analytical solution for a beam loaded with simple bending in places distance from the simetry line

[lopessilva]

Hello,

I want to obtain analytical solution to a beam loaded with simple bending at midspan. There is an equation, but it´s only valid for points located on the simetry line. I want to calculate deflection along the left edge. I know there is a displacement method that uses the stiffness matrix, but I was wondering if there is other way or if you can point a book with a detailed explanation. I´m sending an attachment, to illustrate better.




Regards,
Hugo Silva
Mechanical Eng. PhD student
Materials Eng. MSc.