Statics: Lesson 61 - Shear Moment Diagram, The Equation Method

Statics: Lesson 61 - Shear Moment Diagram, The Equation Method Welcome back to engineering mechanics statics! In Lesson 61, we are exploring a crucial scenario where the graphic method fails and we must rely on "The Equation Method" for drawing Shear Force Diagrams (SFD) and Bending Moment Diagrams (BMD). If you have a beam with a triangular distributed load, finding the maximum bending moment requires setting up precise mathematical functions, and this high-value tutorial shows you exactly how to do it. First, we will calculate the global support reactions using rigid body equilibrium equations. Next, we will sketch the SFD using a clever snow skiing analogy to determine the correct parabolic curve shape. Then, we will expose the biggest trap in statics—proving why the zero shear point ($ V = 0 $) does not align with the triangle's centroid. You will learn how to make a strategic section cut at a distance of 'x', apply similar triangles to determine the changing load height, and derive the official equations for both shear and moment. This algebraic shortcut is an absolute must-watch for your structural analysis, mechanics of materials study, and FE Exam statics prep! 𝐌𝐲 𝐄𝐧𝐠𝐢𝐧𝐞𝐞𝐫𝐢𝐧𝐠 𝐍𝐨𝐭𝐞𝐛𝐨𝐨𝐤 for notes! Has graph paper, study tips, and Some Sudoku puzzles or downtime between classes! https://amzn.to/3pTSZXw 𝐄𝐧𝐠𝐢𝐧𝐞𝐞𝐫𝐬 𝐏𝐮𝐳𝐳𝐥𝐞 𝐁𝐨𝐨𝐤 Sodoku, Mazes, Word Search, Word Scramble - 400 puzzles and solutions - Perfect Gift! https://amzn.to/3KxtS3L 𝐂𝐚𝐩𝐬𝐭𝐨𝐧𝐞 𝐃𝐞𝐬𝐢𝐠𝐧 𝐉𝐨𝐮𝐫𝐧𝐚𝐥 For your senior design project documentation! 100 pages of numbered graph papers. https://amzn.to/3OtZJ6z 𝐅𝐄 𝐑𝐞𝐯𝐢𝐞𝐰 𝐉𝐨𝐮𝐫𝐧𝐚𝐥 For you notes and work while preparing for the FE Exam. 100 pages of graph paper! https://amzn.to/3ONRILn 𝐏𝐄 𝐉𝐨𝐮𝐫𝐧𝐚𝐥 𝐒𝐓𝐀𝐑 𝐋𝐨𝐠 Record your projects in preparation of your PE application or for your annual review at work...(Situation, Task, Analysis, Results) https://amzn.to/3rjyAMp 𝐇𝐨𝐰 𝐭𝐨 𝐀𝐜𝐞 𝐒𝐭𝐚𝐭𝐢𝐜𝐬 Great book to review or have on your shelf to make sure you never forget Statics! https://amzn.to/455QRKM Top 15 Items Every Engineering Student Should Have! 1) TI 36X Pro Calculator https://amzn.to/2SRJWkQ 2) Circle/Angle Maker https://amzn.to/2SVIOwB 3) Engineering Paper https://amzn.to/2K7vYbP 4) Mechanical Pencils 40pk https://amzn.to/2GGRG4y 5) Desk/Bed Clamp Reading Light https://amzn.to/2YzN5qG 6) Stainless Steel Rulers https://amzn.to/31aqMcP 7) Small Stapler https://amzn.to/2ynDOrk 8) Post it Tabs for Page Markers https://amzn.to/2SSIP4q 9) Noise Canceling Wireless Headphones https://amzn.to/3aMLbdY 10) Wireless Mouse https://amzn.to/2ROkY5Y 11) Multicolor Pen/Pencil https://amzn.to/3331AXy 12) Portable Charger https://amzn.to/2RsitHG 13) Backpack Rain Cover https://amzn.to/2Gq4ATM 14) Amazon Dot https://amzn.to/2Gs42g4 15) Portable Bluetooth Speaker https://amzn.to/3aIMZV0 This video is NOT sponsored. Some product links are affiliate links which mean if you buy something we'll receive a small commission. Follow me on Instagram   / jeff_hanson_phd   Please consider supporting the channel by subscribing, commenting, and liking each video. This moves these videos up the search list and helps me greatly. Thank you for watching. My Patreon:   / jeff_hanson   Please help keep the free videos coming by donating. Thank you for the many blessings. This video is copyrighted by the Jeff Hanson for the private use of our audience. Any other use of this video or any pictures, descriptions, or accounts of the video without written consent from Jeff Hanson is strictly prohibited. Please consider supporting the channel by subscribing, commenting, and liking each video. This moves these videos up the search list and helps me greatly. Thank you for watching. My Patreon:   / jeff_hanson   Please help keep the free videos coming by donating. Thank you for the many blessings. This video is copyrighted by the Jeff Hanson for the private use of our audience. Any other use of this video or any pictures, descriptions, or accounts of the video without written consent from Jeff Hanson is strictly prohibited. These videos are not formally endorsed by Texas Tech University. These video resources shall not imply nor infer official representation or approval of or endorsement by Texas Tech University. #statics #jeffhanson #engineeringmechanics #shearmomentdiagram #SFD #BMD