A chiseled slab is a slab (with or without drops) supported (generally without beams) by columns (with or without column minds). It is also defined as a strengthened concrete slab reinforced immediately by concrete columns without the use of beams. Even slabs are one of the very most popular structural systems in domestic buildings, hotels, private hospitals and office properties. Smooth slabs are sturdy concrete slabs that copy the load directly to columns of uniform thickness. One of the important way systems that make level slab systems a very attractive solution is the ease of its construction. Architects prefer the smooth slab systems due to the flexibility in agreement of partitions and columns supplying architects the best use of space.

## Punching shear

## What is punching shear?

Punching shear is a type of failure of reinforced concrete slabs put through high localized forces. In level slab buildings this occurs at column support items. The failure is due to shear:

## Flat slabs and punching shear: encouragement systems

The most popular floor system found in residential car parks, complexes and many other structures (scheduled to large period required) is reinforced concrete chiseled slabs. They may be easy to create floor systems to keep the height between flooring and ceiling. Smooth slabs are preferred to the clients and architects due to economics advantage which is speeding up the building process. But there is a major weakness in chiseled slab from structural anatomist perspective that they are susceptible to punching shear failing at the junctions of columns and columns. The major concern when using level slabs is shear transfer from slab to the columns. Its threat for columns may punch through the slab, it is suitable to utilize drop panels at the column if the live lots surpass 3, if live loads go beyond 6 it's recommended to utilize column head, in case there is heavy live lots (greater than 10) it's advised to use column brain with drop sections as case of industrial structures. With regards to heavy loads it is preferred the chiseled slab floor system such as multistory car parks and multistory properties where large spans with large areas are needed. A column head or drop -panel supports the toned slabs to provide the level of resistance to punching shear throughout the column. But from the architectural viewpoint it isn't preferred to save lots of space between floor surfaces. By far the most serious kind of inability is the shear failing scheduled to punching shear that will arise at the columns. An average punching shear inability is seen as a diagonal crack beginning with the bottom of the slab and making their way to the top at the position of 20-45 degree to the horizontal resulting in the parting of the slab throughout the column in a truncated pyramid form. The intensifying collapse of the framework is produced as one way reaction of punching shear inability. The punching shear capacity of your slab without shear support depends on the effectiveness of concrete, depth of the slab and column size and the region of tension reinforcement. Also the shear capacity can be reduced by any openings near to the column's perimeter like services for multi storey properties.

Uses of column heads:

Increase shear power of slab

reducing the span to reduce as soon as in the slab

if live lots exceed 6

Uses of drop sections:

Increase shear durability of slab

Increase negative second capacity of slab at location of high negative bending and reduces the chance of shear failure

Reduce deflection by stiffen the slab

if the live tons exceed 3

## Shear studs as punching shear support for chiseled slabs:

The use of stud systems for punching shear reinforcement is an efficient solution for concrete toned slabs where punching shear support is on the critical route where experience occurs which indicates the most well-liked form of shear encouragement.

## Analysis of even slabs

Flat slab can be analyzed and created by any methods like:

direct method

equivalent framework method

finite element (SAP) (computer model)

Neither the direct method nor comparative frame method can solve slabs have uncommon geometric configurations or the columns are spaced irregularly, therefore these special cases the floor can be analyzed by using finite aspect analysis, which the slab is divided into small finite elements which is linked by nodes. The element of the tightness matrix is computed and the global rigidity matrix is created. The deformation at each node can be established and the component internal forces can be acquired.

## Direct method

Limitation of the direct method

To ensure that the moments at the critical portions are appropriate, there are design conditions that must be required

A bare minimum spans required is three continuous spans in each path.

The proportion of the a bit longer to the shorter span within a panel shouldn't go over 1. 3

The difference between the successive span measures in each direction shouldn't be more than 10%

The difference between the non-successive span measures in each course shouldn't be more than 20%

Definition of column strip and field strip

The circulation of point in time varies continuously across the width of the slab -panel, to simplify the material arrangement, the design moments are averaged over the width of the column strip.

The column remove width should be taken as half the sort way for slabs without drop sections, in case there is even slab with drop panel, the column strip width equals the drop width. The width of the field strip equals the difference between course length and column strip width.

Statical Moment in time Mo

The immediate design method can be an empirical process of establish the design of critical sections moments. With the supports there is certainly negative moment with the mid span of uniform loaded beams you can find positive moment.

