# RC design

Contents

- Shear and bending moment reduction for RC bar
- Improved RC bar crack calculation
- Min. and max. reinforcement check in Detailed result of RC bars
- Shear reinforcement design
- RC shell design for crack width
- RC shell fire design
- Improved shear capacity results for RC shells
- Improved default colour settings in RC shell Auto design

## Shear and bending moment reduction for RC bar

Reduction of RC beam internal forces at supports are implemented according to EN1992-1-1 in FEM-Design 22. Reduction zones are generated automatically above columns and walls when *entering RC design* mode, and can be individually deactivated or reactivated manually.

Shear (*T _{z}*) and bending moment (

*M*) applied to the RC design will be reduced in the defined zones according to Eurocode.

_{y}**Properties**

- Size of the reduction zone can be set manually, or – in case of
*Columns*and*Walls*– automatically. - Moment and shear reductions can be activated independently from each other.
- An Eurocode-based moment reduction method can be selected depending on the type of support, rigid or hinged (5.3.2.2(3) or 5.3.2.2(4)).

**Visualization**

The zones appear as thick sections on beam axes at supports according to the following colour code:

: both shear and moment reductions are active for the zone*black*: either shear or moment reduction is active for the zone*orange*: inactive zone*grey*

**Results**

The reduced values of bar internal forces in RC bars are shown and listed in the usual internal force figures and results.

**Detailed result**

Based on EN 1992-1-1: 6.2.1(8), the concrete utilization should be checked considering the unreduced shear force.

**Limitations**

Reduction zones are generated (automatically) on *Beams*, whose y axis lies in the global horizontal plane and *Columns* or *Walls* are connected to it from below. One can manually define reduction zones on *Beams*, whose y axis lies in the global horizontal plane.

## Improved RC bar crack calculation

Previous FEM-Design versions calculate the RC bar crack width for second-order internal forces taking into account geometric imperfection (l_{0}/400) and second-order effects (nominal stiffness/curvature method). According to the Eurocode, the following effects do not have to be considered for *SLS* combinations:

- second order effects (EN 1992-1-1 5.1.4 (1))
- imperfections (EN 1992-1-1 5.2 (3))

Thus, in FEM-Design 22, the crack width calculation is performed with the "original" load combination internal forces. Since the standard does not prescribe the second order ones, FEM-Design chooses the more economical solution.

## Min. and max. reinforcement check in Detailed result of RC bars

From now on, the minimum and maximum reinforcement check is added to the detailed result of the RC bars.

# Improved display of concealed bar properties

From now on, the ID, section and material properties can be displayed for *Concealed bars* in the same way as for regular bars.

# Single reinforcement bar

FEM-Design 22 introduces a brand new feature, which is an option to place a single reinforcement bar into concrete walls and slabs. Single bars are placed on the new object layers (*RC shell, appl. reinf., single, top / bottom*) separately from the other reinforcement types and layers.

**Definition**

Activate the proper bottom or top "single" reinforcement layer, then define the new single surface reinforcement by using one of the following four methods (*Manual design* tool):

*1. By Line > By end points: *Define

*Diameter*of the bar(s),

*Number of bars*,

*Space*and

*Offset*and draw a line that defines the direction of the new reinforcement and finally, select the side of the line, where the bar(s) shall be placed.

*2. By line > By shell edge*: Define

*Diameter*of the bar(s),

*Number of bars*,

*Space, Offset*and

*Overhang*and select the shell edges, along which the single bar(s) shall be placed. The final length of the bar is equal to the length of the edge and the overhang value.

*3. By line > By shell corner*: Define

*Diameter*of the bar(s),

*Number of bars*,

*Space, Offset*and

*Length*and select the shell edges that intersect in one corner, next to which the single bar(s) shall be placed. The single bar(s) will be placed perpendicularly to the angle bisector of the two shell edges.

