Reinforced Concrete Columns | List of Symbols

The American Concrete Institute (ACI) 318-11 permits the use of the moment magnifier method for computing the design ultimate strength of slender reinforced concrete columns that are part of braced frames. This computed strength is influenced by the column effective length factor K, the equivalent uniform bending moment diagram factor Cm and the effective flexural stiffness EI among other factors.

 

List of symbols

  • Ag, Ars – Area of gross concrete cross section and of longitudinal reinforcing steel bars
  • Cm – Equivalent uniform bending moment diagram factor
  • Ec, Es – Moduli of elasticity of concrete and steel
  • EI – Effective flexural stiffness of column
  • e – End eccentricity = M2/Pu = Mcol/Pu
  • f′c – Specified compressive strength of concrete
  • fy – Specified yield strength of reinforcing steel bars
  • GA, GB – Relative stiffnesses of column at upper and lower joints
  • G min – Smaller of GA and GB
  • h, hbm, hcol – Overall thickness of cross-section of member, beam, and column taken perpendicular to axis of bending
  • Ig,Ig(bm),Ig(col) – Moment of inertia of gross concrete cross section of member, beam and column
  • Irs – Moment of inertia of longitudinal reinforcing steel bars taken about centroidal axis of member cross section
  • K – Effective length factor
  • ℓ, ℓbm, ℓcol –  Unsupported height (length) of member, beam, and column
  • M, Mbm – Bending moment and beam applied bending moment
  • Mc – Column design bending moment which includes second-order effects
  • Mcs, Mcol – Bending moment resistance of cross section and of member (column)
  • Mmax – Maximum bending moment acting along column length
  • M1, M2 – Smaller and larger of factored moments applied at column ends
  • My, My(bm) – Bending moment acting on member and beam cross section at onset of initial yielding of flexural tension steel computed from ACI Code without using ϕ factors
  • n – Number of data points
  • P – Axial load
  • Pc – Critical axial load strength of column
  • Po – Unfactored pure axial load strength of column cross section
  • Pu – Column axial load strength
  • Pu(des)  – Column axial load strength computed from one of three design procedures selected for this study
  • Pu(th) – Theoretically computed axial load strength of column
  • r – Radius of gyration of column cross section
  • β – Dimensionless factor for nonlinear EI equation 
  • βd – Ratio of maximum factored sustained axial load to total factored axial load associated with same load combination
  • δns – Moment magnifier for columns that are part of braced (nonsway) frames
  • δ1 – Moment magnifier for columns subjected to axial load and equal and opposite end moments causing symmetrical single curvature bending
  • Δ – Deflection of column due to cord effects
  • εcu – Maximum compressive strain in concrete
  • ρ, ρbm, ρcol – Total area of longitudinal reinforcing bars divided by gross area of concrete cross section of member, beam, and column
  • ϕ – Curvature or strength reduction factor
  • ϕk – Stiffness reduction factor