104523993 Behavior of Concrete Moment Resisting Frames Under Seismic Loading (1)

7/30/2019 104523993 Behavior of Concrete Moment Resisting Frames Under Seismic Loading (1)

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Behavior of Concrete

Moment-Resisting Frames

Under Seismic Loading

12/5/2011


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Table of Contents

Abstract ........................................................................................................................................... 2

Introduction ..................................................................................................................................... 2

Objective and Organization ............................................................................................................ 3

Response of Structure to Earthquake Motion ................................................................................. 4

Behavior of Steel Reinforcement .................................................................................................... 4

Behavior of Reinforced Concrete ................................................................................................... 5

Unconfined Concrete .................................................................................................................. 5

Confined Concrete ...................................................................................................................... 6

Moment-Resisting Frames .............................................................................................................. 6

Behavior of Beams .......................................................................................................................... 7

Reversing Plastic Hinges ............................................................................................................ 7

Flexure and Shear ................................................................................................................... 8Unidirectional Plastic Hinges ..................................................................................................... 9

Flexure and Shear ................................................................................................................. 10

Behavior of Columns .................................................................................................................... 11

Influence of an Axial Load on Plastic Hinge Zones ................................................................. 11

Strength Enhancement of Columns .......................................................................................... 12

Behavior of Beam-Column Joints ................................................................................................. 12

Shear Forces in Joint Zones ...................................................................................................... 12

Mechanisms of Resisting Shear Forces .................................................................................... 13Diagonal Strut Action ........................................................................................................... 13

Panel Truss Action ................................................................................................................ 14

Bond in Beam-Column Joints ................................................................................................... 14

Contribution of Mechanisms in Internal Joints ......................................................................... 15

Slabs and Beam-Column Joints ................................................................................................ 16

External Joints ........................................................................................................................... 16

Conclusions ................................................................................................................................... 17

Tables and Figures ........................................................................................................................ 18

List of References ......................................................................................................................... 26


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Abstract

The behaviors of concrete and the steel reinforcement under seismic loading have

become popular topics of current investigation in structural engineering. Compared with

monotonic loading (sustained static loading), the structural responses under seismic loading

(cyclic) account for horizontal and vertical motion, which makes it worth further investigation.

A thorough study of the behavior of moment-resisting frames during earthquake situations has

been carried out. The moment-frames were deconstructed into their three main parts: beams,

columns, and beam-column joints, which were looked at separately. Our study shows the

importance of plastic hinge zone formation in the beam as a means of handling the inelastic

rotation induced by seismic actions. Additionally, it shows the possible positive effect that axial

loads could have on confined concrete columns, which is important since earthquakes impose not

only horizontal loads, but vertical loads on a structure as well. In a structure subjected to

earthquake loading, perhaps the most important part essential to the stability of the structure are

the beam-column joints. We found that these joints are subjected to high amounts of shear stress

during loading and that there are two main mechanisms to handling this stress, diagonal strut

action and panel truss action. With diagonal strut action, we found that the bond stresses

between the concrete and steel reinforcement must be significantly high. However, with panel

action, the bond strength can be as little as 0.25 the magnitude of that required for diagonal strut

action. This is due to the fact that with this type of response, the bond stresses are spread out

over the full width of the reinforcement. We have also found that the interaction between slabs

and beam-column joints plays an important factor in contributing to the flexural strength of the

structure. Our efforts focus solely on the effects in moment-resisting frames, though it has been

recognized that other earthquake-resistant structural systems exist. We conclude that in order to

determine what system should be used in certain circumstances, all possibilities should be

considered.

Introduction

An earthquake is the result of a sudden release of energy in the Earths crust that creates

seismic waves. Earthquakes are mostly caused by rupture of geological faults, but other

activities such as mine blasts and explosions can trigger seismic activity (Nilson). As history has


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(Booth and Key). Finally, these ideas are looked at within the general scope of design of

concrete structures in areas with seismic activity.

Response of Structure to Earthquake MotionSince earthquakes consist ofrandom horizontal and vertical movements of the earths

surface, it can be difficult to predict the effect they would have on structures. The forces which a

structure subjected to seismic action are called upon to resist, result directly from the distortions

induced by the motion of the ground on which it results. As the ground moves, inertia tends to

keep structures in place, resulting in the imposition of displacements and forces that can have

catastrophic results. An example of this behavior is demonstrated in Figure 1. These

displacements are the result of the distortion waves travelling along the height of the structure.

