Reinforced Concrete Structures : Design according to CSA A23.3-04

11. Compression Members: Braced Columns

Chapter 11 Compression Members Braced Columns 11.1 Notation Used in this Chapter A Area of a section in general Ac Area of the core of a spiral-reinforced column, measured from the outside diameter of the spires Ag Total area of section of concrete As1 Cross-sectional area of longitudinal reinforcement in one face of a column with asymmetrical reinforcement As2 Cross-sectional area of longitudinal reinforcement in one face of a column with asymmetrical reinforcement As,max Area of cross-section of maximum longitudinal reinforcement As,min Area of cross-section of minimum longitudinal reinforcement Ast Total area of longitudinal reinforcement Cc Factored compressive force at the ultimate limit state resisted by the concrete Cm Factor relating the moment diagram to an equivalent uniform moment diagram Cs Factored compressive force at the ultimate limit state resisted by the steel reinforcement 360 Chapter 11 Cs1 Factored compressive force at the ultimate limit state resisted by the steel reinforcement As1 Cs2 Factored compressive force at the ultimate limit state resisted by the steel reinforcement As2 Ec Modulus of elasticity of concrete Es Modulus of elasticity of steel reinforcement I Moment of inertia of a section in general Ig Moment of inertia of a gross section of concrete Ist Moment of inertia of a section of longitudinal reinforcement with respect to the column’s centroid M Moment acting on the column M1 Value of the numerically smallest factored end moment acting on the column M2 Value of the numerically largest factored end moment acting on the column Mc Value of the factored end moment, taking into account buckling Mmax Maximum factored moment Mns Moment due to factored gravity loads Mr Factored moment resistance Mrb Factored moment resistance corresponding to the balanced state (e = eb) Mro Factored moment resistance without compressive effect Ms Moment due to factored loads resulting in lateral displacement (sway) P Axial compressive force Pc Critical axial compressive load (Euler) PDf Factored axial compressive force due to dead load acting on the column Pf Axial compressive force acting on the column Pr Factored compressive resistance of the concrete section Prb Factored compressive resistance corresponding to the equilibrium state (e = eb) Pr(max) Maximum factored resistance to the axial compressive force allowed by the standard Pro Factored resistance to the compressive force centred on the concrete section S1 Spacing between a supported bar and an unsupported bar S2 Spacing between two supported bars T Factored tensile force at the ultimate limit state resisted by tension reinforcement W Wind load a Depth of equivalent rectangular stress block b Width of rectangular column (short direction) d Effective depth of a reinforced-concrete section d Distance from extreme tension fibre to centroid of tension reinforcement d′ Distance from extreme compression fibre to centroid of compression reinforcement db Diameter of reinforcing bar Compression Members – Braced Columns 361 db,tie Diameter of reinforcing ties db,stirrup Diameter of reinforcing stirrups dext Outside diameter of the circular area described by spirals dspiral Spiral diameter e Eccentricity (e = M/P) eb Eccentricity corresponding to the equilibrium state (εs = εy and εc = εcu) fc Stress in the concrete fc′ Specified compressive strength of concrete after 28 d fs Stress in tension steel reinforcement fy Specified yield strength of steel reinforcement h Height of column of rectangular section k Effective length factor lu Clear unsupported length of the column r Radius of gyration s Reinforcement spacing x Distance from the extreme compression fibre to the plastic centre of the section xc Distance from extreme compression fibre to centroid of the concrete section Δ Deflection due to column buckling α1 Ratio of the average stress of the stress block to the compressive strength of the concrete αD Factor for factored dead load αL Factor for factored live load αw Factor for factored wind load γ Ratio of the distance between the extreme bars at height h δ Amplification factor for the end moment M2 to provide for the slenderness effect δs Amplification factor for the end moment Ms to provide for the slenderness effect εcu Unit strain at ultimate limit state εs Unit strain of tension steel εs′ Unit strain of compression steel εy Unit strain at elastic limit (corresponding to fy) ρg Ratio of longitudinal reinforcement (ρg = Ast/Ag) ρs Reinforcement ratio φc Resistance factor for concrete φm Member resistance factor (φm = 0.75) φs Resistance factor for steel reinforcement ψ Coefficient for combination of loads 362 Chapter 11 11.2...