Flat slab by keralaguest

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									     Flat slab
               4 z
              Et 3        4z       4 z 
                    2                 q
              
            2  x 4
     12 1 v          x 2y 2 y 4 
                                         

     Column grid L in both directions. Square column size a .
                                                                                              L2 
   Load per unit area, q  w  constant except over columns when q  w
                                                                         1
                                                                        
                                                                                                    .
                                                                                                    
                                                                                          a 2 
                                                                           a
     Consider a periodic function which is zero when x                       kL where k is any positive or
                                                                         2
     negative integer.                                                       
                      
                                        2mx
      hx          a           cos        .                                
                     m
                              m
                                          L                
                                   2rx                         L  L
     Multiply by cos                    and integrate from x   to ,
                                     L                          2  2
    a                                             a
                                                 2r
             2rx                                   2  L sin ra  a L so that a  1 sin ma which
      2

       L dx  2 2r sin
                    L
         cos
                                                  L  r                        m
                                                                     r           m
       a                                                       L                           L
     
         2
                                  a
     includes a0                   .
                                  L
                                                                      
   Hence

                      wL2          2mx        2ny
      w            2                 an cos L
      q                      am cos
                      a m          L n
                  wL2   1           ma     na     2mx     2ny
              w 2 2           sin     sin     cos      cos
                  a m n mn      L       L        L        L
                                 
                  4wL2               ma     na     2mx     2ny
                   2 2 
                               1
                               sin     sin     cos      cos
                   a m1 n1 mn      L       L        L        L
                                                            
                            ma   2mx 2wL 1     na   2ny
                      m sin L cos L  a  n sin L cos L
                 2wL     1
             
                  a m1                  n1






								
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