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Capacity Design

Optimize the design of concrete, steel and timber structures according to Internation codes

 

The uniqueness of GRAITEC Advance Design is to offer a solution that is very efficient because it is dedicated to building professionals: design, calculation and creation of fabrication drawings, easy training, and provides a rapid return on investment, usually from the first project.

ADVANCE Design goes further than ever in helping engineers to optimize the design of concrete, steel and timber structures according to the Eurocodes and Romanian codes. Some of the many new functionalities in regards to Eurocodes are: climatic generator improvements according to latest norms CR 1-1-3/2012 and CR 1-1-4/2012, automatic load combinations according to CR 0-2012, punching verification according to Eurocode 2, checking the overall stability of circular sections of Class 4 according to Eurocode 3, and capacity design according to P100-2006 or Eurocode 8.

 

1. Introduction

Seismic design of structures is mainly focused on developing a favorable plastic mechanism to render the structure strength, ductility, and stability.

The behavior of a structure regarding the action of a major earthquake is anything but ductile, taking into account the oscillating nature of the seismic action and the fact that plastic hinges appear rather randomly. To achieve the requirements of ductility, structural elements, and thus the entire structural system must be able to dissipate the energy induced by the seismic action, without substantial reduction of resistance.

Both Romanian seismic design code P100-1/2006 and Romanian standard SR EN 1998-1, provide a method for prioritizing structural resilience ("capacity design method") in order to better choose the necessary mechanism for dissipation ofenergy. Determination of the design efforts and the efforts for elements will be in accordance to the rules of this method.

2. Constructive measures for meeting the local and global ductility

Depending on the capacity of energy dissipation, structures are classified into the following classes:

  • medium ductility (M),
  • high ductility (H).

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):

Where:

fyd - calculation of yield strength for reinforced concrete;

NEd - the value of axial force (maximum axial force in columns)

Ac - the concrete cross-section area.

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:

Where:

fyk - characteristic yield point of reinforcements;

Designing resistance capacity [MPa] when the concrete strength class is ≤ C50/60
Designing resistance capacity [MPa] when the concrete strength class is > C50/60
Designing resistance capacity

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:

Where:

M(R,b,i/j) - the value of the moment at the end of "i" or "j" of the beam, for the sense of the seismic bending moment;

M(d,b,i/j) - the value of the design bending moment for determining the associated shear forces;

γRd - over strength factor (Table 2.3) which takes into account steel strain-hardening of the longitudinal steel and shrinkage of concrete;

ΣM(R,c) - the sum of the design valuesof the capable moments of the columns in the nodes;

ΣM(R,b) - the sum of the design values of the capable moments of the beams in the node.

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:

Where:

MR,c,i/j - the value of the moment at the end of "i" or "j" of the column, for the sense of the seismic bending moment;

γRd - over strength factor (Table 2.4) which takes into account steel strain-hardening of the longitudinal steel and shrinkage of concrete;

ΣM(R,c) - the sum of the design values of the capable moments of the columns in the node;

ΣM(R,b) - the sum of the design values of the capable moments of the beams in the node.

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.

 

 

3. Designing the resistance capacity using ADVANCE Design

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

The structural system consists of reinforced concrete frames (resistance class C30/37) reinforced by the central vertical bracing (made of S355 steel) around the perimeter and a central core made of reinforced concrete walls (resistance class C30/37). The value of the behavior factor q, for both directions of seismic action, is 4.725 placing the structure in the ductility class M.

Advance Design automatically determines, with the Concrete calculation engine, an optimal solution for actual reinforcement areas from beams and columns and later, verifies the prioritizing method for structural elementsfor the nodes of the analyzed frame. The theoretical areas of reinforcement and also the real areas of reinforcement, for beams and columns are calculated automatically according to the Romanian standard SR EN 1992-1-1 and the National Appendix.

Figure 3.3 gives the longitudinal and transverse reinforcement solution offered by Advance Design for one of the beams.

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.

 

 

4. Conclusions

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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