507 33 Powerpoint-slides DRCS Ch19

5/24/2018 507 33 Powerpoint-slides DRCS Ch19

1/150 Oxford University Press 2013. All rights reserved.

Design of Reinforced

Concrete Structures

N. Subramanian



Chapter 19

Design of Joints



Introduction

In the capacity design of structures, a building is usually envisaged as a

chain and the different components, such as columns, beams, joints,

and walls, as its links.

On the basis of the underlying principle of a chain is as strong as its

weakest link, the overall strength of a building is correlated to the

strength of its weakest component.

If an RC bridge is idealized as a chain, then the piers, deck, and the

knee joints are the links.



Introduction

Fig. 19.1 Capacity design concept (a) Original chain (b) Loaded chain



Introduction

The objective of any design will then be to ensure that the chain (or its

weakest link) does not break when it is pulled with the design force.

In order to ensure this, the designers need to carry out the following:

1. Identify the weakest link

2. Accurately (and conservatively) evaluate the strength of the

weakest link

3. Know with reasonable certainty the higher-bound value of the

design force with which the chain will be pulled



Introduction

If the ductile link is the weak one (i.e., its capacity to take the load is

less), then the chain will show large final elongation (see Fig. 19.1).

Instead, if the brittle link is the weak one, then the chain will fail

suddenly and show small final elongation.

Joints are crucial zones for the effective transfer of forces and

moments between the connecting elements such as beams and

columns.

When a building is located in a non-seismic zone and designed only for

gravity loads, the design check for joints may not be critical and hence is

not usually attempted.

f



Failure of Beam-column Joints

During Earthquakes

Fig. 19.2 Failure of beam-column joints (a) During the Turkey earthquake (b) During

the 1988 Bihar earthquake



Beam-column Joints

The performance of framed structures not only depends upon the

individual structural elements but also upon the integrity of the joints.

In most of the cases, joints of framed structures are subjected to the

most critical loading under seismic conditions.

The joints should be strong enough to sustain the forces (moments,

axial, and shear forces) generated by the loading and to transfer the

forces from one structural member to another (beams to columns, in

most of the cases) for satisfactory performance of structures under all

the loading conditions, especially under seismic conditions.



Beam-column Joints

Beam-column joint is defined as the portion of the column within the

depth of the deepest beam that frames into the column.

The beam-column joints in a moment resistant frame can be classified

as the following (see Fig. 19.3):

1. Interior joints

2. Exterior joints

3. Corner joints

4. Knee joints



Beam-column Joints

Fig. 19.3 Types of beam-column joints and strength coefficients as per ACI 352-02



Beam-column JointsWhen four beams frame into the vertical faces of a column, the joint is

called an interior joint.

When one beam frames into the vertical face of a column and two

more beams frame into the column in the perpendicular direction, it is

called an exterior joint.

A corner joint is one in which the beams frame into two adjacent

vertical faces of a column.

In a roof joint (also called knee joint), the columns will not extend

above the joint, whereas in a floor joint the columns will extend above

the joint as shown in Fig. 19.3.



Requirements of Beam-column Joints

1. A joint should exhibit a service load performance equal to or greater

than that of the members it joins; that is, the failure should not

occur within the joints.

2. A joint should possess strength not less than the maximum demand

corresponding to the development of the structural plastic hingemechanism of the structure.

3. The joint should respond elastically during moderate earth quakes.

4. The deformation of joints should not significantly increase the storey

drift.

5. The joint configuration should ensure ease of fabrication and good

access for placing and compacting concrete in the joint region.



Design and Detailing of Joints

Some of the incorrect detailing practices adopted by the site engineers

in India are as follows:

(a) incorrect bending of beam reinforcement into the beam-column

joint for anchorage

(b) inadequate anchorage of beam bars into the beam-column joint

(c) poor quality concrete at the critical region of the joint, obviously

due to poor quality formwork coupled with inadequate compaction

(d) kinking of column bars near beam-column joints



Corner Joints

The external joints (corner joints) of a frame can be broadly classified

into opening and closing corners.

The corners that tend to open (increase the included angle when

loaded), as circled in Fig. 19.4, are termed opening corners, whereas

those that tend to decrease the included angle are termed closingcorners.

Opening corners occur at the corners of frames, bottom of water

tanks, and in L-shaped retaining walls.

In bridge abutments, the joint between the wing walls and abutment

will act as an opening joint.



Opening Joints

Fig. 19.4 Examples of opening joints (a) Water tank (b) Retaining

wall (c) Bridge abutment (d) Portal frame



Corner Joints

The elastic distribution of stresses before cracking of an opening

corner knee joint is shown in Fig. 19.5(b). Large tensile stresses occur at

the re-entrant corner and the middle of the joint.

Due to these stresses, cracking will develop as shown in Fig. 19.5(c). If

reinforcements are not provided crossing these cracks, the joint will fail

immediately after the development of the diagonal crack.



Corner Joints

Fig. 19.5 Stresses in an opening joint (a) Stresses at ultimate load (b) Elastic distribution of stresses

(c) Possible cracks (d) Strut-and-tie model


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Oxford University Press 2013. All rights reserved.

Corner Joints

When the internal load path in the form of a truss system is envisaged

and steel provided to carry the tension, with concrete carrying the

compression, the resulting details will have a good chance of working

safely. Such a truss system could be determined using the strut-and-tie

modela possible model for the joint is shown in Fig. 19.5(d).

In the normal detailing adopted for an opening joint (Fig. 19.6a), the

flexural efficiency was found to be about 25 per cent of the strength of

the members meeting at the joint.

The detail shown in Fig. 19.6(g) will develop the required moment

capacity without excessive deformation.


