fy = Ff
>>>> This is what we would expect. There needs to be enough friction at the
>>>> floor to keep the bench from moving.
>>>>
>>>> Now lets look at the torques being applied to the leg. Please
>>>> remember that a torque is determined by both the force being applied
>>>> and the distance (moment arm) from the reference point. Lets use
>>>> the floor as our reference point. This gives us:
>>>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>>>> Substituting Fst = Fsc we get:
>>>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>>>> or
>>>> Fy*H - Fsc*W = 0
>>>> or
>>>> FY*H = Fsc*W
>>>>
>>>> This last equation tells us that the torque applied by Fy*H is equal
>>>> to the counter torque being applied by the stretcher Fsc*W.
>>>>
>>>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>>>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>>>> of the equation because the tension at the bottom of the stretcher is
>>>> balanced by the compression at the top of the stretcher.
>>> That really is not supported in reality. I can take a bench with the
>>> same size stretcher and move it from the middle to the bottom and
>>> cause the bench to rack. All things being equal.
>>>
>>>>
>>>> A final note: The width of the stretcher does determine the magnitude
>>>> of the tension/compression in the stretcher needed to balance the torque
>>>> due to the forces being applied to the bench. Since I simplified the
>>>> analysis to just two forces in the stretcher, the magnitude drops
>>>> inversely with the width instead of the square of the width.
>>>>
>>>>
>>>> Your bench is stiff due to your building it with wide stretchers and
>>>> rigid joints and not due to the stretchers being higher above the floor.
>>>>
>>> Certainly it is. I agree that wide stretchers are necessary, but if I
>>> put that wide stretcher at the bottom I have more leverage and
>>> therefore that joint will fail eventually. It
>>> will cause compression of the fibers and the socket will widen if I
>>> were to put that stretcher at the very bottom like I have seen on
>>> benches.
>>>
>>
>> Another way to look at the leverage issue. There are forces from both the
>> your efforts at the top of the bench and counter balancing reaction force
>> from the floor being applied to the bottom of the leg. As you move the
>> location of the stretcher up, you are shortening the lever arm between the
>> top of the bench and the stretcher. However at the same time, you are
>> lengthening the lever arm between the force reaction at the bottom of the
>> leg and stretcher. The decrease in the top torque is balanced by an
>> increase in the bottom torque. The result is the the torque applied to
>> the stretcher/leg joint is constant.
>>
>>
>> Dan
>>
>>
> Ok, added another video. http://youtu.be/F1MlotN9ssY you try it.
If the stretcher were attached to something fixed like a wall then I
would agree with what you have been showing. Indeed if you are fastening
your bench to a wall then you should fasten it near the top of the
bench.
However the stretcher is not attached to a fixed object. It is simply
attached to another leg of the bench. That leg can also move and flex.
Let me give you another example. Take your argument to the extreme and
move the stretcher all the way to the top of the bench. If I understand
your arguments then since this would produce a near zero lever arm then
the bench would be extremely rigid.
However this is basically the same situation as most tables with an apron
around the top. (The stretcher in this case is the same as the apron.)
However to make a table rigid, table makers have to go to great lengths to
make the leg/apron joint very strong and rigid. The problem is that the
table leg makes a very long lever arm connected to the bottom of the
apron/stretcher. You have simply shortened one lever arm and lengthened
another when you move the stretcher.
Dan
On 2/16/2014 8:17 PM, woodchucker wrote:
> On 2/16/2014 10:52 PM, woodchucker wrote:
>> On 2/16/2014 9:52 PM, Dan Coby wrote:
>>> On 2/16/2014 12:10 PM, woodchucker wrote:
>>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>>
>>>> It's all in the engineering.
>>>
>>> You correctly point out that using a wide stretcher will make for
>>> a stiffer bench. If the stretcher is rigidly connected to the leg,
>>> then its contribution to the stiffness of the bench is proportional
>>> to the square of its height. So doubling the height of the stretcher
>>> will quadruple its effect on the bench's stiffness. However other
>>> things like the size of the upper apron, legs, top, and the rigidity
>>> of the joints also affect stiffness. Diagonal braces can also have
>>> a major impact.
