STRUCTURAL DESIGN OF SLABS

STRUCTURAL DESIGN OF SLABS

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The main goal of structural analysis is the accurate determination Design analysis is a significant move for the optimal design of structures. Also for the distribution of moments and internal forces over the whole part of a structure and for identification of critical design parameters and conditions at all respective sections. The type of analysis to be used should be appropriate to the problem in consideration. Considerations of the structure made up of linear elements and plane 2-dimensional and 3-dimensional elements in our case of a limit state. Moments derived from the elastic analysis may be distributed further up to maximum levels of 30% as long as the resultant moment distribution remains at equilibrium state which the loads applied and contingent on design criteria and certain limits example limitations of the extent to the neutral axis.

Inconsiderate of the analysis method used the following doctrines will always apply

• Continuous slab: That is over the support that may be considered not to provide circulatory restraint, the moment calculations at the centre line of the supporting beam may reduce drastically where t is the breadth of support and as the support reaction.
• For the designing of the columns, moments from the frame action used without any form of redistribution to any parts of the structure.
• Monolithic slab: The critical design hogging moment may be used like that at the face of the support, but always taken as less than 0.65 times the full fixed end moment value.

The development of different methods of such study have been evaluated and adequately documented (Simoez and Muttoni, 2016, 82). This paper presents a promising approach analytically assessed as well as numerical through a simple slab with precise dimensions.An optimal of stresses on a prespecified line that will help any profound engineer come up with the right judgement in the selection and selection of appropriate design principles and material use. For the calculation of total loads on the slab, beam, and column we must know about the various load coming on the column and these loads include;

1. Self-weight of column x number of columns
2. Self-weight of beam per running meter
3. A load of wall per running meter
4. The total load of the slab (self-load + live load + dead load)

For Columns

Columns are subjected to bending moments which are considered in the final design. STAAD Pro and ETABS  are advanced structural design software used to come up with the most outstanding designs.

The following are assumptions that we use for structural loading calculations:

Self-weight of concrete should be around 2400kg/

Self-weight of steel is around 800kN/.

Even with the 350mm x 350 mm assuming 1% steel and 3m standard height, the self-weight of the column is around 10kN. So in my calculations, I assume self-weight of the column to be between 10kN to 15kN per floor.

For Beams

Similar calculations are done like for columns. Each meter of the beam has dimensions of 250mm x350mm excluding the thickness of the slab with self-weight of 3kN/

For Walls, the density of one brick varies from 1250 – 2100kilogram per cubic meter. For a 6″ thick wall of 3-meter height and length of  1 meter we can calculate load per turning meter to be equal to 0.15 x 3 x 2000 x1= 900 kilograms, that is 9.0 kN/m. the same technique is used to calculate load per running meter for any type of a construction brick.

For slab

Assuming slab thickness to be 130mm, now each square meter of the slab weight should have a slab weight of 0.13 x 2400 equating to 3KN.  We assume load to be 1kN per meter and superimposed live load to be 2KN per meter. We can calculate the load on the slab to be around 6kN to 7.5KN per square meter.

Shear force  = ∑(forces on one side of the section) = rate of change of bending moment

Bending moment =∑(moment of power on one side of a section) = (shear force) = area of shear force diagram.

STRUCTURAL DESIGN PROCESS

The shear stress of a slab may be calculated by procedures given in BS 8110, CL.3.5.5.2. ( Arangjelovski and Havok. D, 2016, 33 ) Various experiments that have been carried out show that as compared to beams s pieces fail slightly at higher shear stresses, and this is included in the value of design ultimate shear stress.

DESIGN OF A ONE-WAY SLAB

A slab is considered to be one way when it is supported on all the four sides, and the ration of short span to long-span is greater than or equal to 2,

a)minimum thickness values for a one-way slab  have been carefully specified by ACI Code 9.5.2.1

The span length may be taken as equal to the depth slab plus the clear span but should not exceed the distance between the centres of supports.ACI Code 8.7.1. The thickness h of the flexural bars should be 1/3 of the lateral spacing. Also, lateral spacing, according to ACI Code 7.6.5, should not be placed wider apart than five times the thickness of the slab of 18 inches according to ACI Code 7.12.2. also, the reinforcement ratio comes in here as a very important aspect during the design process. It is the ratio of the area of reinforcement to gross concrete area based on the exact total depth of the slab that is going to be used. For our one way slab, the rectangular sections are imperilling of shear and moment. Consequently, the maximum reinforcement ratio corresponds to a net tensile strain in the reinforcement

As from minimum reinforcement ration, two concepts should be understood clearly. One th temperature and shrinkage reinforcement should be because we are using concrete grade “C30” = 37 (ACI Code 7.12.2.1). Secondly, flexural reinforcement should not be less than shrinkage reinforcement that is at minimum or 0.0018

slab

L                                                        L

Support beam

Thickness estimation

h =  for deflection = L/28

L = beam spacing =25ft

Therefore  = (25 x 12)/28 = 10.7142

We will use h = 11.0

Shear

From the three approaches of designing for shear our case has  considered the one when reinforcement is required because even from our original data we have been instructed that reinforcement has been used where checking of shear in the beams is done using strut method