Due to the repeating cycles associated with earthquake loads, the building undergoes a series of

complex oscillations (Duggal). As the materials yield and behave inelastically, a significant

amount of energy is dissipated. This usually translates into increased displacements, which may

require increased ductility and result in major nonstructural damage (Nilson). In this sense, this

response differs from the one that results from wind loads, which is caused by external pressures

and suctions on a structure (Booth).

Behavior of Steel Reinforcement

The behavior of reinforced concrete under cyclic loading is highly non-linear, and, in

particular, depends on the concrete-steel interface. As mentioned above, an earthquake results in

alternating back and forth motion within the structure. When a reinforcing bar is yielded in

tension or compression from the loading applied in one direction and the direction of the stress is

reversed, the distinct yield point in monotonic loading is lost and the stress-strain relation takes

on a curvilinear form (Booth and Key). This is known as the Bauschinger effect and is

demonstrated in Figure 2.

An important result of this effect is that the stiffness of the steel is lowered as it

approaches yield compared with the initial cycle, which makes it more prone to buckle in the

compression cycle. Stress no longer depends on strain, but instead on the strain history.

Increases in initial yield stress of around 20% may occur in mild yield steel due to the high rates


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of loading that result from seismic activity; this increase is lower in high-yield steel. The

increase in yield stress has also been found to be much lower in subsequent yielding cycles.

Therefore, strain rates in reinforcement are likely to be relatively minor for seismic loading

(Booth and Key).

Since the stress is no longer uniquely related to the strain, but is instead related to the

strain history, standard flexural theory no longer applies since it makes the assumption that

stresses and strains are uniquely related. Although the theory is no longer applicable to members

subjected to reversing inelastic load cycles, it can be used to give a reasonable estimate of

strength. Other factors that have been found to influence the stress-strain behavior of steel

reinforcement subjected to inelastic load cycles are the characteristics under monotonic loading,

the strain aging of the reinforcement, the composition of steel, and the temperature of the

reinforcement (Booth). The relationships found are generally too complex, however, their

experimental results can be used to establish perimeters for use with codes and design guides.

Behavior of Reinforced Concrete

Unconfined Concrete

Concrete on its own is weak and brittle in tension; however, in compression it is

somewhat ductile. Ductility can be defined as the ratio of the displacement at maximum load to

the displacement at yield. Ductile members are capable of undergoing large inelastic

deformations with little decreases in strength (Duggal). The flexural design of concrete members

under monotonic loading cannot directly be applied to earthquake loading, because earthquake

loads subject a structure to higher strain rates and an alternating direction of loading. During an

earthquake, the direction of the structural actions reverses as the structure sways backwards and

forwards (Booth). The swaying motion results in one side of the beam being in compression

during one-half of the sway cycle and in tension with extensive yielding of the steel in the

second half of the cycle.

The effect of repeated loading to high strain levels on the behavior of concrete has been

examined in a number of studies. As shown in Figure 3, the envelope to the cyclic loading

curves has been found to lie close to the monotonic stress-strain curve (Karson and Jirsa). Under

the application of high cyclic strains, they found that the concrete strength and stiffness degrade.


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Therefore, it is important that the compression zone in a potential plastic hinge in a beam

contains a minimum area of longitudinal steel reinforcement. This ensures that, as the strength

of the concrete degrades, the reinforcement can pick up a portion of the compression force to

prevent a premature crushing failure (Booth).

Confined Concrete

It has been shown that a lateral confining pressure, when applied to concrete, can greatly

increase both its compressive strength and compressive strain at fracture. The latter feature is

used in seismic design to increase the ductility of members subjected to flexure and axial loads.

In 1928, Richart et al. showed that the compressive strength, f'cc, could be calculated through the

following empirical formula:

f'cc = f'c + 4.1f1

where f'c is the cylinder strength and f1 is the confining pressure. This confining pressure does

not need to come from hydrostatic pressure, but could result from the confining effect of circular

or spiral reinforcement. This is due to the tendency of concrete to expand in directions normal to

an applied compressive stress. This expansion causes the confinement steel to stretch, which, in

turn, allows for the development of tensile forces tending to resist the expansion. Improvements

in compressive stress and compressive strain due to confinement are less dramatic in high-strength concrete, although with its high strength-to-weight ratio, it may have applications in

seismic design for tall buildings (Booth and Key). However, proper considerations should be

made beforehand.

