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Verified by the CalcTree engineering team on August 12, 2024
This calculator designs a reinforced concrete corbel using strut and tie method. It provides the required main tension steel and horizontal (or vertical) links in the corbel. It uses the strut-and-tie method for corbels provided in Reinforced Concrete Design to Eurocode 2 by J. H. Bungey, R. Hulse, and William Henry Mosley.
All calculations are performed 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
Inputs
Load
FEd
:400 kN
HEd
:{"mathjs":"Unit","value":80,"unit":"kN","fixPrefix":false}
ac
:{"mathjs":"Unit","value":200,"unit":"mm","fixPrefix":false}
Corbel Properties
h
:600 mm
b
:{"mathjs":"Unit","value":350,"unit":"mm","fixPrefix":false}
c
:50 mm
Reinforcement
Main tension bars provided:
db
:20mm
n
:3Preferred link size:
dl
:16mm
Bearing Plate
t
:{"mathjs":"Unit","value":10,"unit":"mm","fixPrefix":false}
b1
:{"mathjs":"Unit","value":350,"unit":"mm","fixPrefix":false}
l
:{"mathjs":"Unit","value":120,"unit":"mm","fixPrefix":false}
Material Properties
Concrete:
fck
:{"mathjs":"Unit","value":30,"unit":"MPa","fixPrefix":false}
αcc
:0.85
γc
:1.5Reinforcement:
fyk
:{"mathjs":"Unit","value":500,"unit":"MPa","fixPrefix":false}
γs
:1.15Outputs
Dimension requirement check
d
:540
Remark (i)
:OK!
Bearing stress check
-
σEd
:9.523809523809524
σRd,max
:12.716
Remark (ii)
:OK!
Concrete strut check
- Strut angle,
θ
:61.194769848646466
Remark (iii)
:OK! θ = 61 is used.-
z
:389.1803992791089
Remark (iv)
:OK!
Main tension steel
-
F'td
:299.9494120427436
As,main prov
:942.4777960769375
As,main req
:690 mm2 or 3-H20
Remark (v)
:OK!
Horizontal / vertical links
- If provide horiz links
ac/h
:0.3333333333333333
Remark (vi)
:Provide horizontal links.
As, per link req
:471.23889803846896
As,link req
:4-H16 @ 75 mmExplanation
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.
EC2 provides a couple different methods for the design of corbels:
- 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.
- Strut and 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 and tie approach.
What is a strut and 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 and 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 and tie to analyse a concrete element when it's
.The strut and 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.
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 and tie?
As per Annex J.3 of EC2, the corbel is considered as a short cantilever, and hence the strut and tie method is valid, when the distance
.
Considering the diagram above, the ultimate vertical load,
will be resolved into a strut and tie triangulated model which has components both resisted by the concrete and the main steel reinforcement. The concrete resistance in compression is called a compression strut
and
is the angle of inclination of the strut. The tension resistance will be provided by the main steel reinforcement which acts as the horizontal tension tie
. The equations for
and
are not explicitly provided in EC2. Design guides and textbooks often provide a detailed procedure of using strut and tie. Explore the toggles below for derivation of the equations and the required design checks, based on textbook Reinforced Concrete Design to Eurocode 2.
Compression strut,
Inclination angle of strut,
Tension tie,
This calculator considers the following design checks for a corbel:
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.
References
- Reinforced Concrete Design to Eurocode 2 by J. H. Bungey, R. Hulse, and William Henry Mosley
- Strut-and-tie Models by The Concrete Centre
Related Resources
- Concrete Column Design Calculator to AS3600
- Concrete Beam Design Calculator to AS3600
- RC Rectangular Beam Calculator (IMP) ACI 318-19
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