# Free Comparison between BS8110 and Eurocode BS EN1992 in the Bending and Deflection of Reinforced Concrete Slabs Dissertation Example

BENDING AND DEFLECTION OF REINFORCED CONCRETE SLABS

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Introduction

The deflection of beams in structural applications is a physical phenomenon that depends on several factors such as the span, thickness and the loading characteristics of the beam. The load carrying capacity of slab depends on the load applied to the beam and the beam characteristics (Al-Sunna, 2012). The load causes bending stress within the power-transmitting member that varies from zero (0) at the center of the slab to a maximum at the surface of the slab. The slab will fail as a result of bending stress if it is not properly designed. The bending test can be used to investigate several shearing properties of the specimen. Some of these properties are the proportional limit, yield strength in span, the thickness of the beam resilience and stiffen (Bednář, 2013).

The marine engines generate high loads to propel the vessel through the water. The marine slabs are therefore made of a material that can resist high loads. The slab should also be able to be resistant to corrosion and also high bending strength too. The best material to slab us thus stainless steel of high bending strength (Choo, 2014).

Most of the structural components are tested for their tensile and torsional strengths to ensure that they are safe for the structural components. For the testing of the slab components, the specimen is subjected to bending test as well as bending test. The modes of the failure of the components are examined to come up with the correct material and dimensions in the process of designing the slab (Kong, 2014). The ductility depicts the strength of the metal and the toughness of the metal used. Mostly, stainless steel is used for the structural purposes because it has high strength compared to the other metals. The metal is also resistant to corrosion hence the best fit for the marine applications (McCormac, 2015).

The Analysis of Results

The design of the slab considers working stresses of the application and the level of safety. The material and the dimensions of the designed slab depend on the applicability of the slab. The main feature that is considered in the marine propeller slab is the bending resistance. The marine propeller slabs are subjected to high loads which can result in the failure of the slab if the design was not done properly.

The absolute load transmitted by the slab is due to the tangential force that generates twisting moment (load) (Mosley, 2015). The load generated is used to perform other tasks in the mast like propulsion. The machine elements which are mounted to the slabs make the slab bend. The design of the slab should then take into account the load and bending moments. The slab is mainly connected to the other parts by the use of the splines or universal coupling element (Qian, 2012).

The analysis of the results

Table 1: BSS10 150 mm 3KN/M

b (mm) h (mm) Concrete cover (mm) bar diameter (mm) fck (Mpa) effective depth, d (mm) Mu = 0.156fckbd^2 Span (m) Live Load (kN/m) Dead Load (kN/m) Design Load ω (kN/M) 𝛾𝐺= 1.4 𝛾Q=1.6

1000 150 10 16 30 132 81.54 1 3 5 11.80

1000 150 10 16 30 132 81.54 2 3 5 11.80

1000 150 10 16 30 132 81.54 3 3 5 11.80

1000 150 10 16 30 132 81.54 4 3 5 11.80

1000 150 10 16 30 132 81.54 5 3 5 11.80

1000 150 10 16 30 132 81.54 6 3 5 11.80

1000 150 10 16 30 132 81.54 7 3 5 11.80

1000 150 10 16 30 132 81.54 8 3 5 11.80

1000 150 10 16 30 132 81.54 9 3 5 11.80

1000 150 10 16 30 132 81.54 10 3 5 11.80

The table above shows the results for the 150kn/ m uniformly distribute the load. The breadth of the slab is 100 mm, and the thickness is `150mm. The variation in the span of the slab makes the bending moment to increase. The bending moment of the slab is a function of the length of the beam. The longer the beam, the greater the bending moment. The love load has been kept constant for the whole deflection. The dead load of the slab includes the weight of the beam. The designed loading magnitude is higher than the force applied to the load. The slab has therefore applied the safety factor concept. The bending moment for the slab is given by the load and the distance from the fulcrum. The bending stress is a function of the bending moment, the distance from the centroid and the moment of inertia for the slab. The deflection of the slab is there computed and varies according to the span of the beam. The shorter the beam, the less the bending moment hence the deflection of the beam.

Given the bending moment, the deflection of the beam for the various spans can be shown as in the table below

Table 2: Deflection

Span (m) Med (𝜔𝑙^2)/8 (kNm) k = Med / bd^2 fck

1 1.475 0.002821778

2 5.9 0.011287114

3 13.275 0.025396006

4 23.6 0.045148454

5 36.875 0.07054446

6 53.1 0.101584022

7 72.275 0.138267141

8 94.4 0.180593817

9 119.475 0.22856405

10 147.5 0.282177839

The graph for the area of the steel required against the span of the beam is as shown below

Figure 1: Graph for the As against the span

The results for the EC2 steel is as shown in the table below

Table 3: 150mm 3kn/m for EC2 Slab

b (mm) h (mm) Concrete cover (mm) bar diameter (mm) fck (Mpa) effective depth, d (mm) Mu = klimfckbd^2 (km) 085725δ00δ0466725δ00δ0447675δ200δ2

