Analysisbeam_cantilever.xlsTo determine deflection of a cantilever beam under superimposed loadsBy Alex Slocum, 1/1/04, last modified 06/11/04 by Xue'en YangEnters numbers in BOLD, Results in REDSchematicBeam dimensions and propertiesValuesInstructionsLength, L (mm)100Enter total length of beam in mmWidth, W (mm)25Enter width of beam in mmHeight, H (mm)6Enter height of beam in mmLength increment, Linc (mm)1Enter length increment to be used in finite difference calculationModulus of elasticity, E (N/mm^2)200000Enter elastic modulus in N/mm^2Moment of inertia, I (mm^4)450=1/12*W*H^3Distance from farthest fiber to neutral axis, cc (mm)3= H/2LoadingSee schematic for definitions of loads and positionsPoint load, F (N)10Enter amplitude of the point load, in NLocation of point load, af (mm)0Enter location of the point load, in mmDistributed load amplitude, wa, (N/mm)1Enter amplitude of the distributed load near the cantilever end, in N/mmDistributed load amplitude, wL, (N/mm)1Enter amplitude of the distributed load at the clamped end, in N/mmStarting point of distributed load, aw (mm)50Enter location for wa, in mmMoment load, M (N-mm)10Enter amplitude of the applied moment, in N*mmLocation of moment load, am (mm)25Enter location of the moment load, in mmMaximum deflection (microns)-56.771Return maximum deflection along the beam in micronsMaximum slope (milli radians)0.779Return maximum slope along the beam in milli radiansReactions at beam endsRA, Ra (N)0.000Reaction force at ARB, Rb (N)60.000Reaction force at BMA, Ma (N)0.000Reaction moment at AMB, Mb (N-mm)-2240.000Reaction moment at BqA, ta (radians)0.001Rotation at AqB, tb (radians)0.000Rotation at BdA, da (mm)-0.057Deflection at AdB, db (mm)0.000Deflection at BEquationsNote: For other types of distributed loads, use principle of superposition

Plots

Plots-56.7708333333-55.9921481481-55.2135740741-54.4352222222-53.6572037037-52.8796296296-52.1026111111-51.3262592593-50.5506851852-49.776-49.0023148148-48.2297407407-47.4583888889-46.6883703704-45.9197962963-45.1527777778-44.3874259259-43.6238518519-42.8621666667-42.1024814815-41.3449074074-40.5895555556-39.836537037-39.085962963-38.3379444444-37.5925925926-36.849962963-36.1101111111-35.3731481481-34.6391851852-33.9083333333-33.1807037037-32.4564074074-31.7355555556-31.0182592593-30.3046296296-29.5947777778-28.8888148148-28.1868518519-27.489-26.7953703704-26.1060740741-25.4212222222-24.7409259259-24.0652962963-23.3944444444-22.7284814815-22.0675185185-21.4116666667-20.761037037-20.1157407407-19.4758893519-18.8416-18.213000463-17.5902296296-16.9734375-16.3627851852-15.7584449074-15.1606-14.5694449074-13.9851851852-13.4080375-12.8382296296-12.276000463-11.7216-11.1752893519-10.6373407407-10.1080375-9.5876740741-9.0765560185-8.575-8.0833337963-7.6018962963-7.1310375-6.6711185185-6.2225115741-5.7856-5.3607782407-4.9484518519-4.5490375-4.162962963-3.7906671296-3.4326-3.0892226852-2.7610074074-2.4484375-2.1520074074-1.8722226852-1.6096-1.3646671296-1.137962963-0.9300375-0.7414518519-0.5727782407-0.4246-0.2975115741-0.1921185185-0.1090375-0.0488962963-0.01233379630

Distance along beam, xDistance from left end of beam (mm)Deflection (mcrons)Deflection