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Opening Joints

Fig. 19.6 Measured efficiency of opening joints (a) Detail ASimple detail (b) Detail B

Loop detail (c) Detail CTwo U hooks (d) Detail DVertical stirrups (e) Detail E

Simple detail (f) Detail F

Cross-diagonal spiral (g) Detail G

With diagonal bar


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Closing Corner Joints

The stresses and behaviour of a closing corner joint are opposite to

those in an opening corner joint (see Fig. 19.7). Hence, a major diagonal

crack is formed on the diagonal of the joint, as shown in Fig. 19.7(b).

In these joints, the top tension bars in the beams have to be bent to a

sufficient radius to anchor them in the column to prevent bearing or

splitting failure inside the bent bars at the corner. The tension steel

should be continuous around the corner.

Knee joints may be subjected to load reversals during wind or seismic

loads and hence require greater care in detailing.


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Closing Corner Joints

Fig. 19.7 Closing corner joint (a) Stresses at ultimate load (b) Cracking pattern


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T-joints

T-joints are encountered in exterior column-beam connections,continuous roof beams over columns, and at the base of retaining walls.

The forces acting at a T-joint are shown in Fig. 19.8(a). The shear force

in the joint gives rise to diagonal cracks, thus requiring stirrups in the

joint.

The detailing of longitudinal reinforcement also significantly affects

the efficiency of the joint. A commonly found detail is shown in Fig.

19.8(b) and an improved detail is shown in Fig. 19.8(c).


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T-joints

Fig. 19.8 T-joints (a) Forces and strut-and-tie model (b) Poor detail (c) Satisfactory detail


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T-joints

As the bars are bent away from the joint core in the detail of Fig.19.8(b), the efficiency was found to be in the range of only 2540 per

cent.

However, the detail of Fig. 19.8(c), where the bars are anchored in thejoint core, showed better performance in tests and had efficiency in the

range of 80100 per cent.

However, it has to be noted that stirrups have to be provided to

confine the concrete core within the joint.


25/150


In the case of T-joints at the base of retaining walls, Nilsson and

Losberg (1976) found that the normal detailing as shown in Fig. 19.9(a)

results in wide corner cracks.

To reduce the crack width, they suggest a detail with an inclined

reinforcement as shown in Fig. 19.9(b).

T-joints


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T-joints

Fig. 19.9 Layout of reinforcement in retaining wall corners (a) Normal

detail (b) Addition of diagonal bar


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Beam-column Joints in Frames

The beam-column joint in a multi-storey frame transfers the loads andmoments at the ends of the beams into the columns.

The forces acting on an interior joint subjected to gravity loading is

shown in Fig. 19.10(a). Here, the tension and compression from thebeam ends and the axial loads from the columns are transmitted

directly through the joint.

For a four-member connection as shown in Fig. 19.10(a), if the twobeam moments are in equilibrium with one another then no additional

reinforcement is required.


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Fig. 19.10 Forces in interior beam-column joints (a) Gravity loading (b) Seismic loading


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In the case of lateral loading like seismic loading, the equilibratingforces from beams and columns, as shown in Fig. 19.10(b), develop

diagonal tensile and compressive stresses within the joint.

Cracks develop perpendicular to the tension diagonalABin the jointand at the faces of the joint where the beams frame into the joint.

As concrete is weak in tension, transverse reinforcements have to be

provided in such a way that they cross the plane of failure to resist thediagonal tensile forces.


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Design of Beam-column Joints

Because the joint block area is smaller relative to the member sizes, itis essential to consider localized stress distribution within the joints.

The principal mechanisms of failure of a beam-column joint are as

follows:

1. Shear failure within the joint

2. Anchorage failure of bars, if anchored within the joint

3. Bond failure of beam or column bars passing through the joint

The joint has to be designed based on the fundamental concept that

failure should not occur within the joint.


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Types of JointsTypical beam-column joints are grouped as Type 1 and Type 2 joints, as

per ACI 352 as follows:

Type 1 joints: These joints have members that are designed to

satisfy strength requirements without significant inelastic

deformation. These are non-seismic joints.

Type 2 joints: These joints have members that are required to

dissipate energy through reversals of deformation into the inelastic

range. These are seismic joints.


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Joint Shear and Anchorage

Joint shear is a critical check and will govern the size of the columns of

moment-resisting frames.

For ductile behaviour, it is assumed that the beams framing into the

column will develop plastic hinges at the ends and develop their

probable moment of resistance at the column faces. This action

determines the demands on the column and the beam-column joint.


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Fig. 19.11 Beam-column joint and frame yielding mechanism


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Hanson and Connor (1967) first suggested a quantitative definition ofRC joint shear, namely that it could be determined from a free body

diagram at mid-height of a joint panel.

Figure 19.12 is a free body diagram of the joint for calculation ofcolumn shear.

It is made by cutting through the beam plastic hinges on both sides of

the column and cutting through the column one-half storey heightabove and below the joint.


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Fig. 19.12 Free body diagram of interior beam-column joint


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For a typical storey, it is sufficiently accurate to assume that the pointof contraflexure is at the mid-height of the column.

Once the column shear, Vcolis found, the design horizontal joint shear

can be obtained by considering the equilibrium of horizontal forcesacting on the free body diagram of the joint shear, as shown in Fig.

19.13.

Assuming the beam to have zero axial load, the flexural compressionforce in the beam on one side of the joint may be taken equal to the

flexural tension force on the same side of the joint.


37/150



Fig. 19.13 Free body diagram of joint shear


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Numerous studies have shown the presence

of a slab to have a significant effect on the

performance of Type 2 connections.

Hence longitudinal reinforcement in the slab

within the effective width should be included

to calculate the joint shear force (ACI 352-02).



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The nominal shear strength of the joint Vn,jshould be at least equal to the required

strength Vu,j.

WhereAejis the effective shear area of the joint =

bjhj, bjis the effective width of the joint, and hjis the

effective depth of the joint, is the strength

reduction factor = 0.85, and is the strength

coefficient.



40/150



The area effective in resisting joint shear may not be as large as the

entire cross-sectional area of the column since the (web) width of beam

and of the column may differ from each other. The codes recommend

effective joint shear area based on engineering judgment.

