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Elastic Critical Load Factor λcr

Elastic Critical Load Factor (lcr) is an indicator for buckling sensitivity of a structure. The larger the value is the less sensitive to sway buckling effect the structure is. It can also be used to compute the amplification moment (M) from the moment obtained by a linear analysis ( M') as,

By definition, lcr is a factor multiplied to the design load to cause the structure to buckle elastically and drastically, such that the structure does not exhibit pre-buckling deflection. This condition is impossible to attain in practice since structures deform in all directions, no matter how small, once external loads are applied. As the large deflection and material yielding effects are not considered here, the factor is an upper bound solution that cannot be used directly in design. However, lcr is useful in assessing the stability condition.

The following requirements are imposed in the CoPHK (2011).

  1. When lcr < 5, a structure must be designed by a second-order analysis discussed below (i.e. the P-Δ moment must be considered by a second-order analysis and the first-order linear analysis with or without moment amplification cannot be used)
  2. When 5≤ lcr < 10, the structure is sway-sensitive and moment must be amplified for the sway effect (i.e. the P-Δ moment must be considered and the first-order linear analysis with moment amplification method can be used) and
  3. When lcr ≥10, the frame is sway insensitive that the sway effect can be ignored (i.e. the P-Δ moment can be ignored)

lcr can be determined either by the deflection method in the CoPHK (2011) or in computer. In all cases, the P-δ moment must be considered in using imperfect member in analysis or the buckling curves in design code.

Second-order analysis can be used in all cases above.


 Figure1 The P-Δ and P-δ Moment

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