The flat slab that I analyzed was of the following properties; the distances between the grids are X1, X2, and Y1, Y2 are 6.00m, 6.00m, 6.75m, and 7.00m. the thickness 200mm. and the supporting columns are 300mm square. The loading are the variable loads is 3 kN/m2, the perment loads are partions load 1 kN/m2 and other is the self- weight. The wind load on the building is taken care by the bracing. The thickness of the slab 200mm which is to the nearest 25mm and satisfy the value of the design shear resistance in the EC2without the provision of shear reinforcement.
For the analysis of the flat slabs in accordance to EC2 can be achieved in the following methods: equivalent frame method, finite element analysis, yield line analysis, and the Grillage analogy. The following steps are used in the design of the flat slabs:
Design life – for our case the building is common structure (design life is 50 years)
Asses of the loading on the slab. in this case the ratio of the variable loads to permanent loads should be less than 1.25
Finite element analysis is the use of the ordinary or partial differential equation by a computer to solve wide range of structural problems. The FEA software in our case Midas Gen has the following features applicable that assist in the analysis of the structure, flat slab:
Any model should have nodes, elements, supports, and loads. Nodes can be free points. If not free, they are at the ends and intersection of elements. Elements can be inn our case plates and beams. A plate element is either triangular or quadrilateral with nodes at corners. Meshing is referred to the use of sub-division of surface members into elements. The mesh size I used is 250mm. the supports in the model will ensure that surface will not stand on its own. It provides the result of the bend moments between them which are realistic. The supports for the flat slab are columns. The column moment assist in the generation of punching shear stress.
MIDAS GEN was used to perform the FEA. I did it using the following procedure
Selected the units work with. Distance used Meters. Loading Kilonewton (KN).
The code of preference is EC2-04
Grid creation, used grid line
Named the grid, g
Grid spacing in x-axis 6.00, 6.00, 6.00, 6.00 and y-axis 6.75, 7.00, 7.00, 6.75. used the relative option.
Created nodes and add them in place of the column as the floor plan.
Created column as an element. Assigned properties, used DB option, size 0.3m square and material of grade C40/50. Added them as at the nodes as it had been showed in the plan and the height is -0.5m.
Created virtual beams as an element. Helped in producing the surface. Assigned properties, used users option size 0.001m rounded named it null. Added to connect columns, at position z0.
Modified the interior beams by translating (copying) parallel dy-0.3 and 0.3 those that are parallel to y-axis and did so those in the x-axis. The edge virtual beam translating (copying) to be at the edge of the column in the outwards side and 0.45m in the inwards side.
Auto meshed, by selected all the null elements, mesh type selected both triangle and quadrilateral. Side used is 0.5m. used create by element. The properties used material used C40/50and named slab, thickness of 0.2m, offset plate in ratio of 0.5 in local z. Generated plates on the surface.
Provided distinguishing colors for the plates and column by material.
Defined support at every column.
Created cases, deadload (self-weight and partition) and variable load
Self-weight assigned -4.8KN/m2. Partition load assigned -1.0KN.m2 as a pressure load. Variable load -3.0KN/m2 as a pressure load.
Auto-generated load combination for EC2. ccCB1 for ULS and ccCB2 for SLS
Performed analysis by pressing F5.
Clicked results to generate graphs and contours.
The contours of moment
Contours of stresses
Serviceability Check
Calculation
===============================================================================
[[[*]]] PUNCHING CHECK MAXIMUM RESULT DATA BY STRESS: DOMAIN 1-[10].
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-. Information of Parameters.
Node No. : 6248
LCB No. : 1
Materials : fck = 40000.0000 KPa.
Thickness : 0.2000 m.
Covering : dB = 0.0260 m.
dT = 0.0260 m.
-. Information of Checking.
v_Ed = 12583.8867 KPa.
u1 = 2.1803 m.
d = 0.1740 m.
u0 =1.5708e-008 m.
-. Basic control perimeter
rholy = 0.0042
rholz = 0.0042
rhol = min[ sqrt(rholy*rholz), 0.02 ] = 0.0042
k = min[ 1+(200/d)^0.5, 2.0 ] = 2.0000 (d in mm)
gamma_c = 1.500
v_Rd,c = max[ 0.035*k^1.5*sqrt(fck), (0.18/gamma_c)*K*(100*rhol*fck)^1/3 ]
= 626.0990 KPa.
RatV = v_Ed / v_Rd,c = 20.099 > 1.0 —> Not Acceptable !!!
(Need Vertical Reinforcements.)
fywd = 347826.0870 KPa.
fywd_ef = min[ 250+0.25*d, fywd ] = 293500.0000 KPa.
Asw/sr = (v_Ed-0.75*vRd_c)*(u1*d) / (1.5*d*fywd_ef) = 0.060 m^2/m. ( 0.060 m^2/m.)
(Calculating the outermost perimeter of shear reinforcement.)
uout,ef = v_Ed*(u1*d)/(v_Rd,c*d) = 43.8218 m.
Conclusions and Recommendations
To conclude this report has shown a full finite element model as well as a finite element analysis which shown above are the steps that were made to determine the most appropriate thickness for the slab which was rounded to the nearest 25 mm. Even though the flab flat of thickness 200mm is sufficient for our case. The best for flat slab should have drop heads which will be more sufficient to take the punching stress. This will lead to further reduction of the thickness of the slab of about 150mm.
Bond, A.J., Brooker, O., Harris, A.J., Harrison, T., Moss, R.M., Narayanan, R.S. and Webster,R., 2006. How to design concrete structures using Eurocode 2. FLAT SLABS
Cameron, D.A., 2002. Case Study of Courtyard House Damaged by Expansive Soils: Plan layout of raft slab. [Online] Available at: https://www.researchgate.net/figure/Plan-layout-of-raft-slab_fig3_245289967 [Accessed 26 March 2017].
Deplazes, A., 2005. Constructing Architecture: Materials, Processes, Structures. illustrated ed. Berlin: Springer Science & Business Media.
Joseph Lstiburek, J.C., 1996. Moisture Control Handbook: Principles and Practices for Residential and Small Commercial Buildings. reprint ed. New Jersey: John Wiley & Sons.
Günayd?n, H.M. and Do?an, S.Z., 2004. A neural network approach for early cost estimation of structural systems of buildings. International Journal of Project Management, 22(7), pp.595-602.
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