Construction sites are always bustling with activity as hundreds of employees work round the clock to give architectural dreams a shape and form. But behind the din of machinery and buzz of construction, there is a very stark reality: construction reigns as one of the most dangerous industries for workplace accidents, injuries, and deaths.
The Occupational Safety and Health Administration (OSHA) shows construction accounts for a significant portion of occupational fatalities yearly, with falls, electrocutions, and struck by objects being among the leading causes. Thus, ensuring construction worker safety isn’t just a moral imperative, but a legal requirement avoiding costly legal issues, protecting human lives, and the reputation of construction companies.
Here are the six (6) legal tips to follow when working on-site.
Obtain the Necessary Permits and Licenses
A critical step is getting the necessary permits and licenses before starting any construction project. This involves getting the right paperwork with legal authorizations from relevant authorities, as well as confirmation about the project’s compliance with local regulation standards.
However, failure to acquire permits has really bad legal implications, such as hefty fines, project shutdown, and serious legal action. The required types of permits will range from zoning regulations and building codes to environmental protection protocols, depending on the nature and scope of the project in question.
Comply with OSHA Regulations
OSHA ensures employees’ work environments are safe and healthful through the definition of rules and directions that are in line with many different industries, including construction sites. These policies aim at lessening dangers, stopping harm, and ensuring the well-being of the workers. Ideally, the OSHA regulations provide the basis for:
Legal Obligations and Worker Protection
Complying with OSHA requirements is not just about meeting legal obligations but also about giving the construction worker top consideration for his safety and health. Complying ensures that employers clearly demonstrate strong commitments to providing safe working environments.
Importance of Proper Safety Protocols
Having proper safety protocols under OSHA compliance means spotting the prospective hazards at a construction site, evaluating potential risks, and finding proper ways to control and mitigate those risks. It should cover broader areas for safety protocols, including operating equipment, handling hazardous material, and emergency response procedures.
Key Components of OSHA Compliance
Safety and health, according to OSHA rules, need to be approached with much detail. For example, constant checking helps in the determination of potential risks. Besides, all the workers should be provided with training and a complete set of means of safety needed to carry out the hazards. Moreover, the employer must make records of training, inspections, and incidents to display compliance with OSHA regulations.
Maintain Proper Documentation
Maintaining proper documentation proves vital for construction firms to show compliance with safety rules, conduct thorough inspections, and tackle any incidents or disputes occurring on-site properly. Furthermore, precise paperwork is a vital instrument defending corporate measures during court cases; thus, it is pivotal in lessening legal dangers. To ensure compliance and mitigate these risks, employers should establish clear procedures for documenting various safety measures, and any other relevant documentation pertaining to safety protocols and regulatory requirements.
In the unfortunate event of an injury due to negligence or unsafe working conditions, seeking legal counsel from experienced personal injury lawyers is essential. According to the legal team at Prochaska, Howell & Prochaska, experienced lawyers can help injured workers navigate the legal complexities and pursue rightful compensation. They will also ensure fair settlements on behalf of the injured party through negotiation and gathering essential evidence to build a strong case.
Implement Proper Safety Training Programs
Comprehensive training prepares workers with all the knowledge that they are supposed to have, in addition to the skills necessary to undertake jobs in ways that are safe and minimize risks of accidents and injuries. Thus, the lack of proper training endangers the workers and may place construction companies at risk of legal liability. Employers are to design and develop sound safety training programs, which must be custom-built and in line with the prevailing hazards on site.
For employers to develop good safety training programs, identifying the unique risks workers may face is vital. Conducting thorough assessments and understanding construction regulations is essential. Furthermore, the content should cover those risks like fall protection, equipment use, and emergency plans.
Implementation Strategies
Planning safety training programs needs thoughtful preparation and execution. Firms should schedule frequent training sessions to ensure all workers get proper instruction. Skilled trainers ought to be hired to deliver training, providing hands-on demonstrations and applied guidance.
