### How are load combinations generated with a concomitance matrix?

Software:

Advance DesignModule

GeneralQuestion:

**How are load combinations generated with a concomitance matrix?**Type:

GeneralDifficulty:

****

## Answer

Requirements must be met by resistance, stiffness and ductility when designing a structure, and therefore all relevant design situations must be considered.

Design situations, and implicit load combinations, must be chosen to be sufficiently severe and varied. They must include all conditions that can occur predictably during the analysis and during the post-processing of the structure.

In Advance Design the load combinations can be defined in 3 ways:

- Using the "

**Define**" button through which the user can modify the value of the partial factor for permanent actions (

**ϒ**), as well as the value of the factors for variable actions (

**Ψ**), and then it can generate the load combinations;

- Using the concomitance matrix, which is defined as a table that will generate all necessary load combinations determined by simultaneous concepts between different actions.

In this document we will refer only to the generation of load combinations by using the concomitance matrix. We will consider the steel structure in **Figure 1** and the load combinations in **Table 1**.

**Figure 1.** The analysed structure

Before defining the load combinations, we can set for each family or load case the effect it has in the combinations ("**Favorable**", "**Unfavorable**", "**Favorable or Unfavorable**" for permanent actions and "**Base**", "**Support**", "**Base or Support**" for variable actions), partial factor for permanent actions (ϒ) and factors for variable actions (Ψ_{0}, Ψ_{1}, Ψ_{2}). This can be done in the "**Combinations**" section from the properties window of the family (**Figure 2**) or of the load case.

**Figure 2.** Properties window for the family of load cases

For the analyzed case, the permanent loads (G1, G4) have an unfavorable effect. For variable loads (Q2, Q3) Category A is considered and the effect is as follows: "Base or Support" for Q2, "Support" for Q3, Advance Design automatically displays the corresponding coefficients. For the family of climatic loads, Snw5, we consider a "Base or Support" effect.

To define the load combinations we need to access the "Combinations" window (from the Menu select Assumptions - Define combinations).

Click the "**Concomitance**" button (**Figure 3**) in order to see the concomitance matrix.

**Figure 3.** The window of defining the load combinations

By default, the concomitance matrix will be generated by using the predefined rules. The values that can be used inside this matrix are: "0", "1" and "2". The significance of the numbers is explained below:

**2**" Load case on a white background (line)

__must be combined__with the load case from the column;

"

**1**" Load case on a white background (line)

__can be combined__with the load case from the column;

"

**0**" Load case on a white background (line)

__cannot be combined__with the load case from the column.

**Figure 4** presents the concomitance matrix for the load cases presented in **Table 1**.

**Figure 4.** Concomitance matrix

**Note:** The number of lines and the number of columns in concomitance matrix is unlimited.

Rules for exclusion or forced combination between different load cases or families of load cases can be defined (**Figure 5**).

**Figure 5.** Setting the concomitance rules and generating the load combinations

By clicking the "**Generate**" button we obtain the load combinations corresponding to the previously set concomitance matrix. The load combinations are detailed in **Table 2**.