Table of Contents
1. GENERAL
1.1 Eurocodes
1.2 Units of measurement
1.3 Symbols
2. LIMIT STATES DESIGN
2.1 General
2.2 Actions on structures
2.2.1 Classification of actions
2.2.2 Nominal/ Characteristic values of loads
2.2.2.1 Materials self-weights
2.2.2.2 Floor coverings self-weights
2.2.2.3 Brick masonry loads
2.2.2.4 Imposed loads
2.2.2.5 Snow loads and wind loads
2.2.3 Design values of actions
2.2.3.1 Non-seismic actions
2.2.3.2 Seismic actions
2.2.4 Combinations of actions
2.2.5 Wind influence
2.2.6 Effects of indirect actions
2.3 Effects of actions
2.3.1 Deformation-stress definition of structures for combinations without
seismic actions (STR/GEO) [EC0, 6.4.1.]
2.3.2 Deformation-stress definition of structures for combinations with
seismic (or accidental) actions
2.3.3 Deformation-stress envelope definition
2.4 Strength of structural elements
2.5 Exercise
3. STRUCTURAL MODEL AND ANALYSIS
3.1 Structural model
3.1.1 Effective span of beams and slabs
3.1.2 Effective width of flanges
3.1.3 Rigit bodies
3.1.4 Diaphragmatic behaviour
3.2 Seismic loading model
3.3 Deformations - Stresses
3.3.1 Frame model
3.3.2 Slab analysis
3.3.3 Frame analysis
3.3.4 The effect of torsional stiffness on indirect beam-beam supports
3.3.5 Modelling floor diaphragms using two-dimensional finite elements
3.3.6 Modelling slabs using members and finite elements
3.3.6.1 The frame behaviour in regions of columns
3.3.6.2 Deflection of beams
3.3.6.3 Torsional stiffness of beams
3.3.6.4 Final conclusion
4 SLABS
4.1 General
4.2 Two-dimensional finite elements
4.2.1 Assumptions
4.2.2 Stress resultants and deflections
4.2.3 Unfavourable loadings and envelopes of stresses – deflections
4.2.4 Clarifications
4.3 Analyses using tables
4.3.1 Assumptions
4.3.2 Application width of concentrated load on slab
4.3.3 Distribution width of concentrated load
4.3.4 Support moments of continuous slabs
4.3.5 Contribution of pinned slab supports
4.4 Cantilevers
4.4.1 Static analysis
4.4.2 Deflection
4.5 One-way slabs
4.5.1 Static analysis
4.5.2 Deflection
4.5.3 Effective of live load on the static analysis of one-way slabs
4.5.3.1 Accurate analysis method
4.5.3.2 Simplified method for envelope estimation
4.6 Two-way slabs
4.6.1 Shear forces and support reaction forces
4.6.1.1 Simplified method
4.6.1.2 Czerny’s elasticity method
4.6.2 Fundamental support and span moments – Deflections
4.6.2.1 MARCUS method
4.6.2.2 CZERNY’s elasticity method
4.6.3 Bending moments in continuous two-way slabs
4.6.3.1 Continuous strip method
4.6.3.2 Accurate method (manual)
4.6.3.3 Practically accurate method
4.6.4 Influence of live load
4.7 Slabs supported on three edges
4.8 Slabs supported on two adjacent edges
4.9 Exercises
5. SEISMIC BEHAVIOUR OF FRAMES
5.1 One-storey plane frames (or coupled columns)
5.1.1 Bending and shearing effect on deformations and stresses
5.1.2 The degree of fixity effect of columns
5.1.3 The effect of columns moment of inertia
5.1.4 The effect of columns differential height
5.1.5 Frame column stiffness
5.1.5.1 One-storey frame structural systems
5.1.5.2 One-storey dual structural systems
5.2 Coupled one-storey plane frames
5.3 Multistorey plane frames
5.3.1 Multistorey plane frame systems
5.3.2 Multistorey plane dual systems
5.3.3 Comparison of multistorey frame and dual systems
5.4 Space frames
5.4.1 Diaphragmatic behaviour
5.4.2 Centre of mass and radius of gyration
5.4.3 Centre of stiffness and elastic displacements of the diaphragm
5.4.3.1 Subject description
5.4.3.2 Translation of centre of stiffness CT along x direction
5.4.3.3 Translation of centre of stiffness CT along y direction
5.4.3.4 Rotation of the diaphragm by an angle θz about CT
5.4.3.5 Torsional stiffness ellipse, torsional radii and equivalent system
5.4.3.6 Work methodology
5.4.4 Assessment of building torsional behaviour
5.4.5 One-storey space frame with rectangular columns in parallel arrangemen
5.4.5.1 Analysis using manual calculations, assuming fixed-ended columns (k=12)
