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  • INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

    Volume 2, No 1, 2011

    © Copyright 2010 All rights reserved Integrated Publishing services

    Research article ISSN 0976 – 4399

    Received on October, 2011 Published on November 2011 338

    An economic comparison of Direct displacement based Design with IS-1893

    Response Spectrum method for R.C. Frame Buildings Sunil S. Mayengbam

    1 , Choudhury.S

    2

    1- Research Scholar, Department of Civil Engineering, NIT Silchar, India

    2- Professor, Dept. of Civil Engineering, NIT Silchar, India

    sunil_mayengbam@hotmail.com

    ABSTRACT

    Displacement based design deals with the level of damage of structure by designing a

    structure with a specified target displacement. Traditional codal Force-based method of

    design cannot design structures for target design objectives under a specified hazard level. An

    economic comparison between a simpler form of Direct Displacement-based Design and IS-

    1893 Response Spectrum method for reinforced concrete frame buildings is reported here.

    Buildings of two different plans, three different heights are designed with the method for the

    performance levels achieved from those designed by the codal method and their respective

    costs of structural frame members are compared. It has been found that the frame buildings

    designed with the method is more economical than those designed with the codal method for

    the performance levels achieved by the said codal under similar conditions of modeling and

    performance levels.

    Keywords: Direct displacement based design; IS-1893 response spectrum method;

    differences in procedure; performance levels; similar condition; structural costs.

    1. Introduction

    Seismic design of buildings has traditionally been force-based. In the force-based codal

    method of design, the base shear is computed based on perceived seismic hazard level,

    importance of the building and probable reduction in demand due to nonlinear hysteresis

    effects. The computed base shear is distributed at floor levels with some prescribed or

    estimated distribution pattern. It is widely understood now that it is not the force but

    displacement, which can be directly related to damage. The constancy of stiffness in force-

    based design is also not tenable (Priestley 1993, 2003). Through force-based method of

    design an engineer cannot deliberately design structure for an intended performance level.

    The alternative approaches are displacement-based design and performance-based design

    which are gradually becoming popular in recent times. In these methods the design is done

    for an intended displacement or, an intended performance under a perceived hazard level.

    Displacement-based design procedures have been reported in the literatures (Aschheim 2002,

    Paulay 2002, Qi and Moehle 1991, etc). An offshoot of the displacement-based design is

    Direct Displacement-based Design (DDBD) which has been reported by several authors

    (Pettinga and Priestley 2005; Xue 2001 etc.). The DDBD method for hollow-tube R.C. frame

    buildings by Pettinga and Priestley (2005) appears to be appealing where the building is

    designed for some specified interstorey drift limit (2%) by considering an Equivalent Single

    Degree of Freedom (ESDOF) system of the building. Under the specific modeling and target

    drift condition, dynamic amplification of storey shear, column moment and storey drift are

    considered and modified to achieve the target inter storey drift.

  • An economic comparison of Direct displacement based Design with IS-1893 Response Spectrum method for

    R.C. Frame Buildings

    Sunil S. Mayengbam, Choudhury.S

    International Journal of Civil and Structural Engineering

    Volume 2 Issue 1 2011

    339

    The Performance-Based Design (PBD) apparently started with the Freeman’s Capacity

    Spectrum Method (Freeman 1975), developed fast with the contribution from vast research

    community and with the publication of various documents by Applied Technology Council

    and Federal Emergency Management Agency. The performance levels of the buildings are

    described in terms damage level reflected by inelastic rotation in members differentiated as

    Immediate Occupancy (IO) level, where damage level is least; Life Safety (LS) level, where

    damage level is intermediate and life is not threatened under strong ground motion; and,

    Collapse Prevention (CP) level where damage is substantial and the structure is on the verge

    of collapse.

    2. DDBD design procedure

    The design is done by a simpler DDBD method similar to Pettinga and Priestley (2005). The

    target design drift and performance level of the building are decided. The beam depth has

    been derived from UPBD (S. Choudhury et al, communicated to Earthquake Spectra in

    2011). The beam width varies from one-third to half of beam depth as per general design

    practice. The column sizes are so adjusted that the column steel is restricted 4% of column

    sectional area.

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0 1 2 3 4 5 6

    D is p la ce m en

    t (m

    )

    Period (seconds)

    IS-Displacement Spectra 5%

    10%

    15%

    20%

    25%

    Figure 1: IS-Displacement spectra for 0.36g, medium type soil.

    However, for ready reference the design steps are elaborated below, with mention of

    difference with DDBD method of Pettinga and Priestley (2005), wherever applicable.

    The equivalent single degree of freedom system properties are determined as follows

    ∑ ∑

    ∆ =∆

    ii

    ii

    m

    m 2

    d

    (1)

    d e ∆

    ∆ =∑ iimm

    (2)

  • An economic comparison of Direct displacement based Design with IS-1893 Response Spectrum method for

    R.C. Frame Buildings

    Sunil S. Mayengbam, Choudhury.S

    International Journal of Civil and Structural Engineering

    Volume 2 Issue 1 2011

    340

    ∑ ∑

    ∆ =

    ii

    iii

    m

    hm H e

    (3)

    Here, mi, hi and ∆i are respectively the mass, height from base and displacement for i th

    storey.

    ∆d is target (spectral) displacement, me is equivalent mass, He is the effective height of the

    ESDOF system.

    The displacement spectra corresponding to design acceleration spectra are generated for

    various damping shown in figure 1.

    The deflection profile suggested by Pettinga and Priestley (2005), as shown in Eq. (4a) and

    (4b), has been used. Here, Øi is the mode shape coefficient of building at i th

    floor and n is

    total number of storey.

    n4, H

    hi i

    3

    4 =φ 

      

     − H

    hi

    4

    1 1

    (4b)

    Storey displacement, ∆i in step 3 and 8 is given by

     

      

     ∆ =∆

    c

    c ii φ φ

    (5)

    Where, ∆c and ϕc are the critical storey displacement and the corresponding mode shape

    at the critical storey level.

    The damping in the system is computed from ductility as given below: The yield

    displacement (∆y) of ESDOF system is given by Eq. (6) and frame ductility (µ) is given by

    Eq. (7). Now equivalent effective damping (ξ) in the system is obtained from Eq. (8).

    eyFy Hθ=∆

    (6)

    yd ∆∆= /µ

    (7)

     

      

     − +=

    π µ

    ξ 5.01

    1205 % (8)

    The design base shear is computed as follows. The effective time period (Te) is obtained from

    displacement spectra corresponding to the curve for damping ξ and the value of target

    displacement ∆d. Effective stiffness for ESDOF system is given by Eq. (9) and base shear is

    given by Eq. (11).

  • An economic comparison of Direct displacement based Design with IS-1893 Response Spectrum method for

    R.C. Frame Buildings

    Sunil S. Mayengbam, Choudhury.S

    International Journal of Civil and Structural Engineering

    Volume 2 Issue 1 2011

    341

    2

    e

    e2

    e 4 T

    m K π=

    (9)

    ∆−P effect is considered as per Pettinga and Priestley, (2007) where stability ratio (ӨP∆), post yield stability ratio unaffected (ro=0.01,assumed) and affected (rp) by ∆−P effect and overall moment (MB) are given by Eq. (10a), (10b) and (10c) respectively.

    eB P

    HV

    P∆ =∆θ

    (10a)

    − =

    P

    Po p

    r r

    θ θ

    1

    (10b)

    D

    p

    peDeB P r

    rHKM ∆   

     

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