Concentric and eccentric joints are shown in Fig. 19.14.

ff d h


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Effective Joint Width

Fig. 19.14 Determination of effective joint width (a) Concentric joint (b) Eccentric joint


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Effective Joint Width,bj

i h d h


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The shear strength of the eccentric beam-column connection isreduced by using a smaller effective width if the eccentricity of the

spandrel beam with respect to the column centroid exceeds one-eighth

of the column width.

When beams of different widths frame into opposite sides of the

column in the direction of loading, b should be taken as the average oftwo widths. The average of the beam and column widths usually

governs the effective joint shear width.

D i f Sh R i f


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Design of Shear ReinforcementPaulay, et al. (1978) proposed shear transfer mechanisms of a joint as

shown in Fig. 19.15, referred to as diagonal strut mechanism and trussmechanism.

They assumed that the strength of the diagonal strut controls the joint

strength before cracking.

When the joint shear becomes large, diagonal cracking occurs in the

joint core and the joint reinforcements come into play; finally, the joint

fails by the crushing of the concrete in the joint core.

Both mechanisms are incorporated in the NZS 3101 code.

J i Sh R i M h i


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Joint Shear Resistance Mechanisms

Fig. 19.15 Joint shear resistance mechanisms (a) Concrete strut mechanism (b) Concrete

truss mechanism

D i f Sh R i f


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Design of Shear ReinforcementNZS 3101 requires a large amount of transverse reinforcement in a

joint to resist a dominant part of the joint shear by the trussmechanism, relying on the good bond stress transfer along the

longitudinal reinforcement.

The US codes assume severe bond deterioration of the reinforcingbars in the joint and hence the internal shear forces are resisted only by

the diagonal compressive strut of concrete.

The real behaviour of the structure may be due to the combination ofthe diagonal strut and the truss mechanisms with the bond

deterioration of longitudinal reinforcement to a certain degree during

cyclic loading.

J i C fi d b B


47/150


Joints Confined by Beams

The behaviour of a beam-column joint is influenced by severalvariables, which include concrete strength, arrangement of joint

reinforcement, size and quantity of beam or column reinforcement,

bond between concrete and longitudinal bars in the beam or column,

and axial load in the column.

For Type 1 joints the hoop reinforcement can be omitted when thejoints are confined by beams framing into the sides of the column.

J i t C fi d b B


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Joints Confined by Beams

When such confining beams are not present, ACI 352-02 recommendsthat at least two layers of transverse reinforcement be provided for Type

1 joints, between the top and bottom levels of longitudinal

reinforcement, in the deepest beam framing into the joint.

The primary functions of ties in a tied column are to restrain the

outward buckling of the column longitudinal bars, to improve bondcapacity of column bars, and to provide some confinement to the joint

core.

C fi t R i f t


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Confinement Reinforcement

Confinement of the joint core is intended to maintain the integrity ofjoint concrete, to improve joint concrete toughness, and to reduce the

rate of stiffness and strength deterioration.

For Type 2 joints, when the joint is confined by beams, transverse

reinforcement equal to at least half the confining reinforcement

required at the end of the column should be provided within the depthof the shallowest framing member.

S i f T


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Spacing of Transverse

Reinforcement

C fi t R i f t


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Confinement Reinforcement

When wide beams are used, confining reinforcement should beprovided through the joint to provide confinement for longitudinal

beam reinforcement outside the column core if such confinement is not

provided by a beam framing into the joint.

In the exterior and corner joints, all the 135 hooks of the cross-ties

should be along the outer face of the column.

For best behaviour of the joint, the longitudinal column bars should beuniformly distributed around the perimeter of the column core.

A h f B t J i t


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Anchorage of Bars at Joints

When plastic hinge develops in the beams adjacent to the joint, thetop bars of beams may go into the strain hardening range and yielding

may penetrate into the joint core with simultaneous bond deterioration.

A splitting crack may appear along the bar as shown in Fig. 19.16(a)and the bond stress distribution around the bar will not be uniform.

Column dimensions seldom permit providing the development length

by straight embedment alone; hence, hooks are often required toanchor negative (top) beam reinforcement at the far side of exterior

beam-column joints.

A h f B t J i t


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Fig. 19.16 Anchoring of beam bars in exterior joints (a) Anchorage details (b) Hook

details (c) Location of hoops and headed bars

A h f B t J i t


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If the bottom bars are also required to develop their strength at theface of the joint, they should also be provided with 90 hooks, which

should be turned upwards and extended towards the mid-depth of the

joint.

Hooks should be located within 50 mm of the confined core, as

shown in Fig. 19.16(c).

The development length equation in ACI and NZS codes consider thebeneficial effect of anchoring the bar in the well-confined joint core and

also the adverse effect of the bar being subjected to load reversals

during earthquake.


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Code Provisions for Hooks

Use of Headed Reinforcement


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Use of Headed ReinforcementThe use of hooks in external beam-column

joints often results in steel congestion,difficult fabrication and construction, and

greater potential for poor concrete

placement.

Anchor plates or heads, either welded or threaded to thelongitudinal bar, can be used as an alternative to the use of hooked

bars in exterior beam-column joints.

The use of headed bars offers a potential solution to the problemsposed by hooked bars and may ease fabrication, construction, and

concrete placement.

Beam and Column Bars Passing through


57/150


Beam and Column Bars Passing throughInterior Joint

The uneven distribution of bond stress around a bar may affect thetop beam bars, the underside of which may be embedded in inferior

quality concrete, due to sedimentation.

The following factors influence the bond response of bars at thebeam-column joint:

1. Confinement, transverse to the direction of the embedded bar,

significantly improves bond performance under seismic

conditions.2. The bar diameter has a significant effect on the bond strength in

terms of bond stress.

Beam and Column Bars Passing through


58/150


ea a d Co u a s ass g t ougInterior Joint

3. The bar deformations (i.e., the area of ribs of deformed bars)

improve resistance against slip and increase the bond strength.4. The clear distance between the bars moderately affects the bond

strength.