Moment-Resisting Frames

Moment-resisting frames are one type of earthquake-resistant structural system. They

consist mostly of horizontal beams and vertical columns and derive their lateral strength from the

rigidity of the beam-column connection rather than from diagonal bracing members. The two

main types of moment-resisting frames are grid frames and perimeter frames, shown in Figure 4.

Grid frames comprise of a uniform grid of frames in both directions and their main advantages

are that they are highly redundant and achieve a good resistance to seismic forces both within the


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superstructure and to the foundations. However, all the columns must be designed for biaxial

loads and all members have to be ductile. Perimeter frames are restricted to the outside of the

building. Because internal columns only need to support gravity loads, the column spacing can

be increased, which results in greater architectural freedom. However, the corner columns of

perimeter frames suffer from problems of biaxial loading and possible uplift (Booth and Key).

Moment-resisting frames, if constructed properly, can provide a highly ductile system

with a good degree of redundancy. This could potentially allow for more freedom in the

architectural planning of internal spaces and external cladding, without obstruction from bracing

elements. Additionally, their flexibility may serve to detune the structure from the forcing

motions on stiff soil or rock sites (Booth and Key).

However, there are also problems associated with moment-resisting frames. The low

stiffness of moment-resisting frames tends to cause high story drifts, which may lead to damage

of cladding and other non-structural elements. A more general problem with the flexibility of

moment frames is that design may be governed by deflection rather than strength leading to an

inefficient use of material. Also, the beam-column joint is an area that accumulates a high stress

concentration, and careful consideration needs to be taken in its construction. Therefore, it is

critical to understand the behavior of these joints under cyclic loading. Another consideration is

that joints often require congested reinforcement, for which skillful steel-fixing skills are

necessary (Booth). The behavior of reinforced concrete beams and columns will also be

analyzed in the following sections.

Behavior of Beams

Ductile concrete frames are designed so that the plastic hinges form in the beams under

design earthquake loading. These hinges must be able to sustain inelastic deformation and

dissipate energy without suffering much strength degradation. Under seismic loading, two

different types of hinges can form in beams: reversing plastic hinges and unidirectional plastic

hinges (Booth and Key). It is possible for both reversing and unidirectional hinges to form in a

beam during a severe earthquake.

Reversing Plastic Hinges


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Reversing plastic hinges form where the beam spans are short or where the gravity loads

supported by the beams are light. For uniformly reinforced beams, these hinges occur if the

direction of the shear force in the beam does not change when the plastic hinges have formed.

Specifically, the following inequality must be obeyed:

(MA + MB)/L'> wL

'/2

where MA and MB are the flexural strengths at the ends of the beam, L'is the clear span and w is

the vertical force on the beam per unit length. Figure 5 shows the concept behind the reversing

hinge in beams. Plastic hinges and maximum moments are located against the column faces. As

the structure sways back and forth due to earthquake loading, these hinges yield first in one

direction and then the other. The beam region between the plastic hinges sustains little

deformation as it remains in the elastic range. As a result, the rotation imposed on the plastic

hinges is closely related to inter-story drift (Booth).

Flexure and Shear

Experiments carried out by researchers at Auckland University have demonstrated the

behavior of beams which form reversing hinge zones (Fenwick, Tankat, and Thom). The results

of flexural deformation are shown in Figure 6. They found that the first inelastic displacement

applied to the beam, +2i, causes the top reinforcement in their test beam to yield in tension

while small compressive strains are sustained by the bottom reinforcement. With the reversal of

loading direction in the next half-cycle (-2i), the bottom steel yields in tension and the top

reinforcement goes into compression. Due to the Bauschinger effect, the steel no longer has a

distinct yield point (Fenwick, Tankat, and Thom).

