Example 8: Reinforcement design for both Ultimate and Serviceability Limit States

Data for Cross Section Analysis & Design application

In this example, we will perform a reinforcement design for both Ultimate and Serviceability Limit States (ULS and SLS). Such procedure is very common when designing reinforced concrete beams, since both requirements, regarding ultimate strength and cracking due to service loads should be checked.

Cross Section Analysis & Design can easily handle similar cases by modifying the default Analysis Parameters sets ULS and SLS. If more design situations should be considered, we can create new Analysis Parameters sets.

We will start from the file created in Example 7. So materials and section geometry will not change.

The additional design data are as follows:

Concrete and Reinforcement data

Ultimate Limit State (ULS)

Serviceability Limit State (SLS)

Stress/Strain distribution of concrete

Compressive part

Rectangular according to ACI 318

Parabolic-Constant

Tensile part

Ignored (no tensile strength)

Yes (consider tensile resistance)

Reinforcement stress limits

No limits (use full strength)

Reduce tensile strength to 220 MPa to limit crack width

 

Load cases

Moreover, the reinforcement design procedure will take place for the following loads:

Ultimate loads (ULS)

lc 1-ULS

N = 0

My = -140 kNm

Mz = 0

lc 2-ULS

N = 0

My = 55 kNm

Mz = 0

lc 3-ULS

N = -10 kN

My = -44 kNm

Mz = 0

Service loads (SLS)

lc 1-SLS

N = 0

My = 49 kNm

Mz = 0

lc 2-SLS

N = -3 kN

My = 24 kNm

Mz = 0

 

Solution with Cross Section Analysis & Design

Opening a file from disk

First of all we click on the File menu and select Open in order to open the file we created in Example 7.

Unlock the model

Afterwards, if the model is locked, we click on Edit -> Unlock model, in order to modify the geometry of the cross section.

Unlocking model

In the popup window, we choose Yes to unlock the model.

Unlock confirmation

Review of Analysis Parameters

We need to modify the Analysis Parameters sets “ULS” and “SLS” to match with the design data provided above. This can be done by clicking Analysis -> Analysis Parameters.

First of all, we select “ULS” from the list at the top left corner.

Setting rectangular concrete stress block for Ultimate Limit State

We make sure that the compressive stress strain part of concrete is set to “Default rectangular by code for ULS”. Moreover, the “No Tension” should be selected for the tensile part of concrete. The Stress/Strain limits for reinforcement are not changed as shown in picture above.

Next, we select “SLS” from the list at the top left corner.

Setting parabolic-constant concrete stress/strain curve for Serviceability Limit State

According to the given design data, we make sure that a Parabolic-Constant concrete curve has been selected. The tensile part should have the option “Linear and Drop to Zero” selected, in order to consider the tensile resistance of concrete. Finally, we have applied a tensile stress limit for reinforcement equal to 220 MPa.

We notice that the strength reduction factors are in this case equal to 1.0, since the program automatically adjusts them to be compatible to current design situation SLS. On the other hand, the default values by ACI 318 were applied for the ULS case. We click ok to close this form.

Definition of load cases

We click on the Analysis -> Reinforcement design -> Load cases menu item to enter the load cases.

Delete existing load cases

First of all, we select all the rows and click the Remove load case(s) icon to delete them. Afterwards, we enter the load cases and assign the corresponding Analysis Parameters sets, as shown below.

New load cases for reinforcement design

Carry out the analysis

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

Results

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

Reinforcement design results

We note that the load case is adequate and we can see the placed reinforcement sizes.

Notice that the most unfavourable load case is lc1-SLS, which refers to Serviceability Limit State. Although the loads for SLS are smaller than ULS, the reinforcement demand can apparently be greater, since the reinforcement stress was reduced to 220 MPa.

Furthermore, the reinforcement size constraints applied in Example 2 are considered in this design as well.

These can be verified for each load case. For instance for lc1-ULS, the needed reinforcement for rebars 1, 2, 3 and 4 is 0.99 cm2, whereas the reinforcement demand for rebars 5, 6 and 7 is 0.66 cm2. The size constraint is valid since 0.99 cm2 = 1.5 x 0.66 cm2.

 


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