土木工程专业英语4.4Reinforced Concrete Column4.4.1 Types of ColumnsColumns are defined as members that carry loads chiefly in compression. Usually columns carry bending moment as well, about one or both axes of the cross-section, and the bending action may produce tensile force over a part of the cross-section. Even in such cases, columns are generally referred to as compression members, because the compression forces dominate their behavior . In addition to the common type of compression members, i.e., vertical elements in structures, compression members include arch ribs, inclined rigid frame members, compression elements in trusses or shell.Columns may be classified based on the following different categories:(1)Based on loading, columns maybe classified as follows:a. Axially loaded columns, where loads are assumedacting at the centroid of column section.b. Eccentrically loaded columns, where the loads areacting at a distance e from the centroid of column section .The distance e could be along the x or y axis, causing moments either about the x axis and y axis.c. Biaxially loaded columns , where the loads areapplied at any point on the column section, causing moments about both the x axis and y axis simultaneously.(2) Based on length, columns can be classified asfollows:a. Short columns, where the column”s failure is due to the crushing of concrete or due to the yielding of the steel bars under the full load capacity of the column.b. Long columns（slender columns）, where the buckling effect and the slenderness ratio must be take into consideration in the design, thus reducing the load capacity of the column relative to that of a short column.(3) Based on lateral reinforcement, columns can be classified as follows (Figure 4.24):a. Columns reinforced with longitudinal bars and lateral ties.b. Columns reinforced with longitudinal bars andcontinuous spirals.c. Composite compression members reinforcedlongitudinally with structural steel shapes, pipe, or tubing, with or without additional longitudinal bars,and various types of lateral reinforcement.The main reinforcement in columns is longitudinal, parallel to the direction of the load, and consists of bars arranged in a square, rectangular, or circular pattern.Lateral reinforcement, in the form of individual relatively widely spaced ties or a continuous closely spaced spirals, serves several functions. For one, such reinforcemen is needed to hold the longitudinal bars in positions in the forms while the concrete is being placed. For this purpose, longitudinal and transverse steel are wired together to form cages, which are then moved into the forms and properly positioned before placing the concrete. For another, transverse reinforcement is needed to prevent the highly stressed, slender longitudinal bars from buckling outward by bursting the thin concrete cover.Figure 4.24.4.2 Short Columns1 Behavior or Axially Loaded Short Column When an axial load is applied to a reinforced concrete short column, the concrete can be consideredto behave elastically up to a low stress of about(1/3)f”c. Two different types of failure occur in columns, depending on whether ties or spirals are used . A tied column fails at the load N a(Figure 4.25). At this load, the concrete fails by crushing or shearing outward along inclined planes , and the longitudinal steel bars fail by buckling outward between ties , as shown in Figure 4.26a. The column failure occurs suddenly, much like the failure of a concrete cylinder.In a spirally rein forced column, when the same load N a is reached, the longitudinal steel and the concrete within the core are prevented from moving outward by the spiral. The concrete in the outer shell, however, not being so confined, does fail; i.e., the outer shell spalls off when N a is reached, as shown in Figure 4.26b. It is at this stage that the confining action of the spiral has a significant effect, and if sizable spiral steel is provided, the load will ultimately fail the column by causing the spiral steel to yield. The axial strain when the column fails can be much larger than that at which the shell spallsoff.Figure 4.25 Load-deformation of tied and spirally reinforced concrete columnFigure 4.26 Failure of tied and spirally reinforced concrete columnIf the load on the column is increased to reach its ultimate strength, the concrete will reach the maximum strength and steel will reach its yield strength, f y. See Figure 4.27. the ultimate bearing capacity of a short column reinforced with longitudinal bars and lateral ties can be written as followsN u=f`y A`s +f c A c （4.4.1）Where,A`s=reinforcement areaf`y= reinforcement yield strengthA c=concrete section areaf c=concrete prismatic compressive strength2.Short Columns under Combined Axial Forceand MomentWhen a member is subjected to combined axial compression N and moment M , such as in Figure4.28a , it is usually convenient to replace the axial loadand moment with an equal load N applied at eccentricity e=M/N , as in Figure 4.28b . The two loadings are statically equivalent. All columns may then be classified in terms of the equivalent eccentricity. Figure 4.27 Stress and force at ultimate strength of axial loaded columnFigure 4.28 Equivalent eccentricity of column load(1)Failre modes of columnsUnder the combined actions of axial force and moment , there are two types of failure modes of column (a) balanced failure , (b) compression failure , when the neutral axis is outside the section, causing compression throughout the section , and (c) tension failure , when the neutral axis is within the section , developing tensile strain on the left of the neutral axis .Balanced failureUnder this mode of failure , yielding of the tensile steel on the far side of the column occurs simultaneously with the attainment of limit compressive strain of 0.0033 in concrete .Compression failureCompression failure of the column occurs when (a) therelative eccentricity e o/h o is small , or (b) although the relative eccentricity e o/h o large , the tension reinforcement ratio is large . Columns having small relative eccentricity are generally characterized by compression over the entire concrete section , but columns with large eccentricity are subjected to tension over tension over at least a part of the section. Columns of this type fail by crushing of the concrete and compressive yielding of the steel on the side near the load, while the reinforcement on the side farthest from the load does not yield. See Figure 4. 