Background: The capacity design philosophy permits ductile components of a structural system to yield, whereas the brittle components are not permitted to fail. Therefore, brittle components should have sufficiently higher strength compared to ductile components. The "strong-column/weak-beam" design philosophy ensures good ductility and a preferable collapse mechanism in the building. The failure mode wherein the beams form hinges is usually considered to be the most favourable mode for ensuring good global energy-dissipation without much degradation of capacity at the connections. In order to ensure this favourable failure mode design codes recommend a minimum value of Moment Capacity Ratio (MCR). Methods: MCR is defined as the ratio of cumulative column moment capacity to cumulative beam moment capacity framing to a particular joint. Calculation of MCR is complicated as the column bending strength varies with the axial load. A family of RC framed building models is analysed in this study for earthquake load considering various load combinations given in relevant Indian standards. A range of axial force that may arise in the column sections during an event of design earthquake are obtained. Findings/Applications: A simplified procedure to calculate MCR empirically is proposed. The proposed method is computationally simple for calculating nominal design strength of the column to be used in determining MCR at a beam-column joint.

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Capacity Design of Reinforced Concrete Framed

Building for Earthquake Loading

A. Mistri* and P. Sarkar

Department of Civil Engineering, National Institute of Technology, Rourkela, India;

a.mistri009@gmail.com, sarkarp@nitrkl.ac.in

Abstract

Background: The capacity design philosophy permits ductile components of a structural system to yield, whereas the brittle



ductile components. The "strong-column / weak-beam" design philosophy ensures good ductility and a preferable collapse

mechanism in the building. The failure mode wherein the beams form hinges is usually considered to be the most favourable

mode for ensuring good global energy-dissipation without much degradation of capacity at the connections. In order to en-

sure this favourable failure mode design codes recommend a minimum value of Moment Capacity Ratio (MCR). Methods :

-

ular joint. Calculation of MCR is complicated as the column bending strength varies with the axial load. A family of RC framed

building models is analysed in this study for earthquake load considering various load combinations given in relevant Indian

standards. A range of axial force that may arise in the column sections during an event of design earthquake are obtained.

Findings/Applications-

tationally simple for calculating nominal design strength of the column to be used in determining MCR at a beam-column joint.

*Author for correspondence

1. Introduction

Designing a building to behave elastically during

earthquake without any damages makes the project

uneconomical. So the earthquake-resistant design philos-

ophy allows damages in some predetermined structural

components. e exural capacities of members are

determined on the basis of the overall response of a struc-

ture to earthquake forces. e capacity design procedure

sets strength hierarchy rst at the member level and then

at the structure level. So, it needs adjusting of column

strength to be more than the beams framing into it at a

joint. Mathematically it can be expressed as,

Indian Journal of Science and Technology, Vol 9(30), DOI: 10.17485/ijst/2016/v9i30/99225, August 2016

ISSN (Print) : 0974-6846

ISSN (Online) : 0974-5645

Where, Mc and Mb are moment capacities at the end

of column and beam meeting at a joint respectively. In

order to ensure this favourable failure mode1 design

codes recommend a minimum value of Moment Capacity

Ratio (MCR) which is dened as the ratio of summation

of column moment capacity to the summation of beam

moment capacity at a particular beam-column joint.

Mathematically, it can be expressed as:

.

Keywords: Capacity based Design, Earthquake Load, MCR, Reinforced Concrete, Strong Column Weak Beam

Capacity Design of Reinforced Concrete Framed Building for Earthquake Loading

Indian Journal of Science and Technology

Vol 9 (30) | August 2016 | www.indjst.org

2

Table 1 presents a list of minimum MCR recommended

by major international codes and published literatures

Design codes dene the MCR as the ratio of summation of

moment capacities of column sections framing into a joint

evaluated at the joint faces considering factored axial loads

resulting in the minimum column moment to the summa-

tion of moment capacities of the beam sections framing

into it along the direction of lateral forces.