A strut strength check is done using   and links strength is checked using

Eurocode 2 uses the variable strut method for checking of a member with shear reinforcement

The following definitions are used in this method in shear calculations

= applied shear force which may be checked at d from face support

= resistance of member without shear reinforcement

= resistance governed by the yielding of shear reinforcement

= resistance member, governed by the crushing of compression struts

V ()

d               α                                                                           V       1/2z        z=0.9d

s

Shear reinforcement

α = angle between shear reinforcement and the beam axis

θ  =  angle between concrete compression and the beam axis

z = inner lever arm normally 0.9d is used

= is the minimum width

= Area of the shear reinforcement

design compressive strength =/1.5=  /1.5 = 30/1.5

=1.0 for shear)          =20

= coefficient of stress in compression chord

=strength reduction factor concrete cracked in shear   = V =0.6(/250 )

=0.6(1-30/250) =0.928

Since the width of our beam considered to be 1.0ft

Dead load (DL) will be 150 x 6.5/12 = 81 psf

Live load (LL) =100 psf

Total factored load DL and  LL =100 x1.6 + 81 + 0.928

= 241psf

In designing of the RCC, this paper shows how ultimate load method (ULM)can be used that works based on the ultimate strength of the reinforced concrete known as the load factor that necessitates an appropriate safety margin.

Given the following information;

Width (Lx)=2.4m

Length (Ly)=6.7m

Length (L)=2.8m

Variable load on the slab=3KN/

=30

Characteristic strength of steel  =500

Unit weight of reinforced concrete=24KN/

Volume of the slab= (Lx) x (Ly) x (L)

=2.4m x 6.7m x 2.8m=45.024

If   1=24KN

45.024

Analysis of a singly reinforced bay

Such analysis implies the determination of the ultimate moment of resistance of this section. This is easily obtained from the couple resulting from flexural stresses. (Nguyen and Tanapornraweekit,2016, 117, 121)

Limiting span-to-depth ratio and theoretical deflection assessment are the two methods of designing for deflection.

Where  are the resultant (ultimate) forces in compression and tension, respectively, and z is the lever arm?

.         for

And the line of action of corresponds to the level of the centroid of the tension steel

Concrete stress block in compression

Having in mind Unit weight of reinforced concrete=24KN/

The value of can be computed knowing that the compressive stress in concrete is uniform at 0,447 for a depth of 3/7 and this it varies parabolically over a depth of 4/7

For a rectangular section of width Lx=2.4m

= 0.447

Therefore =0.8664

Also, the line of action of  id determined by the centroid of the stress block located at a distance  from the concrete fibre subjected to the maximum compressive strain. Considering moments of compressive forces   about the maximum compressive strain location

(0.362=0.8664

Solving x =

Depth of neutral axis

For any given section of the depth of the neutral axis should be such that  satisfying equilibrium of forces. Equating  in the expression for

valid only if resulting

Shear stress

The distribution of shear stress in reinforced concrete rectangular beams

Curve line

NA             d      Ly                    straight line

In beams of uniform depth

=

Where =shear force due to design loads

b=Lx=breadth of rectangular beams and d= Ly= effective depth

Design shear strength of reinforced concrete

Experiments confirmed that reinforced concrete in beans has shear strength even without any reinforcement. This shear strength depends on the grade of concrete and percentage of tension steel on the beams. On the other hand, the shear strength of reinforced concrete with reinforcement is restricted to some maximum value

In case of bent up bars, it is to be seen that the contribution towards shear resistance of bent up bars should not be more than 50% that of the total shear reinforcement.

Shear force is given by

For a single bar

Discussion

The method used for the analysis of reinforced concrete slab gives supreme values for the collapse load of slabs. However, in morally same cases of slab geometry and loading calculations, the yield line method can be used as a design method because the fracture pattern can be obtained with reasonable accuracy. We can also practically conclude that the actual collapse load of a slab load may be above the calculated value because of secondary effects such a kinking of the reinforcing steel in the presence of the fracture line and the effect of horizontal edge restraints which includes very high compressional forces in the plane of the slab within a consequential increase in the capacity of a load. Alternatively, to yield line theory, the strip method proposes by Hillerborg,1960 at Stockholm. This method is a direct design procedural technique as opposed to yield line theory which is analytical and therefore applies less here. One of the most notable results corresponds to the combination of load, in our case the maximum negative and positive bending  moments a

In the slab are concentrated at the edges of the wall, and they are greater than those provided by the capacity of the slab for the condition of design of service vertical. When the horizontal load is increased, bending moments increase much more.

Conclusion

The goal of this paper was to evaluate and design a simple bay only of a building that has to be constructed in  Al Mawaleh, Muscat,  Sultanate of Oman. Most of the calculations carried out throughout this study show the shows the behaviour of slabs under variable load. But slabs are often subjected to concentrated loads which is what should be considered in most cases. One-way slab designs are very costly and meant to last for a very long life span. Appearance and durability are designed to be satisfactory; this is possible by limiting the crack widths. The limits outlined in the Eurocode apply to either the size of bar or bar spacing, not both.

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