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- 1. Alhosn University, Abu Dhabi, UAE Department of Civil Engineering Design Assessment of a Reinforced Concrete Building Through Non-Linear Analysis Presented by: Mohammed Mohideen Ismail Ahmad Mahmoud Khier Moaid Ahmed Jumaa Adnan Talal Mayassi Supervised by: Dr George Markou, Assistant Professor 1
- 2. 1. Project Objectives 2. Methodology 3. Modeling 4. Nonlinear Analysis (Theory) 5. Geometry of the Structure 6. Results from the Preliminary Analysis (Linear Static) 7. Modal Analysis 8. Computation of the Seismic Load 9. Nonlinearities and SAP2000 10. Numerical Results (Nonlinear Analysis) 11. Redesign of the RC Structure 12. Conclusions Presentation Contents Wednesday, 29th of May 2013 2
- 3. Study the mechanical behavior of the RC structure. Perform Pushover Analysis. Redesign the building so as to achieve a seismically resistant behavior (if required). Primary Objectives Wednesday, 29th of May 2013 3
- 4. Study the geometry of the structure. Two finite element models were constructed in Etabs and Sap2000 commercial software through which the seismic assessment of the RC structure was performed. Determining whether the structure is capable of carrying a medium seismic excitation according to Eurocode, through the use of pushover analysis. Perform the redesign. Methodology Wednesday, 29th of May 2013 4
- 5. Modeling Finite Element Method (FEM): Is a numerical analysis technique used by engineers, to obtain solution to partial differential equations that describe a wide variety of physical and nonphysical problems. Wednesday, 29th of May 2013 5
- 6. Modeling Types of Finite Elements: The shape of each element gives the ability to discretize different geometries according to the structural element shape. In our model we used beam-column and shell finite elements. Rod and beam elements Plane and shell elements Solid elements Wednesday, 29th of May 2013 6
- 7. Non-linear Analysis Wednesday, 29th of May 2013 When the internal forces are not equal to the externally applied loads due to the materials nonlinearities, then a nonlinear iterative procedure is required to update the stiffness matrix of the structure so as to achieve the equilibrium between the internal and the external forces. This procedure is known as nonlinear analysis. 7
- 8. Non-linear Analysis Analysis type Short description Nonlinearity of material Infinitive displacements and deformations Nonlinear relationship between stress and strain Large displacements and rotations but small deformations Displacements and rotations are large but change of the length and angle is small Linear or nonlinear relation between stress and strain Large displacement ,rotation and deformation Large change in angle and length Linear or nonlinear relation strain- stress Wednesday, 29th of May 2013 It should be noted that when we use material nonlinearity, the nonlinear response is solely due to the stress strain relation. 8
- 9. Non-linear Analysis Wednesday, 29th of May 2013 Newton-Raphson method: This method is an iterative procedure where at each iteration the stiffness matrix of the structure is recalculated and the system of equations is solved iteratively by setting the incremental loading vector equal to the unbalanced forces, the stiffness matrix is calculated at every internal iteration based on computed stress-strain at the previous internal iteration. 9
- 10. Wednesday, 29th of May 2013 10
- 11. Wednesday, 29th of May 2013 11
- 12. Wednesday, 29th of May 2013 The height of the structure is :44.5 m 12
- 13. Results from the Preliminary Analysis (Linear Static) ULS Static Linear Analysis Wednesday, 29th of May 2013 ULS Static (ACI) =1.2(G) +1.6(Q) As it can be seen the maximum developed stresses was 56 MPa. The deformation were not significant while our structures initial design is able to carry the static design loads applied. 13
- 14. Results from the Preliminary Analysis (Linear Static) Wind Load Linear Analysis Wednesday, 29th of May 2013 The maximum stress developed by wind load along the x-axis, which has a value of 5.85 MPa. 14
- 15. Results from the Preliminary Analysis (Linear Static) The maximum stress developed due to the wind load along the y-axis, which has a value of 11.7 MPa. Wednesday, 29th of May 2013 15