>>>
>>> However there are a few problems with your analysis when it comes
>>> to the location of the stretcher.
>>>
>>> If I am interpreting your video correctly, the magnet represents the
>>> stretcher and the bar of the magnetic base represents the leg of the
>>> bench. The joint between the stretcher and leg is free to pivot.
>> Well not exactly the yellow grip tite is the stretcher. But to represent
>> the lever principle simply, they are not connected. The point is that
>> even w/o locking them together solidly, even if you had loose bolts the
>> middle would offer less leverage and the bottom, would be too much
>> leverage.
>>>
>>> Real benches are not normally built with joints that pivot. The
>> You are taking this too literally, it's to show the benefit of a middle
>> stretcher vs a bottom stretcher.
>>> rigidity of many bench designs comes from the rigidity of the joints
>>> between the legs, aprons, top, and stretchers. If none of these joints
>>> were rigid then the bench would simply fall down due to gravity. You
>>> can build a bench with flexible joints but you need to have some form
>>> of diagonal bracing to convert some of the parallelograms into triangles.
>>>
>>>
>>> Lets do a simple analysis of a bench leg. To make things very simple,
>>> I am going to have a bench with only a single leg and without a top or
>>> an apron. Obviously this is not very representative of real benches.
>>> However this is somewhat equivalent to what you were showing in your
>>> video. I am also going to replace the stretcher with just a couple
>>> of forces. When the leg tries to rack (twist) it will apply a force
>>> at the top of the stretcher which is trying to push the stretcher to
>>> the right and a force at the bottom of the stretcher which is trying
>>> to pull the stretcher to the left. The stretcher pushes back on the
>>> leg with equal and opposite forces so the stretcher will push back to
>>> the left at the top and pull to the right at the bottom. With a rigid
>>> joint between the stretcher and leg, the top of the stretcher will be
>>> in compression and the bottom will be in tension as the stretcher tries
>>> to keep the bench from racking. (In a real joint the forces will be
>>> distributed across the joint and vary smoothly from compression at the
>>> top to tension at the bottom.)
>>>
>>>
>>> Fy ----> |---|
>>> | | |
>>> | | |
>>> | | |
>>> | | |
>>> | | |
>>> | |<--- Fsc |
>>> | | | |
>>> | | W H
>>> | |---> Fst | |
>>> | | | |
>>> | | | |
>>> | | | |
>>> | | S |
>>> | | | |
>>> | | | |
>>> |---| <---- Ff | |
>>>
>>> In this diagram:
>>> Fy is the force you are applying to bench while working
>>> Ff is the friction force at the bottom of the leg at the floor
>>> Fsc is the force due to trying to compress the top of the stretcher
>>> Fst is the force due to applying tension to the bottom of the
>>> stretcher
>>> S is the height of the bottom of the stretcher
>>> W is the width of the stretcher
>>> H is the height of the top of the bench
>>>
>>> If we apply Newton's second law to the stretcher we see:
>>> Fsc - Fst = 0
>>> This means that Fsc = Fst. I.e. there is as much tension force at the
>>> bottom of the stretcher as compression at the top. If these forces did
>>> not balance the the stretcher would start to accelerate.
>>>
>>> If we apply Newton's second law to the leg we see:
>>> Fy - Fsc + Fst - Ff = 0
>>> Since Fsc = Fst we get Fy - Ff = 0
>>> Which means Fy = Ff
>>> This is what we would expect. There needs to be enough friction at the
>>> floor to keep the bench from moving.
>>>
>>> Now lets look at the torques being applied to the leg. Please
>>> remember that a torque is determined by both the force being applied
>>> and the distance (moment arm) from the reference point. Lets use
>>> the floor as our reference point. This gives us:
>>> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
>>> Substituting Fst = Fsc we get:
>>> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
>>> or
>>> Fy*H - Fsc*W = 0
>>> or
>>> FY*H = Fsc*W
>>>
>>> This last equation tells us that the torque applied by Fy*H is equal
>>> to the counter torque being applied by the stretcher Fsc*W.
