# 3.6.2: AnalyzeThII 🔷

Last updated

Last updated

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]). 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.

The **“AnalyzeThII”**-component features the following input-plugs:

Fig. 3.6.2 shows the same system as in fig. 3.5.1. 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 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.

**"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.