During an event of earthquake or wind a range of fac-

tored axial loads occurs in the column Design codes try to

capture the upper bound and lower bound of the loads

that may arise during an event of an earthquake through

load combinations considering the cyclic nature of earth-

quake load. erefore, to calculate the MCR at a given

joint, one has to consider the axial forces from various

load combinations which is computationally cumber-

some. is makes the procedure unattractive to the

designer. is paper attempts to simplify this procedure

through empirical formulation.

design of reinforced concrete elements conforming8. All

the building models considered here have six bays (in the

direction of the earthquake) with a uniform bay width

of 5 m. It should be noted that bay width of 4m – 6m is

the usual case, especially in Indian and European prac-

tice. Four dierent height categories were considered for

the study, ranging from 4 to 10 storeys (4-storey, 6-sto-

rey, 8-storey, 10-storey), with a uniform storey height of

3.5 m. All the buildings are assumed to be symmetric in

plan and representative plane frames subjected to loading

only in the primary direction are considered for analyses.

Figure1 presents a typical building frame (8-storey) con-

sidered in this study.

Commercial soware9 is used for modelling and ana-

lysing. Beams and columns in the present study were

modelled as frame elements with the centerlines joined

at nodes. e rigid beam column joints were modelled

by using end osets at the joints. e oor slabs were

assumed to act as diaphragms, which ensure the integral

action of all the vertical lateral load-resisting elements.

e weight of the slab was distributed to the surrounding

beams. M 25 grade of concrete and Fe 500 grade of rein-

forcing steel was used to design the building. e column

end of the foundation was considered as pinned for all the

models in this study.

Documents MCR

Uma and Jain, 200621.1

ACI 318M-1431.2

NZS3101:199541.4×Ω

EN1998-1:200451.3

IS 13920 (dra): 201461.4

Ω is over strength factor for beams

Table 1. Minimum MCR recommended by design

codes and published literature

2. Structural Modelling

e present study is based on analyses of four multi-sto-

ried RC buildings. All of these buildings were designed as

per Indian Standard 7 loading requirements, correspond-

ing to the highest seismic zone (PGA = 0.36g) with the

Figure 1. Typical building frame (8-storey) considered in

this study.

A. Mistri and P. Sarkar

Indian Journal of Science and Technology 3

Vol 9 (30) | August 2016 | www.indjst.org

3.Development of Simplied

Procedure for Estimating MCR

As discussed in the previous section many international

design codes provide a limit of MCR of beam-to-column

joint for capacity design of building frames. e MCR is

dened as the ratio of cumulative column moment capac-

ity to cumulative beam moment capacity framing at a

particular joint. Although this appears to be a simple pro-

cedure the calculation of column moment capacity is a

Storey Level

Exterior Column (4CE) Interior Column (4CI)

G 0.124 0.052 0.245 0.109

1 0.089 0.036 0.176 0.077

2 0.064 0.025 0.127 0.053

3 0.023 0.006 0.046 0.015

mean 0.060 0.025 0.151 0.065

σ0.025 0.008 0.084 0.040

P = maximum axial force carrying capacity of the column; P max and P min =

maximum and minimum column axial force demand of the earthquake; σ =

standard deviation

Table 2. Column axial force for four-storey building

Storey Level

Exterior Column (6CE) Interior Column (6CI)

G 0.180 0.073 0.343 0.157

1 0.148 0.060 0.281 0.128

2 0.135 0.054 0.255 0.114

3 0.097 0.039 0.183 0.081

4 0.064 0.024 0.120 0.050

5 0.024 0.006 0.044 0.014

mean 0.116 0.046 0.219 0.097

σ 0.058 0.024 0.110 0.053

Table 3. Column axial force for six-storey building

Capacity Design of Reinforced Concrete Framed Building for Earthquake Loading

Indian Journal of Science and Technology

Vol 9 (30) | August 2016 | www.indjst.org

4

Normalised Column Axial Force

Normalised Column Axial Force

Figure 3. Column axial force for six-storey building. Figure 2. Column axial force for four-storey building.

matter of concern for the design oce as it depends on the

axial force level the column is subjected to. During cyclic

earthquake loading column experience a range of axial force

due to various combinations of load and unlike beam col-

umn does not have a unique moment capacity. at makes

the calculation of MCR cumbersome. e present study is

an attempt to simplify this procedure. Four code designed

building models are analysed for earthquake load using an

equivalent static approach to nd out the axial force range

of the various columns in the buildings. Tables 2-5 show the

variation of axial force in dierent columns. Axial force has

taken for one representative exterior and one representative

interior column for each building model. Figures.2-5 pres-

ent these data graphically.

