Advanced Package Training Scaffolding 2011.1 - Scia-Software GbR

More documents

Recommendations

Info

10. The second order calculation Timoshenko 42 Advanced Training The first method is the so called Timoshenko method (Th.II.O) which is based on the exact Timoshenko solution for members with known normal force. It is a 2 nd order theory with equilibrium on the deformed structure which assumes small displacements, small rotations and small strains. When the normal force in a member is smaller than the critical buckling load, this method is very solid. The axial force is assumed constant during the deformation. Therefore, the method is applicable when the normal forces (or membrane forces) do not alter substantially after the first iteration. This is true mainly for frames, buildings, etc. for which the method is the most effective option. The influence of the normal force on the bending stiffness and the additional moments caused by the lateral displacements of the structure (the P-∆ effect) are taken into account in this method. This principle is illustrated in the following figure. M(x) = Hx M(L) = HL First Order Theory The local P-δ effect will be regarded further in this course. M(x) = Hx + P δ + P Δx /L M(L)= HL + P Δ Second Order Theory If the members of the structure are not in contact with subsoil and do not form ribs of shells, the finite element mesh of the members must not be refined. The method needs only two steps, which leads to a great efficiency. In the first step, the axial forces are solved. In the second step, the determined axial forces are used for Timoshenko’s exact solution. The original solution was generalised in Scia Engineer to allow taking into account shear deformations. The applied technique is the so called ‘total force method’ or ‘substitution method’. In each iteration step, the total stiffness of the structure is adapted and the structure is re-calculated until convergence. This technique is illustrated in the following diagram.
43 Scaffolding In this figure, the stiffness K is divided in the elastic stiffness KE and the geometrical stiffness KG. The geometrical stiffness reflects the effect of axial forces in beams and slabs. The symbol u depicts the displacements and F is the force matrix. The criterion for convergence is defined as follows: ∑ , + , + , − ∑, + , ∑ , + , + , + , With: ux,i The displacement in direction x for iteration i. uy,i The displacement in direction y for iteration i. The displacement in direction z for iteration i. uz,i Start Calculate KE KG = 0 K = KE - KG Solve K.u = F Convergence in u? Stop Yes Calculate KG ≤ 0,005/( ) This convergence precision (Precision ratio) can be adapted in the solver setup: No
Page 1 and 2: Advanced Package Training Scaffoldi
Page 3 and 4: Contents 1. Introduction ..........
Page 5 and 6: 1. Introduction 5 Scaffolding This
Page 7 and 8: Materials 7 Scaffolding For the mat
Page 9 and 10: FLOOR BOARDS 9 Scaffolding The inpu
Page 11 and 12: END INPUT OF CONSTRUCTION 11 Scaffo
Page 13 and 14: q2: Partial area load (EN12811-1, 6
Page 15 and 16: Load Case 1: Self Weight 15 Scaffol
Page 17 and 18: 17 Scaffolding In the example discu
Page 19 and 20: 1 2 q p ( z) = ce ( z) ⋅ qb = ce
Page 21 and 22: q p e 21 Scaffolding EN 12811-1 §6
Page 23 and 24: 4. Results It is recommended to fir
Page 25 and 26: 6. Scaffolding SLS Check - EN 12811
Page 27 and 28: 7. Steel Code Check ULS Check - EN
Page 29 and 30: Stability Check Buckling data 29 Sc
Page 31 and 32: - Go to the menu “Steel -> Check
Page 33 and 34: 8. Scaffolding ULS Check - EN 12811
Page 35 and 36: 9. Non-Linear Combinations Overview
Page 37 and 38: 1a 5.2.2(3)c lb based on a global b
Page 39 and 40: These inclination functions are ent
Page 41: 41 Scaffolding The buckling curve u
Page 45 and 46: Start Choose ΔF u0 = 0 F0 = 0 F =
Page 47 and 48: 47 Scaffolding As specified, the Ne
Page 49 and 50: 49 Scaffolding In the results menu,
Page 51 and 52: ∙ + ∙ = ∙ The equation f
Page 53 and 54: Example Stability_Imperfe Imperfect
Page 55 and 56: Buckling Shape [-] A polynomial has
Page 57 and 58: 57 Scaffolding Using this combinati
Page 59 and 60: 12. Input Hinge Types and non-linea
Page 61 and 62: The rigidities are filled out and t
Page 63 and 64: 63 Scaffolding It is assumed that t
Page 65 and 66: 13. Scaffolding - Coupler Check Whe
Page 67 and 68: The internal force My for this beam
Page 69 and 70: Example ULS Check - Scaffolding che
Page 71 and 72: 71 Scaffolding
Page 73 and 74: 73 Scaffolding Where L is the membe
Page 75 and 76: 75 Scaffolding
Page 77 and 78: Shear The design value of the shear
Page 79 and 80: For a solid bar, round tube and hho
Page 81 and 82: 17. Template To create a template,
Page 83 and 84: 3. Inserting the user block into an
Page 85 and 86: Annex A: Wind pressure versus Wind

Advanced Package Training Scaffolding 2011.1 - Scia-Software GbR

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?