Depending on the capacity of energy dissipation, structures are classified into the following classes:
In order to design in one of the two classes of ductility, the values of the behavior factor "q" must be first elected. For structures made of reinforced concrete, the behavior factor is limited to the values in Table 2.1, both for P100-1/2006 and for SR EN 1998-1-1.
A favorable plastic mechanism requires a structure of the sections so that the plastic deformations first occur at the end of the beams and later at the base of the column. Also, the nodes between beams and columns must remain in the elastic range of stress.
In order to achieve this, code P100-1/2006 and SR EN 1998-1-1, must be correlated with the design requirements form SR EN 1992-1-1.
The local ductility requirements provide a minimum area of reinforcement for longitudinal reinforcement, both for beams and for columns. Thus, SR EN 1992-1-1 recommends a minimum area of longitudinal reinforcement for columns, As,min, according to chapter 9.5.2 (2):
Another condition for the local ductility of columns refers to the normalized values of the axial force - vd. Table 2.2 lists its limit values.
Similarly, in order to meet the requirements of the local ductility for beams, chapter 5.4.3.1.2 (5) from SR EN 1998-1-1 and chapter 5.3.4.1.2 (4) from P100-1/2006, recommend using a minimum percentage of longitudinal reinforcement for wide areas:
fyk - characteristic yield point of reinforcements;
[MPa] when the concrete strength class is ≤ C50/60
[MPa] when the concrete strength class is > C50/60
Design values of bending moments in beams are determined by the formula (5.3) from P100-1/2006 and (5.8) from SR EN 1998-1-1:
Similarly, design values of bending moments in columns are determined by the formula (5.4) from P100-1/2006 and (5.9) from SR EN 1998-1-1:
According to P100-1/2006 (Chapter 5.2.3.3.2. formula 5.1.) and SR EN 1998-1-1 (Chapter 4.4.2.3. formula 4.29.), structure nodes from ductility classes H and M, located in seismic areas will verify the formula:
For ductility class H, the formula states that the sum of capable moments of the columns which go into a node must be bigger with 20% and with 30%, than the sum of capable moments of the beams.
For the structure in Figure3.1, located in an area with high seismicity (ag = 0.28g) design efforts must be determined, in the elements of the transverse frame (Figure3.2), and also the verification of its nodes.
In Advance Design all verifications can be done automatically according to Romanian standard P100-1/2006 (or SR EN 1998-1-1 with the National Appendix) and SR EN 1992-1-1.
Figure 3.1. 3D view of the analyzed structure
Figure 3.2. Solicited transverse frame
Figure 3.3. Reinforcement solution for a beam
Figure 3.5. 3D view of the reinforced beam casing
Figure 3.4. Theoretical and real areas of reinforcement
Figure 3.6. Longitudinal area of reinforcement and interaction curves for columns
The verification of the design capability done with Advance Design requires the verification of reinforced concrete frame nodes. The verification is done with formula 5.1 (chapter 5.2.3.3.2) if P100-1/2006 is used, and formula 4.29 (chapter 4.4.2.3.) if SR EN 1998-1-1 is used. For the determination of the capable moments from beams and columns (the calculation of parameters MR,c, MR,b from the above relations) real reinforcements will be used, automatically calculated with Advance Design. The nodes which do not meet the verification formula will be marked in a specific calculation note (Figure 3.7).
Figure 3.7. Verification of column-beams nodes in Advance Design
For the reinforced concrete frames nodes which do not meet the verification formula from P100-1/2006 and SR EN 1998-1-1, ADVANCE Design may allow manual modification of the reinforcement solution used or may automatically make iterations in order to find optimal longitudinal reinforcements in columns, so that the specific conditions are met. Manually changing the beam reinforcement solution involves modifying the following parameters: anchorage length, bars longitudinal or transverse diameter, the number of longitudinal or transverse bars.
The Capacity Design method is generally applicable to reinforced concrete frames and enables users a proper sizing of columns and beams by checking the frame nodes, according to SR EN 1992-1-1, SR EN 1998-1-1 or P100-1/2006. Advance Design includes all the norms and requirements, offering civil engineers a superior solution for the structural analysis and design of reinforced concrete.
While resistance capacity should lead to a safer and more accurate design process, engineers should keep in mind that the calculation models are only mathematical simulations of physical phenomena and cannot accurately predict the structural behavior. Too many uncertainties can occur and it is up to civil engineers to characterize as best as they can and as many parameters as they can.
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