NEVER get the Stiffness Method wrong AGAIN in Structural Analysis!

Learn the Stiffness Method (also called the Displacement Method) step by step: from joint movements and bar stiffness to a fully worked continuous beam, checked against the StructTutor solver. By the end, you'll be able to solve a continuous beam by hand. In this lesson you will see: • Which joint movements are possible, and how supports and hinges restrict them • How to count the independent unknowns in beams and frames (with and without sway) • Where the stiffness coefficients come from: unit cases for end rotation and transverse displacement • How loads become fixation actions, and the sign conventions we use • The equilibrium equation f + K·X = P, and the eight steps of the method • A worked example: a continuous beam A–B–C, fixed at A and C, roller at B, two 4 m spans, q = 10 kN/m on AB • Bar end moments, reactions, and the moment diagram, compared with the solver • Equilibrium and compatibility checks, frequent mistakes, and an exercise for you to try Worked example (results): X₁ = θB = 6.667/EI rad · M_AB(A) = +16.667 kN·m · M_BA = −6.667 kN·m · M_BC = +6.667 kN·m · M_CB = +3.333 kN·m · R_A = 22.5 kN · R_B = 20 kN · R_C = 2.5 kN (downward) Conventions and assumptions: plane structures, prismatic bars, linear elastic material, small displacements, bending deformation only. Counter-clockwise rotations and moments are positive. ⏱ CHAPTERS 0:00 Introduction and lesson map 0:27 Which joint movements are possible? 0:47 Three ideas not to mix 1:04 Supports 1:31 Rigid joints and internal hinges 1:49 Counting the unknowns: a continuous beam 2:27 Frames: with and without sway 3:04 Bar stiffness: rotation at end i 3:30 Bar stiffness: rotation at j and transverse displacement 3:58 Axial movement and validity 4:41 Unit cases build the stiffness matrix 5:21 Loads give fixation actions 6:05 The method in eight steps 6:29 The equilibrium equation 7:13 The exercise: data and unknown 7:51 Fixation action 8:13 Unit case and stiffness 8:43 Equilibrium and solution 9:06 End moments of the bars 9:47 Reactions and diagrams 10:30 Comparison with the solver 10:49 Checks 11:27 Recap and frequent mistakes 11:48 Your turn and closing 🧮 Try it yourself: pause at 11:48 and solve the same beam with BC = 6 m, then check your result in the StructTutor solver. 🌐 Platform: structtutor.com If this helped, like the video and subscribe for the next lesson. Disclosure: the narration in this video uses a synthetic (AI-generated) voice. #StiffnessMethod #DisplacementMethod #StructuralAnalysis #CivilEngineering #StructuralEngineering #StructTutor