29b.Figure 4. 29 Failure modes of columnsTension failureTension failure occurs when (a) the relative eccentricity e0/h0 is large, and (b) the tension reinforcement ratio is moderate. The longitudinal steel on the side farthest from the load yields first.Gradually, with the increase of tensile strain, the compressive strain reaches 0.0033 at the compressive edge and compression reinforcement yields.(2)Capacity of short columns under combined axial force and momentUnder the combined actions of axial force and moment, a strength interaction diagram (see Figure 4. 30) generally describes the capacity envelope of a column. The strength interaction diagram defines the failure load and failure moment for a given column for the full ranges of eccentricity from zero to infinity. For any eccentricity, there is a uniquepair of value of (Mu, Nu) that will produce the incipient failure. That pairs of values can be plotted as a point on a graph relating Nu and Mu. Any radical line represents a particular eccentricity e o=M/N. Load demand points (M, N) from all load combinations must fall inside the (M0, N0) capacity envelope; otherwise, the column is considered inadequate and should be redesigned.Figure 4. 30 Strength interaction diagramThe upper point of an interaction curve is the case of pure axial compression. Where the interaction curve intersects with the moment axis, the column is under pure bending, in which case the column behaves^ like a beam. The point of maximum moment on the interaction diagram coincides with the balanced condition. The extreme concrete fiber strain reaches ultimate strain (0. 0033) simultaneously with yielding of the extreme layer of steel on the opposite side (f y/E s=0. 002).The interaction diagram further reveals that as the axial force Nu becomes larger the section can carry smaller Mu before failing in the compression zone. The reverse is the case in the tension zone, where the moment carrying capacity Mu increases with the increase of axial load N…. In the compression failure zone, the failure occurs due to over straining of concrete. The large axial force produces high compressive strain of concrete keeping smaller margin available for additional compressive strain due to bending. On the other hand, in the tensionfailure zone, yielding of steel initiates failure. This tensile steel stress reduces with the additional compressive stress due to additional axial load. As a result, further moment can be applied until the combined stress of steel due to axial force and increased moment reaches the yield strength.Figure 4. 31 shows a member loaded parallel to its axis by a compressive force N at an eccentricity e0 measured from the centerline. The actual geometrical shape of the concrete stresses distribution is shown in Figure 4. 31a. Just as for simple bending, the actual concrete compressive stress distribution is replaced by an equivalent rectangular distribution having depth .r. Equilibrium between external and internal axial forces requires thatFigure 4.31 Actual and equivalent rectangular stress distribution of eccentrically loaded column at ultimate strengthIn addition, sum of the moments of the concrete compressive stress, reinforcement force and the external force N about the centerline of the resultant force in the tension reinforcement must equal to zerowhere.e = distance from the line of action of the axial compression force to the centroid of reinforcement on the side of the column farther from the loadh0= distance from the centroid of reinforcement on the side of the column farther from the load to most extreme concrete compressive fiberQ s— stress in reinforcement on the side of the column farther from the load, for compression failure and for tension failureAdditional eccentricityTo account for the additional eccentricity due to accidental eccentricity from loading, nonhomogeneity of concrete material, unsymmetrical reinforcement and construction tolerances, the initial eccentricity e0 in Equation (4. 4. 4) is replace bywhere the additional eccentricity, e a, is 20mm or 1/30 column depth measured in the direction of eccentricity, whichever is larger.4.4.3Slender ColumnsA column is said to be slender if its cross-section dimension issmall compared with its length. The degree of slenderness is generally expressed in terms of the slenderness ratio l o/i, where l0 is the effective column length and i is the radius of gyration of its cross-section, equal to. For square or circular members, the value of i is the same about either axis; for other shapes i is the smallest about the minor principle axis.Columns having are designated as short and otherwise, they are slender. Short columns fail because both concrete and steel are stressed to their maximum carrying capacities and give away, respectively, by crushing and by yielding. On the other hand, the slender columns may fail at a much lower value of the load whensudden lateral displacement of the member takes place between the ends. Thus, short columns undergo material failure, while slender columns may fail by buckling (geometric failure) at a critical load or Euler’s load, which is much less in comparison to that of short columns having equal area of cross- section.1.Capacity of Axially Loaded Slender ColumnThe ultimate bearing capacity of an axially loaded slender column reinforced with longitudinal bars and lateral ties can be written as followswhere, 0. 