Mark Free End of Cantilever Beam and its Impact on the Analysis & Design of Cantilever Beam

Mark Free End of Cantilever Beam and its Impact on the Analysis & Design of Cantilever Beam

Introduction

In ProtaStructure, all cantilever beams should be correctly marked, to ensure correct design & detailing. 
During the modelling process, whenever a beam is unsupported at one end, the program will automatically mark it as a cantilever. 
A red triangle will appear at the free end of the cantilever, point towards the support as shown below : 


This cantilever mark can be changed manually by selecting the beam > Right-Click > 3 options will be exposed  : 



This article explains the impact of Mark Free End of Cantilever Beam to the analysis, design & detailing cantilever beams. 

Simple Test Model A & B

Two simple models are created as shown below.  

     

  1. Model A- Cantilever beam with Marked Free End
    1. The marking of cantilever beam is automatic - the free end is automatically marked with red triangle
  2. Model B- Cantilever beam with Unmark Free End
    1. The cantilever beam marking is manually removed by selecting option "Both Ends Supported"

Parameters:

All beams are similar size – 250x500
Dead load – 12kN/m applied to all beams

Model A & B Results Discussion

After successfully analysis, the Analytical Model view can be accessed, showing the following :
  1. Analytical wire frame (blue)
  2. The deflected shape (red)

1. Analysis Results:

 i. Bending Moment Diagram for factored load combination 


From the figure above, the bending moment for model A (marked free end) and model B (unmark free end) is exactly the same.
Hence, Mark Free End of Cantilever Beam option doesn't affect the analysis result at all. 
Since ProtaStructure is based on 3D stiffness analysis, the resultant forces are purely based on member sizes & their connectivity. 

 ii. Deflection for factored load combination 


From the figure above, the deflection for model A (marked free end) and model B (unmark free end) is exactly the same. 
Hence, the Mark Free End of Cantilever Beam doesn’t affect the deflection result.  
Since the member forces are all the same, the deflection is also the same as deflection is directly reflective of the member forces.

2. Design and Detailing

i. Beam Design

Go to Beam Section Design to design the beam. Review the design by going to the Beam Section Design - Rebar Tab



The blue figures at the top are the required steel at each location of the beam based on the design moments. 
From the figures above, there are differences in section design for Model A and Model B.

Model A : 
  1. For Model A, there is only 1 no. of blue design figure at the top support of cantilever beam. 
  2. Hence, the cantilever beam is designed for one zone only which is hogging moment at support.  
  3. The same top bar is extended to the end of the beam. It is assumed to be sufficient along the entire length of the beam.
  4. The deflection ratio is calculated & checked based on cantilever beam limits of the chosen code. 
  5. This confirms that model A cantilever beam is correctly marked. 
Model B : 
  1. There are 6 no. of blue design figures at the left, middle & right (top & bottom).
  2. Hence, this beam is designed for three zones which is similar to a normal beam, supported on both beam ends. 
  3. No deflection ratio calculated because there is no sagging moment along the entire length of beam. 
  4. Deflection check for normal non-cantilever marked beams will only be shown and checked if there is sagging moment along the length of the beam. 
  5. This confirms that model B cantilever beam is wrongly "unmarked" as "both ends supported".

ii. Detail Drawings

Click on detail drawings to review the beam detailing.


For Model A, the top bar 3T12 is extended to the end of the beam. This detailing conforms to normal practice of cantilever beam. 

For Model B, the top bar 3T12 is provided at support zone only and 3T10 is provided at mid and end zone. This detailing conforms to normal beam supported on both ends. 

Hence, "Mark Free End" of cantilever beam will only affect the design and detailing a beam. It does not affect the analysis results, i.e. forces and deflection will be the same.
It is important to correctly mark free end of cantilever beam to ensure correct design and detailing for the cantilever beam. 

Simple Test Model C 

We will now look at a more complicated model.
We will focus on this area where cantilever beams meet. 


1B9 is auto-marked as cantilever as expected. 
When cantilever beam 1B20 & 1B22 meets, the program will auto mark the stiffer beam as cantilever : 
  1. The stiffer beam is with a higher ratio of [Moment of Inertia, I] divided by [Length of beam].
  2. Hence 1B22 is marked as cantilever as it is shorter & stiffer (Moment of Inertia of both beams are the same as the size are the same).
  3. 1B20 cannot be marked as cantilever ( as 1B22 is already marked as cantilever

Analysis and Result

i. Bending Moment Diagram
​



From the figure above, 1B9 behaves like a cantilever beam as expected with hogging moment along its entire length. 

1B20 also behaves like a cantilever with hogging moment along its entire length. However, it cannot be marked as cantilever while modelling as it determined to be less stiff than 1B22. 

1B22 has no hogging moment.  So 1B22 does not behave like a cantilever beam but it incorrectly marked as a cantilever beam.

Why a beam marked as cantilever does not behave like a conventional cantilever?
Protostructure analysis is based on 3D stiffness analysis. The final behavior is purely based on stiffness of members and their connectivity. 
Hence the analysis is not affected by the cantilever marking.

Model C Workaround

Since 1B20 bending moment diagram is more akin to cantilever, for more accurate design it should be treated as cantilever.  This can only be done if 1B22 if not connected to the same node or joint. 
As workaround, we can remodel beam 1B20 using another node by created another axis intersection as shown below:






Since 1B20 & 1B22 are no longer using the same node, 1B20 can now be marked as cantilever.  

Summary

The examples above show the importance of marking cantilever beams correctly.  This is to ensure the design & detailing of the cantilever beams is correct according to the chosen code.
Cantilever beam are automatically marked as the beam is created. The cantilever mark should be checked and modified accordingly, if found to be wrong. 
At times, we have to run the analysis and then check the bending  moment diagrams to determine which beams behaves like a cantilever. After checking, if any beam has been wrongly marked, it should be manually rectified.
If a beam cannot be marked as cantilever (due to another adjoining beam), then create a different joint for the cantilever end of the beam (as discussed above). 






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