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Design of Concrete University of Structure II بسم هللا الرحمن الرحيم Palestine Lecture # 3 Instructor: Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns According to ACI Code a structural element with a ratio of height-to least lateral dimension exceeding three used primarily to support compressive loads is defined as column. P h b h l b Instructor: Page 1 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns Columns are vertical compression members of a structural frame intended to support the load-carrying beams. They transmit loads from the upper floors to the lower levels and then to the soil through the foundations. Loads Column Column Beam Sec A Sec A Sec A-A Main beam Instructor: Page 2 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns Usually columns carry bending moment as well, about one or both axes of the cross section, and the bending action may produce tensile forces over a part of the cross section 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 Instructor: Page 3 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Types of Columns 1- Form and arrangement of reinforcement Columns are divided into three types 1- Tied Columns It is a column in which the longitudinal reinforcement bars are tied together with separate smaller diameter transverse bars (ties) spaced at some interval along the column height. (Figure a) 2- Spirally-Reinforced Columns It is a column in which the longitudinal bars are arranged in a circle surrounded by a closely spaced continuous spiral. (Figure b) 3- Composite Columns It is a column made of structural steel shapes or pipes surrounded by or filled by concrete with or without longitudinal reinforcement. (Figure c) Instructor: Page 4 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Types of Columns Instructor: Page 5 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Types of Columns 2- Length of the column in relation to its lateral dimensions. Columns may be divided into two categories 1- Short Columns, for which the strength is governed by the strength of the materials and the geometry of the cross section 2- Slender columns, for which the strength may be significantly reduced by lateral deflections. 3- Position of the load on the cross-section Columns can be classified as 1-Concentrically loaded columns, are subjected to axial force only 2-Eccentrically loaded columns, are subjected to moment in addition to the axial force. Instructor: Page 6 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns Behavior of Tied and Spirally-Reinforced Columns Failure of a tied column Failure of a spiral column Deformation Instructor: Page 7 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns Factored Loads and Strength Reduction Factors Factored Loads For gravity loads only, Pu = 1.2 PD+1.6 PL For dead, live and wind loads, Pu = 1.2 PD+1.0 PL+1.6 PW For dead and wind loads, Pu = 0.9 PD + 1.6 PW or Pu = 1.2 PD + 0.8 PW For dead, live and earthquake loads, Pu = 1.2 PD+1.0 PL+1.0 PE For dead and earthquake loads, Pu = 0.9 PD + 1.0 PE Instructor: Page 8 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Columns Strength Reduction Factors ACI Code specifies Φ values or strength reduction factors for most situations as in the following table Strength condition Φ Tension-controlled sections (εt ≥ 0.005) 0.90 Compression-controlled sections (εt ≤ 0.002) Members with spiral reinforcement 0.70 Other reinforced members 0.65 Instructor: Page 9 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Sway and Nonsway Frames 1- Nonsway Frames (braced) It is a structural frames whose joints are restrained against lateral displacement by attachment to rigid elements or bracing Columns Shear wall Columns Brace X Beams Beams P According to ACI Code M a column in a structure is nonsway if ∆ lc Secondary moment Pu 0.05 Primary momen t vu lc M P Instructor: Page 10 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Sway and Nonsway Frames 1- Nonsway Frames (braced) Moreover, ACI Code assumes a story within a structure is nonsway if: Q P 0.05 u Vu lc Where, Q is the stability index which is the ratio of secondary moment due to lateral displacement and primary moment, ΣPu is the total vertical load in the story, Vu is the story shear in the story under consideration, Lc is length of column measured center-to center of the joints in the frame, and Δ is the first-order relative deflection between the top and bottom of that story. Instructor: Page 11 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Sway and Nonsway Frames 2- Sway Frames (Unbraced) Structural frames, not attached to an effective bracing element, but depend on the bending stiffness of the columns and girders to provide resistance to lateral displacement are called “sway frames” Instructor: Page 12 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect The slenderness of columns is based on their geometry and on their lateral bracing. As their slenderness increases, their bending stresses increase, and thus buckling may occur. Several items involved in the calculation of slenderness ratios, these item unsupported column lengths, effective length factors and radii of gyration. Unsupported lengths (lu) It is clear distance between floor slabs, beams, or other members capable of providing lateral support as shown in figure. Instructor: Page 13 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K The effective length is the distance between points of zero moment in the column Thus, the effective length factor k, is the ratio of the effective length to the original length of column. Typical cases illustrating the buckled shape of the column for several end conditions and the corresponding length factor K Points of inflection Instructor: Page 14 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K For members in a structural frame, the end restraint lies between the hinged and fixed conditions. The actual k value can be estimated from the Jackson and Moreland alignment charts The effective length factor k is a function of the relative stiffness at each end of the column. In these