9 is reduction factor accounting for accidental eccentricity from loading or due to construction tolerances that will induce moment, is stability reduction coefficient of reinforced concrete member 2.Capacity of Slender Column under Combined Axial Force andMomentConcrete design code GB 50010-2002 describes an approximate slenderness- effect design procedure based on the moment magnifier concept. The eccentricity e, in equation (4. 4. 5) is multiplied by an eccentricity magnification factorwhere,h— overall cross-section dimension in the direction of eccentricity= curvature correction factor of the eccentrically loaded column section; is not to be taken greater than 1£2= influence coefficient of slenderness ratio on the cross-section curvature;£z =A= the gross section area4.4. 4 Detailing Requirements for Reinforcement1.Material StrengthConcrete strength has a pronounced effect on the strength capacity of a column. The high strength concrete C30-C40 or higher grade are generally used.Reinforcements of grade HRB335 or HRB 400 are used, and the high strength bars are not recommended.2.Detailing of Column Longitudinal ReinforcementThe ratio of longitudinal steel area to gross concrete, cross-section is in the range from 0. 6 percent to 5 percent. The lower ratio limit is necessary to ensure resistance to bending moment not accounted in the analysis and to reduce the effects of creep and shrinkage of the concrete under sustained compression. Ratios higher than 5 percent not only are uneconomical, but also would cause difficulty owing to congestion of the reinforcement, particularly where the steel must be spliced. Most columns are designed with ratios below 2 percent.Larger diameter bars are used to reduce placement costs and to avoid unnecessary congestion. The diameter of the longitudinalreinforcement should not be less than 12mm. A minimum of four longitudinal bars is required when the bars are enclosed by spaced rectangular or circular ties.Spacing between longitudinal bars measured along the periphery should not exceed 300mm. When the depth of the eccentrically loaded column is greater than 600mm. additional longitudinal bars with a diameter of 10 16mm should be placed on the lateral sides.Longitudinal bars in a column are generally spliced at mid-storey height, away from the section of maximum stress.Where the column cross-section dimensions change, longitudinal bars need to be offset. The slope of the offset bar should not exceed 1 in 6. Horizontal ties are needed within the offset with a spacing not to exceed 10 times the minimum diameter of longitudinal bars or 200 mm, whichever is less.3.Detailing of Column Ties or HoopsTo prevent buckling of longitudinal bars, all bars of tied columns shall be enclosed by lateral ties, as shown in Figure 4. 32. The ties must be at least 1/4 of the maximum longitudinal bar diameter and at least 6mm. The vertical spacing of ties in columns should not exceed 15 times the minimum diameter of longitudinal bars 400mm, or the smallest dimension of the column size, whichever is the least.When the overall reinforcement ratio is greater than 0. 03, hoopsshould be used with a spacing not to exceed 10 times the minimum diameter of longitudinal bars, 'but not larger than 200mm. The minimum hoop diameter is specified to be 8 mm.The ties shall be so arranged that every corner and alternate longitudinal bar shall have lateral support provided by the corner of a tie having an included angle of not more than 135°, and no longitudinal bar shall be farther than 300mm on either side from such a laterally supported bar.Figure 4. 32 shows cross-sections frequently found in buildings. In general, in members with large axial forces and small moment, longitudinal bars are spaced more or less uniformly around the perimeter. When bending moments are larger, much of the longitudinal steel is concentrated at the faces of highest compression or tension, i. e. . at maximum distance from the axis of bending. In heavily loaded columns with large steel percentages, the result of a large number of bars, each of them positioned and held individually by ties, is steel congestion in the forms and difficulties in placing the concrete. In such a case, bundled bars are frequently employed. Bundles consist of three or four bars tied in direct contact, wired, or otherwise fastened together. These are usually placed in the corners.Figure 4.32 Column hoops and ties4.Detailing of Column SpiralsSpiral columns require a minimum of six longitudinal bars. Spacers should be used to maintain the designed spiral spacing and to prevent distortions. The clear spacing between turns of the spiral must not exceed 80mm or 1/5 of its core diameter, whichever is less. In addition, a minimum ratio of spiral steel is imposed such that the structural performance of the column is significantly improved, with respect to both ultimate load and the type of failure, compared with an otherwise identical tied column.Spirals should be anchored at each column end by providing an extra one and one-half turns of spiral bar. Spirals may be spliced by full mechanical or welded splices or by lap splices with adequate lap lengths. While spirals are not required to run through the column-to-floor connection zones, ties should be inserted in those zones to maintain proper confinement, especially if horizontal beams do not frame into these zones .。
