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P x 2
EJ    x  EJ   M x  0  M  x a  
z z 0 0 a M
2 M
P  x a  2  q x a q  3 (6.41)
 P  ,
p a 2! q a 3!

M x 2 P x 3 M x a  2
EJ y   x  EJ y  EJ  0 x  0  0  a M 
z
0
z
z
2 6 M 2! (6.42)
P  x a  3  q x a q  4
 P  .
p a q a
3! 4!
If the beam has some typical loads P , M or q , then, before
the last three items in the equations (6.41) and (6.42) should be put
the sign of summation.
The values M , P and y ,  , are called static and geometric
0 0 0 0
initial parameters respectively.
The values M , P , q are taken as positive if they are trying to
turn the left side of the beam clockwise in respect with the section.
If you accept the rules for signs M , P , q and shown in fig.
6.18 in the direction axes x and y , a positive value y
corresponds to the deflection up and positive values  – turn of a
cross-section counter clockwise.

Figure 6.19
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