Gable lean maths question
Discussion
I have an old french house and the gable wall, both sides, above first floor leans about 150mm over 2m according to spirit level. What degree is that. There is no sign of movement and the house is 400yrs old so I assume it was built like that. the walls are around 700mm thick and solid random stone.
Strangely the first two floor walls are fairly vertical. They lean the same way as well, one toward the house and the other away. I'm thinking I might need to install some pattress plates.
Strangely the first two floor walls are fairly vertical. They lean the same way as well, one toward the house and the other away. I'm thinking I might need to install some pattress plates.
The answer is Shuff4's 4.3 degrees, near as makes no difference (4.289, to be precise, if the dimensions given were absolutely spot on).
The very rough rule of thumb is that if an imaginary vertical plumbline from the top centre of the wall stays within the middle third of the thickness, its fine.
A quick fag-packet calculation suggests that on a wall thickness of 700mm, that amount of lean would be fine up to about 3.11m. of wall height.
If in doubt, consult a structural engineer, of course: there can be other factors involved.
Slightly depressing that we're sending people out from our schools these days who not only can't do basic Trig, but don't have the wits to look up a calculator to do it for them on Google.
The very rough rule of thumb is that if an imaginary vertical plumbline from the top centre of the wall stays within the middle third of the thickness, its fine.
A quick fag-packet calculation suggests that on a wall thickness of 700mm, that amount of lean would be fine up to about 3.11m. of wall height.
If in doubt, consult a structural engineer, of course: there can be other factors involved.
Slightly depressing that we're sending people out from our schools these days who not only can't do basic Trig, but don't have the wits to look up a calculator to do it for them on Google.
Using trig it's:
sin(angle) = opposite / hypotenuse.
Opposite is the amount of lean, 150 mm. Hypotenuse is the length of wall, 2000 mm.
That gives, angle = arcsin(150/2000) = 4.30 degrees.
It also means the peak of the gable is now 6 mm lower than if it were straight.
Just noticed Equus has posted 4.289 which uses tan ranther than sin - the wall is the hyptonenuse as it's not part of the right angle of the imaginary triangle. The lean distance and the imaginary vertical line from the ground to the gable form the right angle, with the wall as the long edge (i.e. the hypotenuse).
sin(angle) = opposite / hypotenuse.
Opposite is the amount of lean, 150 mm. Hypotenuse is the length of wall, 2000 mm.
That gives, angle = arcsin(150/2000) = 4.30 degrees.
It also means the peak of the gable is now 6 mm lower than if it were straight.
Just noticed Equus has posted 4.289 which uses tan ranther than sin - the wall is the hyptonenuse as it's not part of the right angle of the imaginary triangle. The lean distance and the imaginary vertical line from the ground to the gable form the right angle, with the wall as the long edge (i.e. the hypotenuse).
Edited by Flibble on Thursday 22 August 09:42
Flibble said:
Just noticed Equus has posted 4.289 which uses tan ranther than sin - the wall is the hyptonenuse as it's not part of the right angle of the imaginary triangle. The lean distance and the imaginary vertical line from the ground to the gable form the right angle, with the wall as the long edge (i.e. the hypotenuse).
I was assuming that the 2m. was measured as a vertical height, not along the sloping face of the wall, so yes, I was taking that as the adjacent to the angle, and using tan.But if you can measure the difference of 0.01 degrees on an old masonry wall, good luck to you!
Edited to add:
Wayne E Edge said:
There is no sign of movement and the house is 400yrs old so I assume it was built like that.
If it's built with lime mortar, then the mortar is slightly 'plastic' and can 'flow' or deform to some degree before failing (see 4th paragraph, page 11 of this document). It almost certainly wasn't built like that - even 15th Century French cowboys weren't that bad - so you do need to be conscious of the potential for further movement. Edited by Equus on Thursday 22 August 10:37
Equus said:
The answer is Shuff4's 4.3 degrees, near as makes no difference (4.289, to be precise, if the dimensions given were absolutely spot on).
The very rough rule of thumb is that if an imaginary vertical plumbline from the top centre of the wall stays within the middle third of the thickness, its fine.
A quick fag-packet calculation suggests that on a wall thickness of 700mm, that amount of lean would be fine up to about 3.11m. of wall height.
If in doubt, consult a structural engineer, of course: there can be other factors involved.
Slightly depressing that we're sending people out from our schools these days who not only can't do basic Trig, but don't have the wits to look up a calculator to do it for them on Google.
We didn't learn that type of thing in the 'schools' we went to. I left in 1979.The very rough rule of thumb is that if an imaginary vertical plumbline from the top centre of the wall stays within the middle third of the thickness, its fine.
A quick fag-packet calculation suggests that on a wall thickness of 700mm, that amount of lean would be fine up to about 3.11m. of wall height.
If in doubt, consult a structural engineer, of course: there can be other factors involved.
Slightly depressing that we're sending people out from our schools these days who not only can't do basic Trig, but don't have the wits to look up a calculator to do it for them on Google.
Edited by Wayne E Edge on Thursday 22 August 18:38
Equus said:
If it's built with lime mortar, then the mortar is slightly 'plastic' and can 'flow' or deform to some degree before failing (see 4th paragraph, page 11 of this document). It almost certainly wasn't built like that - even 15th Century French cowboys weren't that bad - so you do need to be conscious of the potential for further movement.
Thanks for all your answers. Tje stone is held together with clay Edited by Equus on Thursday 22 August 10:37
It always amazes me how tolerant old buildings are in terms of their stability. This is a clay wall on a listed barn I recently surveyed in support of a planning application for conversion.
The photo is not an optical illusion - the top of that wall is fully outside of its base, let alone the middle third, and remains standing but I would not want to remove the roof structure!
Wayne E Edge said:
We didn't learn that type of thing in the 'schools' we went to. I left in 1979.
That genuinely surprises me! You're around the same age as me, then, and I can still remember the rhyme they taught us:Some Old Hags Collect Apples Hoping To Obtain Ale.
Sin = Opposite over Hypotenuse
Cosine= Adjacent over Hypotenuse
Tan = Opposite over Adjacent
Wayne E Edge said:
The stone is held together with clay
Again (and unlike cement mortar) clay has a degree of plasticity and can 'creep' over the years.It will continue to move, but if it;s only got that far in 400 years, you probably don't need to worry too much in your lifetime.
Equus said:
Again (and unlike cement mortar) clay has a degree of plasticity and can 'creep' over the years.
It will continue to move, but if it;s only got that far in 400 years, you probably don't need to worry too much in your lifetime.
LIt will continue to move, but if it;s only got that far in 400 years, you probably don't need to worry too much in your lifetime.
Think I would remember that. No rhymes in our school.
Edited by Wayne E Edge on Sunday 25th August 21:04
Equus said:
Wayne E Edge said:
We didn't learn that type of thing in the 'schools' we went to. I left in 1979.
That genuinely surprises me! You're around the same age as me, then, and I can still remember the rhyme they taught us:Some Old Hags Collect Apples Hoping To Obtain Ale.
Some Old Houses Creak And Howl Through Old Age
Sheepshanks said:
I went to school around that time and certainly did trig. The rhyme we used, perhaps more appropriate to your line of business than the above, was:
Some Old Houses Creak And Howl Through Old Age
I like that! Yes, definitely more appropriate for construction professionals... I shall have to remember that, for my Part II students!Some Old Houses Creak And Howl Through Old Age
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