Data0.77870370370.77864814810.77848148150.77820370370.77781481480.77731481480.77670370370.77598148150.77514814810.77420370370.77314814810.77198148150.77070370370.76931481480.76781481480.76620370370.76448148150.76264814810.76070370370.75864814810.75648148150.75420370370.75181481480.74931481480.74670370370.74398148150.74125925930.73842592590.73548148150.73242592590.72925925930.72598148150.72259259260.71909259260.71548148150.71175925930.70792592590.70398148150.69992592590.69575925930.69148148150.68709259260.68259259260.67798148150.67325925930.66842592590.66348148150.65842592590.65325925930.64798148150.64259259260.63709074070.63146666670.62570925930.61980740740.613750.60752592590.60112407410.59453333330.58774259260.58074074070.57351666670.56605925930.55835740740.55040.54217592590.53367407410.52488333330.51579259260.50639074070.49666666670.48660925930.47620740740.465450.45432592590.44282407410.43093333330.41864259260.40594074070.39281666670.37925925930.36525740740.35080.33587592590.32047407410.30458333330.28819259260.27129074070.25386666670.23590925930.21740740740.198350.17872592590.15852407410.13773333330.11634259260.09434074070.07171666670.04845925930.02455740740

Distance from left end of beam (mm)Slope (milli radians)Slope

ProE Mechanica0-10-20-30-40-50-60-70-80-90-100-110-120-130-140-150-160-170-180-190-200-210-220-230-240-250-250-260-270-280-290-300-310-320-330-340-350-360-370-380-390-400-410-420-430-440-450-460-470-480-490-500.5-512-524.5-538-552.5-568-584.5-602-620.5-640-660.5-682-704.5-728-752.5-778-804.5-832-860.5-890-920.5-952-984.5-1018-1052.5-1088-1124.5-1162-1200.5-1240-1280.5-1322-1364.5-1408-1452.5-1498-1544.5-1592-1640.5-1690-1740.5-1792-1844.5-1898-1952.5-2008-2064.5-2122-2180.5-2240

Distance from left end of beam (mm)Moment (N-mm)Moment

0-0.0666666667-0.1333333333-0.2-0.2666666667-0.3333333333-0.4-0.4666666667-0.5333333333-0.6-0.6666666667-0.7333333333-0.8-0.8666666667-0.9333333333-1-1.0666666667-1.1333333333-1.2-1.2666666667-1.3333333333-1.4-1.4666666667-1.5333333333-1.6-1.6666666667-1.6666666667-1.7333333333-1.8-1.8666666667-1.9333333333-2-2.0666666667-2.1333333333-2.2-2.2666666667-2.3333333333-2.4-2.4666666667-2.5333333333-2.6-2.6666666667-2.7333333333-2.8-2.8666666667-2.9333333333-3-3.0666666667-3.1333333333-3.2-3.2666666667-3.3366666667-3.4133333333-3.4966666667-3.5866666667-3.6833333333-3.7866666667-3.8966666667-4.0133333333-4.1366666667-4.2666666667-4.4033333333-4.5466666667-4.6966666667-4.8533333333-5.0166666667-5.1866666667-5.3633333333-5.5466666667-5.7366666667-5.9333333333-6.1366666667-6.3466666667-6.5633333333-6.7866666667-7.0166666667-7.2533333333-7.4966666667-7.7466666667-8.0033333333-8.2666666667-8.5366666667-8.8133333333-9.0966666667-9.3866666667-9.6833333333-9.9866666667-10.2966666667-10.6133333333-10.9366666667-11.2666666667-11.6033333333-11.9466666667-12.2966666667-12.6533333333-13.0166666667-13.3866666667-13.7633333333-14.1466666667-14.5366666667-14.9333333333

Distance from left end of beam (mm)Stress (Pa)Stress

0-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-11-12-13-14-15-16-17-18-19-20-21-22-23-24-25-26-27-28-29-30-31-32-33-34-35-36-37-38-39-40-41-42-43-44-45-46-47-48-49-50-51-52-53-54-55-56-57-58-59-60

