> For the complete documentation index, see [llms.txt](https://manual.karamba3d.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://manual.karamba3d.com/3-in-depth-component-reference/3.5-algorithms/3.5.2-analyzethii.md).
# 3.6.2: AnalyzeThII
The "Analyze ThII"-component exist for convenience. Second order theory analysis can also be specified per load-case-combination via the ["Load-Case-Combination Settings"-component](/3-in-depth-component-reference/3.2-load/3.2.4-load-case-combinations/3.2.5.3-load-case-combination-settings.md) and calculated by an ["Analyze"-component](/3-in-depth-component-reference/3.5-algorithms/3.5.1-analyze.md).
Section [3.2.5.3](/3-in-depth-component-reference/3.2-load/3.2.4-load-case-combinations/3.2.5.3-load-case-combination-settings.md) contains details regarding second order theory calculations.
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 [\[10\]](/appendix/bibliography.md)). 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 results of 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
{% file src="/files/3yb7XtE96JcgOzg8B5FB" %}
Fig. 3.6.2 shows the same system as in fig. [3.5.1](/3-in-depth-component-reference/3.5-algorithms/3.5.1-analyze.md). 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]$$ due to the effect of the axial compressive load.
The **“AnalyzeThII”**-component features the following input-plugs:
| | |
| ---------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| **"Model"** | Model to be considered |
| **"LCases"** | List of names of load-case or load-case-combination from which to take the normal force $$N^{II}$$ which cause second order theory effects. By default the minimum normal force of all load-cases is considered. The hint in section [Load-Case-Combinations](/3-in-depth-component-reference/3.2-load/3.2.4-load-case-combinations.md) explains how load-cases and load-case-combinations can be excluded from the default list. |
| **"InitialNII"** | The initial value of $$N^{II}$$ can be specified at the element level by using a ModifyElement-component. If **"InitialNII"** is **"True"** these values get used during the first iteration of the ThII-Analysis |
| **"CombiNII"** |
If set to True, the minimum normal force across all load cases is used for each element, resulting in a single stiffness matrix applied to all load cases. This approach can lead to overly conservative results. If set to False, a separate stiffness matrix is computed for each load case based on its corresponding normal force, producing less conservative results but requiring greater computational effort.
|
| **"NoTenNII"** | Tension forces increase a structure’s stiffness. When **NoTenNII** is set to **True**, the value of $$N^{II}$$ is restricted to negative values by default. The upper limit of $$N^{II}$$ can be adjusted to any value via the **niiLt0Limit** parameter in *karamba.ini*. |
| **"NoComNII"** | Compressive forces decrease a structure’s stiffness. For membranes, this can cause wrinkling and thus local buckling. When **NoComNII** is set to **True**, $$N^{II}$$ is restricted to positive values by default. The lower limit of $$N^{II}$$ can be customized via the **niiGt0Limit** parameter in *karamba.ini*. |
| **"RTol"** | The determination of $$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.