5. The compression strength of concrete is not a significant

parameter.To limit the slippage of beam and column bars through a joint, ACI

352: 2002 suggests the following limits:

Draft IS 13920 stipulates(Clause 7.1.2):

Beam and Column Bars Passing


59/150


Larger development lengths are highly

desirable, especially when the joint is

subjected to high shear stresses and when the

column-to- beam flexural strength ratio is low.

Larger beam-to-column flexural strength ratios

considerably improve the behaviour ofconnections.

Beam and Column Bars Passing

through Interior Joint

Constructability Issues


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A three-stage procedure for installing the horizontal ties in a beam-column joint is shown in Fig. 19.17 (see next slide):

In stage 1, as shown in Fig. 19.17(a), top bars of the beam are not

placed and horizontal ties in the joint region are stacked up.

In stage 2, top bars of the beam are inserted in the beam stirrups,

and beam reinforcement cage is lowered into the formwork.

In stage 3, ties in the joint region are raised in their final locations

and tied with binding wires, and column ties are continued.



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Fig. 19.17 Three stages of providing horizontal ties in beam-column joints (a) Stage 1

(b) Stage 2 (c) Stage 3



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Multiple layers of longitudinal reinforcement should be avoided

wherever possible, as they make the placement difficult, especially in

exterior beam-column joints.

In this case, as well as in cases where shallow columns are joined with

relatively deep beams, the beam bars may be terminated in an

extended beam stub as shown in Fig. 19.18(a). In this case, ties shouldbe extended into the beam stub to control cracks.



63/150



Fig. 19.18 Measures to improve constructability



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To avoid unfavourable plastic hinge mechanism and to reduce

congestion at beam-column joints, the beam plastic hinge region can be

moved slightly away from the face of the beam-column joint.

This will eliminate the bond deterioration between the beam bars and

the surrounding concrete in the beam-column joint. Moving the beamplastic hinge region can be achieved by detailing the beam as shown in

Figs 19.18(b) and (c).


Beam to beam Joints


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Beam-to-beam Joints

Strut-and-tie models for the flow of forces of interconnected systems

as shown in Fig. 19.19.

The strut-and-tie models of Fig. 19.19 indicate tensile stresses at the

beam-to-beam junction, and hence additional vertical stirrups are to be

provided to support them. Such stirrups are also referred to as hanger

reinforcement orhanger stirrups.

Strut-and-tie Model for Beam-to-beam


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Joints

Fig. 19.19 Strut-and-tie model for beam-to-beam joints (a) System A (b) System B

Beam to beam Joints


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Beam-to-beam Joints

The main reaction from the secondary beam to the girder was foundto be delivered by a diagonal compression strut, as shown in Fig. 19.20,

which tends to apply its thrust near the bottom of the supporting girder.

This inclined compressive force will tend to push the bottom of the

supporting girder/main beam, eventually splitting the concrete at the

bottom of the girder and resulting in the subsequent failure of thegirder.

Beam to beam Joints


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Beam-to-beam Joints

Fig. 19.19 Strut-and-tie model for beam-to-beam joints (a) System A (b) System B

Fig. 19.20 Girder supporting secondary beams (a) System of beams (b) Section through secondary beam

(c) Section XX through the girder

Beam-to-beam Joints


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Beam-to-beam Joints

These compressive forces should be resisted by providing hangerstirrups, which are designed to equilibrate the downward component of

the diagonal compression struts (see Fig. 19.20a).

It has to be noted that the hanger stirrups are to be provided inaddition to the normal girder stirrups required for shear, as shown in

Fig. 19.20.

The transfer of beam reaction into the girder may be visualized usingthe strut-and-tie model, as shown in Fig. 19.20(c).

Beam-to-beam Joints


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Beam-to-beam Joints

The hanger stirrups should be distributed within a zone extending to adistance of half the depth of the relevant beam on each side of the

point of intersection of the beam axes. This zone is referred to as the

transitionor transfer zone (see Fig. 19.21).

The hanger stirrups should be well anchored at the top and the

bottom.

When the beam and girder are of the same depth, the lower layer ofreinforcement in the supported beam can be cranked up at the junction,

so that it is above the lower layer of reinforcement of the supporting

girder.

Location of Hanger Stirrups


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Location of Hanger Stirrups

Fig. 19.21 Location of hanger stirrups (a) As per Canadian code (b) As per Leonhardt and Mnnig

(1977) and Euro code

Beam-to-beam Joints


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Beam-to-beam Joints

When the reaction due to the secondary beam is large, SP 34- 1987

suggests using bent- up bars in addition to hanger stirrups as shown in

Fig. 19.22.

Such reinforcement helps reduce cracking and should be placed within

the transition zone.

Bent-up Hanger Bars


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Bent up Hanger Bars

Fig. 19.22 Bent-up hanger bars

Design of Corbels


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Design of CorbelsCorbelsorbrackets are short stub-like projections from the column or

wall faces (see Fig. 19.23).

The term corbel is generally used to denote cantilevers having shear

span to effective depth ratios less than or equal to 1.0.

They are generally found in the columns of industrial buildings to

support gantry girders, which, in turn, support rails over which overhead

cranes are mounted.

They are extensively used in precast concrete construction to provide

seating for beams; in such cases, corbels are cast integrally with precast

columns.

Typical Corbel


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Typical Corbel

Fig. 19.23 Typical corbel (a) Reinforcement details (b) Strut-and-tie model

Design of Corbels


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Design of Corbels

The principal function of corbels is to support the prefabricated beamand at the same time transmit the reactions to vertical structural

members such as walls or columns.

Corbels are usually provided with a steel-bearing plate or an angle onits top surface, as shown in Fig. 19.23a, to distribute the reaction evenly

and to have uniform contact surface.

A similar bearing plate or angle will be provided in the lower part ofthe supported beam.