charts, k is determined as the intersection of a line joining the values of ψ at the two ends of the column. The relative stiffness of the beams and columns at each end of the column ψ is given by the following equation E c I c / lc E b I b / lb Instructor: Page 15 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Braced frame Instructor: Page 16 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Unbraced frame Instructor: Page 17 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K E c I c / lc where, E b I b / lb lc = length of column center-to-center of the joints lb = length of beam center-to-center of the joints Ec = modulus of elasticity of column concrete Eb = modulus of elasticity of beam concrete Ic =moment of inertia of column cross section about an axis perpendicular to the plane of buckling being considered. Ib =moment of inertia of beam cross section about an axis perpendicular to the plane of buckling being considered. Σ indicates a summation of all member stiffness connected to the joint and lying in the plane in which buckling of the column is being considered Instructor: Page 18 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K Consider the two-story frame shown in Figure. To determine the effective length factor k for column EF C F I E ( I / h ) Ec ( I EF / h2 ) E c DE 1 Eb ( I BE / l1 ) Eb ( I EH / l2 ) h2 and B E H Ec ( I EF / h2 ) h1 F A D G Eb ( I CF / l1 ) Eb ( I FI / l2 ) L1 L2 For ψ = ------ and for ψ = ------ ACI Code specifies that for columns in nonsway frames, the effective length factor k should be taken as 1.0 Instructor: Page 19 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K To calculate the ψ values it is necessary to use realistic moments of inertia. Usually, the girder will be appreciably cracked on their tensile sides, whereas the columns will probably have only a few cracks. In the ACI code, it is stated that for determining ψ values for use in evaluating K factors, the rigidity for beams = 0.35 Ig and for columns= 0.7 Ig as follows Where, Ig is the gross moment of inertia Instructor: Page 20 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K ACI Code provides the following simplified equations for computing the effective length factors for nonsway and sway frame members For Nonsway frames, k 0.7 0.05 A B 1.0 K is the smaller of k 0.85 0.05 min 1.0 Where, ψA and ψB are the values of ψ at the two ends of the column, ψmin is the smaller of the two values. Instructor: Page 21 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Slenderness effect Effective length factors K For Sway frames, a) Restrained at both end For ψm > 2.0 , 20 m k 1 m 20 For ψm ≥ 2.0 , k 0.9 1 m Where, ψm is the average of ψ at the two ends of the column b) Hinged at one end k 2.0 0.3 Where, ψ is the values at the restrained end of the column Instructor: Page 22 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine The ACI Procedure for Classifying Short and Slender Columns According to ACI Code, columns can be classified as short when their effective slenderness ratios satisfy the following criteria: For Nonsway frames k lu M 34 12 1 40 r M2 For sway frames k lu 22 Where, r k = effective length factor lu = unsupported length of member r = radius of gyration, for rectangular cross sections r = 0.30 h, and for circular sections, r = 0.25 h h = column dimension in the direction of bending. Instructor: Page 23 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine The ACI Procedure for Classifying Short and Slender Columns M1 = smaller factored end moment on column, positive if member is bent single curvature, negative if bent in double curvature. M2 = larger factored end moment on column, always positive. [M1/M2] = ratio of moments at two column ends [Range -1 to 1] M1 M1 0 0 M2 M2 Single curvature Double curvature Instructor: Page 24 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Chart summarizes the process of column design as per the ACI Code Column Design Non-sway frame Non-sway frame Neglect k lu k lu M 22 Slenderness 34 12 1 40 r [ Short ] r M2 Moment k lu magnification k lu M 22 100 100 34 12 1 . r [ long ] r M2 Exact P ∆ k lu k lu 100 analysis 100 r [ long ] r Instructor: Page 25 Eng. Mazen Alshorafa Design of Concrete University of Structure II بسم هللا الرحمن الرحيم Palestine Example # 1 Instructor: Eng. Mazen Alshorafa Design of Concrete University of Structure II بسم هللا الرحمن الرحيم Palestine Example # 1 The frame shown in Figure consists of members with rectangular cross sections, made of the same strength concrete. Considering buckling in the plane of the figure. Categorize column bc as long or short if the frame is: a)Nonsway 270 kN.m 0.6x0.3 0.6x0.3 b)Sway 0.3x0.35 4.0 m 0.6x0.3 0.6x0.3 400 kN.m 0.3x0.35 4.5 m 9.0 m 7.5 m Instructor: Page Ex1-1 Eng. Mazen Alshorafa Design of Concrete University of Structure II بسم هللا الرحمن الرحيم Palestine Solution a- Nonsway For a column to be short, k lu M1 34 12 40 r M2 Lu = 4-0.3-0.3=3.40 m k is conservatively taken as 1.0 k lu 1(3.4) 32.38 r 0.3(0.35) M1 27 34 12 34 12 42.1 taken as 40 32.38 M2 40 i.e., column is classified as being short Instructor: Page Ex1-2 Eng. Mazen Alshorafa Design of Concrete University of Structure II بسم هللا الرحمن الرحيم Palestine Solution b- Sway For a column to be short, k lu 22 (0.3)(0.35)3 r 0.7 C 12 (4) 0.406 (0.3)(0.6) 3 (0.3)(0.6) 3 0.7 0.7 12 (9) 12 (7.5) (0.3)(0.35) 312 (0.3)(0.4) 3 0.7 0.7 12 (4.5) b 12 (4) 0.945 (0.3)(0.6) 3 (0.3)(0.6)3 0.7 0.7 12 (9) 12 (7.5) Using the appropriate alignment chart, k = 1.21, and k lu 1.21(3.4) 39 .18 22 r 0.3 (0.35 ) i.e., column is classified as being slender Instructor: Page Ex1-3 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Short axially loaded columns For tied reinforced columns Pu 0.52 Ag [0.85 fc ' g ( fy 0.85 fc ' )] For spirally reinforced columns Pu 0.595 Ag [0.85 fc ' g ( fy 0.85 fc ' )] Instructor: Page 26 Eng. Mazen Alshorafa Design of Concrete University of Structure II Palestine Design Considerations Maximum and Minimum Reinforcement Ratios Instructor: Page 27 Eng. Mazen Alshorafa

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