*4. By rectangle*: Define

*Diameter*of the bar(s),

*Number of bars*,

*Space,*and

*Cover,*and then - in the model space - draw a line for the bar direction and the rectangular area, where the given number of bars will be distributed at equal distances.

*Space*cannot be defined using this input method

**Design**

In the design calculations, single bar reinforcement is transformed into specific surface reinforcement, and added to the other surface reinforcements.

## Shear reinforcement design

Shear capacity calculation and shear reinforcement design of concrete shells according to Eurocode is now available for both *Load combinations* and *Load groups* in the *RC design *module.

### Calculation process

As shear resistance of concrete shells depends on the longitudinal reinforcement, the recommended workflow is to first perform the longitudinal surface reinforcement design, then the shear reinforcement design. Shear checking of concrete shells consist of maximum three different calculations:

**1. Shear capacity of concrete compression strut**

According to EN 1992-1-1: 6.2.3, the shear capacity of concrete compression strut (*v _{Rd,max}*) is determined and compared with the resultant shear force (

*v*). This criterion always needs to be fulfilled for the overall adequacy of the shell. If this shear capacity is not large enough, greater thickness or stronger concrete material should be applied.

_{Ed}*2. Shear capacity without shear reinforcement*

The shear capacity without shear reinforcement (*v _{Rd,c}*), calculated according to EN 1992-1-1: 6.2.2, is based on the shear resistance of the concrete and the longitudinal reinforcement. As Eurocode allows the reduction of the shear forces near the supports (see settings and details at

*Shear control regions*), this shear capacity is checked against the reduced resultant shear force (

*v*). If this criterion is not fulfilled, the application of shear reinforcement is required.

_{Ed,Red}*3. Shear capacity with shear reinforcement*

According to EN 1992-1-1: 6.2.3, the shear capacity with shear reinforcement (*v _{Rd,s}*) is calculated purely on the basis of the applied quantity of shear reinforcement, and similarly to

*v*, it is also compared with the reduced resultant shear force.

_{Rd,c}The *cot(ϴ)* and the equivalent reinforcement quality, which is used to express the quantity of the equivalent applied and missing shear reinforcement can be set at *Calculation parameters*. The *final utilization* is obtained according to the following logic:

- no applied shear reinforcement
*:*

- shear reinforcement is applied
*:*

### Shear control regions

These specific regions are providing extra settings for the shear capacity calculation, and can be used for two special purposes:

*1. Ignore shear check*

In this case, no shear capacity calculation is performed within the region. To specify the extent of this region, a multiplier on the effective depth (*d = 0.9 * h*) of the section can be set. This extension is measured from the physical dimension of the object. For example, in case of a *Column/Wall*, it is measured from the perimeter of the cross-section, in case of a *Point/Line support*, it is measured directly from the centre point/line of the support.

*2. Apply shear reduction*

According to the standard (EN 1992-1-1: 6.2.1 (8)), the shear force diagram can be cut off at *d* distance measured from the face of the support (defined by the perimeter of the *Physical extension*). The *Physical extension* in the dialog is measured in the same way as in the previous case, from the physical dimension of the object.

Upon entering *RC design* mode, automatic *Shear control regions* are generated for RC plates:

- at
*Column*intersection points, - along
*Wall*intersection lines, and - at
*Point*and*Line supports*.

In case of *Columns*, the default setting is *Ignore shear check*, due to the probable punching reinforcement around it. Arbitrary shapes and positions can be created manually with the *Define* command and its sub-tools.

**Comment**

For manual region drawing, the *User coordinate system* (*UCS*) must be placed in the plane of the shell element to be designed.

### Shear reinforcement design

In FEM-Design, shear reinforcement is implemented as shear links defined by diameter, steel quality and spacing in two directions (*x’* and *y’* direction of longitudinal reinforcement). There is no need to select the actual type of reinforcement in the program (shear dowel, stirrup, U-shaped, etc.), as it does not affect the calculation.

