Cấu tạo thép tòa nhà - P4

Every building consists of a load bearing frame, usually created by reinforced con-crete, or by steel, or by the combination of both areas with usual earthquake activity. Although the load bearing frame is not visible after the completion of the construc

2 THE BEHAVIOR OF THE FRAME

The reinforced concrete consists of two ingredients, the concrete and the ment The reinforcement is usually made out of steel and rarely (for the time being) from composite materials

reinforce-The reinforcement is divided into two main categories: (a) the longitudinal forcement which consists of reinforcement bars and (b) the traverse rein-forcement which mainly consists of stirrups

rein-In order to fully explain the behavior of the frame, we will examine two simplified structures, a simple slab supported in the two opposing sides and a panel consisting of two columns and a beam which connects the columns

1.4.1 Slab reinforcement and behavior

Because of the loads (self weight, marble coverings, loads from humans etc) that it bears and because of the elasticity that it has, a slab will be deformed as illustrated in the following picture Although the real deformation is very small, invisible to the hu-man eye and can only be measured in mm (millimeters), it always has the form illus-trated in the picture

Concrete has very high compression strength and therefore does not need any tudinal reinforcement in the areas of compression On the contrary, the tensile strength of concrete is minimal and therefore it is required to use longitudinal rein-forcement in the areas of high tension

longi-The cooperation of concrete and steel reinforcement results in the ideal combination of materials in order to achieve both high compression strength and adequate tensile

ates small hair cracks invisible to the human eye However, these cracks do not fluence the static behavior of the slab

in-Diagonal stresses are developed at the edges of the slab but these stresses are ways dealt with by the concrete and thus there is no requirement for additional trans-verse reinforcement

al-Because of the development of tensile stresses in the upper fibers of the support eas of the slab, it is obligatory to use a minimum longitudinal reinforcement This re-inforcement can either be autonomous or can originate from the main body of the slab or even both

ar-In the particular example of the above picture, the upper or ‘negative’ reinforcement originates from the main body of the slab (bended reinforcement bars)

Slab reinforced with an industrial steel mesh

In general, slabs do not have to cope with forces imposed vertically to their level of reference and therefore it is not reinforced to cope with seismic forces

When it is decided to use a reinforcement mesh for reasons of simplicity and omy, the only additional reinforcement needed is that of the longitudinal bars in the support areas of the slab, as illustrated in the above picture

econ-1.4.2 Column and beam reinforcement and behavior

PANEL WITHOUT SEISMIC INFLUENCE

The following panel consists of two columns and a beam and is only stressed by the gravitational loadings and not by any seismic loadings

The following picture illustrates the deformations and the possible concrete crackings in a very large scale in order to emphasize the behavior of the elements under the influence of gravitational loadings In reality, both the deformations and the crackings are too small to be visible by the human eye

The tension developed in specific areas of the panel will most definitely result in the development of crackings Therefore, it is obligatory to use the required reinforce-ment in every tension area of the panel When the crackings are perpendicular to the main axis of the element we must use longitudinal reinforcement (bars) in order to avoid the further developed of these hair cracks When the crackings are diagonal we must use transverse reinforcement (stirrups) in order to constrain these hair cracks When the panel is not supposed to receive any seismic loadings it is also possible to constrain all diagonal hair cracks by the use of special diagonal reinforcement

PANEL WITH SEISMIC INFLUENCE

The panel illustrated in the following picture is identical to the one describe above During its entire life span, it will function in exactly the same way as the previous panel, except for the crucial moments of the earthquake The behavior of the panel during an earthquake is illustrated in the following two pictures

During the earthquake there are mainly horizontal movements developed These movements create horizontal inertia forces (forces created due to the sudden change in the kinetic condition of an element

During the earthquake, the imposed horizontal forces constantly change their tion This results in the constant alternation of the panel’s behavior Therefore, the tensile stresses and their result, the hair cracks, constantly change their position and direction This periodical alternation of the panel’s behavior under the influence of an earthquake is what determines the level of difficulty in designing earthquake resistant structures It also determines the importance of using and correctly implementing the adequate reinforcement for the building’s frame, in areas with frequent seismic activ-ity

direc-Essential rules for reinforcing an earthquake resistant frame

The following requirements – rules are derived from the behavior of a frame during

the earthquake: Columns:

