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Computer Applications in Structural Engineering

Computer Applications in Structural Engineering. Dr. Abdul Razzaq Touqan Department of Civil Engineering. Define Structural Engineering?. Chapter 1: Introduction. Contents: Define Structural Engineering? Implicit Modeling

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Computer Applications in Structural Engineering

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  1. Computer Applications in Structural Engineering Dr. Abdul Razzaq Touqan Department of Civil Engineering

  2. Define Structural Engineering?

  3. Chapter 1: Introduction • Contents: • Define Structural Engineering? • Implicit Modeling • Implicit Modeling: degreeof physical versus designmathematical models • Developing mathematical models: structural systems • Developing mathematical models: Loadings and materials assumptions • Developing Ideas: laws versus theories • Discretization of mathematical models: Classification of finite elements • Important details

  4. Implicit Modeling: degree of physical versus design mathematical models

  5. Developing mathematical models: structural systems • Elements • 1D • 2D • 3D • Structures • 1D structure with 1D elements • 2D structure with 1D, 2D elements • 3D structure with 1D, 2D, 3D elements

  6. Developing mathematical models:Loadings and materials assumptions • Loadings assumptions: • Static versus Dynamic • Concentrated versus distributed • Materials assumptions: • Linear versus Nonlinear • Isotropic versus anisotropic • Homogeneous versus heterogeneous

  7. 1D, 2D or 3D modeling 1D: slab-beam-column

  8. 1D, 2D or 3D modeling 1D: slab-beam-column/ continued

  9. 1D, 2D or 3D modeling 2D: plane frame

  10. 1D, 2D or 3D modeling 3D: space frame with slabs/walls

  11. Developing Ideas: laws versus theories • Structural Analysis laws • constitutive (stress-strain) relationships: essential • equilibrium equations: essential • compatibility equations: optional/present challenge • Structural Analysis theories: • Based on assumptions • Assumptions based on available knowledge • Available knowledge is constrained with available tools like hand calculators and personal computers • Computer programs are based on assumptions on which the theoretical basis of the software was developed.

  12. Discretization of mathematical models

  13. Important details

  14. Homework 1 • Select a physical structural system • Provide a photo or photos of it • Do a mathematical model of it • Explain how to verify and validate your model

  15. End of structural modelings Let Learning Continue

  16. Chapter 2: 3D static analysis for lateral forces • Contents: • Implicit modeling • Idealization • Solution • Verification and validation of results • 2D versus 3D analysis • Rigidity of diaphragms • Coincidence of center of mass with center of rigidity

  17. Idealization

  18. Solution: speed of different computers

  19. Solution: SAP Program SAP in English language

  20. Solution: SAP Program SAP in English language

  21. Verification and validation of results • 1D and 2D Models cannot achieve compatibility • When using FE method make sure that the three laws (constitutive + equilibrium + compatibility) are all satisfied • Try to verify FE program before using it by comparing its results with the results of using another method (theoretical, experimental or empirical) • Make sure that results are used to enforce or correct engineering sense.

  22. 2D versus 3D analysis:rigidity of diaphragms • Lateral forces are distributed to elements according to relative rigidity between diaphragm and lateral load resisting units: • For large ratios lateral loads are distributed in proportion to stiffness of lateral units (e.g. …) • For small ratios lateral loads are distributed in proportion to tributary diaphragm areas.

  23. 2D versus 3D analysis:rigidity of diaphragms (cont) a one-story flat plate reinforced concrete building subjected to an earthquake force of 360kN in the x-direction and a live load of equal magnitude distributed on the whole floor. Columns are square having 20cm dimensions, 3m elevation, and the distance between them is 6m, elastic modulus Econ=20GN/m2

  24. 2D versus 3D analysis:rigidity of diaphragms (cont) Column reactions in kN for floor systems with different rigidities

