Determine the vertical component of force that each of the three struts at A, B, and C exerts on the silo if it is subjected to a resultant wind loading of 250 lb which acts in the direction shown.ġ6 Example 26-02 (cont.) Establish Cartesian Coordinate System Draw FBDġ7 Example 26-02 (cont.) What Equilibrium Equation Should be Used? Mo = 0 Why? Find moment arm vectors x y z TBC TBD F1= 3 kN F2 = 4 kN Ax Ay AzĮxample (cont.) Moment Equation x y z TBC TBD Due to symmetry TBC = TBD F1= 3 kN F2 = 4 kN Ax Ay Azġ1 Example 26-01 (cont.) Moment Equation z TBD F1= 3 kN TBC F2 = 4 kN Azġ2 Example 26-01 (cont.) Force Equilibrium z TBD F1= 3 kN TBC F2 = 4 kNġ3 Example 26-01 (cont.) Force Equilibrium z TBD F1= 3 kN TBC F2 = 4 kNġ4 Example 26-01 (cont.) Force Equilibrium z TBD F1= 3 kN TBC F2 = 4 kNġ5 Example 26-02 The silo has a weight of 3500 lb and a center of gravity at G. Unit vectors x y z TBC TBD F1= 3 kN F2 = 4 kN Ax Ay AzĨ Example 26-01 (cont.) Ball-and-Socket Reaction Forces Unit vectors zĩ Example 26-01 (cont.) What Equilibrium Equation Should be Used? Determine the components of reaction at the ball-and-socket joint A and the tension in the supporting cables BC and BD.ĥ Example 26-01 (cont.) Draw FBD Due to symmetry TBC = TBD z TBDĦ Example 26-01 (cont.) What are the First Steps?ĭefine Cartesian coordinate system Resolve forces Scalar notation? Vector notation? x y z TBC TBD F1= 3 kN F2 = 4 kN Ax Ay Azħ Example 26-01 (cont.) Cable Tension Forces Position vectors 28 Preferred option Schedule time on Thursday Nov.15 or 22 Please Advise Class Representative of Preferenceģ Lecture 26 Objective to illustrate application of scalar and vector analysis for 3D rigid body equilibrium problemsĤ Example 26-01 The pipe assembly supports the vertical loads shown. 9 Two Options Use review class Wednesday Nov. Altogether, our results may help in better understanding and controlling the particle interfacial instabilities with potential uses in synthesis of new materials, environmental sciences and microfluidics.1 Lecture 26: 3D Equilibrium of a Rigid BodyĮNGI 1313 Mechanics I Lecture 26:ēD Equilibrium of a Rigid BodyĢ Schedule Change Postponed Class Two Optionsįriday Nov. We also discuss possible metastable states. We develop stability diagrams in terms of f, N (we study 7 ≤ N ≤ 61), and the contact angle θp at the particles and identify three unstable regimes corresponding to (i) collective detachment of the whole cluster from the interface, (ii) ejection of individual particles, and (iii) both detachment and ejection. In the cases with an initial hexagonal arrangement of the particles, upon f approaching fcrit, our simulations additionally reveal the emergence of curvature-induced defects and 2D stress anisotropy. The scaling remains valid in the whole regime of forces f, i.e., even close to the stability limit fcrit. In the case of incompressible clusters, we find that the equilibrium 3D interface profiles are uniquely determined by the length scale γ/(fn0), where n0 is the particle surface number density, and a non-dimensional shape parameter f2Nn0/γ2. We employ analytical theory, numerical energy minimization (Surface Evolver) and computational fluid dynamics (the Lattice-Boltzmann method) to study the equilibrium deformation of the interface and structural mechanics of the clusters, in particular at the onset of instability. We investigate clustering of particles at an initially flat fluid-fluid interface of surface tension γ under an external force f directed perpendicular to the interface.
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