Hmm, depends upon what you are analyzing. However, it usually is tied to the use of 1st and 2nd order differential equations. As such when you have a load applied to a structure, 1st order is shear and 2nd order is bending moment. In wave analysis it is slightly different applying to the primary and secondary waves, or the major driving wave function and the secondary driving wave function.
A first order analysis, as applied to structures, is an analysis which does not consider secondary effects of deformation of the structure. A second order analysis considers primary effects plus secondary effects.
For example, consider a column cantilevered from a fixed base with a vertical load and a horizontal load applied at the top. A first order analysis considers the bending moment resulting from the horizontal force combined with the axial stress resulting from the vertical load. A second order analysis considers the additional bending moment resulting from the eccentricity of axial load due to the sway of the column.
In a simple warehouse building, columns may be subjected to vertical and lateral loads. A first order analysis considers only these loads but does not take into account how the bending moments are modified as a result of horizontal movement. A second order analysis takes that into account.
It is sometimes termed the P-delta effect where P (the axial load) is acting at an eccentricity, delta which adds to the bending moments in the columns. There are a variety of approximate methods for estimating secondary effects, but they can be calculated more precisely by carrying out a first order analysis, then iteratively adding the magnitude of joint deformations to the the joint co-ordinates and re-calculating the revised forces and moments until the results of successive runs are close enough to be accepted.
The analysis of any member with axial load combined with bending must consider second order effects. Axial load produces bending equal to P.Δ where P is axial load and Δ is displacement of the member. This moment must be added to the bending moments of a first order analysis.
Whether it is taken into account by second order analysis or by approximate moment magnifiers is the choice of the designer. When hand calculations were used, moment magnifiers were much easier to apply and were preferred by most practicing engineers. With computer analysis, second order analysis will likely become the norm.
1st and 2nd order analysis
Re: 1st and 2nd order analysis