- 16. Results from the Preliminary Analysis (Linear Static) Linear Quasi – Static (Seismic analysis) Wednesday, 29th of May 2013 The maximum stress applied by seismic load on the horizontal direction, which has a value of 17.1 MPa. The code that has been used for generating the seismic load was UBC 97. 16
- 17. Results from the Preliminary Analysis (Linear Static) The corresponding maximum horizontal displacements were found to be equal to 0.77cm and 1.37cm for model wx and wy, respectively. It is evident that the y- direction is the weak one, thus it results larger displacements Wednesday, 29th of May 2013 Maximum Story Displacement due to Wind Load 17
- 18. Results from the Preliminary Analysis (Linear Static) When the seismic load is applied on the structure, for the case of the x-axis the maximum horizontal displacement was found to be equal to 1.7 cm and in the case of the y-axis the maximum horizontal displacement was found to be equal 3.53 cm Wednesday, 29th of May 2013 Maximum Story Displacement due to Seismic Load 18
- 19. Modal Analysis Deformed shape of Mode 1. T=1.83 sec Deformed shape of Mode 2. T=1.587 sec Deformed shape of Mode 3. T=1.043 sec Wednesday, 29th of May 2013 19
- 20. Computation of the Seismic Load Wednesday, 29th of May 2013 Area T(thickness) Self Weight G(dead loads) Q (Live Loads) Weight From Loads Total Weight M Total Ground floor 325.2m² 0.1m 796.74kN 5kN 5kN 2113.8kN 57267.3kN 5837.64kg Mezzanine floor 325.2m² 0.25m 1991.85kN 5kN 5kN 2113.8kN 1st floor 389.2m² 0.25m 2383.85kN 5kN 2.5kN 2237.9kN 2nd floor- 9th floor 389.2m² 0.25m 2383.85kN 5kN 2.5kN 2237.9kN Roof 389.2m² 0.35m 3337.39kN 5kN 7.4kN 2810.024kN Top Roof 389.2m² 0.25m 2383.85kN 5kN 2.5kN 2237.9kN 20
- 21. Our structure was found to have a 1st fundamental period of 1.83 seconds, thus the 3rd part of the response spectrum graph will result the required design spectrum acceleration Sd(T) describes the part of the response spectrum diagram given that we assume that the structure has a ground type C. According to Eurocode the factor S =1.15 and Tc =0.6 sec when the ground type is C. Sd (T) = ag * S*(2.5/q) * ( Tc/T), Vtotal = Sd (T) * M Total Base Shear: Vtotal = 22.62 MN` Computation of the Seismic Load The assumed design acceleration in this case was assumed to be equal to ag = 0.15g. According to the response spectrum diagram of EC8, the design spectrum acceleration is computed. Wednesday, 29th of May 2013 21
- 22. Computation of the Seismic Load Distribution of the Total Base Shear FLOOR mi zi mi*zi ∑mi*zi (mi*zi)(∑mi*zi) Horizontal Load F1 2910.54kg 1m 2910.54 1419366kg.m 0.00205 47kN F2 4105.65kg 4.4m 18064.86 0.0127 288kN F3 4621.75kg 7.8m 36049.65 0.0254 575kN F4 4621.75kg 11.5m 53150.13 0.0374 846kN F5 4621.75kg 15.2m 70250.6 0.0495 1120kN F6 4621.75kg 18.9m 87351.08 0.0615 1392kN F7 4621.75kg 22.6m 104451.6 0.0735 1663kN F8 4621.75kg 26.3m 121552 0.08564 1938kN F9 4621.75kg 30m 138652.5 0.09768 2210kN F10 4621.75kg 33.7m 155753 0.1097 2482kN F11 4621.75kg 37.4m 172853.5 0.12178 2755kN F12 6147.414kg 41.1m 252658.7 0.178 4027kN F13 4621.75kg 44.5m 205667.9 0.1449 3278kN Wednesday, 29th of May 2013 22
- 23. ∗ Plastic hinges: Concentrated hinges that were assigned to the frame and shell elements, which may experience nonlinear behavior. ∗ Layered Shell Elements: In order to account nonlinearities in all shell finite elements, Area Properties in SAP2000 were created. These properties were assigned with a nonlinear layer property. Nonlinearities and SAP2000 Wednesday, 29th of May 2013 23
- 24. Wednesday, 29th of May 2013 Deformed shape and the plastic hinges (step 1). Deformed shape and plastic hinges (step 2). Deformed shape and plastic hinges (step 3). Numerical Results (Nonlinear Analysis) 24
- 25. Wednesday, 29th of May 2013 Deformed shape and plastic hinges (step 4). Deformed shape and plastic hinges prior to failure (front view). Deformed shape and plastic hinges prior to failure (Back view). Numerical Results (Nonlinear Analysis) 25
