弧长计算(拱形).已知:弦长2700mm,高300mm,求弦长?

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弧长计算(拱形).已知:弦长2700mm,高300mm,求弦长?
弧长计算(拱形).已知:弦长2700mm,高300mm,求弦长?

弧长计算(拱形).已知:弦长2700mm,高300mm,求弦长?
已知:弦长L=2700mm,高H=300mm,求弧长C?
弧半径为R,弧所对的圆心角为A.
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=300/2+2700^2/(8*300)
=3187.5,
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2700/2)/3187.5)
=50.115度
=50.115*PI/180
=0.874676弧度
C=R*A=3187.5*0.874676=2788.03mm