A. Mistri and P. Sarkar

Indian Journal of Science and Technology 5

Vol 9 (30) | August 2016 | www.indjst.org

Storey Level

Exterior Column (8CE) Interior Column (8CI)

G 0.218 0.085 0.407 0.187

1 0.190 0.074 0.352 0.162

2 0.183 0.072 0.339 0.155

3 0.151 0.060 0.278 0.126

4 0.137 0.054 0.251 0.113

5 0.099 0.039 0.181 0.079

6 0.066 0.025 0.120 0.050

7 0.025 0.007 0.044 0.014

mean 0.144 0.057 0.265 0.119

σ 0.066 0.027 0.124 0.059

Table 4. Column axial force for eight-storey building

Storey Level

Exterior Column (10CE) Interior Column (10CI)

G 0.227 0.062 0.407 0.189

1 0.222 0.067 0.395 0.183

2 0.204 0.059 0.363 0.169

3 0.193 0.060 0.342 0.158

4 0.186 0.060 0.328 0.150

5 0.153 0.051 0.269 0.122

6 0.133 0.045 0.232 0.104

7 0.096 0.034 0.167 0.073

8 0.060 0.020 0.102 0.042

9 0.023 0.005 0.038 0.011

mean 0.170 0.055 0.298 0.136

σ0.070 0.020 0.127 0.061

Table 5. Column axial force for 10-storey building

Capacity Design of Reinforced Concrete Framed Building for Earthquake Loading

Indian Journal of Science and Technology

Vol 9 (30) | August 2016 | www.indjst.org

6

e above tables and gures show the statistical

range of axial forces that generally the building columns

experience. In order to investigate what moment capac-

ity a column may pose under these ranges of axial force,

respective column interaction diagrams given10 are super-

posed with the obtained axial force. A typical example is

shown in Figure.6. e results are summarised in Table6.

e above discussions conclude that the ratio of axial

force with the ultimate capacity of the section normally

lies between 0.12-0.41 or by rounding o 0.1-0.4. is

range of vertical force gives a minimum moment car-

rying capacity of 0.8-1.05 times the column moment at

zero axial force as per the corresponding design chart

of SP16:1980. Table6 shows that the value of the multi-

plier is less for interior joint and more for exterior joint.

Considering a conservative value of the multiplier a sim-

plied procedure for estimating MCR is proposed as

follows:

Normalised Column Axial Force

Normalised Column Axial Force

Normalised Co lumn Axial Force

Normalised Co lumn Axial Force

Figure 5. Column axial force for 10-storey building. Figure 4. Column axial force for eight-storey building.

A. Mistri and P. Sarkar

Indian Journal of Science and Technology 7

Vol 9 (30) | August 2016 | www.indjst.org

Col. Id

4CE 0.21 0.22 0.08 0.22 0.22 0.24 0.92

4CI 0.42 0.23 0.19 0.26 0.23 0.26 0.88

6CE 0.26 0.18 0.10 0.19 0.18 0.18 1.05

6CI 0.50 0.13 0.22 0.17 0.13 0.15 0.87

8CE 0.27 0.18 0.11 0.19 0.18 0.18 1.00

8CI 0.51 0.14 0.23 0.17 0.14 0.17 0.82

10CE 0.30 0.13 0.08 0.16 0.13 0.13 1.00

10CI 0.52 0.12 0.25 0.16 0.12 0.15 0.80

Table 6. Column Moment Capacities

Figure 6. Column axial force range (typical) shown in

design chart of SP 1610.

Capacity Design of Reinforced Concrete Framed Building for Earthquake Loading

Indian Journal of Science and Technology

Vol 9 (30) | August 2016 | www.indjst.org

8

Where, the column moment capacity is to be calcu-

lated from zero axial force. is multiplier of 0.8 is arrived

at from the limited results presented in Table6. Additional

studies are required for a statistically signicant value of

this multiplier.