Shear reinforcement can be created manually (*Manual design*) and automatically (*Auto design*).

#### Manual design

The manual definition of shear reinforcement is very similar to the definition of longitudinal bars: the program assigns the drawn region to the RC shell(s) with the parameters set in the default settings. The specific value of the applied area is also displayed in the tool window, calculated with the current diameter and two-directional spacing.

#### Auto design

The *Auto design* method first calculates the amount of missing shear reinforcement, which is basically checking whether the shear capacity without shear reinforcement is sufficient to withstand the reduced shear forces or not. If yes, the design stops, otherwise the program generates shear reinforcement region(s) on the shell based on the design parameter settings.

**Design parameters**

At *Shear reinforcement*, in addition to the quality and applicable diameters, it is possible to decide whether to use the same diameter for the entire shell (even in the case of multiple applied shear reinforcement regions), or to find the optimal (smallest) one for each region.

At *Spacing*, one can choose from three options:

*Base net: bottom space**Base net: top space**User defined values*

The *Base net* refers to the spacing of the longitudinal reinforcement in the *x’* and *y’* directions (set in the design parameter of the *Surface reinforcement: longitudinal*).

At *Design approach*, just as with longitudinal reinforcement, three design strategies are available, depending on the priorities of geometric simplicity and the amount of the applied reinforcement.

### Results

The following results are available in the model space:

*Utilization*: full shear capacity utilization, based on the formulas defined at*Calculation process*section

*Design forces*:*v*: resultant shear force_{Ed}*v*: the reduced value of the resultant shear force, if the node is in a shear reduction region, otherwise_{Ed,Red}*v*_{Ed}

*Reinforcement**Applied*: the specific value of the applied shear reinforcement*Missing*: the specific value of the missing shear reinforcement, if the shear capacity is insufficient without shear reinforcement, otherwise it is zero

- Shear
*capacity**v*: shear resistance of concrete compression bars_{Rd,Max}*v*: shear resistance without shear reinforcement_{Rd,c}*v*: shear resistance with shear reinforcement_{Rd,s}

*Utilizations**v*: 100 *_{Rd,Max}*v*_{Ed}/ v_{Rd,Max}*v*: 100 *_{Rd,c}*v*_{Ed,Red }/ v_{Rd,c}*v*: 100 *_{Rd,s}*v*_{Ed,Red}/ v_{Rd,s}

**Note: **

In the *Check > Utilization* table, the *v _{Rd,c}* column contains only the maximum of nodes where either there is no shear reinforcement or the utilization for

*v*is lower than that for

_{Rd,c}*v*.

_{Rd,s}**Detailed results**

The *Detailed result* refers to a certain point of the shell (*Result points*) that can be selected/re-selected in the tool window of the detailed result of the RC shell. As calculation input, it includes the shell *Geometry*, *Concrete* material, *Applied* and *Equivalent* *reinforcement*, *Internal and design forces* of the selected point.

As a result, the program details the calculation of the concrete compression strut and the shear capacity with and without reinforcement (including missing reinforcement, if relevant). The final *Utilization* table shows the individual and overall utilizations (the latter is based on the formula defined at *Calculation Process*).

## RC shell design for crack width

It is now possible to automatically design the reinforcement of RC shells for crack width. This process is performed by iterative placing new reinforcement regions around cracks that exceed the crack width limit.

**Note**

Due to the principle of this solution, in case one is aiming for minimizing the usage of steel, in many cases, it will not be the most economical result. Better result can then be achieved by modifying the existing reinforcement regions (*Manual design*).

