Example 5: Control of concrete cracking: Estimation of the stress at reinforcement (Serviceability Limit State)

Data for Cross Section Analysis & Design application

We will extend the file created in Example 2 in order to calculate the stress at each rebar under the loads defined below.

As many regulations propose, the effect of cracking can be controlled by considering a reduced reinforcement stress which is specified by other parameters, such as allowable crack width, rebar diameters, rebar spacing etc.

The concrete stress/strain curve is assumed to be linear.

Load cases

 

lc 1:

N = 0

My = -120 kNm

Mz = 0

lc 2:

N = 0

My = 37 kNm

Mz = 0

lc 3:

N = 20 kN

My = -54 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 2.


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 specify the corresponding Analysis Parameters set by clicking Analysis -> Analysis Parameters. We will use the default “SLS” set. The concrete stress block is linear and the corresponding strain values are defined according to ACI 318. Strength reduction factors φ do not need to be changed since we are performing an analysis in Serviceability Limit State (stress calculation). The concrete tensile strength is ignored. You can override these values by modifying any of the fields of the form.

Analysis parameters for Serviceability Limit State

Definition of load cases

We click on the Analysis -> Deformed configuration -> Load cases menu item and next on the Add load case button in order to insert a new load case under the name “lc 1”. Afterwards we fill the values for loads and make sure that the “SLS” Analysis Parameters set is enabled. We can create the remaining load cases lc 2 and lc 3 likewise.

Load cases for deformed configuration analysis

We click OK to close the form.

Carry out the analysis

We just click Analysis -> Deformed configuration -> Analyze, to perform the analysis.

Results

The results can be obtained from the Analysis -> Deformed configuration -> Show results menu item.

On this form, we choose the “lc 1” load case at the top left corner, in order to view the results related to the first defined load case.

The following data can be found on this form.

  • Neutral axis location
  • Strain distribution
  • Equivalent force couple
  • Stress contour on the cross section area
  • Reinforcement forces/stresses
  • Stress information per material

Calculated neutral axis, strain distribution, stress contour

As we can see, the maximum stress values at reinfordcement are reported as expected for rebars 1 to 4 (bottom layer reinforement) and have a value of 222.72 MPa.

By the above mentioned way, we can obtain the results for the remaining load cases “lc 2” and “lc 3” by changing the selected load case item at the top left corner of the results form.



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