# 3.6.2: AnalyzeThII 🔷 Axial forces in beams and in-plane forces in shells influence the structural stiffness. Compressive forces decrease a structure’s stiffness, tensile forces increase it. The influence of compressive forces on displacements and cross section forces may be neglected as long as their absolute value is less than 10% of the buckling load. In Karamba3D distinction is made between normal forces $$N$$ which cause stresses in the members and normal forces $$N^{II}$$ which result in second order effects (see also [\[10\]](https://manual-2.karamba3d.com/appendix/bibliography)). At first sight this concept seems weird. How can there be two kinds of normal forces in the same beam? Well, in reality there can’t. In a computer program it is no problem: stresses get calculated as $$\sigma = N/A$$ and $$N^{II}$$ is used for determining second order effects only. The advantage is, that in the presence of several load-cases one can chose for each element the largest compressive force as $$N^{II}$$. This gives a lower limit for the structure's stiffness. A re-evaluation of the load-cases using these $$N^{II}$$ values leads to a structural response which is too soft. However the different load-cases may then be safely superimposed. Use the **“AnalyzeThII”**-component for automatically determining the normal forces $$N^{II}$$ from cross section forces $$N\_{x} \cdot N ^{II}$$influences a structure's stiffness which in turn impacts the distribution of cross section forces $$N\_x$$. Thus an iterative procedure with repeated updates of $$N^{II}$$-forces needs to be applied. ![Fig 3.6.2: Deflection of simply supported beam under single load in mid-span and axial compressive load](https://442610158-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MCkDlhlZpqUmakSqOrp%2Fsync%2Fa8a9dc77dd10e33980335b9aaea06d2e5eb29f97.png?generation=1595316033682891\&alt=media) Fig. 3.6.2 shows the same system as in fig. [3.5.1](https://manual-2.karamba3d.com/3-in-depth-component-reference/3.5-algorithms/3.5.1-analyze). This time with results according to first and second order theory. When comparing the transverse deflections in load-case two one can see that the maximum deflection increased from $$0.24\[m]$$ to $$0.28\[m]$$ due to the effect of the axial compressive load. The **“AnalyzeThII”**-component features the following input-plugs: | | | | -------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **"Model"** | Model to be considered | | **"LC"** | Number of load-case from which to take the normal force $$N^{II}$$ which cause second order theory effects. If set to −1 (the default) the minimum normal force of all load-cases is considered | | **"RTol"** | The determination of $$N^{II}$$ is an iterative process. The value of **“RTol”** is the upper limit of displacement increments from one iteration to the next. | | **"MaxIter"** | Supply here the maximum number of iterations for determining $$N^{II}$$. The default is 50. In case **“RTol”** can not be reached within the preset number of iterations the component turns orange. | | **"NoTenNII"** | Tension forces increase the stiffness of a structure. Setting **“NoTenNII”** to **“True”** limits $$N^{II}$$ to negative values. | The normal forces $$N^{II}$$ get attached to the model and will be considered in all further analysis steps. They impact the results of the **“Analyze”**-, **“Buckling Modes”**-, **“Natural Vibrations”**- and **“Optimize Cross Sections”**-components. For imperfection loads $$N^{II}$$-forces have a direct impact on the applied loads. Use the **“NII”** button in submenu **“Tags”** of the **“ModelView”**-component to display $$N^{II}$$-forces. {% file src="" %}