Finite element analysis of frame structures

In this video application of finite element methods in analyzing a 2D frame structure is elaborated in a step-by-step manner using a worked example below. Theory: Members in a frame are considered to be rigidly connected in that both forces and moments can be transmitted through their joints. In developing the equations and methods for the solution of plane frames and grids, first, we develop the stiffness matrix for a beam element arbitrary oriented in a plane. Then, we include the axial nodal displacements degree of freedom in the local beam element stiffness matrix. Finally, we combine these results to develop the stiffness matrix, including axial deformation effects, for an arbitrary oriented beam element. Example: Using the matrix displacement method, determine the nodal bending moments for the rigid-jointed plane frame shown (see video). It may be assumed that the axial stiffness of each element is large compared to the flexural stiffness. 👇 SUBSCRIBE TO THIS YOUTUBE CHANNEL 👇 https://youtube.com/channel/UCaszVnxZ5T_EIKyiKN3IR4Q/?sub_confirmation=1 We have started a new #lectureseries dubbed: Introduction to #FiniteElementMethods (for beginners). We shall be having a live lecture every week from 8.30 AM (UTC+3). The lessons will be archived in this playlist https://bit.ly/FEMintro. See you in class. Cheers. And always remember to subscribe to this channel. Watch individual lectures here 1. Introduction to finite element methods https://youtu.be/yAnkX8gz8ls 2. Linear spring as a finite element https://youtu.be/wR7U0Akccac 3. Finite Element equation for a bar element https://youtu.be/OiOCNLp_bLg 4. Finite element equation formulation for a Bar element in 2-D space https://youtu.be/Ay_9kNkiU_k 5. Analysis of Beams in Finite Element Method https://youtu.be/_HL5GzDk7vM Tutorials/Solved problems 1. FEA solved problems on springs, tapered bar and beam//Tutorials https://youtu.be/r7jtrg4NC9Y 2. Derivation of stiffness matrix for a beam element https://youtu.be/ZmyyOifNGRI If you would like to support the channel, below are various ways in which you can - 1. Join my Youtube Members club and enjoy special perks: https://bit.ly/drYTMembers 2. Become a patron: https://www.patreon.com/drgathimba 3. Become a member: https://bit.ly/BMC-Member 4. Donate via PayPal: https://bit.ly/2TmSTHL This will allow me to create more educative videos covering various engineering topics. Below are some useful text for beginners - Daryl L. Logan, A First Course in the Finite Element Methods. 6th Ed., - CENGAGE Learning, 2017 - Wahyu Kuntjoro, An Introduction to the Finite Element Method. McGraw-Hill Education (Asia), 2005 For those of you who would like to explore the topic in more detail, I recommend the books: - Fundamentals of Finite Element Analysis by David Hutton and, - The finite element method: linear static and dynamic finite element analysis by Thomas J. R. Hughes. You can now download notes and other materials related to the lectures on this link https://bit.ly/4Downloads Disclosure: Product links are 'affiliate links'.