  25. 2D versus 3D analysis:rigidity of diaphragms: Conclusions • Case 1: • Eq distributed according to rigidity • LL 15:45:120=1:3:8 compared to 1:2:4 according to tributary. If use of reactions and taking frames 1:2 for fixed ends to 3:10 (1:3.33) for pinned ends. Thus 15:45=1:3 in between, and also 45:120=1:2.66 in between. • Case 2: • Eq distributed according to tributary area • LL almost no change • Case 3: • Eq distributed almost according to rigidity (semi-rigid) • LL almost no change

  26. 2D versus 3D analysis:rigidity of diaphragms Recommended Changes: • Change interior column to 40cm square and discuss effect of changes on live and EQ. • Change exterior frame columns to 1.5m height instead of 3m and discuss effects. • Main conclusion: tributary or reaction method is almost ok for gravity • For rigid diaphragm (RC structures) distribute according to rigidity • For steel structures of light coverings distribute according to tributary area.

  27. 2D versus 3D analysisCoincidence of center of mass with center of rigidity a one-story flat plate (40cm thick) reinforced concrete building subjected to an earthquake force of 360kN in the x-direction and a live load of equal magnitude distributed on the whole floor. Columns are square, 3m elevation and the distance between them is 6m, elastic modulus Econ=20GN/m2

  28. 2D versus 3D analysisCoincidence of center of mass with center of rigidity

  29. 2D versus 3D analysisCoincidence of center of mass with center of rigidity Column reactions (kN) for symmetric and asymmetric systems

  30. Coincidence of center of mass with center of rigidity: conclusions • 1. rigid diaphragm: Coincidence + equal rigidity of all columns: equal force in all columns • 2. semi-rigiddiaphragm: Coincidence + variable rigidity: force distributed in 9.5/1 ratio instead of 16/1 for rigid diaphragm • 3. semi-rigiddiaphragm: non-coincidence + variable rigidity: force distributed in 5/1 ratio instead of 6.2/1 for rigid diaphragm

  31. Homework # 2 (research) • Study effect of earthquakes on asymmetric structures

  32. Exercise: P-delta effects • Study previous structure with 40cm square columns and 0.3g earthquake acceleration (i.e. 3KN/m force applies in x-direction) but as a minaret of 12m, 24m, 48m and 96m height. Study effect of structure P-delta. • Research: Study effect of earthquakes on minaret structures

  33. 2D versus 3D analysisCoincidence of center of mass with center of rigidity Exercise: a one-story reinforced concrete building subjected to an earthquake force of 320KN in the y-direction distributed on the whole floor. Columns are rectangular 30cmX60cm, 6m elevation and the distance between them is 5m in x-direction, 8m in y-direction, slab is solid 25cm depth, all beams 30cm width, elastic modulus Econ=22GN/m2, density=25KN/m3 .

  34. Exercise: Comparison between SAP and tributary with 10% acceptance criterion

  35. Exercise: Further modifications • If height of column B is reduced to half, and depth of beam is 80cm, find reaction due to earthquake in columns A and B both analogically and by SAP. • (Ans.: FA=19kN, FB=144kN ratio 7.6 instead of 8) • If also height of columns A and C are reduced to half, and depth of beam is 80cm, find reaction due to earthquake in columns A, B and C both analogically and by SAP. (Answer: FA=73kN, FB=94kN, FC=53kN, instead of FA=76kN, FB=97kN, FC=55kN: details next page)

  36. x=6.61m, y=1.29m,, J=2092k, • FA=76KN, FB=97KN, FC=55KN

  37. Homework #3 • A reinforced concrete frame structure of 3m elevation and 6m bay widths having the plan shown in Figure next page. The foundations are assumed pinned. If the elastic modulus is 22GPa, and the Poisson's ratio is 0.2. All columns were assumed of rectangular cross section 20cm x 40cm; the slab is flat 40cm thickness. • If the structure is subjected to a horizontal earthquake force 1000KN applied on the slab in the y-direction, find the largest reaction in the y-direction due to the earthquake force and show where it occurs by assigning joint A? RAy= • Verify your result manually

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