5.4.5.2 Analysis using the Excel file, assuming fixed-ended columns (k=12)
5.4.5.3 Analysis using the Excel file, assuming columns with k=6
5.4.5.4 Analysis using software, assuming actual beam and column
torsional stiffnesses
5.4.6 Multistorey space frame of rectangular columns in parallel arrangement
5.4.6.1 Analysis using manual calculations, assuming fixed-ended columns (k=12)
5.4.6.2 Analysis using the Excel file, assuming fixed-ended columns (k=12)
5.4.6.3 Analysis using the Excel file, assuming columns with k=6
5.4.6.4 Analysis using software, assuming actual beam and column
torsional stiffnesses
5.4.7 Exercises
6. SEISMIC ACCELERATIONS AND LOADINGS OF BUILDINGS
6.1 Seismic response of buildings
6.1.1 Seismic zones [EC8, §3.2.1]
6.1.2 Importance factors [EC8, §4.2.5]
6.1.3 Ground type [EC8, §3.1.2]
6.1.4 Viscous damping
6.1.5 Behaviour factor
6.1.5.1 Structural types [EC8 §5.2.2.1]
6.1.5.2 Regularity in plan [EC8 §4.2.3.2]
6.1.5.3 Regularity in elevation [EC8 §4.2.3.3]
6.1.5.4 Ductility classes [EC8 §5.2.1]
6.1.5.5 Basic value of the behaviour factor qo [EC8 §5.2.2.2]
6.1.5.6 Failure mode factor kw [EC8 §5.2.2.2]
6.1.5.7 Conclusion
6.1.6 Design spectrum of horizontal seismic actions [EC8, §3.2.2.5 & §3.2.1(3)]
6.1.7 Design spectrum of vertical seismic actions [EC8, §3.2.2.5(5)]
6.2 Dynamic analysis και natural periods of structure
6.3 Seismic stresses
6.3.1 Seismic accelerations
6.3.2 Seismic forces, shear forces, bending moments
6.3.3 Approximate method for the calculation of seismic accelerations [EC8, §4.3.3.2.2]
6.3.4 Cracking and plasticity effects
6.4 Applications
6.4.1 Frame type structure
6.4.2 Wall-equivalent dual type structure
6.4.3 Approximate analysis of the frame and wall type structures
6.5 Loading envelopes
6.6 Special cases
6.6.1 Columns not belonging in a diaphragm
6.6.2 Vertical component of seismic action [EC8, §4.3.3.5.2]
APPENDICES
APPENDIX A: MODELLING SLABS WITH FINITE ELEMENTS
Α.1 Modelling slabs with finite elements in a structural frame
Α.1.1 The frame behaviour in the regions close to columns
Α.1.1.1 Model using members
Α.1.1.2 Model with finite elements
Α.1.1.3 First Conclusion
Α.1.2 Deflection of beams
Α.1.2.1 Model using members
Α.1.2.2 Model using finite elements
Α.1.2.3 Second Conclusion
Α.1.3 Torsional stiffness of beams
Α.1.3.1 Model using members
Α.1.3.2 Model using finite elements
Α.1.3.3 Third Conclusion
Α.1.3.4 FINAL CONCLUSION
APPENDIX B: STIFFNESS OF MULTISTOREY PLANE FRAMES
Β.1 Stiffness of frame crossbar
Β.2 Equivalent multistorey frame – crossbar relative stiffness
Β.3 Relative stiffness of crossbar column
Β.4 Effect of slabs on stiffnesses using finite elements
Β.5 Effect of walls on stiffnesses using finite elements
APPENDIX C: DIAPHRAGMATIC BEHAVIOUR OF ONE-STOREY SPACE FRAME – GENERAL CASE
C.1 Subject description
C.2 Axis transformation
C.3. Case 1: Translation of centre of stiffness CT along x direction by δxο
C.4 Case 2: Translation of centre of stiffness CT along y direction by δyο
C.5 Case 3: Rotation of the diaphragm by an angle θz about CT
C.6 Torsional stiffness ellipse, torsional radii and equivalent system
C.7 Superposition of the three cases
C.8 Work Methodology
C.9 Expressions relating the initial system X0Y and the principal system xCTy
C.10 One-storey space frame with rectangular columns in random arrangement
C.10.1 Analysis using manual calculations, assuming fixed columns (k=12)
C.10.2 Analysis using the Excel file, assuming fixed-ended columns (k=12)
C.10.3 Analysis using the Excel file, assuming columns with k=6
C.10.4 Analysis using software, assuming actual beam and column torsional stiffnesses
APPENDIX D: DIAPHRAGMATIC BEHAVIOUR OF MULTISTOREY SPACE FRAME – GENERAL CASE
D.1 Subject description
D.2 General method for the calculation of the diaphragm i data
D.3 Diaphragm lateral stiffnesses
D.4 Diaphragm torsional stiffness
D.5 Torsional stiffness distribution
D.6 Equivalent system – Relative lateral stiffness – Relative torsional stiffness
D.7 Examples