>>>
>>> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
>>> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
>>> of the equation because the tension at the bottom of the stretcher is
>>> balanced by the compression at the top of the stretcher.
>> That really is not supported in reality. I can take a bench with the
>> same size stretcher and move it from the middle to the bottom and cause
>> the bench to rack. All things being equal.
>>
>>>
>>> A final note: The width of the stretcher does determine the magnitude
>>> of the tension/compression in the stretcher needed to balance the torque
>>> due to the forces being applied to the bench. Since I simplified the
>>> analysis to just two forces in the stretcher, the magnitude drops
>>> inversely with the width instead of the square of the width.
>>>
>>>
>>> Your bench is stiff due to your building it with wide stretchers and
>>> rigid joints and not due to the stretchers being higher above the floor.
>>>
>> Certainly it is. I agree that wide stretchers are necessary, but if I
>> put that wide stretcher at the bottom I have more leverage and therefore
>> that joint will fail eventually. It will cause compression of the fibers
>> and the socket will widen if I were to put that stretcher at the very
>> bottom like I have seen on benches.
>>>
>>>
>>> Dan
>>
>>
> I'll build a small mortise and tenon setup (2) to show middle pressure vs end pressure.
>
> This is about leverage and lever arms. A longer lever has more ability to break the joint down, that a shorter one.
See my comment in another post about there being two lever arms to consider.
The first is the lever arm between the top and the stretcher. The second is
the lever arm between the bottom and the stretcher. As you make one shorter,
the other is getting longer. The resulting torques remain constant.
Dan
woodchucker wrote:
> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>
> It's all in the engineering.
Jeff - cannot hear you well enough to understand you.
--
-Mike-
[email protected]
On 2/16/14, 3:43 PM, Bill wrote:
> Mike Marlow wrote:
>> woodchucker wrote:
>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>
>>> It's all in the engineering.
>>
>> Jeff - cannot hear you well enough to understand you.
>
> No problem here. Maybe your speakers?
>>
>
No, the gain is way too low. I had to turn the speakers way up to hear.
Nonetheless... great information and totally correct about the racking
force and moving the stretchers up or making them wider to avoid racking.
--
-MIKE-
"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com
[email protected]
---remove "DOT" ^^^^ to reply
Bill wrote:
> Mike Marlow wrote:
>> woodchucker wrote:
>>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>>
>>> It's all in the engineering.
>>
>> Jeff - cannot hear you well enough to understand you.
>
> No problem here. Maybe your speakers?
No - my speakers are just fine. Maybe my ears...
You have to admit - Jeff's volume is very low.
--
-Mike-
[email protected]
On 2/16/2014 9:52 PM, Dan Coby wrote:
> On 2/16/2014 12:10 PM, woodchucker wrote:
>> See: http://www.youtube.com/watch?v=Ktihu6UR0tM&feature=youtu.be
>>
>> It's all in the engineering.
>
> You correctly point out that using a wide stretcher will make for
> a stiffer bench. If the stretcher is rigidly connected to the leg,
> then its contribution to the stiffness of the bench is proportional
> to the square of its height. So doubling the height of the stretcher
> will quadruple its effect on the bench's stiffness. However other
> things like the size of the upper apron, legs, top, and the rigidity
> of the joints also affect stiffness. Diagonal braces can also have
> a major impact.
>
> However there are a few problems with your analysis when it comes
> to the location of the stretcher.
>
> If I am interpreting your video correctly, the magnet represents the
> stretcher and the bar of the magnetic base represents the leg of the
> bench. The joint between the stretcher and leg is free to pivot.
Well not exactly the yellow grip tite is the stretcher. But to represent
the lever principle simply, they are not connected. The point is that
even w/o locking them together solidly, even if you had loose bolts the
middle would offer less leverage and the bottom, would be too much leverage.
>
> Real benches are not normally built with joints that pivot. The
You are taking this too literally, it's to show the benefit of a middle
stretcher vs a bottom stretcher.
