# Analysis

Contents

# Deflection check for shells

Deflection check for any kind of plates and walls has been added (except for the fictitious ones), available for load combinations, maximum of load combinations and maximum of laod groups.

## Configuration settings

Shells and bars share the same configuration settings, thus the deflection check is performed for only the selected type(s) of load combinations and/or load groups.

## Checking process

In case of shells the base value of the checking process can be either the deflection or the rotation. Of course, in both cases it requires the comparison of two quantites, a base value and a limit value, node by node.

### Checking based on rotation

*Base value* of rotation is the resultant of the local x' and y' rotations (in the shell's local coordinate system).*Limit value* is defined by the User (1.5° by default), corresponding to the so called deflection regions (see later). It can be different for each type of serviceability limit states.*Utilization* result obtained on the bases of these values is independent on the geometry, supporting system, orientation and rigid body motion of the shell.

### Checking based on deflection

If deflection is used as the base value, the calculation is not that unambiguous neither for base nor for limit value.

#### Deflection limit values

Both *relative* (e.g. L/300) and *absolute* (e.g. 50mm) limit values can be specified. During the calculation, the program will find the relevant one, and use it as the final limit value. While the evaluation of absolute limit is quite straightforward, the relative needs some detailed explanation, because the value of the "L" characteristic length in case of an arbitrary shaped plate is not obvious at all.

*Calculation of relative deflection limit*

For a rectangular plate "L" is usually the shortest span, but for complex polygonal/curved geometry it is highly depend on the supporting system (e.g. a large slab of an office building drawn with one plate in FD). For the general usability of this feature, FEM-Design introduces the concept of *Deflection regions*. These regions are aimed to take into account the supporting structures, which arrangement fundamentally affects the value of the charateristic length. As typical supports of a plate (e.g. columns, walls, etc.) are positioned onto the nodes/lines of the axes, by default every plate is split by the axis system to generate the corresponding deflection regions.

##### Deflection region modification

These regions can be arbitrarly modified by the Define option, or set to default by the exclamation mark. If there are no axes in the model, or a plate has no intersetion with any of the axes, one deflection region is assigned to it. Similarly to the RC shell buckling regions, there are some restricitons on them: these regions must not overlap neither to other shells nor to each other, also they must completely fill the region of the shell. After the definition of a new region, the program automatically cuts the parts hanging out of the plate, and fills the empty ones on it.

All deflection region have its own, indvidual checking criteria, characteristic length calculation method, and limit values for the different serviceability limit states.

In this dialog, in the Checking criteria section a Not relevant option is also available besides the Deflection and Rotation based checking. It can be useful when User wants to exclude a region from the checking process: in this case, similarly to the bars, zero utilization is set for the whole region. For the determination of the Characteristic length there are three options: it can be either the shortest/longest edge of the defleciton region or a User defined value (in case of a full circle, the shortest and longest edges are both calculated as the diameter of the circle).

#### Calculation of deflection base value

For the calculation of deflection base value the EC does not give any specification about the elimination of the rigid body motions, in other words how to obtain the actual, pure value of deflection. Imagine that we have a multi storey building, and the aim is to perform the deflection check of the plate located on the top storey. In this case, the use of vertical translational displacement (analysis result) as base value is highly overestimate the actual value of deflection, becasue it contains the compression of all the lower storeys. In order to eliminate this effect, FEM-Design measures the deflections from a *Reference plane*. Each Deflection region has its own reference plane, more precisely it has its own reference plane for each load combination. There are two options for calculation of this plane, both depend on the displacement result.

The first option is the *cantilever mode* (default), when the reference plane is obtained by the shifting of the plane of the deflection region parallel with itself to the node with the smallest positive deflection.

The second option is to manually *select three points* on the deflection region: during the calculation FEM-Design is fitting the reference plane to the displaced position of these points combination by combination.

#### Different deflection direction for plates and walls

It is worth to note that the direction in which the deflection is measured is different for plates and walls. For walls (and vertical plates) it is always the resultant of the global x and y translational displacement, in other words the horizonal displacement (always positive). For horizontal and inclined plates the deflection direction is perpendicular to the plane of the plate, also it has a positive/negative sign according to that its vertical compont points downwards/upwards. Besides the usual utilization result, the calculated value of deflections can be also checked for each load combination, maximum of combinations and maximum of load groups.

# Resultant for Labelled sections

Labelled sections have been supplemented with a new result, the resultant of the internal forces acting along the section line. It is available for Load cases, Construction stages, Load combinations, Maximum of load combinations and Seismic analysis.

#### Conditions for displaying resultant

All the labelled sections are capable to display their resultant for which the following conditions are met:

- the section consist of one straight line
- it has common part with at least one plate or wall.

#### Extra parameters for displaying resultant

These labelled sections have two additional parameters for the calculation of the resultant:

*Base point*is the point where the internal forces are reduced to, in other words the resultant of the internal forces is calulcated at this point. By default, it locates at the middle of the section line, but its position can be arbitrary set on this line from the labelled section's tool window:

*Coordinate system*of the resultant is always taken as the following: the z' axis is taken as the shell's z' axis, the y' axis is parallel with section line, and the x' axis is normal to the line. These conditions allow two possible coordinate systems, which basically differ in their normal direction. Changing between these systems can be done according to the following picture:

#### New result

The resultant of labelled sections is an independent, new result item, only available, if there is at least one labelled section with resultant possibility in the model.

These resultant values are calculated right after the defintion of the labelled section (also during the Load case, Load combination, etc. calculation), thus no extra checking is needed to obtain these results. Creating/modifying/deleting a labelled section does not invalidate them. As these values are obtained from the shell internal forces acting along the section line, their physical direction depends on the normal direction of the section (orientation of the x' axis of the resultant's coordinate system). Let us consider the following example for the representation:

The plate is subjected to pure tension. The direction of the resultant (which consist of one normal force now) depends on the normal direction of the section.

# Von Mises stresses

Von Mises stress result is available for bar elements, similar to sigma x' stress for load case, combination, construction stages, max of combination, max of load groups, max of moving load and moving load influence line calculations.

Detailed result is also available for the above mentioned calculation:

Von Mises stresses can be listed under *Bar, stresses* tables.