Design of beam, slab and column

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Nov 24, 2024

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Contents I. Introduction: ............................................................................................................................. 2 II. Design of beam: .................................................................................................................... 2 III. Design of column: ................................................................................................................. 8 IV. Slab Design ......................................................................................................................... 10 V. Discuss briefly, a minimum of five sustainable factors considered in the RCC design, and provide different sustainable methods of design? .......................................................................... 14 VI. Describe the 5 top elements that affect the design process, including climate change as a factor. …………………………………………………………………………………………….15 VII. Result and discussion .......................................................................................................... 17 VIII. Conclusion ...................................................................................................................... 18 IX. References ........................................................................................................................... 18

Structural Design I. Introduction: This study uses Eurocode design standards to develop and assess residential construction beams, slabs, and columns. All these elements must be built to assure the safety, lifespan, and sustainability of the structure. The project's goal is to include students in the entire design and assessment of a supplied plan, with an emphasis on the practical use of theoretical knowledge and analytical abilities in the context of structures. The primary goal is to build a greater grasp of the concepts behind structural design and analysis. The significance of this research rests in its capacity to bridge the gap between theoretical knowledge and actual implementation. Students gain critical problem-solving, critical thinking, and decision-making abilities in the subject of structural engineering by participating in the design and assessment process. This hands-on training not only improves their academic performance but also prepares students for real-world workplace issues. Finally, this task is critical because structural elements design and analysis assure the safety of the building and its occupants. Due to poor design or construction, structural breakdowns can result in property damage, injury, or death. As a result, building structural components must be correctly designed and evaluated to meet safety and performance standards. II. Design of beam: From the following figure I have to design any beam of Bedroom 1 having L = 5 m. So, Ly/Lx = 5/5 = 1 < 2 Therefore, it’s a two-way slab in square shape i.e., Ly = Lx = 5 m. So load will transfer to beams equally.

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Design perimeters Length (L) of Slab Panel = 5m Width (W) of Slab Panel = 5m Grade of concrete = 30 MPa Live Load = 5.5 kN/m 2 Take Fy = 500 N/mm 2 Estimate Preliminary Size of beam: Assume simply supported beam having dimensions,

h = Span/15 h = 5000/15 h = 333.33 mm b = 0.5*h b = 0.5*333.33 b = 166.66 mm Try beam Size 200x500. Loads Calculation: As the slab panel is square shaped therefore load will transfer equally on all beams of the panel.

Assume beam size 200×500 and simply supported. Cover = 35mm for XC2 exposure (Table 4.1) Assume 20 mm diameter bar, and 10 mm diameter bar for stirrups. d = 500 – 35 – 20/2 - 10 = 445 mm Load Calculations: Load transfer to B-1 will be = Area of triangle*W Live load transfer = (5*5/4) *5.5 = 34.375 kN Uniform distributed load of slab on beam = 34.375/5 = 6.875 kN/m Self-weight of the slab = Slab thickness*Concrete Unit weight Self-weight of the slab = 0.175*25 = 4.375 kN/m2 Dead load transfer = = (5*5/4) *4.375 = 27.34 kN Uniform distributed load of slab on beam = 27.34/5 = 5.46 kN/m Self-weight of the beam = 0.55*0.2*25 = 2.75 kN/m Total dead Load = 5.46 + 2.75 = 8.21 kN/m Ultimate load (w) = 1.35G k + 1.5Q k = 1.35×8.21+1.5×6.875 = 21.396 KN/m Design moment (M Ed ) = wl 2 8 = 21.396 × 5 2 8 = 66.86 KN-m Ultimate moment of resistance (M Rd ) = 0.167f ck bd 2 Ultimate moment of resistance (M Rd ) = 0.167×30×200×445 2 ×10 -6 Ultimate moment of resistance (M Rd ) = 198.42 KN-m Since M Rd > M Ed design as a singly reinforced beam. K o = M Ed f ck bd 2 = 66.86 × 10 6 30 × 200 × 445 2 = 0.056