(a) The reinforcement bars should be fitted symmetrically in the perimeter of the column since the tensile stresses (and as a result, the crackings) constantly change their direction

(b) There is a high requirement for transverse reinforcement (accurately fitted rups of high strength) This reinforcement secures the elements from intense diagonal crackings that periodically change their direction which are created due to the diagonal tensile stresses (shearing)

stir-Beams:

(a) The lower reinforcement bars should be accurately anchored- in the same way as the upper reinforcement bars- since the tensile stresses and the re-sulting crackings constantly change their direction and the area of develop-ment due to the periodical alternation of the earthquake’s direction The phe-nomenon of constant direction shifting may result, during critical earthquakes, in the development of tensile stresses in the lower areas of the supports

(b) There is a high requirement for transverse reinforcement with accurately fitted stirrups of high strength in order to cope with the intense interchanging diago-nal tensile stresses and their results- the diagonal crackings

Even when a structure is properly designed, there is a possibility that some of the elements will exceed their bearing capacity before the rest, either due to an intense earthquake that has not been accounted for, or due to unpredictable conditions in certain parts of the structure In order to deal with these possibilities, we use two ‘lines of defense’:

must satisfy the requirement for adequate bearing capacity of the columns

In this line of defense we should ensure that elements will fail due to bending which has a plastic behavior and not due to shearing that will result in a friable behavior of the damaged elements

While by using a high seismic coefficient we can minimize the possibilities of sive overall failures during an intense earthquake, by securing the plasticity and bear-ing capacity of the elements we can avoid any localized failures in ‘weak’ areas of the structure These local failures can arise for a number of reasons and may result in the overall failure of the structure

exten-The requirement for plastic behavior (plasticity) of the structural elements

There is a high requirement for the implementation of a large number of stirrups both for columns and beams in the joint areas These stirrups are fitted not only to cope with the diagonal tensile stresses but also in order to ensure the high plasticity which is necessary during very intense earthquakes

The plasticity is the ability of an element made out of reinforced concrete to continue to deform even after it exceeds its bearing strength, without failing

During an intense earthquake there will be one element – the most vulnerable- that will be the first to exceed its bearing strength If this element has a plastic behavior it will continue to cope with the imposed stresses and will allow the second most vul-nerable element to also contribute its bearing strength If this second element also has a plastic behavior it allow the next most vulnerable element to contribute and fi-nally all the elements will be able to contribute in coping with the intense stresses de-veloped

Summarizing, if all the elements of a structure have the adequate plasticity then the bearing capacity of the frame will depend upon the capacity of the to-tal of the elements On the other hand, if at least one of the elements does not have the adequate plasticity then the bearing capacity of the frame will depend upon the capacity of the most vulnerable of the elements

after it has exceeded its bearing strength, is associated with the bending stresses developed and requires the adequate shearing strength For this reason we should always design against shearing by taking into account the shearing capacity of the elements in order to minimize the possibilities of an element failing due to shearing stresses

The failure of a column or beam usually takes place in the joint area which is the area that the column and the beam are connected together Therefore it is essential to en-sure the plastic behavior of both the columns and the beams in their connection ar-eas What is more, when there is a possible danger of embolism of the column by a staircase or a wall, then the entire body of the column must have the required plastic-ity

A 50x50 column that has three stirrups in every layer as required by regulations in order to ensure its plastic behavior

A beam with plasticity requirements

A beam with increased plasticity requirements

The requirement of bearing capacity for columns

The capacity design ensures that the column will always have a higher bearing strength than the beams which they support As a result, however intense an earth-quake might be, the beams will always be the elements that fail and not the columns When the beams fail, they absorb the concentrated energy that was produced by the earthquake and relief the frame What is more the natural frequency of the structure changes and thus avoid resonance In general, the failure of one or more beams does not result in a chain failure even during a very intense earthquake As a result, the building can still function satisfactory to allow for the evacuation of the residents