Span (m)

Live Load (kN/m) Dead Load (kN/m) Design Load ω (kN/M)

1000 150 10 16 30 132 87.82 1 3 5 11.25

1000 150 10 16 30 132 87.82 2 3 5 11.25

1000 150 10 16 30 132 87.82 3 3 5 11.25

1000 150 10 16 30 132 87.82 4 3 5 11.25

1000 150 10 16 30 132 87.82 5 3 5 11.25

1000 150 10 16 30 132 87.82 6 3 5 11.25

1000 150 10 16 30 132 87.82 7 3 5 11.25

1000 150 10 16 30 132 87.82 8 3 5 11.25

1000 150 10 16 30 132 87.82 9 3 5 11.25

1000 150 10 16 30 132 87.82 10 5 5 14.25

For the EC2 slab, the dimensions and the loading conditions are the same. However, the bending moments and the deflection are different from the BS8110. The trend of the moments and the deflection increases with the increase in the span of the slab. The live loading and the applied loads are, however, kept constant. The BS8110 slabs appear to be stronger than the EC2 slabs. The difference is caused by the modulus of elasticity of the beams and the reinforcement materials used. BS8110 slab requires less deflection than EC2 for the same span due to the difference in the modulus of elasticity (Soutsos, 2012). The design of the slab depends on the properties of the metal which the bending test was done. The characteristics of the metal which are investigated include the bending strength, the Poisson ratio and the modulus of rigidity. The isotropic metal’s properties are determined by the use of the uniaxial bending testing. In the case of the anisotropic metals, the biaxial bending testing is carried out.

The graph below shows the deflection of the slab per given span.

Table 4: Deflection results for the EC2

Span (m) Med (𝜔𝑙^2)/8 (kNm) k = Med / bd^2 fck1 1.40625 0.002690255

2 5.625 0.010761019

3 12.65625 0.024212293

4 22.5 0.043044077

5 35.15625 0.067256371

6 50.625 0.096849174

7 68.90625 0.131822486

8 90 0.172176309

9 113.90625 0.21791064

10 178.125 0.340765611

Figure 3: AS against the span for EC2

The analysis and the comparison of the results for the value of q = 4kN/m and thickness of the slab as 150mm

Table 5: q = 4kN/m BS 110

b (mm) h (mm) Concrete cover (mm) bar diameter (mm) fck (Mpa) effective depth, d (mm) Mu = 0.156fckbd^2 Span (m) Live Load (kN/m) Dead Load (kN/m) Design Load ω (kN/M) 𝛾𝐺= 1.4 𝛾Q=1.6

1000 150 10 16 30 132 81.54 1 4 5 13.40

1000 150 10 16 30 132 81.54 2 4 5 13.40

1000 150 10 16 30 132 81.54 3 4 5 13.40

1000 150 10 16 30 132 81.54 4 4 5 13.40

1000 150 10 16 30 132 81.54 5 4 5 13.40

1000 150 10 16 30 132 81.54 6 4 5 13.40

1000 150 10 16 30 132 81.54 7 4 5 13.40

1000 150 10 16 30 132 81.54 8 4 5 13.40

1000 150 10 16 30 132 81.54 9 4 5 13.40

1000 150 10 16 30 132 81.54 10 4 5 13.40

The span of the beam affects the bending moments acting on them. The deflection of the beam is a function of the bending moment. If the bending moment is increased, the deflection of the slab increases and vice versa.

The bending moments on the cantilever depending on the loading characteristics of the cantilever and the dimensions of the beam. The density of load applied might be varying or constant. If the load varies then the bending moment for the slab also keeps varying according to the magnitude of the load applied (Schladitz, 2012).

The rise in the varying load applied results to growth in deflection hence the area of steel required to decrease the deflection. The rise in the span length for the load applied leads to the multiplication in the warping of the slabs hence the deflection (Subramanian, 2013). The table below shows the effect of the varying load on the deflection of the beam.

Table 6: Deflection BS110

Span (m) Med (𝜔𝑙^2)/8 (kNm) k = Med / bd^2 fck1 1.675 0.003204392

2 6.7 0.01281757

3 15.075 0.028839532

4 26.8 0.051270279

5 41.875 0.08010981

6 60.3 0.115358127

7 82.075 0.157015228

8 107.2 0.205081114

9 135.675 0.259555785

10 167.5 0.320439241

The graph for the area of steel required versus the span of the beam is as shown below.

