Example 1: Reinforcement design of a beam section

Data for Cross Section Analysis & Design application

The bottom required reinforcement of a beam section 25 cm x 60 cm is to be estimated. Top reinforcement is 3ø12. Extra side reinforcement is 2ø12. Top and side reinforcement bars are constant and do not need to be designed.Cross section

Regulation: ACI 318

Concrete (cylinder) strength: 25 MPa

Yield stress of reinforcement steel: 500 MPa

Reinforcement cover to rebar center: 4 cm

Tensile concrete strength is ignored.

Stirrup type: Tied

Frame type: Intermediate

All remaining data (concrete stress block, φ reduction factors, other coefficients etc.) to be taken according to ACI 318.

Load cases

 

lc 1:

N = 0

My = -250 kNm

Mz = 0

lc 2:

N = 0

My = 20 kNm

Mz = 0

lc 3:

N = 15 kN

My = -45 kNm

Mz = 0

lc 4:

N = -7 kN

My = -65 kNm

Mz = 0

 

Solution with Cross Section Analysis & Design

First of all define the corresponding Reinforced Concrete Code, by clicking on the Project -> Reinforced Concrete Code menu item.

Selection of Reinforced Concrete Code

Reinforced concrete code selection

Selection of ACI 318 regulation and definition of Stirrup type (Tied) and Frame type (Ordinary, Intermediate)

Since the examined section does not belong to a column, we can select the “User values” option in the Reinforcement ratio limits box. We set a minimum ratio equal to 1.5‰ and keep the maximum value to 4%. Since the program is intended to handle generic cross sections, you should review the limits for reinforcement ratios, as they can differ depending on the frame elements which the examined section is assigned to. But in case of columns, you can keep the option “Default by code for columns”.

Definition of material properties

Next, we are going to specify the material properties.

Concrete can be specified by selecting Materials -> Concrete

Definition of concrete materials

The Default Concrete material can be overridden by changing its properties, as shown in the form below.

A C25 grade is defined

Value “Concrete strength” has been set equal to 25 MPa. The concrete is not assumed confined and the elasticity modulus is to be calculated according to ACI 318, so we do not need to change anything else. The concrete defined here is now accessible through the name “C25”. Alternatively we could click the “Add new” button in order to define a new concrete material.

The reinforcement can respectively be defined from the Material -> Reinforcement menu item.

S500 reinfoircement grade is defined

We modify the Default Reinforcement material by specifying a new name (S500) and a yield stress of 500 MPa.

Drawing the geometry

We are now ready to draw the geometry of the cross section, by clicking the Draw -> Rectangle using dimensions. The center point of the rectangular section can be inserted by entering its coordinates (0,0) and then clicking the Button to use current value button, or just by clicking on the point (0,0) with the mouse. Then the Length and Width values should be set to 0.25 and 0.60 respectively. Finally, the C25 concrete should be selected for the rectangle we are drawing.

Drawing a rectangle

After we have clicked the “OK” button, the rectangle is shown in the drawing area.

Beam concrete section

Before drawing the rebars, we have to make sure that a proper rebar set is available for the design. This can be checked by selecting Project -> Available Rebars.

Definion of reinforcemt bar sizes

The rebars shown above are available in the project. This means that we can draw rebars of these diameters and additionally the program will only choose from these rebar sizes when performing a reinforcement design.

So, we can now draw the reinforcement bars by clicking on the Draw -> Rebar Line menu item.

We can enter a value (0.04 m) for the reinforcement cover to the rebar center in the field, which becomes active when inserting reinforcement bars, as shown below. The program automatically draws help lines at the specified distance from the concrete rectangle edges and enables mouse snapping at their intersections.

Inerting rebar line

To draw the bottom rebars, we click on both green circles successively.

Bottom face reinforcement of beam section

Start and end point coordinates have been automatically filled in the corresponding form. The remaining properties of the bottom reinforcement can be specified, by selecting a rebar count (4), a material (S500) and a reinforcement size (ø20).

Note: The specified reinforcement (ø20) is not important at this point, since their diameter will be calculated by the program automatically and the required rebar will be assigned to them during the design procedure.

Rebar line properties

After clicking the “OK” button, the lower rebars are shown in the drawing area.

We take the same steps in order to draw the top rebars. After clicking on the top points, we can define the corresponding properties, as below.

Setting constant reinforcement size

Note that the rebar count is now set to 3 and the reinforcement size is ø12. Moreover, the option “Constant size for design” has been selected, so that the rebar sizes will not change during the design. After clicking the “OK” button, we can continue to draw the side reinforcement bars.

Drawing side reinforcement

The rebar count is now set to 2 and both s1, s2 distances to 0.15 m. The option “Constant size for design” is still enabled since we do not want these rebars to be re-dimensioned.

side reinforcement properties

In order to draw the side reinforcement bars on the right, we can take advantage of the replicate option.

First of all, we click on the reinforcement line that has been defined before in order to select it.

Selecting a rebar line

The line appears now thicker with its related dimensions, which informs us that it is selected. In order to replicate it to the right side (16 cm to the right), we click on Edit -> Replicate menu item and on the “Linear” tab enter a dy distance equal to 0.17 m.

Replicating a rebar line

After clicking “OK”, the side reinforcement on the right is shown correctly.

Beam section with rebars

Note that the rebars have automatically been numbered. When referring to specific rebars (for example when reporting the reinforcement forces), these numbers will be used.

Review of Analysis Parameters

We need to specify the corresponding Analysis Parameters set by clicking Analysis -> Analysis Parameters. We will use the default “ULS” set. All parameters related to ACI 318 code can be found in this form. The concrete stress block is rectangular according to ACI 318, the tensile resistance of concrete is ignored and all remaining data have the default values according to the code. You can override these values by modifying any of the fields of the form.

Setting analysis parameters

Definition of load cases

The load cases can be selected by clicking on the Analysis -> Reinforcement design -> Load cases menu item. The 4 load cases can be entered in the corresponding table. A new load case can be inserted by clicking the Add load case button. We make sure that the assigned Analysis Parameters set to each load case is ULS.

Load cases for reinforcement design

Carry out the design

We just click Analysis -> Reinforcement design -> Analyze, to perform the reinforcement design procedure.

The program asks if it should assign the calculated rebars to the existing ones. We click on “Yes”.

Replace existing rebars

Results

The results can be obtained from the Analysis -> Reinforcement design -> Show results menu item.

As we can see, the cross section is adequate and the bottom rebars have been chosen to be ø18. Remaining rebars (top and side reinforcement) did not change (ø12), as we previously checked the “Constant size for design” option. Furthermore, the calculated rebars have been assigned to the reinforcement bars we provided in the beginning.

Note: The program has calculated the required rebar sizes so that the provided reinforcement ratio lies between the limits specified in the Reinforced Concrete Regulation form.

Reinforcement design results



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