Failure Modes of Corbel


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1. Flexural tension failure is the most common mode and results in thecrushing of the concrete at the bottom of the sloping face of the

corbel after extensive yielding of the tension reinforcement.

2. Flexural compression failure results in the crushing of the concretestrut at the base of the corbel before the yielding of the

reinforcement.

3. Diagonal splitting failure leads to sudden splitting along the linefrom the bearing plate to the base of the corbel.



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Fig. 19.24 Failure modes of corbel (a) Diagonal splitting failure (b) Shear failure (c) Direct shear failure

(d) Vertical splitting (too shallow outer face) (d) Shearing of a portion outside the reinforcement



79/150



4. Shearing failure results in a series of short inclined cracks along theweakened plane. Another possibility is the failure in direct shear

along a plane more or less flush with the vertical face of the column.

5. If the reinforcement is not detailed properly, shearing of a portionoutside the reinforcing bars takes place.

6. If the corbel depth is too shallow, the diagonal cracks may intersect

the sloping surface of the corbel.

Design of Corbels


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Design of Corbels

In corbels with proper detailing, all these failure modes tend toconverge into a single failure mode called the beamshear failure.

This failure mode is characterized by the opening of one or morediagonal cracks followed by shear failure in the compression strut.

The behaviour of a corbel may be visualized using the strut-and-tie

model shown in Fig. 19.23(b).

Design of Corbels


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Design of Corbels

The downward reaction is resisted by the vertical component of thediagonal compression strut, which carries the load down into the

column.

The horizontal load is directly resisted by the tension in the bars keptat the top of the corbel; these bars also resist the outward thrust at the

top of the concrete strut.

At the other end of the corbel, the tension in the ties is kept inequilibrium by the horizontal component of the second compression

strut.

Design of Corbels


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Design of Corbels

Fig. 19.25 Anchorage of main reinforcement in corbels (a) Required anchorage (b) Details of welding

main bar to anchor bar

Design of Corbels


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Design of CorbelsThe vertical component of the thrust in the strut acts as a tensile force

acting downwards into the supporting column. The requiredreinforcement to resist the forces as per the strut-and-tie model is

shown in Fig. 19.23(a).

The reinforcement should be anchored by the following:

1. Welding the primary tension reinforcement to the underside of

the bearing plate or angle, especially when corbels are designed

to resist horizontal forces, or welding to a transverse bar of equaldiameter, in which case the bearing area should stop short of the

face of the support by a distance equal to the cover of the

reinforcement (see Fig. 19.25b).

Design of Corbels


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Design of Corbels2. Bending back the bars to form a loop, in which case, the bearing

area of the load should not project beyond the straight portionof the bars forming the main tension reinforcement.

U-shaped bars in a horizontal plane provide effective end hooks for

wide brackets and when loads are not applied close to the edge. It is

also important to provide a 90 hook for anchorage at the other side of

corbel as shown in Fig. 19.25(a).

The closed stirrups with areaAh(see Fig. 19.23a) must be provided to

confine the concrete in the two compression struts and to prevent the

splitting in the direction parallel to the thrust.

The area of flexure and shear reinforcement may be calculated using

Clause 11.8 of ACI code.

Double-headed Studs in Corbels


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Double headed Studs in Corbels

Double-headed studs provide sufficient anchorage when used as topreinforcement in corbels.

The double-headed studs when placed in the compression zone, inthe direction normal to the corbel face, significantly improve the

ductility of the corbel.

For best efficiency the confining studs should be placed at the bottom

face just outside the column corbel interface (see Fig. 19.26).

Double-headed Studs in Corbels


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Double headed Studs in Corbels

Fig. 19.26 Double-headed studs in corbels

Design of Anchors


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Design of Anchors

Anchors (fasteners) are embedded in concrete and used to connectand support structural steel columns, light poles, highway sign

structures, bridge rail, equipment, and many other applications.

They are basically used to connect two elements of a structure andare increasingly used in both retrofit and new constructions.

The type of anchors used in practice may be broadly classified as cast-

in-place anchorsand post-installed anchors.

Cast-in-place Anchors


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Cast in place Anchors

These include the following types:1. Headed hexagonal bolt

2. L-bolt

3. J-bolt

4. Welded headed stud

In the precast concrete industry, precast components are typically

connected by the use of an embedded plate, which is usually anchored

with welded headed studs.

The size of anchors ranges from 16 mm to 60 mm in diameter.



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p

Fig. 19.27 Cast-in-place anchors (a) Headed hexagonal bolt with washer (b) L-bolt

(c) J-bolt (d) Welded headed stud



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Cast-in-place anchors are set in place inside the formwork along with

the steel reinforcement prior to concrete placement.

Anchor groups may be set using a steel or plywood template to ensure

proper geometry and placement. As these preinstalled anchors do not

allow any clearance, they need very accurate positioning.

Cast-in-place anchors are recommended when the applied loads

require large embedment lengths and high tensile strength.

The headed anchors transfer tensile load by mechanical bearing of the

head, nut, or bent portion and possibly by the bond between the anchor

shank and the surrounding concrete.

p

Post-installed Anchors


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Installed in hardened concrete, these are classified as the followingbased on their load transfer mechanisms (see Fig. 19.28):

1. Adhesive anchors

2. Mechanical anchors

Post-installed Anchors


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Fig. 19.28 Post-installed anchors (a) Adhesive or bonded anchor (b) Undercut anchor (c) Torque-

controlled expansion anchorssleeve and stud types (d) Drop-in type displacement-controlled

expansion anchor

Adhesive Anchors


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Adhesive or bonded anchors (Fig. 19.28a) are inserted into hardened

concrete with an anchor hole diameter not greater than 1.5 times theanchor diameter.

These anchors transfer tensile loads to the concrete by the bond

between the anchor and the adhesive as well as the bond between theadhesive and the concrete.

Steel elements for adhesive anchors include threaded rods, deformed

reinforcing bars, or internally threaded steel sleeves with externaldeformations.

