**VOLUME A**

The art of construction and detailing- Introduction
- The structural frame
- Construction methods
- Reinforcement
- Quantity surveying
- Estimation of the concrete’s quantity
- Estimation of the formworks’ quantity
- Estimation of the spacers’ quantity
- Estimation of the reinforcements' quantity
- Total estimation of the materials’ quantities
- Optimization of the reinforcement schedule
- Estimation of the structural frame’s cost
- Electronic exchange of designs - bids - orders

- Detailing drawings
- General
- The drawings’ title block
- Carpenter’s drawings
- EXCAVATIONS and FOUNDATION FLOOR (Drawing C.10)
- FORMWORK OF THE FOUNDATION and the basement floor (Drawing C.20)
- FORMWORK of the BASEMENT’S ceiling (Drawing C.30)
- FORMWORK of the GROUND FLOOR’S ceiling (Drawing C.40)
- FORMWORK of the MEZZANINE’S ceiling (Drawing C.50)
- FORMWORK of the MEZZANINE’S ceiling with thermal insulation (Drawing C.55)

- Steel fixer’s drawings

- Tables
- Drawings
- Model (exemplary) construction
**VOLUME B**

Static and Dynamic Analysis- General
- Limit States Design
- Models Analysιs
- Slabs
- Seismic behaviour
- One-storey plane frames
- Coupled one-storey plane frames
- Multistorey plane frames
- Space frames
- Diaphragmatic behaviour
- Centre of mass and radius of gyration
- Centre of stiffness and elastic displacements of the diaphragm
- Assessment of building torsional behaviour
- One-storey space frame with rectangular columns in parallel arrangement
- Multistorey space frame of rectangular columns in parallel arrangement
- Exercises

- Seismic accelerations and loadings
- Tables
- APPENDIX A
- APPENDIX B
- APPENDIX C
- APPENDIX D
- APPENDIX D7

« Dynamic analysis και natural periods of structure Frame type structure » | |||||||||||||||

Seismic stresses
The seismic accelerations a
The nodal seismic forces H Seismic accelerations are quantities calculated directly by superimposing modal responses through CQC method. The CQC method always produces quantities with positive sign, as it is the square root of a sum of modal quantities. In this respect, only the comparison of their absolute values has a meaning. If the sign is required e.g. to calculate the seismic forces and then the position of the centres of stiffness, then a good choice would be to use the sign of the fundamental mode shape, e.g. of that with the maximum effective mass participation factor (effective modal mass). In the related software two combination methods are used for the calculation of the stress resultants: According to this method, masses are assumed at the centres of mass of diaphragms and at the end nodes if diaphragms are not present. The seismicaccelerations i of the structure (i.e. diaphragms centres of mass and nodes not belonging to a diaphragm) due to j component of the seismicaction. The corresponding seismic forces are thus obtained by the expression H_{i}_{,}= _{j}a_{i}_{,}_{j} · m_{i} at thevarious discreet positions i of the structure under the horizontal and vertical components of the seismic action j= Χ, j=Υ και j=Ζ. The stress resultants for each combination are calculated, using classic structural analysis, based on the seismic forces. This method is used by default by the software (but it can be changed by the user), having the advantage that the signs of the stress resultants are compatible to those of the classic structural analysis, which is the base and the reference of EC8 and EC2. According to this method, all the seismic quantities are calculated using CQC, i.e. forces, displacements, bending moments, shear forces with sign that of the corresponding modal quantity of the fundamental mode shape. Modal response spectrum analysis assuming masses placed in the centres of diaphragms is required in both methods. In the second method four additional dynamic analyses are required assuming masses placed at the four points of accidental eccentricities (see §6.5). Of course, the accidental eccentricities actually refer to the relative displacements of the centres of mass and stiffness and it may be more logical to consider their influence on the seismic forces of the first method. The seismic forces are not quantities calculated by the analysis but a derivative one, obtained by multiplying the seismic acceleration by the diaphragm mass, or by the mass of the beams and columns framing into the joints that do not belong to the diaphragms. Seismic shear forces are also derivative quantities as, for each storey, they are the sum of seismic forces in X and Y direction of the overlying stories. The sum of columns and walls shear forces of each storey is calculated by the analysis and should be equal to the seismic forces of the storey considered. This is a simple and efficient check for any software. Internal forces and moments of each structural member are calculated through classic structural analysis using the seismic forces of the diaphragmatic nodes, or/and of the nodes not belonging For educational reasons and for verification of the order of magnitude of the dynamic analysis results, the base shear and the distribution of seismic accelerations and seismic forces of a structure may be calculated by a simple approximate method. This method may be applied to buildings with heights up to 40 m, meeting the criteria for regularity in elevation whose response is not significantly affected by contributions of modes higher than the fundamental mode in each principal direction. · H ^{3/4}-
H is the building height, in m, from the foundation or from the level of the rigid basement top. -
C _{t}is frame system factor- For the i direction frame system, C _{t,i}=0.075- For the i direction wall system, C _{t,i}=0.050
According to the Eurocodes [EC8, §4.3.1(7)], structural elements may be considered as cracked, thus their stiffness properties may be taken to be equal to 50% of the corresponding stiffness of the uncracked elements. When the stiffnesses of columns, walls and beams change, the dynamic behaviour of structures i.e. natural periods, effective masses, seismic accelerations and eventually seismic forces, displacements and stress resultants, are affected. Beyond the dynamic response differences due to the decreased stiffnesses, the static behaviour of the structures is also affected. Considering the same seismic forces when stiffnesses are taken as half (0.50E I) ones, then flexural displacements double, but shear and axial displacements remain intact. Therefore the total displacements (flexural + shear + axial) are less than double. In predominantly frame type structures (where bending effect dominates) the total displacements are roughly less than double, while in mainly wall structures (where shear effect is significant) the downward deviation from double can be significant. · The development of deformations is continued even after the cracking of columns, walls and beams, in the actual plastic region. The increase rate of the plastic deformations depends on the ductility of the elements, i.e. their capacity to exhibit post-yield deformations. In case of reinforced concrete, ductility is accomplished by using dense and well closed stirrups and suitable longitudinal reinforcement placed in the perimeter (see volume Α' §1.4.2). The final displacements are the plastic displacements equal to the displacements of the cracked elements multiplied by the behaviour factor q taken under consideration in the base shear calculation (see also §5.4.7, exercise 2). The determination of the maximum plastic displacement of a building is necessary in cases of an existing or eventual adjacent structure, e.g. as in attached buildings, to provide for an adequate seismic joint [EC8, §4.4.2.7 & §4.3.4], required to protect them from earthquake-induced pounding
Applications |
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« Dynamic analysis και natural periods of structure Frame type structure » |
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