Under cyclic loading, the concrete does not contribute directly to the flexural

compression force. The cracks, which opened with the tensile yield of the reinforcement in the

previous half-cycle, do not close. This happens for two reasons. First, aggregate particles tend

to become dislodged and wedge the cracks open. Second, the truss-like action with the stirrups

and the diagonal compression forces, which develop to resist the shear, causes the flexural

compression forces to be smaller than the tension force. The cracks may close if the

compression force exceeds the yield resistance of the steel on the compression side of the beam.

These flexural forces redistribute themselves to the longitudinal reinforcement in the plastic

hinges, and as a result, the high compression forces in the steel combined with the Bauschinger


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effect make this reinforcement more susceptible to buckling than in the monotonic case (Booth

and Key).

To ensure plastic hinge zones in beams have adequate rotational ductility, three design

guidelines should be adhered to. First, there should be lower and upper bounds on the amount of

longitudinal steel that can be used. Second, there should be a limit on the ratio of the steel on

one side of the beam to that on the other side. Third, there should be minimum requirements for

the spacing and size of stirrups to restrain buckling of the longitudinal reinforcement (Booth).

Due to the cyclical nature of earthquake loads, the shear force changes with the direction

of plastic rotation. Diagonal cracking occurs, and combined with the yielding of the longitudinal

reinforcement, render the shear-resisting mechanisms of aggregate interlock and dowel action

ineffective. Therefore, the shear has to be resisted entirely by a truss-like action formed by the

flexural steel and shear steel as tension members and diagonal concrete compression struts.

Present day codes recognize the loss of the shear resistance of the concrete in reversing plastic

hinges and require web reinforcement to be provided to carry the total shear (Booth).

Under inelastic cyclic loading, the diagonal compression forces can develop at steeper

inclinations than standard codes of practice state. When the stirrups yield, the inclination of the

crack adjusts itself such that it intersects just enough stirrups to carry the shear not resisted by the

inclination of the compression force. Increasing the quantity of shear reinforcement increases

the angle of inclination. Each time the critical curvature that causes the stirrups to yield is

exceeded due to the loading cycle, additional yielding occurs (extension of the stirrups) and the

diagonal cracks widen (Booth and Key). The critical value at the curvature can be increased by

increasing the amount of web reinforcement, which reduces the shear deformation. A

representation of shear force versus shear deformation in a reversing hinge is shown in Figure 7.

The opening and closing of diagonal cracks in the web can lead to strength degradation of

the concrete, which results in a diagonal compression failure after a number of load cycles at

stresses lower than those that can be sustained under monotonic conditions. Under these

conditions, failure usually occurs close to one of the major cracks in the plastic hinge and is

accompanied by high shear displacements. This has been termed sliding shear failure (Booth).

Unidirectional Plastic Hinges


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In situations where the inequality above is not satisfied, unidirectional hinges may form.

This usually occurs when beams in a seismic frame carry significant gravity loads (Booth and

Key). In these hinges, the maximum positive bending moments occur in the span some distance

away from the column face. In this situation, four plastic hinges will form during earthquake

loading. First, a negative-moment plastic hinge forms at one end of the beam with positive-

moment plastic hinge located at the position of maximum positive bending moment (zero shear).

When the seismic action is reversed, a second negative-moment plastic hinge forms at the other

end of the beam, and a second positive-moment plastic hinge forms in the beam span at the other

location of maximum positive bending moment (Booth). This concept is illustrated in Figure 8

below.

Because the positive and negative plastic hinges are located at different locations, each

hinge rotates in one direction only. Therefore, each unidirectional hinge can handle about twice

as much rotation as a reversing hinge. However, there is no way that the inelastic rotations can

decrease during an earthquake because of this fact. With this hinge, the inelastic rotation

increases progressively during an earthquake with the deflection of the beam also increasing, as

seen in Figure 8. Although unidirectional hinges have greater inelastic rotation capacities than

reversing hinges, one thing to consider is that forming unidirectional hinges rather than reversing

hinges reduces the ductility of the structure as a whole. This is due to the fact that these hinges

have to sustain greater rotations as the inelastic rotations accumulate with each inelastic

displacement of the structure during an earthquake (Booth and Key).

Flexure and Shear

The deflection under lateral loading of a structure which forms unidirectional plastic

hinges differs from that for a comparable structure in which reversing plastic hinges develop.

