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Beam_curved.xls
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To determine deflection of a curved beam
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By Alex Slocum, 11/26/2004
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Enters numbers in BOLD, Results in RED
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Beam dimensions and propertiesValues
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If round cross-section (enter "yes" or "no")no
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Outside diameter, Do (mm)0
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Inside diamter, Di (mm)0
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If rectangular cross-sectionyes
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Outside height, ho (mm)1
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Outside width, wo (mm)10
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Inside height, hi (mm)0
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Inside width, wi (mm)0
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Radius of curvature, Rr (mm)5
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Length, L (mm)5
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Modulus of elasticity, E (N/mm^2)68947
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Poisson ratio, v0,33
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Maximum allowable stress, sigmax (N/mm^2)250
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Results summary for the complete "U" shaped spring
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Y deflection (microns)19,4
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Y stiffness (N/mm)51,5
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X deflection (microns)7,2
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Bending stress, sigbend (N/mm^2)4,5
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Safety factor (sigmax/sigbend)56
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Detailed calculations
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Shear modulus, G (Pa)25920
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Moment of inertia, I (mm^4)1
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Distance farthest fiber to neutral axis, cc (mm)0,5
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Cross section area, A10
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EA6,89E+05
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GA2,59E+05
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EI5,75E+04
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Loading
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Point load, Fy (N)1Check: Bending (from Roark) for phi = p/2
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Moment, Mo (N*mm)2,5Beam disp.Beam Abbe4x Total
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X direction displacement (microns)AxialShearBendingBendingratio
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Due to Fy0,0000,0001,0880,0914,7141,0881
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Due to Mo0,0000,0000,6212,4840,6211
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Total7,1971,7090
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Y direction displacement (microns)AxialShearBending
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Due to Fy0,0060,0151,7090,0911,94215,0491,7091
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Due to Mo0,0000,0001,0884,3511,0881
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Total19,4012,7960
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Slope (milliradians)Bending
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Due to Fy0,4350,4351
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Due to Mo0,3420,3421
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Total0,7770,7771
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Maximum moment
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Mmax (N-mm)7,5
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Mmax (N/mm^2)4,5
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Angle, phid (degrees)90
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Angle, phi (radius)1,571
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Equations
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