The smallest distance at the intersection between your slab and column is D. if the attributes of the rectangle aren't parallel to the period or the encouraging element doesn't have rectangular mix section, then it is treated as square getting the same area.

The total static instant Mo is divided into a positive minute at mid span and a poor instant at the support.

Definition of D for different even slab systems (with drop panel or with column brain or both with column head and drop panel)

Distribution of Static Moment

The actual circulation of the transverse occasions by two regions of constant moment. As soon as is the tiniest at the guts strip where it is called field remove (or middle strip) and as soon as is the largest at the strip in the column areas where it is called the column remove. This to simplify the research of the smooth slab floor surfaces.

Column strips and field strips

As shown in this amount (column whitening strips and field pieces), the circulation of the occasions can be described between your field strip and the column strip. The column strip can be represented at beam A; field remove can be symbolized at beam B and beam C. since beam B and beam C are backed on beam A and beam A is rested directly on columns. The developed twisting second in beam A is bigger than that in beam B and beam C. because all beams are put through uniform fill (w) and beam A holds the effect WL/2 from beam B and c as well as the same uniform load (w). For an actual even slab, the percentage between your field strip minute and column strip moment is variable and depends on the flexural rigidity and the rectangularity proportion of the surface beams over the building perimeter (if any exists).

Distribution of Mo between column remove and field strip

As shown in this figure the total Statical instant (Mo) is divided into positive second and negative minute. In the interior spans, 40% of the Mo is distributed to the negative point in time and 60% of the Mo is distributed to the negative minute. This is roughly the situation for a beam set from both ends and uniformly packed where the positive second is (/24) 33% of the total moment of (/8) and the negative moment in time is (/12) 67% of the full total moment in time of (/8).

The syndication of the negative instant between the field remove and column strip varies based on the tightness of the edge beam. In case the border beam depth is significantly less than 3 x the slab width, 25% of the Mo is given to column remove. Regarding floors that are different in spans (within 20% difference), the negative point in time section of the slab is suitable for the bigger of both moments.

strip type

marginal beam

exterior bay

Interior bay

negative moment(exterior)

positive moment

positive moment(internal)

negative moment

positive moment

column strip

no beam

25

30

50

45

25

with beam

20

field strip

no beam

5

20

20

15

15

with beam

10

Column remove negative moment in time (45%)

Negative point in time (60%)

Field strip negative second (15%)

Mo (100%)

Column remove positive point in time (25%)

Positive second (40%)

Field remove positive minute (15%)

Moment syndication in inter sections (with or without marginal beam)

Column remove negative moment (35%)

Negative minute (50%)

Field strip negative minute (15%)

Mo (100%)

Column remove negative moment (30%)

Positive minute (50%)

Field remove negative second (20%)

Moment syndication in exterior sections with marginal beam

Provision for routine loading

If heavy live loads are subjected to the slab, negative moments shall form at mid span in addition to positive bending occasions. In the event the live insert (p) is greater than 1. 5 the dead tons (g), the negative bending in column remove in L1 way can be approximated as following equation

M (negative) = (g -) x () x

And the negative moment in the field strip in L1 route is

M (negative) = (g -) x () x

Where:

L1 = course in course 1

L2 = period in course 2

D = width of the column at slab intersection

g= uniform inactive loads

p= homogeneous live loads

Punching shear power of Flat Slabs

Punching shear strength is one of the very most critical design aspects in demining the width of the even slab. A couple of two shear failing mechanisms that may be encounter in a flat slab system.

One way shear

Two way shear

One way shear is comparable to that in beams, this kind of shear is almost never controls the smooth slab flooring surfaces design, the two way shear the failing surrounds the column creating a pyramid condition. The two way shear has stresses higher than a proven way shear. Two way shear failing device is usually come across in footing and in level slab. The interior columns are usually subjected to shear with negligible instant copy from slab to columns. Interior columns minute are not clear by the blend of shear but the mixture of shear and unbalanced second is evident at area and edge column locations, as a result of lateral lots and unequal spans. Elimination of punching inability of column lab connections transferring moment in time depends on exact calculations of shear tensions produced by the transfer of the moment. This research is produced by the ACI and Egyptian code of practice.

Design steps matching to Direct Design Method

Choose the appropriate chiseled slab system in line with the depth of the live fill and architectural requirements.

Assume the thickness of the slab in line with the code requirements.

Calculate the full total static minute to be resisted in the two directions.

Distribute the static point in time between column remove and field strip.

Divide the resulting moments by remove width to obtain the moment in time per meter.

Design the section to choose the support.

