CorbelsPrepared By: Ahmed Osama KhattabSupervised By: Dr. Abdel Wahab El-
Ghandour
Introduction
In architecture a corbel (or console) is a piece of stone jutting out of a wall to carry any weight. A piece of timber projecting in the same way was called a "tassel" or a "bragger".
The technique of corbelling, where rows of corbels deeply keyed inside a wall support a projecting wall or parapet
Introduction
Introduction
In Structural Engineering, a corbel is a cantilever protrusion that has a length to depth ratio below unity.
Structural Usage
• Used mainly to carry precast concrete members (design in BS is described under the precast concrete section)
• Supporting steel sections
• Forming real hinges when necessary
• To provide support for members slightly off the columns (e.g. Our Building)
Behavior
• Differs from cantilever due to high depth to length ratio
• Behaves more like a two dimensional element than a linear element
• Shear cracks are steeper (assumed along the column face)
• Can be demonstrated using the Strut and Tie Model
SAP 2000 Model
• To analyse the two dimensional behaviour of a corbel, a vertical slab supported from one side is loaded under different conditions.
• What straining actions are we interested in?
FMax or FMin, Check: show Fmax and Fmin as arrows
SAP 2000 Model
SAP: a/d=0.5
SAP: a/d=1
SAP: a/d=1.5
SAP: a/d=3.5
Methods of Analysis and DesignWe will cover:
• Traditional– ECP– ACI– BS
• Strut and Tie
Failure Modes
Bearing Failure or tension failure may also occur
Failure Modes
Experimental and numerical cracks
Failure Modes
Experimental and numerical cracks
Failure Modes - Shear
Traditional shear failure (cracks at 45o will not occur), different mechanics will act, a different theory will be applied to resist shear
Shear Friction Theory
• Concrete resistance to shear is completely neglected
• Shear resistance is provided only by friction generated from bearing between the two faces
• Steel required to generate the friction can be used to resist flexure, but tension reinforcement should be provided separately
Shear Friction Theory
Shear Requirements
Concrete dimensions:
Usually the governing constraint that determines the final dimensions and is such that:
ECP:
ACI:
Shear Requirements
Concrete dimensions:
Usually the governing constraint that determines the final dimensions and is such that:
BS: < 5 MPa
This value can be increased by 2(d/a) due to the forced steep angle of shear failure, however most designers prefer not to do this.
Shear Requirements
Concrete dimensions:
Note: When comparing the above values to qmax we find that they are generally larger
The value used for BS is qmax
Shear Requirements
Reinforcement:
BS:
Half the reinforcement needed for flexure is placed as horizontal closed stirrups, and distributed evenly along the upper two-thirds of the effective depth.
Shear Requirements
Reinforcement:ACI and ECP:Required total shear reinforcement is calculated as:
ACI drops the second term (more logic)
The reinforcement is then distributed as follows:
Shear Requirements
Reinforcement:
2/3 of the Asf will be placed with the top main reinforcement (tension reinforcement calculated separately)
The remaining 1/3 will be placed as horizontal stirrups along the upper (2/3)d of the corbel
Shear Requirements
Reinforcement:
However if Af is greater than 2/3 Asf then the BS criteria will apply, or simply follow the following table:
Shear Requirements
Reinforcement:
To compare the μf values of ECP and ACI:
ECP ACI Condition
1.2 1.4 Monolithic
0.8 1 Roughened > 5mm (0.25” ACI)
0.5 - Roughened < 5mm
- 0.6 Un-roughened
Shear Requirements
PCA Quote:An upper limit of unity for a/d is set forth for two reasons:
First, for shear span to-depth ratios exceeding unity, the diagonal tension cracks are less steeply inclined and the use of horizontal stirrups alone as specified in 11.9.4 is not appropriate
Second, this method of design has only been validated experimentally for a/d of unity or less
An upper limit is provided for Nuc because this method of design has only been validated experimentally for Nuc less than or equal to Vu including Nuc equal to zero.
Tension Requirements
ECP and ACI specify that a corbel must be designed to carry a minimum normal tension load equal to (0.2Qu )that should be treated as a live load.
BS specifies (0.5Qu)
Flexure Requirements
ECP procedure states that a corbel can be simplified as a cantilever, Mus can be calculated directly from the statical system and reinforcement calculated using first principles, R-μ curves, or c1–j curves.
Note: Af and An should be calculated separately
Flexure Requirements
ACI and BS use a simplified model of the strut and tie model to design a corbel
Flexure Requirements
BS Designer handbook provides curves to avoid trial ad error
Flexure Requirements
Main Steel Minimum Reinforcement:
ECP:
ACI:
BS:
Bearing Requirements
From Precast Concrete:
ECP:
ACI:
BS:
Example on ACI
Example on ACI
Example on ACI
Example on ACI
Example on ACI
Example on ACI
Example on ACI
Example on ACI
Comparing Results with BS and ECP (solved on paper)
ECP BS (μmin governs) ACI
383 296 298 As(mm2)
149 104 105 Ah(mm2)
Strut and Tie
An imaginary truss of “struts” and “ties” forms within the concrete body, joined by “nodes”
If a stable, safe truss can exist within the concrete boundaries, the system is safe
Ties are basically the reinforcement steel under tension
Struts are formed in the dimensions needed to carry the loads
Strut and Tie
An imaginary truss of “struts” and “ties” forms within the concrete body, joined by “nodes”
If a stable, safe truss can exist within the concrete boundaries, the system is safe
Ties are basically the reinforcement steel under tension
Struts are formed in the dimensions needed to carry the loads
Example on Strut and Tie
Example on Strut and Tie
Determining the Bearing Plate Dimensions
Example on Strut and Tie
Dimensions chosen for shear constraint and satisfying corbel definition:
Example on Strut and Tie
Creating the Model:
Example on Strut and Tie
Creating the Model:
To determine locations of A,B and C:
• These points lie on ties• Draw the reinforcements• A lies on the lower edge
and the column bar• B lies on the intersection
of the bars• C lies on the resultant line
and the main steel bars
Example on Strut and Tie
Creating the Model:
To determine width of DD’:
• Sum the moments about A
• Form an equation with required force and strut dimensions
• fc=φfcu
• Get ws
• Locate D and join to the other nodes as shown
Example on Strut and Tie
Ties:
For all ties:
Example on Strut and Tie
Nodes and Anchorage:
Only node C needs to be checked (Node D was designed):
wt=3.2”
Must be at least equal to
(SAFE)
Example on Strut and Tie
Struts:
Only node C needs to be checked (Node D was designed):
wt=3.2”
Must be at least equal to
(SAFE)
Reinforcement Details
Example’s method (based on strut and tie anchorage)
Reinforcement Details
ACI and BS
Reinforcement Details
ECP:
Special Cases
Double Corbel
Special Cases
Analysis of Column with the corbel
Special Cases
Corbel with opening
Prestressed Corbel
• Usually carried out after the construction to increase the load capacity for new usage
• Special technique needed for short cables