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Equations for P

Module by: Michael Terk. E-mail the author

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Summary: (Blank Abstract)

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What is P?

The abbreviation, PP, is used to describe the axial load on a member.

Basic requirements

The basic requirements for compression members are covered in Chapter E of the AISC Specification (page 16.1-27). The relationship between loads and strength takes the form:

P u ≤ φ c P n P u φ c P n (1)
where:
  • P u P u = sum of factored loads
  • P n P n = nominal compressive strength = A g F cr A g F cr
  • F cr F cr = critical buckling stress
  • φ c φ c = resistance factor for compression members = 0.85

Design strength equation

The design strength equation,

P n = A g F cr P n A g F cr (2)
has the variable F cr F cr which is a function of λ c λ c , the slenderness parameter. The equation for λ c λ c is:
λ c =Klrπ F y E λ c K l r F y E (3)
The equation for F cr F cr , then depends on the value of λ c λ c . For instance:
  • For λ c ≤1.5 λ c 1.5
    F cr =0.658 λ c 2 F y F cr 0.658 λ c 2 F y (4)
  • For λ c >1.5 λ c 1.5
    F cr =0.877 λ c 2 F y F cr 0.877 λ c 2 F y (5)

Slenderness parameter

The slenderness parameter incorporates the material properties. If it is less than 1.5, the compression member is said to be elastic. Then, if the value is over 1.5, F cr F cr must be reduced to account for the effects of initial crookedness.

Put in figure p96.

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