Design the slab for punching shear.

## The Equivalent Frame Method

In 1948 the Equivalent Framework Method was presented. It is used to analyze moments in any sensible frame building. Equal Structure Method is more basic than the Direct Design Method. In the event the structures do not gratify the geometrical and launching conditions or if the lateral weight due to earthquake or wind is present required by the code, then your building necessary to be analyzed by the Equivalent Frame Method. The Equivalent Frame Way for smooth slab system design is more correct method of examination than the Direct Design Method. A series of two dimensional frames are symbolized for the building, that are then analyzed for loads behaving in the planes of the structures. The statical moment in time (Mo) in the immediate method is computed for each period and divided between negative and positive moment regions in line with the code coefficients.

This method can be summarized as:

Moments are sent out at the critical areas by employing an elastic evaluation. Cases of loading need to be considered for the critical launching conditions.

Dimensions or launching have no limits.

Drop panels need to be considered in the research in the versions in the moment of inertia.

Equivalent frame is capable of doing the computation of lateral examination.

The total statical second calculated by using the Equivalent structure method cannot go over the moment (Mo) required by the immediate design method.

Structural analysis

The slab of comparative frames is split into a string in two perpendicular guidelines. These frames contain the slab, projected beams, drop panel and the columns above and below the considered floor. Then your frames are divided into field whitening strips and column pieces. To reach the maximum moment for the users, live insert is placed at the positioning where it can produce maximum moment. The total strip width can determine the inertia for the slab in case of analyzing vertical loads. As the column width plus three times the slab width from each area (can't exceed span / 3) can analyze as soon as of inertia for slab in case there is lateral load analyses. In lateral examination, the differences of earthquake and blowing wind forces must be modeled of full level of the building at each level. Calculations can be simplified by the examination of every floor and its own attached column singularly if the analysis is limited to gravity loads. Fixation is considered at the beginning and ending of the column at the intersection with the ground (slab). Changes in column combination section along the distance of the column due to the second of inertia of columns may be predicated on the gross area uncracked cement causing difference. Resisting moment in time is an outcome from the column which equivalent to the applied torsional strength. The torsional deformation because of the outdoor ends of the slab remove turn more than the central section. An comparative column replaces the real column and the transverse slab strip to take into account the rotation and deformation.

Elements of the equivalent frame method

The sum of the flexibilities of the genuine column and slab strip is equal to the overall flexibility of the equivalent column.

## = +

The stiffness of a member is the inverse of the versatility of this member, these formula can be written as

## =

## =

From above formula can be explained by making a similarity between the system of two springs and the equivalent column. The amount of both individual displacements equals the total deformation of both systems. If an individual planting season with an similar stiffness is being replaced by both springs. When indistinguishable fill (P) is applied by the end, the next system and the initial system must deflect in the same way. By equating the deflection of system someone to that of the same system two, it gives

‹ = +

The connection between drive and displacement for a planting season is P = K ‹, the aforementioned equation can be expressed in terms of the stiffness and applied fill (P)

K = spring and coil stiffness

## + =

By dividing both factors with p, it offers the following equations

## + =

The above equation is comparable to that of code but includes a summation sign to take into account the possibility of contributions from columns at the start and ending of the slab. Torsional member has an approximate manifestation for it's rigidity, predicated on the results of three dimensional analysis of varied slab configurations is distributed by the following equation

= ( )

= modulus of elasticity of concrete

= the transverse dimensions of the column, comparative column, capital

= the center to middle distance assessed perpendicular to the evaluation direction

Cross sectional continuous (C) can be told specify torsional properties as

C = ((1-0. 63 ) )

X = shorter sizing for the member

Y = longer dimensions for the member

Torsional member involves slab and beam; section can be divided into a number of rectangles.

moment type

percentage of point in time from total moments

column strip

field strip

negative moment in interior panel

75

25

negative moment in external surfaces panel

80

20

positive moment

55

45

Distribution of column remove and field remove in equivalent body method

Equivalent column and similar spring and coil system

Column remove and field remove in the same frame method

Use of computer in the equivalent frame method

The equivalent framework method was derived by let's assume that the structural analysis would be carried out utilizing the moment circulation method, fixed end point in time, stiffnesses and equivalent column stiffnesses are computed for use in this analysis. If a standard frame examination program based on the tightness method is usually to be used. The frame must be specially modeled to get answers that agree with those from the equivalent frame method. The Portland concrete relationship has written and preserves the computer program ADOSS "Analysis and Design of Slab Systems".