The iterative calculation can sometimes be time-consuming. By default, therefore, the consideration of *Crack width* is inactive. It can be activated with the *Design by increasing the amount of reinforcement* option and the calculation can be influenced with the following parameters:

*Convergence rate*: In case of a high convergence speed (*Convergence rate*), there is a greater chance of generating more additional bars than necessary, but the results will be ready faster, with fewer iterations. A low convergence rate increases the chance of generating a smaller amount of additional bars, but one can expect a longer calculation time, requiring more iterations.*Maximum allowed iteration number:*If the*Maximum allowed iteration number*is not sufficient, a warning will be sent and there will be places where the RC shell will not be suitable for the crack width design. In this case, increasing the*Convergence rate*and/or increasing the*Maximum allowed iteration number*can be a solution.

From now on, there are four different types of applied reinforcement regions:

*Manual**Auto - base net**Auto - additional**Auto - crack width*

This information can be seen in the tooltip of the region:

**Comments**

- Applied reinforcement regions loaded from previous FEM-Design versions will be considered as
*Auto - additional*type. - In case of editing or modification of the properties of any automatic reinforcement region, it is changed to the
*Manual*category.

## RC shell fire design

Eurocode offers three design methods for calculating reinforced concrete elements in case of fire: “tabulated data”, “simple calculation models” and “advanced calculation models”.

Since the applicability of “tabular data” is very limited, and the standard basically lacks guidance for “advanced calculation models”, FEM-Design 22 uses the methods of “simple calculation models” - namely the “500°C isotherm” and “Zone” methods for fire design of reinforced concrete slabs and walls.

### Concept

The implementation concept follows that one used for RC bars fire design (introduced in FEM-Design 20). For concrete elements, the standard approach in fire design is that at the end of the fire duration, it must be checked whether the damaged element still has sufficient load-bearing capacity, taking into account the reduction in thickness and material parameters.

The *Calculation parameters* of concrete shells have been expanded with the *Fire* tab to specify the fire effect and the fire protection settings.

### Temperature distribution

The essence of the design is to determine the temperature distribution of the cross-section, and based on this, we obtain the reduced thickness and material properties. During this preliminary process, a regular design check can be performed to verify the fire condition of the shell. The thermal effects required for temperature analysis are given in EC 1991-1-2 Section 3, which describes the net heat flux through convection and radiation on the fire exposed object surface(s) (based on standard fire curves).

In order to determine the correct temperature distribution in the section, FEM-Design performs a non-linear, transient finite element heat transfer analysis by using explicit time integration scheme. The temperature dependent thermal properties of the structural steel and concrete are taken according to the EN 1992-1-2 & 1994-1-2.

The *Calculation parameters* define the temperature distribution are highlighted in yellow in the previous figure.

Since an explicit solver is used for the numerical calculation, the correct selection of the *Time step* parameter is essential. It affects both the numerical stability of the solver and the accuracy of the solution. Before the solution procedure, FEM-Design calculates the critical time step of the problem (taking into account the initial room temperature) and chooses the smaller one between critical and requested for numerical stability. Since the critical time step can change over time, but its calculation would be extremely time-consuming before each time step, FEM-Design only calculates it at the beginning. Thus, the divergence of the solution may still occur, in which case the calculation is restarted with a smaller time step until a limit value is reached (warning message). For the calculation, the program generates the finite element mesh of the cross-section. In our experience, from an engineering point of view, medium density provides adequate accuracy in most cases.

**Hint**: In general, a higher mesh density leads to a lower critical time step, so the required computation time increases exponentially with a denser mesh.

At *Section exposure*, three types of boundary conditions can be defined on the top and bottom (defined by the local coordinate system) surfaces of the shells: fire, ambient and insulation.

### Calculation methods

To verify the fire resistance, the member analysis approach of Eurocode 1992-1-2 is used, combined with the simplified calculation methods *Zone* and *500°C isotherm*.

Both methods are based on the temperature distribution. A transient heat transfer module calculates the actual temperature distribution within the cross-section, according to set value of *Duration of fire*. It takes into account the temperature dependence of specific heat, density and thermal conductivity.

Both methods reduce the cross-section of the concrete and change the material properties (and the concrete in the case of the *Zone* method) and perform a regular design based on these reduced inputs.