4. Summary and Conclusion

Design codes recommend minimum MCR for capacity

design of the RC moment resisting frame. MCR is dened

as the ratio of cumulative column moment capacity to

cumulative beam moment capacity framing to a par-

ticular joint. e nominal design strength of beams are

a function of the beam section only and therefore there is

no diculty to calculate it. However, the nominal design

strength of columns depends on the level of axial force

in the column in addition to the column section proper-

ties. Dierent axial forces may arise in a column when

the building is subjected to the dynamic loading like an

earthquake. It is computationally very dicult to nd

the appropriate axial force which results least column

nominal design strength. e present study develops a

computationally simple procedure for calculating nomi-

nal design strength of the column (0.8 times the column

strength at zero axial force) to be used in determining

MCR at a beam-column joint.

5. References

1. Banihashemi MR, Mirzagoltabar AR, Tavakoli HR.e

eects of yield mechanism selection on the performance

based plastic design of steel moment frame. Indian Journal

of Science and Technology. 2015 May; 8 (S9):157–66.

2. Uma SR, Jain SK. Seismic design of beam-column joints in

RC moment resisting frames – Review of codes, Structural

Engineering and mechanics. 2006; 23(5):579–97.

3. ACI 318-14. Building Code Requirements for Structural

Concrete (ACI 318M-14) and Commentary (ACI 318R-

14), American Concrete Institute, ACI Committee 318,

Farmington Hills, MI, 2014.

4. NZS 3101:1995 (Part 1), Concrete Structures Standard.

New Zealand: New Zealand Standards.

5. EN 1998-1:2004, Design provisions for Earthquake

Resistant Structures-Part 1: General Rules, Seismic Actions

and Rules for Buildings, Brussels.

6. IS 13920 (dra):2014, Ductile Design and Detailing of

Reinforced Concrete Structures Subjected to Seismic

Forces Code of Practice. New Delhi, India: Bureau of Indian

Standards.

7. IS 1893:2002, Indian Standard Criteria for Earthquake

Resistant Design of Structures. New Delhi, India: Bureau of

Indian Standards.

8. IS 456:2000, Indian Standard Plain and reinforced con-

crete-code of practice (Fourth revision). New Delhi, India:

Bureau of Indian Standards.

9. SAP 2000. Integrated Finite Element Analysis and Design

of Structures, CSI, Berkeley, California, 2014 Sep.

10. SP 16:1980, Design Aids for Reinforced Concrete to IS:456-

1978. New Delhi, India: Bureau of Indian Standards.

... 3. Calculation of Mb is straightforward as beam moment capacity is a unique value in the absence of any axial force. However, as the column axial forces vary significantly (Mistri and Sarkar, 2016;Mistri, 2016) among the different load cases associated with the seismic load, it is quite ambiguous to calculate the column moment capacity. This issue makes the computation of MCR unattractive for practicing engineers. ...

  • Abhijit Mistri Abhijit Mistri

Capacity design philosophy is the basis of behind the strong column weak beam concept for the improvement of earthquake resistant design. Damages at some in some pre-determined structural members may allowed in the earthquake-resistant design philosophy in order to have a good global behaviour of the building. In order to ensure a favourable failure mode, design codes recommend minimum value of Moment Capacity Ratio(MCR)which is defined as the ratio of summation of column moment capacity to summation of beam moment capacity at a particular beam-column joint. During cyclic earthquake loading column experience a range of axial force due to various combinations of load, and unlike beam, column does not have a unique moment capacity. That makes the calculation of MCR cumbersome. There are discrepancies among the major international codes with regard to MCR. Indian standard codes for design of RC framed buildings are silent on this aspect. Draft 13920(2014)code suggests a value of MCR similar to other international codes without proper theoretical basis. Hence a rational study is required on the values of MCR.A computationally attractive procedure for calculating flexural capacity of column developed for determining MCR at a beam-column joint. To reach at an appropriate and acceptable MCR for capacity design of RC framed building reliability based approach is done. This research deals with the fragility and reliability analysis of four storey RC frames designed using various values of MCR ranging from 1.0 to 3.2. The RC frames are designed as per IS 1893(2002)for all seismic zones. Hazard curves required of various seismic location in India(like zone II, III, IV and V)has been selected from National Disaster Management Authority, Government of India. Seismic risk assessment of all the designed buildings is conducted and based on the achieved Reliability Index and the Target Reliability Index minimum value of MCR is suggested.

