We perfer to explain the difference using an example:

- A column loaded with a bending moment M and a point load P needs to be calculated (Figure A =
**intitial****state**). - Using the geometry and supports the reactions M
_{0}and deformation δ_{0}can be calculated (Figure B =**iteration****1**). - You could stop the calculation but because of the deformation δ
_{0}, the load P has an eccentricity (Figure C=**iteration****2**).

Resulting in an additional moment ΔM_{1}. Increasing the total moment M_{1}= M_{0}+ ΔM_{1}.

Resulting in additional deformation Δδ_{1}. Increasing the total deformation δ_{1}= δ_{0}+ Δδ_{1}. - Again you could stop the calculation but because of the additional deformation Δδ
_{1}, the load P has an additional eccentricity (Figure D =**iteration 3**).

Resulting in an additional moment ΔM_{2}. Increasing the total moment M_{2}= M_{1}+ ΔM_{2}.

Resulting in additional deformation Δδ_{2}. Increasing the total deformation δ_{2}= δ_{1}+ Δδ_{2}. - You could continue the calculation and do an additional iteration, but it will almost not affect the final result. Δδ
_{2}has become quite small during iteration 3, that the affect of Δδ_{2}will be neglectable. You stop the calculations

Conclusions:

- The calculation in ‘Iteration 1’ is called a
**first order calculation**.

Equilibrium expressed as function of the**initial geometry**.

If the boundary conditions are adequately defined,**a solution will always be found**.

Because of the simplicity, this type of calculation is used in**hand calculations**. - The calculation from ‘Iteration 1’ to ‘Iteration 3) is called
**a second order calculation**.

Equilibrium expressed as function of the**a priori unknown deformation state.**Results in larger internal forces and additional deformations relative to a 1st order calculation. The additional effects are called ‘

**second order effects**’.is no certainty. For some structures the deformations and internal forces will keep increasing until it collapses.

**Convergence**Because of its complexity, this type of calculation is done

**by software.**