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... using differential equations

EId4wdx4=qz-EI \cfrac{\text{d}^4w}{\text{d}x^4} = -q_z

This is treated in chapter 8.1 and 8.2 (except for example 4) of the book Engineering Mechanics Volume 2 Hartsuijker & Welleman, 2007.

Exercises

References
  1. Hartsuijker, C., & Welleman, J. W. (2007). Engineering Mechanics: Volume 2: Stresses, strains and displacements. Springer Netherlands. 10.1007/978-1-4020-5763-2