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