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You can use the classic method to find the "Fixed End Moment" or utilize a table as shown below by superposition - separate the beam with two loading cases, either case 1 + case 7, or case 7 with each UDL on its corresponding location.

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Here be dragons. Or, to paraphrase a hadith of the Prophet Mohammed, "There are seventy ways to compute element stresses, and all of them are wrong." The naive approach is to differentiate the element shape functions to find the strain at a point, and then use the stress-strain relationship for the material. The problem is that since the shape ...

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A shell element is similar to the plate element that having both in-plane and out-plane stiffness (note that membrane has the in-plane stiffness only), and have different bending theories: Mindlin Theory for thick shells, and Kirchhoff-Love Theory for thin shells. Here is a good book to read, "Theory and Analysis of Elastic Plates and Shells", by ...

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You formulate the matrices in a local coordinate system where local $x$ axis is along the length of the beam, and the local $y$ and $z$ axes are the principal axes of the beam section. In that coordinate system, $I_{yz} = 0$ by definition. ($I_{xy}$ and $I_{xz}$ are also zero). Finally, you transform the equations in the the global coordinate system using ...

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