- 26. Numerical Results (Nonlinear Analysis) Wednesday, 29th of May 2013 The first plastic hinges occur for a total horizontal load of 5.1 MN and the maximum current capacity of our structure was found to be 17 MN with a total displacement of 6.1 cm at the top floor. As it derives from the above curve, the carrying capacity of the structure is not sufficient in carrying the applied seismic load (22.62MN). 26
- 27. Redesign Wednesday, 29th of May 2013 The compressive strength of the concrete is changed to 35 MPa as opposed to the old 28 MPa. The modulus of elasticity was increased also to 33 GPa. 27
- 28. Redesign of the Shear Walls Wednesday, 29th of May 2013 Section of 35x300 shear walls were added to increase the structures carrying capacity. 28
- 29. Redesign Wednesday, 29th of May 2013 The rectangular section of the shear walls at the ground and mezzanine floors were changed from section of 40x100 to 30x210. 29
- 30. Redesign Wednesday, 29th of May 2013 The beams that were added have a section size of 35x70 cm except the perimetric beams that had a 20x25 cm section which was not modified. 30
- 31. Final Modal Analysis Wednesday, 29th of May 2013 Deformed shape of Mode 1. T=1.23 sec Deformed shape of Mode 2. T=1.22 sec Deformed shape of Mode 3. T=1.1 sec 31
- 32. Results of Pushover curve After Redesign Wednesday, 29th of May 2013 The new carrying capacity of the redesigned frames was found (22688.135kN) which satisfies the demand of EC8. 32
- 33. Conclusion Wednesday, 29th of May 2013 1- Assessing our structures by using software such as ETABS and SAP2000, is of significant importance in terms of safety and accuracy. ETABS and SAP2000 automatically generate and assign code-based loading conditions for gravity, seismic, wind, and thermal forces thus performing the design and assessment becomes a very efficient procedure. 2- Our numerical results and overall experience showed that modeling RC structures is a procedure that requires both theoretical knowledge and practical experience. 33
- 34. Conclusion Wednesday, 29th of May 2013 3- After performing a modal analysis it was found that the 1st mode was rotational thus the geometry of the frame and the stiffness distribution of the shear walls were irregular. In addition to that, we found that the 1st fundamental period was equal to 1.83 seconds that underlines the fact that the flat slab system used derived a flexible mechanical behavior despite the use of relatively large shear walls. 4- It was found that for the at hand RC structure the controlling design load type is the seismic load given that the wind loads did not generate larger deformations and stresses in comparison to those resulted when the seismic loads were generated and applied. This finding strengthens the rule that says "RC structures do not suffer in wind loads". 34
- 35. Conclusion Wednesday, 29th of May 2013 5- In order to perform the pushover analysis we changed the shell FEs used to model all shear walls with frame elements. This was done so as to overcome the computational demand issue that resulted when using shell FEs. It was required to run the nonlinear solver for more than 14 hours when shell FEs were used, so as to finish a single nonlinear analysis. 6- The 12-storey RC building was found inadequate in carrying the 22.62MN seismic load according to EC8 according to the numerical results that derived from the non-linear analysis. For this reason a redesign of the frame was performed so as to overcome this issue. 35
- 36. Conclusion Wednesday, 29th of May 2013 7- When the initial frame was reinforced with beams, the mechanical behavior of the structure changed, while the redesign of the shear walls (add extra shear walls and increase the thickness of existing shear walls) led to a strengthening of the carrying capacity of the structure. After applying the redesign, we managed to increase the carrying capacity according to the code’s demand. In addition to that the fundamental modes were changed given the normalization procedure of the stiffness distribution of the initial frame. 8- The procedure of seismic design and assessment of RC structures is much more complicated than standard design for the static and wind loads through the use of linear elastic analysis. 36
- 37. Thank you for your Attention! Wednesday, 29th of May 2013 37
- 38. Questions? Wednesday, 29th of May 2013 38

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