Radius along neutral axis = 147 [155-8] Arc length @ cl= 1/4 th of circumference of circle with radius 147 and therefore, (147π/2) Net pipe length= 479.907mm
I doubled the measurement - 155 - which gave me the diameter of the circle (if the bend was a circle) then I multiplied that - 310 - by pi - 3.142 - which gave me the circumference of the circle - 974.02 - and divided it by four (because the right angle bend was only quarter of a circle) = 243.505 then added the two legs + 87 = 330.505 and 162 = 492.505 which is the total length.
apprenticemath Ahhh. Thank you very much for your kind encouragement. I thought that since the bend "straightens out" into two straight bits, the ends would be "flat" thus the 16mm would not be a factor (I beg your pardon for my clumsy terminology and thinking!) If it MUST be a factor then I assume that half the diameter would be taken off the measurement at the top and the bottom of that quarter circle - so 492.505 less 16mm = 476.505 I'm sure there is a more "mathematical" way to put that. Perhaps it should have only been 8mm but I don't know why.
***** For fun I tried that another way. I took 155 less half the pipe diameter multiplied by two = diameter is now 294, which multiplied by pi = 923.748 divided by four for the right angle is now 230.937 plus the legs 87 = 317.937 and 162 which gives the final length as 479.937 That one is probably right because it's much more "mathematical". Thank you for this lovely problem.
Good hunch, thinking, all correct. Now the proof for this comes from materials science: @watch?v=JiARfu5ww4k This video is a student assignment as intro to bend calculations, to spark some debate. Thanks for playing along. There is no way one could get any related solution out of any math book. There is no way of students definitely solving this as they have no previous background knowledge or experience relating to the concept of neutral axis in bending. There is no math proof for reality either, it is just so. The link explains, thanks for checking out my class.
Radius along neutral axis = 147 [155-8]
Arc length @ cl= 1/4 th of circumference of circle with radius 147 and therefore, (147π/2)
Net pipe length= 479.907mm
10/10
thanks for watching
49.25 cm total lenght
I doubled the measurement - 155 - which gave me the diameter of the circle (if the bend was a circle) then I multiplied that - 310 - by pi - 3.142 - which gave me the circumference of the circle - 974.02 - and divided it by four (because the right angle bend was only quarter of a circle) = 243.505 then added the two legs + 87 = 330.505 and 162 = 492.505 which is the total length.
Excellent approach, good thinking, almost perfect but incorrect answer. The 16mm dimension has to be part of the picture too somehow.
apprenticemath Ahhh. Thank you very much for your kind encouragement. I thought that since the bend "straightens out" into two straight bits, the ends would be "flat" thus the 16mm would not be a factor (I beg your pardon for my clumsy terminology and thinking!) If it MUST be a factor then I assume that half the diameter would be taken off the measurement at the top and the bottom of that quarter circle - so 492.505 less 16mm = 476.505
I'm sure there is a more "mathematical" way to put that.
Perhaps it should have only been 8mm but I don't know why.
***** For fun I tried that another way. I took 155 less half the pipe diameter multiplied by two = diameter is now 294, which multiplied by pi = 923.748 divided by four for the right angle is now 230.937 plus the legs 87 = 317.937 and 162 which gives the final length as 479.937
That one is probably right because it's much more "mathematical".
Thank you for this lovely problem.
Good hunch, thinking, all correct. Now the proof for this comes from materials science: @watch?v=JiARfu5ww4k
This video is a student assignment as intro to bend calculations, to spark some debate. Thanks for playing along. There is no way one could get any related solution out of any math book. There is no way of students definitely solving this as they have no previous background knowledge or experience relating to the concept of neutral axis in bending. There is no math proof for reality either, it is just so. The link explains, thanks for checking out my class.
26 15/16"
155 + 155 - 8 (half of the pipe diameter) + Leg 1 (87)+ Leg 2 (162) = 551mm ?
Need to include (pi) in the calculation of the arc length