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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Mathematical calculations for deflection due to slope and bending.

Identifier  ExFiles\Box 127\1\  scan0370
Date  27th May 1938
  
-4-

(2) Deflexion of B below A due to slope.
Let Ø = slope at A
Ø = 1/EI (14,500a - 500a² - 4,000a + 200a²)
= 1/EI (10,500a - 300a²)
Deflexion = Ø (10 - a)
= 1/EI (105,000a - 3,000a² - 10,500a² + 300a³)
= 1/EI (105,000a - 13,500a² + 300a³)

(3) Deflexion of B relative to A due to bending.
Mx{John H Maddocks - Chief Proving Officer} = (10 - a - x) 400
EI d²y/dx² = -400 ((10 - a) - x)
EI dy{F R Danby}/dx = -400 ((10 - a)x - x²/2) + Y
EI y = -400 ((10 - a)x²/2 - x³/6) + Yx + δ
as before Y = δ = 0
EIyB = -400 ((10 - a)³/2 - (10 - a)³/6)
= -133 (10 - a)³
  
  


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