Epoxy is the most widely used adhesive.

Mechanical Anchors


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These transfer load by friction or bearing and include expansionanchors and undercut anchors.

Expansion anchors work by the expansion of a wedge or sleeve

mechanism against the surrounding concrete.

Undercut anchors (Fig. 19.28b) are placed in a drilled hole, which is

locally widened at the bottom (called the undercut) using a special

drilling tool. These are then set by projecting elements from the anchoragainst the sides of the undercut portion of the hole, usually by applying

a torque to the anchor.

Mechanical Anchors


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In torque-controlled expansion anchors (Fig. 19.28c), the expansion is

generated by applying a predetermined torque.

In displacement-controlled expansion anchors (Fig. 19.28d), the

expansion is generated when the anchors are driven inside the hole.

Mechanical anchors loaded in tension apply reaction forces to the

concrete at the expansion mechanism, usually near the end of the

embedded part of the anchor.

A grouted anchor is a headed bolt or a threaded rod with a nut at the

embedded end, placed in a drilled hole filled with a pre-mixed grout or a

Portland cementsand grout.

Failure Modes for Anchors underT il L di


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As shown in Fig. 19.29, anchors under tension loading can exhibit fivedifferent types of failures:

1. Steel anchor failure (Fig. 19.29adue to yield and fracture of the

anchor shank)

2. Pull-out or pull-through failure (Fig. 19.29bdue to the

progressive crushing of concrete over the anchor head)

3. Concrete breakout (Fig. 19.29c, where a cone-shaped concrete

failure surface propagates from the head of the anchor; this is

usually the most critical failure mode)

Tensile Loading

Failure Modes for Anchors underTensile Loading


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Tensile Loading

Fig. 19.29 Failure modes for anchors under tensile loading (a) Steel failure (b) Pull-out

(c) Concrete breakout (d) Concrete splitting (e) Side-face blowout (f) Bonded anchors

Failure Modes for Anchors underTensile Loading


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4. Concrete splitting (Fig. 19.29d, which is characterized by theformation of cracks vertically along the length of the anchor)

5. Side-face blowout (Fig. 19.29e, which involves the side-face

blowing out of concrete surface adjacent to the anchor head;studs cannot be closer to an edge than 40% of the effective

height of the studs)

Failures in bonded anchors may occur due to pull-out of a cone ofconcrete, slip out of the hole, or steel failure (see Fig. 19.29f).

Tensile Loading

Code Provisions for Design


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gThere are no provisions for the design of anchors in IS 456.

In the early 1970s, formal design concepts for headed-stud anchors

were introduced in the Precast/Prestressed Concrete Institutes (PCI) PCI

Design Handbook (1971).

ACI 349-90 used a 45 cone breakout model for determining the

concrete breakout strength.

This method assumed a constant tensile stress of fc/3 acting on theprojected area of a 45 cone radiating towards the free surface from the

bearing edge of the anchor (see Fig. 19.30).

Concrete Breakout Bodies


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Fig. 19.30 Concrete breakout bodies according to ACI 349 (a) Tensile loading (b) Shear loading

Code Provisions for Design


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The kmethod suggested a truncated pyramid failure model (with a

35 slope of failure cone), which was incorporated in the Eurocode.

This corresponds to the widespread observation that the horizontal

extent of the failure surface is about three times the effectiveembedment depth (see Fig. 19.31).

Additional refinement of the Kappa method at the University of Texas,

Austin, to make it user friendly, resulted in the CCD approach tofastenings in concrete, based on the 35 truncated pyramid failure

model.

Concrete Breakout Failure


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Fig. 19.31 Concrete breakout failure under tensile loading according to ACI 318

(a) Tensile loading on anchor (b) Assumed truncated pyramidal concrete breakout

Steel Strength of Anchor in Tension


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In the ACI 318 code, design equations are presented to check the

following different failure modes:

1. Steel capacity (tension and shear)

2. Concrete breakout capacity (tension and shear)

3. Pull-out strength and side-face blowout strength (only in tensionand cast-in-place anchor)

4. Concrete pryout strength (only in shear)

5. Bond strength (only for adhesive anchor)

The designer should aim to achieve steel failure as it will be ductile

and will provide sufficient warning before failure.

Concrete Breakout Strength of


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Anchor in Tension

As per ACI 318, the nominal concrete breakoutstrength of a single anchor in tension in

cracked concrete, Nno

ais the factor for lightweight concrete

hef is the effective embedment depth kc= 7 for post-installed anchors and as 10 for

cast-in-situ headed studs /bolts



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Nominal concrete capacity considering edgeand spacing of anchors is:

For a group of anchors:

ANis the projected concrete failure area(see

next slide),Ano= , and iare the

modification factors

Anchor in Tension


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Fig. 19.32 Projected areas for single and group of anchors (a) Single anchor (b) Group of anchors

Modification factor for


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Eccentrically Loaded Anchors

1is modification factor for anchor groupsloaded eccentrically in tension

Fig. 19.33 Definition of e'Nfor a group of anchors (a) All anchors are in tension, (b)

Only a few anchors are in tension

Modification factor for Edge Effects


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Modification factor for edge effects

Modification factor 4(applicable to post

installed anchors only)

Modification factor for Edge Effects

Critical and Minimum Edge


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Distances

IF there is no cracking at service load levels, then themodification factor,

Pull-out Strength in Tension


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Pull-out capacity is dictated by a failure of the concrete around the

head of the anchor.

When the bearing area of the head is small, crushing of concrete

occurs at the head and the anchor can pull-out and crush the concretewithout forming a concrete breakout cone (see Fig. 19.29b).

Local crushing under the head of the anchor significantly reduces the

stiffness of the anchor connection and increases displacement.