*Zone* method

The standard *Zone* method is more accurate. In reality, since the temperature can be different at every point of the section, the concrete material model can also be different from point to point. This method proposes to take the coldest point along the thickness of the shell (reference temperature) and reduces the dimensions of the original thickness in such a way that this reduced thickness with constant concrete material (based on the reference temperature) is equivalent to its original thickness with variable concrete material. To calculate this damaged part, the thickness is divided into 20 "zones" using formula B.12 for *Plates* and formula B.13 for *Walls* (Annex B). Based on the temperature distribution, the reduced concrete and steel material models are used. The concrete reference temperature is the coldest point in the cross-section used to evaluate the reduction factor(s) for the room temperature properties. Since the required reinforcement calculation is based on the rectangular concrete material model, a modified version of the standard's proposed material model is used. First, similar to RC bars, the landing branch is not considered (on the safe side). Second, the parabolic reduced material model is transformed into a rectangular one in such a way that the area, the maximum strain (*ε _{c1,ϴ}*) and the reduced compressive strength (

*f*) remain unchanged.

_{c,ϴ}In the case of reinforcing steel bars, the reduced material model of the standard must also be transformed (preserving its original area, ultimate strain, reduced yield strength), in this case to a linearly elastic perfectly plastic one, to ensure compatibility.

*500°C isotherm* method

The basic idea of the *500°C isotherm* method is that damaged parts, which are greater than 500°C, are removed along the thickness and the rest (so-called reduced thickness) can be modelled with the original (room temperature) concrete properties (except for the design values, which are also calculated with the safety factor for fire). Therefore, it is very important that the concrete material model is not temperature dependent. Both methods use the same reduced material model to model the rebar.

According to Annex D of EN 1992-1-2, shear failure is very rare in fire situations, and the calculation methods in this Annex are not fully proven.

Since the standard does not directly support the calculation of shell buckling, it is optional and can be controlled with the *Check fire resistance against shell buckling* option. At room temperature, the shell buckling is converted to an RC beam/column calculation, considering second-order effects. In the event of a fire, the substitute bar is produced from the reduced thickness according to the selected design method. However, since the fire design of RC bars uses the standard's parabolically reduced material models (for both concrete and rebar), these models are also used to calculate shell buckling in fire.

### Design

Both checking and auto-design for fire are available for *Load combinations* and *Load groups*. In case of *Load combinations*, the check/design is applied for accidental combinations that include a *Load case* of type *+Fire*. For *Load groups*, an *accidental* *Load group* is required with a *+Fire Load case*.

### Results

In the model space, the different RC shell results (*Utilization*, *Required reinforcement*, *Missing reinforcement*, *Shear capacity* and *Shell buckling*) represent the fire results of accidental fire combinations. *Detailed results* for RC shells have been expanded to include *Temperature distribution* and *Reduced section* for fire combinations and maximum results where fire combinations are relevant.

In the *Concrete* section, the original (room temperature) calculation/strength parameters are expanded with the “*Reduced*” ones, if relevant.

The chapters *Applied reinforcement* and *Equivalent reinforcement* contain the original and/or reduced parameters of the reinforcement, depending on the relevancy in further calculations.

The chapters *Minimum reinforcement*, *Maximum reinforcement*, *Required reinforcement*, *Interaction curve* and *Shell buckling* apply the reduced section and material properties in fire combinations.

## Improved shear capacity results for RC shells

According to EN 1992-1-1 6.2.1 (6), RC shells both with, and without shear reinforcement, should be checked against *V _{Rd,max}*

_{ }(6.2.3 (3)).

The previous shear capacity calculation has been supplemented with this, and also shown in the detailed results. The *ν _{1}* and

*α*values must be given according to the individual annexes.

_{cw}## Improved default colour settings in RC shell Auto design

From now on, by default, all applied reinforcement is displayed in different colors by type and direction. Of course, different colouring can be specified by position.