With the unidirectional hinge, little or no shear reversal occurs. The actions in a unidirectional

hinge are shown in Figure 9. The steel on one side of the beam yields in tension, but not on the

other side, which allows the concrete in the compression zone to remain intact longer than it

would in a reversing hinge. The yielded tension steel is subjected to compression if the direction

of the bending moment reverses (as occurs in earthquake situations); however, these stresses are

below yield level. Therefore, the tendency to buckle is not as great as in a reversing hinge

(Booth and Key).


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In unidirectional hinges, only one major set of diagonal cracks form, and the direction of

the diagonal compression forces in the web does not change. In unidirectional hinges, the

diagonal compressive strength of concrete is much higher than in the case of the reversing hinge,

therefore the peak shear forces in beams are likely to be greater for unidirectional than for

reversing hinges (Booth).

Behavior of Columns

Column failure is likely to have more disastrous consequences than beam failure, because

the loss of the support extends to all floors above the failed column. In this regard, they need

additional protection to guard against flexural or shear failure. Columns must be able to sustain

the deformations imposed on them in a severe earthquake while maintaining their required

strength. The differences between beam and column behavior under cyclic loading arise from

the compressive load that a column carries (Booth).

Influence of an Axial Load on Plastic Hinge Zones

In a column, the presence of an axial load and intermediate column bars requires the

concrete to resist some compression, which results in a different load-deflection response when

compared to that of beams. Under the application of repeated strain, the compressive strength of

the concrete degrades. Since the column reinforcement is unable to pick up the entire force,

column crushing could occur. Also, the compression force in the concrete ensures that cracks,

which opened up in the previous half-cycle with the tension yield of the reinforcement close with

the reversal. The resultant compression force can be inclined, as shown in Figure 10, and the

transverse component of this force can resist some shear. Therefore, an increasing axial load can,

at first, increase the shear carried by the concrete. However, at high levels of axial load, this

value decreases (Priestly and Park).

It is important to note that in unconfined columns, increasing the axial load decreases theductility. Confined concrete can sustain much higher strains without strength degradation

compared to unconfined concrete. However, this enhanced performance can only be achieved

when the unconfined concrete cover has failed and spalled, and is based on the requirement that

the increase in strength of the concrete in the confined core is sufficient to compensate for the

loss of strength associated with the spalling of concrete cover (Booth).


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Strength Enhancement of Columns

Confinement in a reinforced concrete column can lead to an increase in strength as well

as ductility. This strength enhancement can be important where the energy dissipation

mechanism involves a primary hinge in a column. The increase in strength in the concrete andthe magnitude of the strains it can sustain allows the reinforcement to resist greater strains due to

strain hardening. In some cases, under cyclic loading, the reinforcement may be able to work

more efficiently than is implied by standard flexural theory. The reinforcement which has been

previously yielded in tension may be able to sustain compressive stresses on load reversal while

still under a tensile strain. This could lead to some strength enhancement for columns sustaining

light loads (Booth). However, the section strength decreases where the confinement

reinforcement stops.

Behavior of Beam-Column Joints

Most potential plastic hinges are located in the beams close to a beam-column joint.

Under earthquake loading, the joint is a highly stressed region, where shear stresses are many

times greater than those in a frame subjected solely to gravity loads. These high shear forces

lead to high concrete diagonal compressive forces, which require adequate confinement of the

joint region to be sustainable. Furthermore, horizontal and vertical steel is needed to transmit thediagonal tension. The bond stresses between flexural steel and concrete in the joint zone are also

quite high, because bars passing through the joint are expected to yield in pure compression on

one side of the joint and in pure tension on the other. Therefore, there is a need to restrict the

diameters of such bars, since bond resistance per unit length decreases with increasing bar

diameter. The anchorage length of the reinforcement bar protruding into the column is also an

important consideration, because the length is restricted on one side of the joint (Booth and Key).

Different form the case of monotonic loading, the opening and closing of joints needs to be

considered during an earthquake, due to the reverse loading situations which can occur

(Buyukozturk).

