The earthquake resistant concrete frame building with special focus on beams and columns - Dissertation Example

?THE EARTHQUAKE RESISTANT CONCRETE FRAME BUILDING – WITH SPECIAL FOCUS ON BEAMS AND COLUMNS In this paper we are going to compare two s on the basis designing the earthquake resistance concrete frame building. The comparison focuses around beam and columns of the building. Two codes are compared here. First is Iranian concrete code and the second one is Eurocode Beam Design: A beam is the structural member which carries load, which are many times vertical to its longitudinal axis. Table 1 states the maximum reinforcement ratio. Iranian Code 8% Euro code 4% Table 1 For Eurocode the effective flanged width is ‘bff’ and for Iranian code it is ‘b’ Figure 1 Special condition should be followed when the beam elements are being designed such as the difference between rectangular beam and flanged beam should be known. Flanged beams are generally the rectangular beams which work with slabs and the part of slab element acts with the top part of the beam. If it is below the flange, then the section needs to be designed by taking into consideration the specific area of concrete section for compression part. The most crucial part in design is the design for flexure and shear. The flexure design has to be repeated twice, one for support condition and another for span condition. Design of Beam Sections under Iranian Standard: Isolated T-Beam Figure 2 Figure 3 Rectangular beams with tensile reinforcing: For this type the beam width b equals to 12 in (305mm) when the moment and shear are expressed per foot (m) of width. The working stress design formula for this is as follows: b = width of beam [equals 12 in (304.8 mm) for slab], in (mm) d = effective depth of beam, measured from compressive face of beam to centroid of tensile reinforcing M = bending moment, lb . in (k .Nm) fc = compressive stress in extreme fiber of concrete, lb/in2 (MPa) fs = stress in reinforcement, lb/in2 (MPa) As = cross-sectional area of tensile reinforcing, in2 (mm2) j = ratio of distance between centroid of compression and centroid of tension to depth d k = ratio of depth of compression area to depth d p = ratio of cross-sectional area of tensile reinforcing to area of the beam (= As /bd) 1. T beams with tensile reinforcing only: The portion of the slab acts as the upper flange of beam when the concrete slab is constructed monolithically. In this case the effective flange width should not exceed 1/4th the span of the beam The width of the web portion of the beam plus 16 times thickness of the slab The centre to centre distance between beams T beams should have a flange thickness with minimum one half the width of the web and flange width not more than four times the width of the web Coefficient K, k, j, p, for Rectangular Sections Beams with tensile and Compressive Reinforcing This kind of beams is generally used when the size of the beam is limited. The notations for detailing in both Iranian code and Euro code are same. The only difference is for the effective flange width which for Euro code is “beff” and for Iranian code b Beam Design According to Eurocode Design load 1.25*35 + 1.5*20 = 73.75 kN/m Bending Moment wl^2/8 = 73.75*6^2/8 = 331.9 kNm Shear Force wl/2 = 73.75*6/2 = 221.25 kN K 0.145 < 0.167 = Kbal Compression R/F not required As 1626 mm2 A's 0 mm2 Shear R/F T10 @ 415 mm c/c Shear Reinforcement: Shear force which acts to the beam can have a substantial deformation. This deformation occurs particularly to the both ends of the beam. Shear reinforcement according to Iranian code: The ultimate shear capacity Vn of a section of a beam equals the sum of the nominal shear strength of the concrete Vc and the nominal shear strength provided by the reinforcement Vs; that is, ?Vn = Vc = Vs. The factored shear force Vu on a section should not exceed where ? = capacity reduction factor (0.85 for shear and torsion). Except for brackets and other short cantilevers, the section for maximum shear may be taken at a distance equal to d from the face of the support. The shear Vc carried by the concrete alone should not exceed 2vfc_ bwd is the width of the beam web and d, the depth of the centroid of reinforcement. (As an alternative, the maximum for Vc may be taken as Рw = Aslbwd and Vu and Mu are the shear and bending moment, respectively, at the section considered, but Mu should not be less than Vud If Vu is larger than ?Vc’ the excess shear has to be resisted by web reinforcement. The area of steel required in vertical stirrups, in2 (mm2), per stirrup, with a spacing s, in (mm), is Here f = yield of strength of the shear reinforcement A= area of stirrups cut by horizontal plane Vs = should not exceed in sections with web reinforcement fy = should not exceed 60ksi A minimum area of shear reinforcement is required in all members, except slabs, footing, and joists or where Vu is less than 0.5Vc’ Shear Reinforcement (Eurocode) Design of the flanged Beam Sections Under Eurocodes Design for flexure: Beff is to be determined by using the following equation (Concrete Centre 2010) Beff = bw + Beff1 + Beff2 Beff1 = (0.2b1 + 0.1l0)? 0.2 /0? b1 Beff2= (0.2b1 + 0.1l0)? 0.2 /0? b2 Definition of l0 for calculating of effective flange width Effective flange with parameters The critical region is the major thing in Eurocodes. The critical region is assumed much shorter in Eurocode 8. The middle section of beams is not critical. It uses the the normal detailing rules from Eurocodes 2 At support At span Flexural Design process of flanged beam (After Concrete Centre Code 2010) Lcr = has to be at least 1.5 x depth of beam (hw) for DCH (ECB -1, 2004) Figure 4Shear Reinforcement (from Concrete Centre, 2010 Design for Flexure (Iranian Code) Basic equation: factored resistance ? factored load effect ?Mn ? Mu Mu = Moment due to factored loads (required ultimate moment) Mn = Nominal moment capacity of the cross-section using nominal dimensions and specified material strengths. f = Strength reduction factor (Accounts for variability in dimensions, material strengths, approximations in strength equations. Design for Shear Links: The critical region is the major thing in Eurocodes. The critical region is assumed much shorter in Eurocode 8. The middle section of beams is not critical. It uses the the normal detailing rules from Eurocodes 