... 3. Calculation of Mb is straightforward as beam moment capacity is a unique value in the absence of any axial force. However, as the column axial forces vary significantly (Mistri and Sarkar, 2016;Mistri, 2016) among the different load cases associated with the seismic load, it is quite ambiguous to calculate the column moment capacity. This issue makes the computation of MCR unattractive for practicing engineers. ...

The major international design codes recommend a minimum value of the column-beam moment capacity ratio (MCR) to ensure a preferred collapse mechanism in multi-storey buildings. The aim of the work presented in this paper was to understand the basis of the discrete values of the MCR recommended in design codes through a probability-based seismic risk assessment method. The results obtained suggest that MCR criteria need not be imposed for buildings located in low-seismicity zones as other design criteria ensure an acceptable level of safety for buildings in these seismic zones. On the other hand, it was found that even a very high MCR cannot ensure a preferred collapse mechanism for buildings in zones of higher seismicity. The code approach of a single value of the MCR is therefore not adequate for consistent performance in different seismic zones or for performance objectives.

This study concentrates on the efect of selecting a desirable yield mechanism that has a significant efect on seismic design and response of structures designed by Performance Based Plastic Design (PBPD) method. In PBPD method, the design base shear is obtained on the basis of energy-work balance equation implementing pre-selected target drift and yield mechanism. With considering the importance of selection of yield mechanism, a parametric study has been done considering the diferent types of yield mechanisms to design a model of steel moment frame. The results obtained by nonlinear time history analyses shown that the complete sway mechanism (strong columns-weak beams) is the most efficient in terms of required design base shear for a given target story drift. It also should be noted that it is often impossible to estimate the column moment demand during the event of sever ground motions because they undergo large moments not only from those delivered from beams but also from their own deformation. Therefore, assuming only the criteria of strong column-weak beam mechanism in PBPD method can't prevent the yielding in columns. In this paper to improvement of PBPD method, some solutions are represented to precisely obtain the required moment of columns to prevent their yielding. Because the yielding of columns leads to form undesirable mechanisms before the structure reaches the pre-selected target drift. For example, a 10 story frame has been designed based on PBPD method using strong column-weak beam mechanism. The frame has been redesigned considering all represented equations of this study (modified PBPD frame). The results obtained by nonlinear static and dynamic analyses show that the modified PBPD frame perform according to expectations in terms of yield mechanism and target drift levels whereas the PBPD frame sufer large story drifts due to flexural yielding of the columns.

  • Sr Uma Sr Uma
  • Sudhir K. Jain

The behaviour of reinforced concrete moment resisting frame structures in recent earthquakes all over the world has highlighted the consequences of poor performance of beam column joints. Large amount of research carried out to understand the complex mechanisms and safe behaviour of beam column joints has gone into code recommendations. This paper presents critical review of recommendations of well established codes regarding design and detailing aspects of beam column joints. The codes of practice considered are ACI 318M-02, NZS 3101: Part 1:1995 and the Eurocode 8 of EN 1998-1:2003. All three codes aim to satisfy the bond and shear requirements within the joint. It is observed that ACI 318M-02 requires smaller column depth as compared to the other two codes based on the anchorage conditions. NZS 3101:1995 and EN 1998-1:2003 consider the shear stress level to obtain the required stirrup reinforcement whereas ACI 318M-02 provides stirrup reinforcement to retain the axial load capacity of column by confinement. Significant factors influencing the design of beam-column joints are identified and the effect of their variations on design parameters is compared. The variation in the requirements of shear reinforcement is substantial among the three codes.

  • Sa'id Towfighi

A computer program is used to obtain design tables for rectangular reinforced concrete columns subjected to axial load and biaxial bending. The user has the option of condensing the results using Bresler's load contour method. Tables constructed from the condensed results provide a design tool that is both accurate and easy to use.