Ongoing Evaluation and Improvement
Safety training programs require ongoing appraisal and enhancement. This involves getting worker feedback to gauge training effectiveness and pinpoint improvement areas. Training programs should be revised as required to tackle any shortcomings or emerging risks. Furthermore, through commitment to continual learning and progress, employers can ensure their safety training programs stay effective and relevant over time.
Importance of Comprehensive Safety Training
Comprehensive safety training is vital for several reasons. For instance, it:
Ensures workers are competent and prepared to handle the challenges and hazards that come with the job.
It helps in safeguarding against injuries, creating a safer workplace for everyone.
It helps avoid legal implications associated with inadequate training.
Ensure Compliance with Building Codes and Regulations
Construction projects must follow building rules. These regulations set standards for materials, designs, and construction methods. In addition, they protect people inside and outside the buildings. However, not following the rules can lead to fines, delays, or stopping work. So, construction companies need to know the latest codes for their projects. They must plan and build with these rules from the start, as it prevents legal issues and promotes safety during construction.
Establish Clear Contracts and Agreements
Putting clear contracts, agreements, and deals in writing is key for building projects. These papers show who does what, when, and how. Furthermore, they map out the plan, due dates, pay terms, and safety rules. Clear papers also help prevent mix-ups by giving guidance and settling disputes. Hence, by stating everyone’s jobs and rights, builders avoid legal issues, facilitating work to move on smoothly. Plus, open deals build trust among team members, contributing to the overall success of the projects.
Keeping sites safe matters for workers, passersby, and the environment – legally and ethically. Following the law, training workers, keeping records, and signing clear contracts creates safer places. In addition, firms reduce risks to workers and legal troubles. Caring about safety helps workers and projects as it shows the field acts properly. Moreover, it fosters a culture of responsibility and benefits all involved, thus boosting the image of construction.
Reinforced concrete (RC) slabs are a fundamental component of reinforced concrete structures, providing a versatile platform for floors, building occupancy, and various structural elements. They are material-intensive structural elements that take a lot of human and material resources to construct. Accurately calculating the quantity of materials for a reinforced concrete slab is very important for cost estimation, material procurement, and efficient construction planning.
It is very pertinent to point out that the quantity of materials required for the construction of reinforced concrete slabs is dependent on the architectural and structural design requirements of the building. Large-spanning floors will require more materials to construct compared to shorter floor spans. Furthermore, special structural features such as cantilever slabs will demand more construction materials compared to simply supported or continuous floors.
The basic materials required for the construction of suspended floor slabs in a building are;
(1) Concrete (cement, sand, stones, and water) (2) Reinforcement (floor mats and beam reinforcements) (3) Formwork (temporary wooden support platform consisting of joists, plywoods/planks, and props).
This article discusses the key steps involved in the calculation of the quantity of these materials required for the successful execution of any building construction project. We will use the floor slab layout in Figure 1 as a case study. All the supporting beams are 230 x 400 mm beams.
Figure 1: Typical layout of a floor slab
Step 1: Determine Slab Geometry
The first step involves defining the slab’s geometric parameters. These include:
Length (L): The horizontal dimension of the slab measured in meters (m) or feet (ft).
Width (W): The perpendicular horizontal dimension of the slab measured in meters (m) or feet (ft).
Thickness (T): The vertical dimension of the slab measured in meters (m) or inches (in).
For the slab layout above,
Length (L) = 5000 + 5000 + 5000 + 230 = 15230 mm = 15.23 m Width (W) = 6000 + 5000 + 230 = 11230 mm = 11.23 m Thickness = 150 mm = 0.15 m
Step 2: Calculate Slab Volume
Once the geometry is defined, the volume (V) of the concrete required can be calculated using the formula:
V = L x W x T V= 15.23 m × 11.23 m × 0.15 m = 25.654 m3
This volume represents the total amount of concrete needed to cast the slab.