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Z = d[0.5+(0.25-3K o /3.4) 1/2 ] Z = 445[0.5+(0.25-3×0.056/3.4) 1/2 ] Z = 421.80 mm A s = M Ed 0.87 f yk z = 66.86 × 10 6 0.87 × 500 × 421.80 = 364.4 mm 2 Hence from table 3.10, provide 2H16 (A s = 402 mm 2 ) at the tension zone of the beam. Provide 2H12 as a nominal steel on compression zone. Design shear Force: Design shear force (V Ed ) = 0.5*w*L Design shear force (V Ed ) = 0.5*21.396*5 = 53.49 KN Shear resistance of concrete f ck = 30 N/mm 2 C R, dc = 0.18/ ɣ c = 0.18/1.5 = 0.12 N/mm 2 K = 1+(200/d) 1/2 = 1+(200/445) 1/2 = 1.67 < 2 (O.K.) Assuming all the tension reinforcement is taken onto support and anchored. ρ 1 = A st /b w d = 402/200×445 = 0.0045 < 0.02 (O.K.) σ cp = 0 υ min = 0.035K 3/2 f ck 1/2 = 0.035×1.67 3/2 ×30 1/2 = 0.41 V R, dc = [C R, dcK (100ρ 1 f ck ) 1/3 + K 1 σ cp ]b w d V R, dc = [0.12×1.67(100×0.0045×30) 1/3 + 0]200×445 V R, dc = 41745.47 N ≥ (υ min + K 1 σ cp ) b w d = 0.41×200×445 = 36490 N Since V R, dc < V Ed shear reinforcement must be provided. Compression capacity of compression strut (V RD, max )

Assume θ = 21.8 o υ 1 = 0.6(1-f ck /250) = 0.6(1-30/250) = 0.52 f cd = α cc f ck / ɣ c = 0.85×30/1.5 = 17 N/mm 2 V RD, max = b w z υ 1 f cd /(cotθ+tanθ) V RD, max = 200× (0.9×445) × 0.52×17/(cot21.8+tan21.8) × 10 -3 V RD, max = 222.40 KN > V Ed (O.K.) Dimeter and spacing of link. V R, dc > V Ed ρ w, min = (0.08f ck 1/2 )/f yk = (0.08×30 1/2 )/500 = 8.7×10 -4 ρ w,min = A sw / sb w sinα A sw / s = 8.7×10 -4 ×175×1 = 0.174mm (assuming the use of vertical link) Maximum spacing of link, s max is. S max = 0.75d = 0.75×445 = 333.75mm Hence from table 3.13 provide H8 at 300mm centers, A sw / s = 0.335mm

III. Design of column: Let’s take Column C-2 which is a uniaxial column. The slab panel is square shaped so both beams will create same moments at the column. Mx = My = 66.86 kN-m Axial load on the column = tributary area*Intensity of loads Ultimate load (n) = 1.35G k + 1.5Q k = 1.35 × 7.1 + 1.5 × 5.5 = 17.83 KN/m 2 Actual load on corner column = 17.83*2.5*2.5 = 111.43 kN Let’s take column size b = 350 mm h = 400 mm Consider H25 as main bars. H8 for ties Take cover = 45 mm Fy = 500 MPa Fc = 30 MPa Clear height of column = 3200 – 550 = 2650 mm. Effective height of column = 0.75*2650 = 1987.5 mm Eccentric bending moment: 1. h/30 = 13.3 mm 2. 1987.5/400 = 4.96 mm 3. E = 20 mm (governs) Me = 111.42*0.02 = 2.22 kN-m Mtotal = 66.86 + 2.22 = 69.08 kN-m