  • Yao-Peng Liu Yao-Peng Liu

xxiii, 280 leaves : ill. ; 30 cm. PolyU Library Call No.: [THS] LG51 .H577P CSE 2009 Liu This thesis discusses the findings of a research project on analysis and design of bare and wall-framed steel structures. Extensive numerical examples have been employed to verify the proposed theory. The thesis further proposes an efficient and reliable computational tool for routine and advanced design of structures of steel material. It is common to note that many structural failures and collapses are due to structural instability which is more difficult and complex to consider than material yielding in the design context. For columns and bracings under large axial forces flexural buckling would tend to occur, whereas beams subjected to bending moments about their major axes may have lateral-torsional buckling. Meanwhile, the initial imperfections, including the global frame imperfection and the local member imperfection, should always be taken into account. In the first aspect, the consideration of initial imperfections transforms idealized bifurcation buckling to realistic load-deflection type buckling. On the other hand, the inclusion of initial member curvature is mandatory in modern design codes such as Eurocode-3 (2005) and BS5950 (2000) either in implicit (via use of different buckling curves) or explicit (via element formulation) consideration. Apart from the foregoing problems in practical engineering design, the contribution of structural walls and floor slabs are also commonly ignored in most previous second-order analysis. Thus, the applications of previous research are limited to bare steel frames. This cannot keep pace with the development and requirement in design of modern structures in which uses of structural plate elements are unavoidable. Furthermore, both researchers and engineers have been increasingly aware of the severe damage due to earthquake, especially after the impact of the Wenchuan Earthquake (2008) in China, and therefore there is a need to refine or improve the current seismic design methods with allowance for imperfections and wall and slab elements. In view of the above observations, there is an urgent need to develop a computational tool for stability analysis allowing for initial imperfections. Also, the common structural elements such as beams, columns, shear walls and floor slabs can be taken into consideration. In this thesis, a curved stability function element is formulated for nonlinear second-order analysis and design of steel frames. The proposed second-order analysis takes both the P-Δ and P-δ effects as well as the initial imperfections into account and as a result the traditional tedious member design can be replaced by the simple section capacity check. The proposed method is a system-based approach rather than a member-based method and therefore the true behavior of the structures can be reflected. Further, a flat shell element superimposed by a membrane element and a Mindlin type plate bending element is proposed for modeling and analysis of plated skeletal structures. The membrane part of the proposed shell element possesses the drilling degree of freedom and is free from 'zero-energy mode'. The bending part of the proposed shell element is based on the Reissner-Mindlin plate theory and the Timoshenko's beam theory. The convergence for the very thin plate is theoretically ensured and the 'shear locking' phenomenon is avoided. By introducing a simple geometric stiffness matrix, this shell element shows high performance and accuracy in tracing the post-buckling path both for 'snap-through' and 'snap-back' problems. To account for the lateral-torsional buckling, an integrated elastic buckling analysis by shell finite element and empirical equation as per the modified Perry-Robertson formulae is proposed to predict the design lateral-torsional buckling moment of beams. The drawbacks of the complicated large deflection and elasto-plastic shell finite element analysis which include uncertainty in modeling of residual stress and initial imperfection and excessively long computer time are overcome by the proposed method. The results by the present theory compare well with the closed form solutions and the one-dimensional beam element for simple cases. Using the proposed semi-empirical method, buckling resistance of beams with complex boundary conditions, geometries, loading types such as castellation in beams, loads above the shear centre and restraints at top flange have been effectively determined. To capture both the in-plane and out-of-plane behavior of structural walls, a shell element model is proposed for second-order analysis and design of wall-framed structures. Also, a simple floor element is suggested for consideration of the floor slabs while the imperfect stability function element is employed for modeling beam-column elements. Hence, the main structural elements of a typical building structure can be modeled in a nonlinear analysis and design and as a result the proposed second-order analysis method can be extended to typical composite building structures and not limited to the bare steel frames. In response to severe damage due to earthquake, a practical application by extending the proposed second-order analysis method for performance-based seismic design based on the pushover analysis procedure is developed. A simple and effective plastic hinge method is proposed here for inelastic pushover analysis. Meanwhile, the traditional nonlinear incremental-iterative procedure for proportional loads is modified to allow for non-proportional loads for simulation of pushover analysis which is carried out under constant gravitational loads with monotonically increasing lateral loads. Feature contained in this study is that it includes both the P-Δ and P-δ effects and their initial imperfections in global frame and local member levels which have not been mentioned in previous research. Moreover, the contribution of shear walls is considered by the proposed shell element. Therefore, a comprehensive method considering important effects is proposed for the performance based seismic design which can also be conducted using one element per member, being consistent with its counterpart for static load which is based on the one element per member model. This simplified modeling reduces the data manipulation effort and required computer time. Ph.D., Dept. of Civil and Structural Engineering, The Hong Kong Polytechnic University, 2009

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