Abrgis the net bearing area of the head of anchor bolt, p = 1.4 (nocracking) p = 1.0 (there will be cracking)

Concrete Side-face Blowout


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Concrete Side face Blowout

For a single headed anchor with deepembedment close to an edge (hef> 2.5 c1), the

nominal side-face blow out strength

For multiple headed anchor with (c1< 0.4 hef),

and anchor spacing < 6c1, the nominal side-

face blow out strength

Failure Modes in Shear Loading


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In the case of shear loading with large edge distance, the mode of

failure of anchors will normally be by steel fracture as shown in Fig.

19.34(a) preceded by spalling of concrete.

Fastening with short anchors may fail by prying out a concrete cone on

the side opposite to the load application as shown in Fig. 19.34(b).

Concrete breakout failures may be due to concrete spalling and lateral

cone or edge failures as shown in Fig. 19.34(c).

As with tension loading, the failure load will be influenced by the

concrete tensile capacity, side cover, flexural stiffness of the anchor

shaft, and embedment depth.

Failure Modes in Shear Loading


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Fig. 19.34 Failure modes for anchors under shear loading (a) Steel

failure (b) Concrete pryout failure (c) Concrete breakout failure

Concrete Breakout Strength ofAnchor in Shear


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Anchor in Shear

Calculations for the basic concrete breakout capacity in shear of an

individual anchor in cracked concrete are given in Page 768 of the book.

Projected area for single and group of anchors under shear loading is

shown in Fig. 19.34.

Fig. 19.35 shows multiple fastening with cast in situ headed studs

close to edge under eccentric shear loading.

The modification factor for edge effects for single anchor or anchor

groups loaded in shear is shown in Fig. 19.36.


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Fig. 19.35 Projected area for single and group of anchors under shear loading (a) Single anchor

(b) Group of anchors

Steel Strength of Anchor in Shear


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Steel Strength of Anchor in Shear

The nominal steel strength of an anchor inshear(cast-in headed stud anchor)

WhereAse,Vis the effective cross-sectional area of ananchor in shear (mm2), andfutais the specified tensilestrength of anchor steel

For cast-in headed bolt, post installed anchorswhere sleeves do not extend through the shearplane


h h


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The basic concrete breakout capacity in shearof an individual anchor in cracked concrete, is

the smaller of the following two equations:

Anchor in Shear

le= heffor anchors with constant overall stiffness over the fulllength, le= 2dafor torque-controlled expansion anchors, le8dain all other cases. c1is the edge distance in loadingdirection and dais the diameter of the anchor

Modification factor for

ll d d h


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Eccentrically Loaded Anchors

5is modification factor for anchor groupsloaded eccentrically in tension

Fig. 19.36 Example of multiple fastening with cast in situ

headed studs close to edge under eccentric shear loading


h h


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Nominal concrete breakout strengthconsidering edge and spacing of anchors is:

For a group of anchors:

Avis the projected area of failure surface on

the sides of member,Avo= , and iare

the modification factors

Anchor in Shear

Modification factors for Edge Effectin Shear


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in Shear

Fig. 19.37 Edge effect in shear

Other Modification Factors for

Sh L di


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Shear Loading

When there is no cracking at service load

For anchors in cracked concrete without

supplementary reinforcement or with edgereinforcement smaller than 12 mm bars

with supplementary reinforcement or with

edge reinforcement > 12 mmbars

Other Modification Factors for

Sh L di


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Shear Loading

The modification factor,8,for anchorslocated in concrete members where ha< 1.5c1



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Anderson and Meinheit (2000, 2008) showed that for a multiple-studconnection the breakout capacity in shear is defined by the cattycorner

stud, that is, the stud diagonally opposite to the geometric corner (see

Fig. 19.37).

On the basis of their work, the PCI code introduced the concept of

side edge distance to the cattycorner stud.

It has been shown that corner influences are much better modelled by

the WJE/PCI equations than the ACI code provisions and ACI provisions

are very conservative for small side edge distances.



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Fig. 19.38 Corner concrete breakout when headed stud anchor is

located near a member corner

Concrete Pryout Strength ofAnchor in Shear


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Pryout failure normally occurs when short, stocky studs or

post-installed anchors are loaded in shear away from an edge(see Fig. 19.33b).

The nominal strength for single anchor:

The nominal strength for a group of anchors:

kcp= 1.0 for hef< 65 mm and kcp= 2.0 for hef 65 mm.

Bond Strength of AdhesiveAnchor in Tension


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The basic bond strength of a single adhesive anchor in tension incracked concrete

The characteristic bond strength in cracked concrete, cr, should be

taken as five per cent fractile of test results conducted as per ACI355.4M.

When analysis indicates no cracking at service load levels,

characteristic bond stress of adhesive anchor in uncracked concrete,ucr,may be used instead of the characteristic bond strength in cracked

concrete.

Bond Strength of AdhesiveAnchor in Tension


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Minimum characteristic bond strength, ucr, may beused, provided:

Anchors meet the requirements of ACI 355.4M,

Anchor holes are drilled with a rotary impact drillor rock drill,

Concrete has a compressive strength of 17MPa

and has attained a minimum age of 21 days at the

time of installation, andConcrete temperature at that time is at least 10C.

Minimum Characteristic Bond

St th (ACI 318 2011)


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Strength (ACI 318:2011)

Bond Strength of Adhesive

Anchor in Tension


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The nominal bond strength of single adhesiveanchor in tension is:

The nominal bond strength of group ofadhesive anchor in tension is:

Anchor in Tension

The modification factors for Bond

Strength of Adhesive Anchor


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Adhesive anchor groups loaded eccentrically intension

For edge effects

For uncracked concrete without supplementary

reinforcement

Strength of Adhesive Anchor

Case Study


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Bostons Big Dig Ceiling Collapse


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g g g p

Source:http://www.ntsb.gov/doclib/reports/2007/HAR0702.pdf

Required Strength of Anchors


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q g

After calculating the nominal strength, thefollowing condition has to be satisfied as per

ACI 318-11

Where, is the strength reduction factor and

Nuaand Vuaare the applied factored tensionand shear loads on anchor respectively

Strength reduction factor,

(ACI 318:2011)


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(ACI 318:2011)

Interaction of Tensile and Shear Forces


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Anchors and group of anchors that are subjected to shear and tensileloads should be designed to satisfy

When Vua/(Vn) 0.2 for the governing strength in shear, then full

strength in tension may be permitted.