Shear Forces in Joint Zones


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The forces acting on an internal beam-column joint are shown in Figure 11 along with

the joint zone ties and intermediate column bars which are necessary to resist the shear within

this zone. The equation for horizontal shear force is given by the following:

Vjh = Cb1 + Tb2Vcol

If the beam sustains no axial force and the plastic hinges form at the column faces, the equation

is reduced to:

Vjh = (Ast + Asb)foyVcol,

where Ast and Asb are the top and bottom areas of longitudinal reinforcement in the beams, foy is

the maximum sustainable stress of the reinforcement, and Vcol is the shear in the column.

Vertical shear forces can be computed similarly, although it is slightly more complicated.

To avoid complicated analysis and calculation, Vjv is generally found by multiplying Vjh by the

ratio of the beam depth to column depth (Booth).

Mechanisms of Resisting Shear Forces

Two basic shear-resisting mechanisms have been identified for joint zones: diagonal strut

and panel truss actions. The contribution that each makes to shear-resistance depends on the

elastic yielding condition of the reinforcement in the members connected by the joint, and the

number of cycles to which the beam-column joint is subjected (Booth).

Diagonal Strut Action

The mechanism of diagonal strut action is shown in Figure 12. The compression forces

in the concrete meet to sustain the diagonal compression force across the joint. In order to resist

the joint zone shear introduced by the tension bars, high bond stresses must be sustained in the

compression corners of the joint zone. Hence, bond failure is likely to occur, particularly if the

reinforcement has been yielded in tension at the column face at an earlier stage of loading. The

extension of the steel between the anchorage position and the tension corner of the joint results in

a wide crack opening up at the face of the column, as seen in the figure. Both the top and bottom

reinforcement are in tension, as well as the beams adjacent to the joint. A reduction in the

flexural strength of the beam at the column face occurs because the compression force increases

to satisfy the equilibrium conditions.


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using too big of a bar diameter may also result in bond failure (Booth). Leon carried out tests on

beam-column joints to investigate the effects of the bar diameter on the influence of the bond

under cyclic loading conditions. He varied the ratio of the column depth to beam bar diameter

using ratios of 16, 20, 24, and 28. Under cyclic loading in the elastic range, he observed

significant degradation in the bond performance in tests using the ratios 16, 20, and 24.

Therefore, he concluded that a ratio of 28 was necessary to maintain adequate performance of the

capacity of the diagonal strut mechanism to resist joint shear (Leon).

Contribution of Mechanisms in Internal Joints

The magnitude of shear that can be resisted by diagonal strut action depends on three

criteria: the level of axial load in the column, the location of the plastic hinge zones, and the ratio

of the areas of the top and bottom reinforcement in the beams. Increasing the axial load can

actually improve the bond conditions for the beam reinforcement passing through the beam-

column joint, which increases the contribution of diagonal strut action. It also reduces the area

of intermediate column bars required for panel truss action. If the axial load is less than that

corresponding to balanced conditions, increasing the axial load increases the flexural resistance

of the column (Booth).

The formation of plastic hinges on either side of the joint can reduce shear resistance;

however, if the plastic hinges are kept away from the column faces, a large portion of shear can

by resisted by diagonal strut action. Although the majority of beam-column subassemblies are

constructed with this in mind, due to the elongation of the beams which results from the

formation of plastic hinges, plastic hinging may occur simultaneously in the beams and the

columns. In this situation, to maintain panel truss action, it is likely that the area of intermediate

column bars would have to be increased.

In tests of subassemblies where low axial load levels were applied to the column and the

beams contained equal areas of top and bottom reinforcement, the joint zone ties should resist the

horizontal zone shear if stiffness degradation is to be avoided. In others, it has been shown that

reducing the area of the bottom reinforcement compared to the top requires fewer joint ties to

obtain good ductile performance (Park and Ruitong). The smaller area of steel enables the crack

at the column face to close and allows some diagonal strut action to contribute to the shear

resistance in one-half of the shear zone (Booth and Key).


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Slabs and Beam-Column Joints

In structural tests in full-scale reinforced concrete multi-story buildings, it was found that

the composite action of the slab with the beams made a major contribution to lateral strength,

which is very important to consider under the case of cyclic loading (Wight). Under assessmentof the flexural strength of the beams can lead to erosion of the intended margin of strength

between the columns and beams, which could possibly lead to a column sway mechanism.

Composite action with a slab affects beams, as well as beam-column joints.