Distance from left end of beam (mm)Transverse Shear (N)Transverse Shear

Distance along beam, xShear (N)Moment (N-mm)Stress (Pa)Slope (mrad)Deflection (microns)0000.00.779-56.81-10-10-0.10.779-56.02-10-20-0.10.778-55.23-10-30-0.20.778-54.44-10-40-0.30.778-53.75-10-50-0.30.777-52.96-10-60-0.40.777-52.17-10-70-0.50.776-51.38-10-80-0.50.775-50.69-10-90-0.60.774-49.810-10-100-0.70.773-49.011-10-110-0.70.772-48.212-10-120-0.80.771-47.513-10-130-0.90.769-46.714-10-140-0.90.768-45.915-10-150-1.00.766-45.216-10-160-1.10.764-44.417-10-170-1.10.763-43.618-10-180-1.20.761-42.919-10-190-1.30.759-42.120-10-200-1.30.756-41.321-10-210-1.40.754-40.622-10-220-1.50.752-39.823-10-230-1.50.749-39.124-10-240-1.60.747-38.325-10-250-1.70.744-37.626-10-250-1.70.741-36.827-10-260-1.70.738-36.128-10-270-1.80.735-35.429-10-280-1.90.732-34.630-10-290-1.90.729-33.931-10-300-2.00.726-33.232-10-310-2.10.723-32.533-10-320-2.10.719-31.734-10-330-2.20.715-31.035-10-340-2.30.712-30.336-10-350-2.30.708-29.637-10-360-2.40.704-28.938-10-370-2.50.700-28.239-10-380-2.50.696-27.540-10-390-2.60.691-26.841-10-400-2.70.687-26.142-10-410-2.70.683-25.443-10-420-2.80.678-24.744-10-430-2.90.673-24.145-10-440-2.90.668-23.446-10-450-3.00.663-22.747-10-460-3.10.658-22.148-10-470-3.10.653-21.449-10-480-3.20.648-20.850-10-490-3.30.643-20.151-11-501-3.30.637-19.552-12-512-3.40.631-18.853-13-525-3.50.626-18.254-14-538-3.60.620-17.655-15-553-3.70.614-17.056-16-568-3.80.608-16.457-17-585-3.90.601-15.858-18-602-4.00.595-15.259-19-621-4.10.588-14.660-20-640-4.30.581-14.061-21-661-4.40.574-13.462-22-682-4.50.566-12.863-23-705-4.70.558-12.364-24-728-4.90.550-11.765-25-753-5.00.542-11.266-26-778-5.20.534-10.667-27-805-5.40.525-10.168-28-832-5.50.516-9.669-29-861-5.70.506-9.170-30-890-5.90.497-8.671-31-921-6.10.487-8.172-32-952-6.30.476-7.673-33-985-6.60.465-7.174-34-1018-6.80.454-6.775-35-1053-7.00.443-6.276-36-1088-7.30.431-5.877-37-1125-7.50.419-5.478-38-1162-7.70.406-4.979-39-1201-8.00.393-4.580-40-1240-8.30.379-4.281-41-1281-8.50.365-3.882-42-1322-8.80.351-3.483-43-1365-9.10.336-3.184-44-1408-9.40.320-2.885-45-1453-9.70.305-2.486-46-1498-10.00.288-2.287-47-1545-10.30.271-1.988-48-1592-10.60.254-1.689-49-1641-10.90.236-1.490-50-1690-11.30.217-1.191-51-1741-11.60.198-0.992-52-1792-11.90.179-0.793-53-1845-12.30.159-0.694-54-1898-12.70.138-0.495-55-1953-13.00.116-0.396-56-2008-13.40.094-0.297-57-2065-13.80.072-0.198-58-2122-14.10.048-0.099-59-2181-14.50.025-0.0100-60-2240-14.90.0000.0

Beam dimensions and propertiesValuesProE MechanicaLength, L (mm)100100Width, W (mm)2525Height, H (mm)66Length increment, Linc (mm)11Modulus of elasticity, E (N/mm^2)200000200000Moment of inertia, I (mm^4)450450Distance from farthest fiber to neutral axis, cc (mm)33Loading ConditionPoint load, F (N)1010Location of point load, af (mm)00Distributed load amplitude, wa, (N/mm)11Distributed load amplitude, wL, (N/mm)11Starting point of distributed load, aw (mm)5050Moment load, M (N-mm)1010Location of moment load, am (mm)2525Maximum deflection (microns)-56.771-56.017Maximum slope (milli radians)0.779Reactions at beam endsRA, Ra (N)0.0000RB, Rb (N)60.00060MA, Ma (N)0.0000MB, Mb (N-mm)-2240.000-2238qA, ta (radians)0.001qB, tb (radians)0.0000dA, da (mm)-0.057-0.056dB, db (mm)0.0000

MBD001C644F.unknown

MBD04342044.vsd

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MBD001AE517.unknown