Beam Cantilever | Beam (Structure)

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  beam_can To determine deflection of a cantilev By Alex Slocum, 1/1/04, last mo SchematicBeam dimensions and propertiesValues #en t$, # %mm& 100 'idt$, ' %mm& 25 (ei $t, ( %mm& 6 #en t$ increment, #inc %mm& 1 )odulus of elasticity, * %+/mm-& 200000 )oment of inertia, . %mm4& 450 istance from fart$est fiber to neutral axis, cc %mm& 3Loading oint load,  %+& 10 #ocation of point load, af %mm& 0 istributed load amplitude, 2a, %+/mm& 1 istributed load amplitude, 2#, %+/mm& 1 Startin point of distributed load, a2 %mm& 50 )oment load, ) %+3mm& 10 #ocation of moment load, am %mm& 25 )aximum deflection %microns& -56.771 )aximum slope %milli radians& 0.77!eactions at eam ends0.00060.0000.000-2240.0000.0010.000-0.0570.000#$uations *nters numbers in B%   A , a %+&  B , b %+&) A , )a %+&) B , )b %+3mm& θ A , ta %radians& θ B , tb %radians& δ A , da %mm& δ B , db %mm& − −  (ote) *or other t+pes o, distri uted loads' use principle o, superposition ( )( ---5- 5 --- - 6- 6 6 a f wwa w A A f   f   a A A A f   A A A A V F x a x aw L a x aw M x F x a M R F x a x aw x x M R EI EI EI EI  F x a x x M R x EI EI EI  θ  θ δ  θ δ  = − − − − −−−= + − − − −− −= + + − −−= + + − −+ ( ) ( ) (( )  ( ) ( ) ( )  ( )( -555 - 5 -- 6 4- 556 -4  L a w B B f   L aw A a f   f  w A a  L aw w F F L R M  F  L a L a w ww EI EI a F a L L L aw EI EI  θ δ  + −= + = −−  − −= + + −   − − + −= −   ilever.xls  er beam under superimposed loads dified 06/11/04 by Xueen !an nstructions *nter total len t$ of beam in mm*nter 2idt$ of beam in mm*nter $ei $t of beam in mm*nter len t$ increment to be used in finite difference calculation*nter elastic modulus in +/mm- 71/1-8'8(5 7 (/- See schematic for definitions of loads and positions *nter amplitude of t$e point load, in +*nter location of t$e point load, in mm*nter amplitude of t$e distributed load near t$e cantilever end, in +/mm*nter amplitude of t$e distributed load at t$e clamped end, in +/mm*nter location for 2a, in mm*nter amplitude of t$e applied moment, in +8mm*nter location of t$e moment load, in mmeturn maximum deflection alon t$e beam in micronseturn maximum slope alon t$e beam in milli radianseaction force at Aeaction force at Beaction moment at Aeaction moment at Botation at Aotation at Beflection at Aeflection at B  L&'  esults in !#& -  )( )( )( )( ) 505 44  6-4-4 w L a wmw L aw w mwa L aw  x aw M x a L a x a M x aw w EI L a EI  x a x aw w EI  − −+ −−− − −− +−− − −− ( ) - 1-0 - w mw  M x a EI L a EI  −+− )  ( ) ( )( )) ( ) ( )  ( ) --- - 54 -  L awa f  wm L a ww  L a w wa M w M L a EI  M a L L aw wa EI   − −− − + +   −−− ++ + +
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