Under the action of a severe earthquake, positive and negative hinges may be expected to

develop against the column faces. This is shown in Figure 14. Large tensile strains are induced

in the slab due to the negative-moment plastic hinge on the right-hand side of the column, which

results in the yielding of the reinforcement steel. The flexural actions induced in the

subassembly arise from the flexural reinforcement in the beam and the reinforcement in the slab.

Tests have shown that the action of the slab is similar to a space truss (Cheung and Paulay). The

tension force in the lab on the right-hand side is balanced by diagonal compression in the

concrete and tension forces in the transverse slab steel. The slab contributes to the flexural

resistance on the right-hand side of the column. This flexural strength can only develop if the

transverse reinforcement can handle the transverse tension forces. In a three-dimensional beam-

column sub assembly, the interaction of the longitudinal and transverse forces in the slabs results

in the flexural contribution of this reinforcement for seismic actions acting along the diagonal

being reduced to approximately half of the value that is sustained for unidirectional actions

(Booth).

External Joints

The forces acting on an external beam-column joint are shown in Figure 15. Panel truss

and diagonal strut actions combine to resist the joint zone shears. For external joints, the

anchorage of the beam bar by bending them into the column helps to sustain diagonal strut action

even when a plastic hinge forms in the beam at the face of the column. Also, these joints require

fewer ties than interior joints to sustain the same shear level.

The provision of an anchorage stub (see Figure 16) for the beam reinforcement improves

the performance of external joints in numerous ways. First, the spalling of concrete on the

outside face of the joint zone is prevented, which eliminates the loss in flexural strength of the


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column. Second, it increases the diagonal strut action. Third, the arrangement reduces steel

congestion as the beam bars can be anchored clear of the column bars (Booth).

ConclusionsA clear understanding of the behavior of the beams, columns, and beam-column joints

during an earthquake is necessary before designs can be considered. Present day building codes

have been engineered to reflect these considerations; however, with the unpredictability of the

extent to which earthquakes can have an effect on structures, sometimes, they may be considered

insufficient or outdated. It was not the intent of this paper to go into depth about design

specifications and building code.

Using the behavior of the members of the structural members described above, several

general design guidelines can be formulated regarding the design of moment-resisting frames to

withstand earthquake loading. To summarize, total collapse is preventable if the failure is ductile

rather than brittle. Second, beams should fail before columns, because column failure affects

everything above it. Third, flexure failure should precede shear failure, especially for reinforced

concrete columns. Fourth, proper design and construction of the beam-column joint connections

is critical because high stress concentrations occur in the joint zone. Fifth, the joint zone areas

within a beam-column joint should be engineered carefully, as the reinforcement required to

allow the diagonal strut and panel truss actions to resist the shear induced within the joint during

a major earthquake could result in a complicated cross-sectional design.

Earthquakes have resulted in numerous structural catastrophes around the world that have

had serious repercussions, both directly and indirectly. The unpredictability of earthquake

dynamics makes the design of earthquake-resistant structures a challenge. Through and

understanding of the behavior of structural members in a moment-resisting frame subjected to

seismic loading, buildings can be designed to sustain such loads, therefore preventing structural

collapse. Further studies to pursue would be to analyze the structural response of shear walls due

to earthquake loads, and then to analyze the behavior of dual systems, since those seem to

combine the benefits of both structural systems and could be the best structural systems to

resisting the effects that earthquake loading imposes.


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Figure 3: Stress-strain relationship for concrete subjected to repeated loading. The figure shows

that the envelope to the cyclic loading curves has been found to lie close to the monotonic stress-

strain curve, and it is accepted as being coincident with it (from Booth).

Figure 4: Top view of a grid frame system (left) and a perimeter frame (left). There are

advantages and disadvantages associated with each type (from Booth and Key).


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Figure 5: Clockwise from top left: Crack pattern, deflected shape, shear forces, and bendingmoment diagrams of a reversing plastic hinge. Plastic hinges and the maximum bending

moments are located against the column faces. The beam region between the plastic hinges

sustains little deformation as it remains in the elastic range (from Booth).

