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This calculator designs a reinforced concrete corbel using strut & tie method. It provides the required main tension steel and horizontal (or vertical) links in the corbel.
📝 This calculator has been designed in accordance with BS EN 1992-1-1: 2004 Eurocode 2 Design of concrete structures - Part 1-1 : General rules and rules for buildings. This code is typically referred to as "EC2".

Calculation

Assumptions

Symbols used in this calculator

Corbel symbols used in this calculator



Inputs

Corbel Properties



h
:500mm​



b
:350​



c
:40mm​



db
:13mm​



dl
:10mm​



Load



FEd
:200kN​



HEd
:50​



ac
:200​



Bearing Plate



t
:25​



b1
:250​



l
:120​



Material Strength



fck
:30​



fyk
:500​



Outputs

Dimension requirement check






d
:453.5​



Remark (i)
:OK!​



Bearing stress check



Actual bearing stress
:6.666666666666667​



Safe bearing stress
:12.672​



Remark (ii)
:OK!​



Concrete strut check

  1. Strut angle, θ


Remark (iii)
:OK! θ = 61 is used.​

  1. 
    
    


z
:379.1158189048094​



Remark (iv)
:OK!​



Main tension steel



F'td
:163.052523431531​



As,main
:375 mm2 or 3-H13​



Horizontal / vertical links

  1. 
    
    


Remark (v)
:Provide horizontal links.​



As,link
:187 mm2 or 2-H10 @ 150 mm​


Explanation

What is a corbel?

A corbel is a structural element provided whenever a horizontal member, such as a beam, is not directly supported by a column.
Concrete column with two corbels supporting beams

EC2 provides a couple different methods for the design of corbels:
  1. Shear approach - EC2 Section 6.2.2(6) or Section 6.2.3(8) - where the applied vertical shear force on the corbel within a certain distance from the column face can be reduced by
    
    for checking against the corbel's concrete shear resistance. See the referenced code clauses for more details.
  2. Strut & tie approach - EC2 Section 5.6.4, Section 6.5 and additional information in Annex J.3 - uses a truss analogy to simplify stress patterns in a concrete member into a triangulated model.
This calculator uses the strut & tie approach.

What is a strut & tie model?

We typically design structural elements based on Euler–Bernoulli beam theory which has the fundamental assumption that plane sections remain plane after bending. Strut & tie is an alternative approach to beam theory, used when non-linear strain distribution exists (e.g. deep beams, at supports). A common rule-of-thumb is to use strut & tie to analyse a concrete element when it's

.
The strut & tie model assumes the stress distribution in a structural element is resolved as a theoretical truss, consisting of a concrete strut in compression and two steel ties in tension formed by the longitudinal and shear reinforcement.
Strut & tie model of a corbel

As per EC2 clause 5.6.4, the forces in the elements of a strut-and-tie model should be determined by maintaining the equilibrium with the applied loads in the ultimate limit state.

How to design a corbel using strut & tie?

As per Annex J.3 of EC2, the corbel is considered as a short cantilever, and hence the strut & tie method is valid, when the distance

.
Strut-and-tie system diagram of a corbel

Considering the diagram above, the ultimate vertical load,

will be resisted by the concrete. The concrete resistance in compression is called a compression strut,

.
The initial tension resistance will be provided by the main steel reinforcement,

, which acts as the horizontal tie. It will be resolved to

when there is a horizontal force

applied, acting at top level of the bearing plate. Moreover, as per EC2 ENV, clause 2.5.3.7.2 - (5), a minimum of

=

should be considered unless special provision is made to limit horizontal forces on the support. The 0.2 factor is taken from coefficient of friction.
The angle of inclination of the strut,

, can be solved by using summation of vertical forces.

Equation of the compression strut,



Equation of the tension ties,

&



Equation of inclination angle of strut,




This calculator considers the following design checks for a corbel using strut & tie methods:

1) Dimension Requirement Check

2) Bearing Stress Check

3) Concrete Strut Check

4) Main Tension Steel Design

5) Horizontal or Vertical Links Design


Also, refer to the toggle below for corbel detailing requirements.

Detailing Requirements

Acknowledgements

This calculation was built in collaboration with Eric Castillo. Learn more.

Related Resources

  1. Concrete Column Design Calculator to AS3600
  2. Concrete Beam Design Calculator to AS3600
  3. RC Rectangular Beam Calculator (IMP) ACI 318-19
Check out our full library of CalcTree templates here!

References

1. Bill Mosley, John Bungey and Ray Hulse, Reinforced Concrete Design to Eurocode 2, Seventh Edition
2. "Strut and tie." The Concrete Centre. https://www.concretecentre.com/Codes/Eurocode-2/Stut-and-Tie.aspx#:~:text=Strut%20and%20tie%20modelling%20(STM,many%20elements%20of%20concrete%20structures. Accessed 28 March 2024.