# 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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