Figure 6: Extension of reinforcement at different loading stages for a reversing hinge. The

coefficient in from ofthe indicates the degree to which the beam is experiencing displacementductility, the (+) or (-) indicates the direction of displacement, and the i denotes that the first

displacement has been applied. The first inelastic displacement applied to the beam, +2i,causes the top reinforcement to yield in tension while the bottom reinforcement is sustaining

compression force (from Booth).


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Figure 7: Shear versus deformation in reversing hinge. The pinched shape of the curve arises

from the shear displacement that is associated with the crack closure that occurs at low load

levels (from Booth).

Figure 8: Clockwise from top left: Crack pattern, deflected shape, shear forces, and bending

moment diagrams of a unidriectional plastic hinge. Note the location of the maximum bendingmoments within the beam. As the inelastic rotation increases progressively, the deflection of the

beam also increases (from Booth).


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Figure 11: Forces in an internal beam-column joint. The figure on the right implies that the top

and bottom parts of the joint are being subjected to counterclockwise bending moments and the

left and right parts of the joint are being subjected to clockwise bending moments (from Booth).

Figure 12: Diagonal strut mechanism of resisting the shear force in beam-column joints. With

diagonal strut action, the reinforcement forces have to be sustained over a small length in the

compression corner of the beam as show in the picture on the right (from Booth).


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Figure 13: Panel truss action of resisting the shear force in beam-column joints. With paneltruss action, the bond stresses are spread over the full width, therefore, compared to diagonal

strut action, the bond force required is less (from Booth).

Figure 14: Beam-column sub-assembly with slab. With the negative-moment plastic hinge on

the right-side of the column faces, large tensile strains are induced in the slab, causing the

longitudinal reinforcement to yield (from Booth).


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List of References

Booth, E., ed., Concrete Structures in Earthquake Regions: Design & Analysis, UK: Longman Group UKLimited, pp. 72-121, 1994.

Booth, E., and Key, D.,Earthquake Design Practice for Buildings, 2nd end, London: Thomas Telford, pp.102-115, 141-152, 2006.

Buyukozturk, O., Beam Column Joints. Mechanics and Design of Concrete Structures. Massachusetts

Institute of Technology. Cambridge, 31 October 2011.

Cheung, P.C., Paulay, T., Mechanisms of slab contribution in beam-column subassemblages,Design

for Beam-Column Joints for Seismic Resistance American Concrete Institute, Special Publication SP123-10, pp. 259-289, 1991.

Duggal, S.K.,Earthquake Resistant Design of Structures, Oxford: Oxford University Press, pp. 12-29,2007.

Fenwick, R.C., Tankat, A.T., Thom, C.W.,Deformation of Reinforced Concrete Beams Subjected to

Inelastic Loading-Experimental Results University of Auckland School of Engineering Report No 374,1981.

Karson, D., Jirsa, J.O., Behavior of concrete under compressive loadings,ASCE Journal StructuralDivision, 95(St.12), pp. 2543-2563, 1969.

Leon, R.T., Interior joints with variable anchorage length,ASCE Journal of Structural Engineering,Vol. 115, No. 9, pp. 2261-2225, 1989.

Leon, R., Jirsa, J.O., Bi-directional loading of reinforced concrete beam-column joints,Earthquake

Spectra, EERI, Vol. 2, No. 3, pp. 537-564, 1986.

Nilson, Arthur H., Darwin, David, Dolan, Charles W., Seismic Design,Design of Concrete Structures,14

thed, New York: McGraw-Hill, pp. 714-750, 2010.

Park, R., Ruitong, D., A comparison of the behaviorof reinforced concrete beam-column joints designedfor ductility and limited ductility,Bulletin of the New Zealand Society for Earthquake Engineering, Vol.

21, No. 4, pp. 255-278, 1986.

Priestly, M.J.N., Park, R., Strength and Ductility of Bridge Substructures RRU Bulletin No 71, National

Roads Boards, Wellington, 1984.

Richart, F.E., Brandtzaeg, A., Brown, R.L.,A Study of the Fracture of Concrete under Combined

Compressive Stresses, University of Illinois, Engineering Experimental Section, Bulletin No. 185, 1928.

Wight, J.K. ed,Earthquake Effects on Reinforced Concrete Structures American Concrete Institute,Special Publications SP84, 1985.

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104523993 Behavior of Concrete Moment Resisting Frames Under Seismic Loading (1)