tailieunhanh - Fundamentals of Structural Analysis Episode 1 Part 5

Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Truss Analysis Force Method Part II by Work done by external force left and work done by interanl force right -case 1. The conservation of mechanical energy principle calls for n M 2 iP Ái 2 iFV 15 2 The case of virtual unit load acts alone. The figure below illustrates the forcedisplacement histories. Work done by external force left and work done by interanl force right -case 2. Again the energy conservation principle calls for ỳ l 4o 1 i fjVj 16 3 The case of the virtual unit load being applied first followed by the application of the real loads. The force-displacement histories are shown in the figures below. 75 Truss Analysis Force Method Part II by Work done by external forces left and work done by interanl forces right -case 3. Application of the energy conservation principle leads to 1 1 n 1 M 1 M M 1 1 A 1 y P A 1 A 1 y fv 1 y Fy y fy 17 2 2 tn 2 J 1 2 J 1 J 1 Substracting Eq. 17 by Eq. 15 and Eq. 16 yields M 1 Ao y fy 14 J 1 which is the principle of virtual force statement expresssed in the unit-load context. Example 15. Find the vertical displacement at node 2 of the truss shown given E 10 GPa 100 cm2 for all bars. 76 Truss Analysis Force Method Part II by Example to find a nodal displacement by the unit load method. Solution. Using the unit load method requires the solution for the member elongation Vi under the appied load and the virtual member force fi under the unit load as shown in the figure below. A unit load applied in the direction of the displacement to be solved. The computation in Eq. 14 is carried out in a table as shown keeping in mind that the virtual member forces are associated with the virtual unit load and the nodal displacement is associated with the member elongation as indicated below. 1 4 V f f Since both the real loading problem and the virtual unit load problem have been solved in earlier examples we shall not go through the process again except to note that in order to find member elongation V L we