When Nua/(Nn) 0.2 for the governing strength in tension, then fullstrength in shear may be permitted.

When Vua/(Vn) >0.2 for the governing strength in shear and Nua

/(Nn) > 0.2 for the governing strength in tension, ACI 318-11 suggests

the following interaction equation:

Interaction of Tensile and Shear Forces


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Fig. 19.39 Interaction diagram for combined tension and shear

Seismic Design Requirements


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When the seismic component of the total factored tension demand on

an anchor or group of anchors exceeds 20 per cent, the following four

options are suggested:

1. Ensure failure of ductile steel anchor ahead of brittle failure of

concrete. This involves the new concept of stretch length.

Observations from earthquakes indicated that a stretch length of

about eight times the diameter of anchor results in good

structural performance (see Fig. 19.39).

Provision of Stretch Length in Anchors


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Fig. 19.40 Provision of stretch length in anchors (a) Anchor chair (b) Sleeve

Seismic Design Requirements


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2. Design anchor for the maximum tension force that can be

transmitted to the anchor based on the development of a ductile

yield mechanism in the attachment in flexure, shear, or bearing, or

its combinations, and considering both material over-strength and

strain hardening effects of the attachment.

3. Design anchor for the maximum tension force that can be

transmitted to the anchor by a non-yielding attachment.

4. Design anchor for the maximum tension force obtained from design

load combinations involving earthquake load E, with E multiplied by

an amplification factor (0) to account for over-strength of the

seismic force-resisting system.

Influence of Reinforcements to Resist Shear


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In general, the procedure to predict the strength of anchors exhibitingconcrete cone failures assumes absence of reinforcement in the

anchorage area.

Parallel reinforcement near the anchor heads (e.g., hairpinreinforcement) has been shown to increase the ultimate load when the

reinforcement is well anchored, as shown in Fig. 19.41.

To ensure yielding of the anchor reinforcement, the reinforcementshould be in contact with the anchor and must be placed as close to the

concrete surface as possible, as shown in Fig. 19.41.

Hairpin Anchor Reinforcement for Shear


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Fig. 19.41Hairpin anchor reinforcement for shear (a) U-loops (b) V-loops (c) Section A-A

Edge and Anchor Reinforcement for Shear

The reinforcement could also consist of stirrups and ties enclosing the


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The reinforcement could also consist of stirrups and ties enclosing the

edge reinforcement embedded in the breakout cone and as close to the

anchors as possible (see Fig. 19.42).

The anchor reinforcement should be developed on both sides of the

breakout surface; edge reinforcement is also necessary for equilibrium

considerations (see Fig. 19.42).

The use of anchor reinforcement is attempted only in the case of cast-

in-place anchors.

Reinforcing bars are to be provided along all concrete surfaces to

minimize concrete damage in front of anchors for consistent seismic

shear behaviour.

Edge and Anchor Reinforcement for Shear


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Fig. 19.42 Edge and anchor reinforcement for shear (a) Plan (b) Section BB

Required Edge Distances and Spacing toPrevent Splitting of Concrete


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The following minimum edge distances and spacings are specified topreclude splitting failure, unless supplementary reinforcements are

provided to control splitting:

1. The minimum centre-to-centre (c/c) spacing of anchors should

be 4dafor cast in anchors that will not be torqued and 6dafortorqued cast in anchors and post-installed anchors.

2. The minimum edge distances of anchors that will not be torqued

should be based on specific cover requirements forreinforcements (Table 16 of IS 456), and for torqued cast-in

anchors the minimum edge distance should be 6da.

Required Edge Distances and Spacing toPrevent Splitting of Concrete


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3. The minimum edge distances for anchors should not be less than thecritical and minimum edge distance for post-installed anchors.

4. The value of heffor an expansion or undercut post-installed anchorshould not exceed two-thirds of member thickness and member

thickness minus 100 mm.

Obtuse-angled and Acute-angled Corners


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Corners with obtuse and acute angles occur in bridge abutments

between the wing walls and the front wall and in folded plate roof.

Tests on V-shaped beams with 135 to 145 corners have been

conducted for various reinforcement details based on which the

following have been concluded:

1. The efficiency of the joint detail is improved when inclined bars

are added to take up the tensile force at the inner corner. Loopswith inclined bars, as shown in Fig. 19.43(a), are preferable for

continuous corners between lightly reinforced slabs.

Reinforcement Details for Obtuse andAcute Corners


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Fig. 19.43 Reinforcement details for obtuse and acute corners (a) Obtuse angle (b) Acute angle

2 The efficiency of the corners improved significantly when the



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2. The efficiency of the corners improved significantly when the

thicknesses of the adjoining members were different. Further,

the mode of failure changed from diagonal tensile failure to

flexural failure.

3. The efficiency of the corner increased by about 32 per cent

when the length ratio of the two legs was changed from one to

two.

The main reinforcement should be restricted to about 0.651.0 per

cent of the section in order to avoid brittle failure of the corner. If the

reinforcement percentage is higher than this, the corner must be

provided with a reinforced haunch and stirrups.



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A reinforcement layout is shown in Fig 19.43(b) where the inclined

reinforcement in acute-angled corner is laid in a haunch.

The length of this haunch is at least one-half the thickness of the wing

wall and the reinforcement is less than 0.50.75 per cent and at least

equal to the thickness of wing wall when it is about 0.81.2 per cent.

The bars must not be spliced in the corner region.

Further, recesses or openings should not be made at or in the

immediate vicinity of corners or joints, since they considerably reduce

the strength and stiffness of the connection.

Thank You!


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Documents

507 33 Powerpoint-slides DRCS Ch19