snt mod 2

• Compression members


  Structural elements that are subjected only to axial compressive forces
• The stress in compression members can be taken as Fa = P/A, where Fa is considered to be uniform over the entire cross section
• The ideal state of uniform stress is never achieved in reality, because some eccentricity of the load is inevitable
• Columns


  • Vertical members whose primary function is to support vertical loads
  • Also called upon to resist bending, in which case they are beam-columns
• Compression members


  • Used in trusses and as components of bracing systems
  • Smaller compression members not classified as columns are sometimes referred as struts
• Buckling load


  The load at which a compression member becomes unstable
• Euler load or Euler buckling load

  1. Pcr is the load at which the compression member becomes unstable

  2. Depends on the length, cross-section, and end conditions of the column and the stiffness of the material
• Effective length


  The length of the column used in the Euler equation, which depends on the end conditions
• Effective length factor (K)

  A factor that accounts for the end conditions of the column
• Slenderness ratio


  KL/r, where KL is the effective length and r is the radius of gyration
• The AISC specification recommends limiting the column slenderness ratio such that KL/r ≤ 200
• Braced frame


  A building where the lateral loads are resisted by diagonal bracing or shear walls
• Unbraced or moment frame

  A building where the lateral loads are resisted through bending of the beams, girders, and columns
• Effective length factor (K) for braced frames

  Assumed to be 1.0 for all columns
• Effective length factor (K) for unbraced frames with pinned column bases

  2.4 for ground floor columns
• Effective length factor (K) for unbraced frames with fixed column bases

  1.2 for ground floor columns
• Nominal compressive strength (Pn)

  Ag * Fcr, where Ag is the gross cross-sectional area and Fcr is the flexural buckling stress
• Design compressive strength (ΦPn)

  Nominal compressive strength multiplied by the resistance factor Φ = 0.90 for LRFD
• Allowable compressive strength (Pn/Ω)


  Nominal compressive strength divided by the safety factor Ω = 1.67 for ASD
• Determining the flexural buckling stress (Fcr)

  Depends on whether the column exhibits inelastic or elastic buckling behavior
• Compact section


  Reaches its cross-sectional material strength before local buckling occurs
• Non-compact section


  Only a portion of the cross-section reaches its yield strength before local buckling occurs
• Slender section


  The cross-section does not yield and the strength of the member is governed by local buckling
• Stiffened and unstiffened elements

  Compression elements that are classified based on their width-to-thickness ratios
• The AISC specification prescribes limits to the width-to-thickness ratios of the plate components that make up the structural member to avoid or prevent local buckling
• The allowable column stress varies with the slenderness ratio, with inelastic buckling occurring when the slenderness ratio is less than or equal to the critical slenderness ratio (Cc), and elastic buckling occurring when the slenderness ratio is greater than Cc
• Determining the allowable compressive stress (Fa) for intermediate columns (KL/r ≤ Cc)


  Fa = (1 - (KL/r)^2 / (2Cc^2)) * Fy / FS, where FS is a factor that depends on KL/r and Cc
• Determining the allowable compressive stress (Fa) for long columns (KL/r > Cc)


  Fa = 12π^2 * E / (23 * (KL/r)^2), where Cc = 2π^2 * E / Fy
• The critical slenderness ratio (Cc) is the value of the slenderness ratio that separates inelastic and elastic buckling behavior
• The A-36 steel W6x20 column is pin connected at its ends and is subjected to the axial load P. The column is laterally supported about its weak axis.