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d2 = 45+8+25/2 = 65.5 mm d2/h = 65.5/400 = 0.164 from the design chart M total f ck bh 2 = 69.08 × 10 6 30 × 350 × 400 2 = 0.041 N f ck bh ❑ = 111.43 × 10 3 30 × 350 × 400 ❑ = 0.016 Asfky f ck bh = = 0.1 As = 0.1 x 350 x 400 x 30 500 = 840 mm2 As per the above data Provide 2H25 – As = 982 mm 2 /m (Not practical because minimum four bars to be use in rectangular columns) Therefore, use 1. 4H20 – As = 1257 mm 2 /m Tie bars: Tie bars must be (1/4) times of the main bars size. 20/4 = 5 mm, use 350H8 Ties bars spacing 1. No more than 20*Dia of bars = 20*25 = 500 mm 2. The least column dimension. (350mm, 400 mm)

IV. Slab Design Materials f ck = 30 N/mm 2 . f yk = 500 N/mm 2 Unit weight of reinforced concrete = 25 kN/m 3 Assumed diameter of bars = 10 mm Slab Panel: L y = 5 m L x = 5 m

L y L x = 5 5 = 1 (Two-way slab) Assumed nominal cover 35 mm. From table 4.7 try slab thickness = 150 mm. From table 7 a sx = 0.062 a sy = 0.062 Load calculation from table 6.1 and 6.2 Permanent, Gk Finishes = 0.6 kN/m 2 Services and ceiling = 1 kN/m 2 Live load = 5.5 kN/m 2 Design life 50 years Exposure class XC2 Slab self-weight = 0.22×25 = 5.5 KN/m 2 Total dead load = 0.6+1+5.5 = 7.1 KN/m 2 Ultimate load (n) = 1.35G k + 1.5Q k = 1.35 × 7.1 + 1.5 × 5.5 = 17.83 KN/m 2 Design for Bending (short span) Assume d = 220 mm d = h – cover – Dia/2 d = 220 – 35 – 10/2 d = 180 mm

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M sx = a sx nl x 2 = 0.062× 17.83 × 5 2 M sx = 27.63 kN-m M sx bd 2 f ck = 27.63 × 10 6 1000 × 180 2 × 30 = 0.028 Determine A s A sx = M sx 0.87 z f yk Where, z = [0.5+(0.25-0.882k) 1/2 ] d ≤ 0.95d Z = 0.95× 180 = 171 mm A sx = 27.63 × 10 6 0.87 × 171 × 500 = 371.44 mm 2 /m Provide H10 – 200 centers, A s = 393 mm 2 /m Check basic (span/d) ratio. Percent reinforcement = 100 A sx, req bd = 100 × 371.44 1000 × 180 = 0.20% This corresponds to basic (span/d) ratio of 34. Check actual (span/d) ratio = 5000 180 = 27.7 < 34. Hence d = 105mm is adequate Design for Bending (long span) M sy = a sy nl y 2 = 0.062× 17.83 × 5 2 M sx = 27.63 kN-m Since the reinforcement for this span will have a reduced effective dept, d = 180 – 10 = 170mm M sx bd 2 f ck = 27.63 × 10 6 1000 × 170 2 × 30 = 0.031

Determine A s A sy = M sy 0.87 z f yk Where, z = [0.5+(0.25-0.882k) 1/2 ] d ≤ 0.95d Z = [0.5+(0.25-0.882×0.031) 1/2 ] ×170 = 165.21 mm ≤ 0.95× 170 = 161.5mm Hence use z = 161.5 mm A sy = 27.63 × 10 6 0.87 × 161.5 × 500 = 393 mm 2 /m Provide H10 – 300 centers, A s = 393 mm 2 /m Check basic (span/d) ratio. Percent reinforcement = 100 A sx, req bd = 100 × 393 1000 × 170 = 0.23% This corresponds to basic (span/d) ratio of 32. Check actual (span/d) ratio = 5000 170 = 29.41 < 32. Hence d = 95mm is adequate