Figure 4: As against the span

The analysis and the comparison of the results for the value of q = 4kN/m and thickness of the slab as 150mm for EC2 slab

Table 7: 4kN/m EC2

b (mm) h (mm) Concrete cover (mm) bar diameter for middle spans (mm) fck (Mpa) effective depth of span, d (mm) Mu = klimfckbd^2 (kNm) 085725δ00δ085725δ00δ085725δ00δ0466725δ00δ0447675δ200δ20466725δ00δ0447675δ200δ2

Span (m)

Live Load (kN/m) Dead Load (kN/m) Design Load ω (kN/M)

1000 150 10 16 30 132 87.82 1 4 5 12.75

1000 150 10 16 30 132 87.82 2 4 5 12.75

1000 150 10 16 30 132 87.82 3 4 5 12.75

1000 150 10 16 30 132 87.82 4 4 5 12.75

1000 150 10 16 30 132 87.82 5 4 5 12.75

1000 150 10 16 30 132 87.82 6 4 5 12.75

1000 150 10 16 30 132 87.82 7 4 5 12.75

1000 150 10 16 30 132 87.82 8 4 5 12.75

1000 150 10 16 30 132 87.82 9 4 5 12.75

1000 150 10 16 30 132 87.82 10 4 5 12.75

The loading effect of 4kN /m on the EC2 slab is greater than for the 3kN/m load. The increment of the load leads to higher bending moments hence the deformation of the beam. Compared with the BS110 slab, it is weaker just as the latter case. The material for the component brings the difference. The live load for the component is raised from 3kN/m this case hence higher area of steel is required in this case than the other case. The love loading makes the material fatigued hence it deforms gradually. The dead weight remained constant hence the amount of the defection increment is due to the increase in live loading and the uniformly distributed load. The thickness of the material remained unchanged hence the moment of the area was constant for this case. The graph below shows the amount of the area of steel required against the length of the component.

Figure 5: Graph of As against the Span

For the values of 200kN/m for the BS110 Slab of thickness 200mm.

Table 8: 200kN/m BS110

h (mm) Concrete cover (mm) bar diameter (mm) fck (Mpa) effective depth, d (mm) Mu = 0.156fckbd^2 Span (m) Live Load (kN/m) Dead Load (kN/m) Design Load ω (kN/M) 𝛾𝐺= 1.4 𝛾Q=1.6

200 10 16 30 182 155.02 1 3 5 11.80

200 10 16 30 182 155.02 2 3 5 11.80

200 10 16 30 182 155.02 3 3 5 11.80

200 10 16 30 182 155.02 4 3 5 11.80

200 10 16 30 182 155.02 5 3 5 11.80

200 10 16 30 182 155.02 6 3 5 11.80

200 10 16 30 182 155.02 7 3 5 11.80

200 10 16 30 182 155.02 8 3 5 11.80

200 10 16 30 182 155.02 9 3 5 11.80

200 10 16 30 182 155.02 10 3 5 11.80

Conclusion

The increase of the breadth of the slab leads to the reduction of the deflection effect. The growth of the breadth leads to the multiplication into the moment of area. The moment of area is a function of the breadth. The increase of the live load and the varying load leads to the increment of the deflection. The area required for the steel against the span of the cantilever is less than the one for the 200KN/M for the EC2 slab.

The effect of the live load makes the deflection to be severe for the slabs of the given dimensions. The dimensions of the slabs and the reinforcement dictate the deflection of the beam. The bending moment of the two slabs for the constant loading is different due to the material characteristics.

References

Al-Sunna, R., Pilakoutas, K., Hajirasouliha, I. and Guadagnini, M., 2012. Deflection behaviour of FRP reinforced concrete beams and slabs: an experimental investigation. Composites Part B: Engineering, 43(5), pp.2125-2134.

Bednář, J., Wald, F., Vodička, J. and Kohoutková, A., 2013. Experiments on membrane action of composite floors with steel fibre reinforced concrete slab exposed to fire. Fire Safety Journal, 59, pp.111-121.

Choo, B.S. and MacGinley, T.J., 2014. Reinforced concrete: design theory and examples. CRC Press.

Kong, F.K. and Evans, R.H., 2014. Reinforced and prestressed concrete. CRC Press.

McCormac, J.C. and Brown, R.H., 2015. Design of reinforced concrete. John Wiley & Sons.

Mosley, W.H., Hulse, R. and Bungey, J.H., 2012. Reinforced concrete design: to Eurocode 2. Palgrave macmillan.

Qian, K. and Li, B., 2012. Slab effects on response of reinforced concrete substructures after loss of corner column. ACI Structural Journal, 109(6), p.845.

Schladitz, F., Frenzel, M., Ehlig, D. and Curbach, M., 2012. Bending load capacity of reinforced concrete slabs strengthened with textile reinforced concrete. Engineering structures, 40, pp.317-326.

Soutsos, M.N., Le, T.T. and Lampropoulos, A.P., 2012. Flexural performance of fibre reinforced concrete made with steel and synthetic fibres. Construction and building materials, 36, pp.704-710.

Subramanian, N., 2013. Design of reinforced concrete structures. Oxford University Press.

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