The Structural Engineer's Corner

Eng. Onorio Francesco Salvatore

Methods of Structural Analysis according to AS 4100 – Part 2: Elastic Analysis

Written By: Lexatus - Sep• 14•13

Second-order Onorio

In the Australian Standard 4100, the second-order effects for elastic analysis are defined in the Clause
It is stated that the analysis shall allow for the effects of the design loads acting on the structure and its members in their displaced and deformed configuration.

Second-order bending moments caused by the member axial forces and the displacements are neglected in the first-order (linear) methods of elastic analysis. The problem is that when we have compressive forces, the second-order bending moments may increase the first-order bending moment. In this case we need to allow for this effect.

As stated in any Structural Engineering books, also the AS 4100 differentiate between two different types of second-order effects. We have:

PΔ effects, which arise from the joint displacement Δ;

Pδ effects, which arise from the member deflections δ from the straight lines joining the member’s ends.

The following picture gives idea of a PΔ effect:

PDelta-1 Onorio

 The following picture, instead, gives idea of a Pδ effect:

PDelta-2 Onorio

Hence, in a first-order analysis we have:

First-order Onorio

In a second-order analysis we have:

Second-order Onorio

These effects shall be taken into account by using either:

a) a first-order elastic analysis with moment amplification in accordance with the Clause 4.4.2, provided the moment amplification factors (δb) or (δs) are not greater than 1.4;


b) a second-order elastic analysis in accordance with Appendix E.

According to the above, it is clear that the second-order effects can be neglected in the following cases:

– triangulated structures which may be assumed to have axial force actions only and which become statically determinate as a result of the assumption of simple construction;

– structures in which there are negligible axial compression forces;

– second-order effects of less than 10%.

When the second-order effects are moderate (less than 40%), they may be allowed for amplifying the bending moments obtained from a first-order elastic analysis. This is in accordance with the Clause 4.4.2 of the Australian Standard. The following cases are identified in the Australian Standard 4100:

  • Moment amplification for a braced member;
  • Moment amplification for a sway member;
    • sway member in rectangular frames;
    • sway member in non-rectangular frames.

The amplification factors δ used are based on estimates of the relative magnitudes of the design loads on the element compared to elastic buckling loads.

The moment amplification method is often conservative and is unreliable for frames with higher second-order effects. The Australian Standard requires that in this latter case a second-order elastic analysis method should be used, as per Appendix E.


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Eng. Onorio Francesco Salvatore

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