V. Discuss briefly, a minimum of five sustainable factors considered in the RCC design, and provide different sustainable methods of design? Because of its strength, durability, and adaptability, reinforced concrete (RCC) is a commonly utilized construction material in buildings and infrastructure. However, due to the enormous amount of energy required to make cement, a fundamental element in concrete, the production of concrete is known to have a considerable environmental impact. As a result, sustainable aspects and design approaches are significant concerns for RCC constructions. Here are five sustainable considerations that are taken into account in RCC design: i. Material Selection: The use of environmentally friendly materials may greatly minimize the environmental effect of RCC constructions. The utilization of recycled aggregates, such as crushed concrete or masonry fly ash or slag, can help to minimize demand for virgin resources while also reducing waste . ii. Water conservation: Construction waste is reduced by careful planning and effective material utilization during the construction process. Prefabrication and modular building approaches are being used to decrease on-site waste and improve overall construction

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efficiency. Furthermore, permeable concrete can minimize stormwater runoff and replenish groundwater. iii. Energy efficiency : structure energy efficiency may be enhanced by using insulated concrete forms, which lower the amount of energy required to heat and cool the structure. Optimizing the structural layout to reduce the quantity of concrete needed and, as a result, the total embodied energy. Incorporating thermal mass into the design helps improve energy efficiency by dampening temperature variations. iv. Construction waste management: Construction waste management may limit the quantity of garbage delivered to landfills while also conserving resources. The usage of precast concrete components can help to decrease construction waste. v. Life cycle analysis: Life cycle analysis (LCA) is a method for assessing a product's environmental effect across its full life cycle. LCA may be used to design RCC structures with a lower environmental effect. To summarize, sustainable RCC design entails a comprehensive strategy that takes into account material sustainability, energy efficiency, structural durability, waste reduction, and carbon emission reduction. Implementing these sustainable criteria via diverse design methodologies helps to the building industry's total environmental responsibility. Eurocode, a European standard for building and civil engineering design, specifies many sustainable design methodologies for RCC structures. Among these techniques are: I. Design for disassembly: This strategy entails developing RCC constructions with the goal of allowing the materials to be easily dismantled and reused. This cuts down on the quantity of garbage produced during demolition and construction. II. Durability design: Durability design is constructing RCC buildings to survive for a long period without requiring extensive maintenance or repair. This lessens the structure's environmental effect over its life cycle. III. Low carbon design: Low carbon design entails lowering the carbon footprint of RCC structures by using low-carbon materials like recycled aggregates and optimizing the design to utilize less cement.

IV. Life cycle assessment: As previously stated, LCA is a method used to assess a product's environmental effect across its full life cycle. Eurocode includes standards for doing LCA on RCC structures in order to maximize their sustainability. V. Energy-efficient design: Optimizing the energy performance of RCC buildings through the use of insulation, passive solar heating, and efficient lighting and ventilation systems is what energy-efficient design entails. VI. Describe the 5 top elements that affect the design process, including climate change as a factor. I. Environmental conditions : Geographical environmental factors, such as earthquakes, prevailing winds, and soil composition, all play an important impact in structural design. The seismic zone, speed of wind, and soil type all impact the materials, building systems, and design of the foundation. Climate change can cause changes in weather patterns, an increase in the frequency of severe occurrences (such as hurricanes and floods), and temperature variations. To ensure structural resilience and sustainability, design procedures must adapt to changing conditions. II. Building Function and Use : The structure's intended purpose and use have a considerable influence on the design approach. Building kinds, such as residential, commercial, and industrial, have various needs that impact material choices, spatial arrangements, and load-bearing capacity. Changing the climate may have an impact on building usage and demand patterns. Increased temperatures, for example, may need extra cooling system considerations, while alterations in precipitation patterns may impact drainage and flood-resistant design. III. Economic Considerations: Budget limitations, building expenses, and the project's economic viability all affect design selections. Cost-effective solutions that fulfil safety and regulatory criteria are critical design concerns. Climate-resilient designs may have greater initial costs, but the long-term advantages, such as reduced exposure to climate- related hazards, may offset the initial costs. Financial considerations might include preparing for the possible influence of climate change on the structure's lifespan and operation.