> rigidity of many bench designs comes from the rigidity of the joints
> between the legs, aprons, top, and stretchers. If none of these joints
> were rigid then the bench would simply fall down due to gravity. You
> can build a bench with flexible joints but you need to have some form
> of diagonal bracing to convert some of the parallelograms into triangles.
>
>
> Lets do a simple analysis of a bench leg. To make things very simple,
> I am going to have a bench with only a single leg and without a top or
> an apron. Obviously this is not very representative of real benches.
> However this is somewhat equivalent to what you were showing in your
> video. I am also going to replace the stretcher with just a couple
> of forces. When the leg tries to rack (twist) it will apply a force
> at the top of the stretcher which is trying to push the stretcher to
> the right and a force at the bottom of the stretcher which is trying
> to pull the stretcher to the left. The stretcher pushes back on the
> leg with equal and opposite forces so the stretcher will push back to
> the left at the top and pull to the right at the bottom. With a rigid
> joint between the stretcher and leg, the top of the stretcher will be
> in compression and the bottom will be in tension as the stretcher tries
> to keep the bench from racking. (In a real joint the forces will be
> distributed across the joint and vary smoothly from compression at the
> top to tension at the bottom.)
>
>
> Fy ----> |---|
> | | |
> | | |
> | | |
> | | |
> | | |
> | |<--- Fsc |
> | | | |
> | | W H
> | |---> Fst | |
> | | | |
> | | | |
> | | | |
> | | S |
> | | | |
> | | | |
> |---| <---- Ff | |
>
> In this diagram:
> Fy is the force you are applying to bench while working
> Ff is the friction force at the bottom of the leg at the floor
> Fsc is the force due to trying to compress the top of the stretcher
> Fst is the force due to applying tension to the bottom of the
> stretcher
> S is the height of the bottom of the stretcher
> W is the width of the stretcher
> H is the height of the top of the bench
>
> If we apply Newton's second law to the stretcher we see:
> Fsc - Fst = 0
> This means that Fsc = Fst. I.e. there is as much tension force at the
> bottom of the stretcher as compression at the top. If these forces did
> not balance the the stretcher would start to accelerate.
>
> If we apply Newton's second law to the leg we see:
> Fy - Fsc + Fst - Ff = 0
> Since Fsc = Fst we get Fy - Ff = 0
> Which means Fy = Ff
> This is what we would expect. There needs to be enough friction at the
> floor to keep the bench from moving.
>
> Now lets look at the torques being applied to the leg. Please
> remember that a torque is determined by both the force being applied
> and the distance (moment arm) from the reference point. Lets use
> the floor as our reference point. This gives us:
> Fy*H - Fsc*(S + W) + Fst*S - Ff*0 = 0
> Substituting Fst = Fsc we get:
> Fy*H - Fsc*S - Fsc*W + Fsc*S = 0
> or
> Fy*H - Fsc*W = 0
> or
> FY*H = Fsc*W
>
> This last equation tells us that the torque applied by Fy*H is equal
> to the counter torque being applied by the stretcher Fsc*W.
>
> PLEASE NOTE THAT THE HEIGHT OF THE STRETCHER ABOVE THE FLOOR DOES NOT
> APPEAR IN THE FINAL EQUATION. The height of the stretcher dropped out
> of the equation because the tension at the bottom of the stretcher is
> balanced by the compression at the top of the stretcher.
That really is not supported in reality. I can take a bench with the
same size stretcher and move it from the middle to the bottom and cause
the bench to rack. All things being equal.
>
> A final note: The width of the stretcher does determine the magnitude
> of the tension/compression in the stretcher needed to balance the torque
> due to the forces being applied to the bench. Since I simplified the
> analysis to just two forces in the stretcher, the magnitude drops
> inversely with the width instead of the square of the width.
>
>
> Your bench is stiff due to your building it with wide stretchers and
> rigid joints and not due to the stretchers being higher above the floor.
>
Certainly it is. I agree that wide stretchers are necessary, but if I
put that wide stretcher at the bottom I have more leverage and therefore
that joint will fail eventually. It will cause compression of the fibers
and the socket will widen if I were to put that stretcher at the very
bottom like I have seen on benches.
>
>
> Dan
--
Jeff