2 Minimum and maximum concrete strut capacity in terms of stress Design of Columns Below is the figure of a typical reinforced concrete column. Due to the influence of the earthquake actions, the columns of the building are suffered in various directions. These seismic loadings may affect huge moments as well as huge shear forces. It is off course very dangerous for the columns. The irregularity of structure may result into torsion failure. The uplift failure can occur due to the vertical acceleration. Consequently the building has to experience complete collapse. That is why the columns need to be designed by considering these things. For that certain criteria need to be developed, especially for RC frame columns. It results minimum loss during the earthquake. Two major reasons are their behind the total failure of the construction during earthquake, first is lack of shear reinforcement and incorrect detailing of beam column joints. Strong column weak beam condition: The major objective of designing Moment resistant ductile frame of reinforced concrete structure is to acquire sufficient strength and ductility. Strength is associated with optimum capacity of the structural member to resist the earthquake load while ductility is associated with maximum deformation beyond the yield stress without loss of strength. So to prevent earthquake loss it is necessary to build the column members stronger than the beam members. Iranian concrete code the sum of the moment of resistance of the columns shall be at least 1.2 times the sum of the moment of resistance of the beams. Over-strength coefficient of the design codes for columns (Iranian Concrete Code (ABA) and Eurocode) Yd Eurocode 8 1.3 Iranian Code 1.2 One of the determining factors to ensure a weak beam in a DMRF structure is R M , the ratio of column-to-beam flexural capacity given by, Where ? C M and ? B M are respectively the sum of the flexural capacities of the columns and beams intersecting at the joint. Experimental results indicate that in order to avoid the formation of a plastic hinge in the joint, R M should be a minimum of 1.4 [Iranian Concrete Code ABA] Column Design Under Iranian Codes: Principal columns – minimum diameter 10 in (255mm) Rectangular columns minimum thickness of 8 in (203mm2) Minimum gross cross-sectional area of 96 in2 (61935mm2) Short columns with closely spaced spiral reinforcing which encloses a circular concrete core reinforced with vertical bars have a maximum allowable load as follows: P = Ag(0.25fc+ fspg) P = total allowable axial load, lb (N) Ag = gross cross-sectional area of column, in2 (mm2) Fc= compressive strength of concrete, lb/in2 (MPa) fs = allowable stress in vertical concrete reinforcing, lb/in2 (MPa), equal to 40 percent of the minimum yield strength, but not to exceed 30,000 lb/in2 (207 MPa) pg = ratio of cross-sectional area of vertical reinforcing steel to gross area of column Ag The center-to-center spacing of the spirals should not exceed one-sixth of the core diameter. The clear spacing between spirals should not exceed one-sixth the core diameter, or 3 in (76 mm), and should not be less than 1.375 in (35 mm), or 1.5 times the maximum size of coarse aggregate used. The ratio Pg for tied column should not be less than 0.01 or more than 0.08. Longitudinal reinforcing should consist of at least 4 bars and the minimum size is 5 No. Long Columns: 1. If the ends of the column are fixed so that a point of contraflexure occurs between the ends, the applied axial load and moments should be divided by R from (R cannot exceed 1.0) 2. If the relative lateral displacement of the ends of the columns is prevented and the member is bent in a single curvature, applied axial loads and moments should be divided by R from (R cannot exceed 1.0) Where h = unsupported length of column, in (mm) r = radius of gyration of gross concrete area, in (mm) = 0.30 times depth for rectangular column = 0.25 times diameter for circular column R = long-column load reduction factor For spiral columns: eb = 0.43 pgmDs + 0.14t For tied columns: eb = (0.67pgm +0.17)d Shear reinforcement for columns (Iranian code) Design for punching shear should be based on ?Vn = ? (Vc + Vs) ? = capacity reduction factor (0.85 for shear and torsion) with shear strength Vn taken not larger than the concrete strength Vc calculated from Where Bo = perimeter of critical section and ?c = ratio of long side to short side of critical section However if the shear reinforcement is provided, the allowable shear may be increased a maximum of 75% if shearheads consisting of two pairs of steel shapes are used. Minimum reinforcement ratio according to Iranian code should be approximately 0.5% Braced Column Design under Eurocodes: Eurocodes need some checks before designing column. Slenderness level (?) is necessary for estimating the consideration of second order effects. If the second order effects can be ignored , then the normal braced column can be designed. If the slenderness of column is above the limit, then the column is slender. The following equation is for determining slenderness and slenderness limit for a rectangular column ?=3.46 lo l h lo = effective length of column = l l 2< lo< l h = depth of the column ?limit =10.8 / vn (National Annex CYS EN 1992 -1- 1:2004) n = Relative axis force = Ned l (Acfcd) Asfyk l bhfck = The value from column design chart Min 3 bars per side (EC8) Braced column under Iranian codes: According to the code the frame may be considered braced if the bracing elements such as shear walls, shear trusses and other factors which resist the lateral moment in a story have a total stiffness at least six times the sum of the stiffness of all the columns resisting lateral movement in story. It is possible to neglect the slenderness under two conditions 1. For column braced against sideway Where M1 = smaller of two end moments on column as determined by conventional elastic frame analysis, with positive sign if column is bent in single curvature and negative sign if bent in double curvature M2 = absolute value of larger of the two end moments on column as determined by conventional elastic frame analysis. 2. For columns not braced against sideway Concrete column design charts for d2 / h = 0.1 (from concrete centre, 2010) Concrete column design charts for d2 / h = 0.2 (from concrete centre, 2010) Read More