IV. Structural requirements: The most essential aspects influencing RCC design are the structural needs of a building or infrastructure project. These criteria are defined by the structure's function, load-bearing capability, estimated lifespan, and the safety features necessary to assure occupant and public safety. V. Sustainable and green design: As the emphasis on sustainability grows, designers are being encouraged to include eco-friendly practices, energy-efficient technologies, and materials that are renewable into their creations. The goal of sustainable design is to reduce the environmental effect of a structure during its existence. The increased awareness of climate change has increased the emphasis on sustainable design. To limit their contribution to climate change, designers are urged to examine the environmental consequences of their choices, such as material selection, energy use, and carbon footprint. Finally, the design process is a multidimensional endeavor driven by environmental circumstances, building use, economic considerations, regulatory constraints, and long-term sustainability aims. It is critical to address the influence of climate change within these aspects in order to create resilient, sustainable, and adaptable buildings. VII. Result and discussion The design drawing offered includes both the layout for a simply supported beam and a slab. The beam is 200 by 500 millimeters and has a 35-millimeter cover; the H20 bar is used for exposure. The load is calculated by taking into account both the self-weight of the beam and the load from the slab. The ultimate load has been determined to be 21.396 KN/m, and the design moment is calculated to be 198.42 KN-m. Because the ultimate moment of resistance will be greater than the moment intended for, the beam will be constructed as a single reinforced beam. The 2H16 bars are what are used to create the tension steel and 2H12 in compression zone. The shear force is measured at the center of support for shear design purposes, and the resultant computation is 53.49 KN. Shear reinforcement is critical, and it has been found that the compression strut's compression capacity must be greater than the shear force intended into it. The equations for the minimum and maximum spacing of links are used to calculate not only the diameter of the links but also their spacing. The minimal reinforcement ratio has been established to be 0.0045, which is less than 0.02. As a result, give H8 at 300mm centers.

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RCC columns are critical elements of structure that provide structures with strength and stability. Their adaptability enables architects and engineers to design a wide range of buildings, while the reinforcing steel included in the concrete increases load-bearing capability. Because of their durability and fire resistance, reinforced concrete columns are essential to the lifespan and safety of modern structures. Columns are the critical members of the structures. The dimensions of the slab are recorded on the plan as Lx = 5 meters and Ly = 5 meters. When calculating the dead load, it is assumed that there is a live load of 5.5 KN/m2 and that the unit weight of the slab is used as input. The ultimate load has been determined to be 17.83 KN/m2. It is vital to account for both the positive and negative moments that occur at the supports when computing the design moment and shear force. The thickness of the slab is defined by the span- to-depth ratio, and H10 bars are utilized for reinforcement. The results of the proposed computation may be used in the design of reinforced concrete beams in the field of civil engineering. To ensure that the beam can safely bear the predicted loads, the computed values of maximum moment capacity and shear capacity may be used to determine the required beam size as well as the reinforcements that need be added to it. VIII. Conclusion The reported calculations for design for the beam, columns and slab appear to be correct and in accordance with standard design methods. The calculations offer the necessary information for selecting suitable reinforcement and slab and beam sizes to safely handle the induced stresses. Nonetheless, it is critical to ensure that the design is in accordance with the project's specific conditions and requirements, as well as local building rules and regulations. It is also recommended that the design be reviewed and approved by a professional structural engineer before construction begins. IX. References 1. Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings. (2004). European Committee for Standardization. 2. Wight, J. K., & Leonards, F. (2015). Reinforced concrete: mechanics and design. Pearson. 3. Nilson, A. H., Darwin, D., & Dolan, C. W. (2010). Design of concrete structures. McGraw-Hill.

4. Zohrevand, P., & Kaveh, A. (2017). Optimum design of reinforced concrete buildings using an artificial bee colony algorithm. Advances in Engineering Software, 112, 22-31. 5. Al-Salloum, Y. A., & Almusallam, T. H. (2009). Load-carrying capacity of reinforced concrete columns strengthened with FRP under eccentric loading. Construction and Building Materials, 23(3), 1383-1393.