what is the function used to give parabolic load on the free end of the cantilever beam

i want to find out the load variation with respect to the distance, the verticle distance (D) is 12 meter (as shown in figure). if i take n points along the D( say y= 0, 3, 6, 9, 12). the total load should be P=1000N.

For this if i use Load (x)=P*sin(pi*y)/D. im getting maximum load as 1000 when theta is eqaul to 90 degree and the total load is exceeding 1000N.

so that what function i suppoese to follow to the total load equal to 1000 with parabolic variation.

Answer 1

[Asad (Mehrzad) Khoddam]

The q value (shear stress) is equal to

Then you need to inegrate from for example -3 to 3 , 3 to 9 to find P value

[VENGATESAN S]

5 points are there in the y axis as I have mentioned in the question. So that how can I find out the load at each point? If I substitute the limit -6 to +6 then I will get only one value. But I need to find the load on 5 points.

I'm having some doubts in applying the limit for the integration.