In order to find the equilibrium equations in polar coordinates. Page 2 of: (soest.hawaii.edu/martel/Courses/GG703/GG711c_Lec_10.pdf)
Do you have to use the Taylor expansion to get from 10.4 to 10.5? Also, how is this equation altered if there are shear stresses?
ps. Add w ww & h ttp to access page
To answer your question and access the specific page you mentioned, I'm sorry but as a text-based AI, I cannot browse the internet or access specific web pages. However, I can still help you understand the process of finding the equilibrium equations in polar coordinates.
In the context of structural mechanics, the equilibrium equations are derived by considering the balance of forces acting on a body or structure. In polar coordinates, these equations take into account the radial and tangential components of the forces.
Regarding your question about the Taylor expansion, I cannot specifically refer to equations 10.4 and 10.5 without the page, but I can explain the general concept. The Taylor expansion is a mathematical technique used to approximate functions by expanding them into an infinite series of terms. It is often employed to simplify complicated equations and obtain useful approximations.
If shear stresses are present, the equilibrium equations in polar coordinates are altered to include additional terms related to shear forces. In polar coordinates, there are two shear components: the azimuthal shear stress (τθr) and the radial shear stress (τrr). These shear stresses need to be taken into account when determining the equilibrium equations in order to accurately describe the state of equilibrium for a structure.
I hope this explanation helps you understand the process of finding equilibrium equations in polar coordinates.