Note: It’s important to ensure all units are consistent (e.g., all in meters or all in feet) to obtain accurate results.
Step 3: Account for Formwork
Formwork is the temporary structure that shapes and supports the concrete during the curing process. While not directly a concrete material, formwork influences the overall material quantity.
Figure 2: Typical floor slab construction in a low-cost low-tech building construction
Two approaches can be considered:
Direct Measurement: If the formwork design details are available, the volume of formwork materials (plywood, lumber, etc.) can be directly calculated using their dimensions and quantities.
Percentage Addition: A common practice involves adding a percentage buffer to the concrete volume to account for formwork material absorption and potential overestimation errors. This percentage typically ranges from 5% to 10% depending on the formwork complexity and project tolerances.
For the project layout under consideration, the floor slab will supported by 250 mm x 3500 mm boards (planks) typically called 1″ x 12″ boards in Nigeria. Ideally, the width of the board is supposed to be 300 mm, but experience has shown that the boards available in local markets rarely meet the dimensional requirements. These boards will be supported by 2″ x 3″ softwood joists/stringers spaced at 600 mm c/c, which will be supported on bamboo props spaced at 600 mm c/c.
Wooden plank (sheathing) requirement
Area of floor slab = L x W = 15.23 m × 11.23 m = 171 m2 Area of wooden plank = b x h = 0.25 × 3.5 = 0.875 m2 Number of 1″ x 12″ planks required = 171/0.875 = 196 pcs
Making a 10% allowance for waste, damages, and offcuts = 1.1 × 196 = 216 pcs (Note: This quantity does not account for the beam formwork requirements which should be calculated using the beam dimensions). If 1.2m x 2.4m marine boards are to be used, the quantity required will be approximately 60 pcs without accounting for waste and offcuts.
Figure 3: Boarding of a floor slab using 1″ x 12″ planks
Side edge formwork The thickness of the slab = 150 mm (therefore 1″ x 6″ board will be adequate for the edge formwork) Perimeter of slab = 2(15230) + 2(11230) = 52920 mm Number of 1″ x 6″ edge formwork required = 52920/3500 = 16 pcs
Timber Joist Requirement
To calculate the quantity of timber joists required, the recommended spacing of the joists is required. Using the length and width of the slab floor plan, you can calculate the total length of the timber joist required if the spacing is known. The number of wood materials required can then be obtained by dividing the total length of the timber joist by the supply length.
The supply length of most softwood timber beams in Nigeria is 12 ft (3.6m), but for quantification purposes, it is wise to use a shorter length, say 3.5 m. It is important to also ensure that good quality wood with the appropriate dimensions is supplied.
Recommended timber joist = 2″ x 3″ softwood (supply length is usually 3500 mm) Spacing = 600 mm
Pick the length of the slab L = 15230 mm Number of joists required along the length = 15230/3500 = 4.35 pcs Number of rows of joists required along the width of the slab = (11230/600) + 1 = 20 rows
Therefore the number of 2″ x 3″ wood required = 20 × 4.35 = 87 pieces Making a 10% allowance for waste, damages, and offcuts = 1.1 × 87 = 96 pcs
Alternatively, number of rows along the length (it can work with either the length or width) = (15230/600) + 1 = 27 rows Length per row = 11230 mm Total length of 2″ x 3″ required = 27 × 11230 = 303210 mm Number of pieces required = 303210/3500 = 87 pieces
Figure 4: Typical joist and bamboo arrangement in a low-cost low-tech building construction
Bamboo prop requirements
To obtain the quantity of bamboo props required, the same steps can be followed as were done for the joists. However, we should know that the bamboo props are individual ‘posts’ standing on their own at a given spacing. Using the recommended spacing of the bamboo, it is possible to calculate the number of bamboo along the length of the floor slab and multiply it by the number of rows along the width of the slab. This should give the total quantity of bamboo required for the slab.
Spacing of bamboo props = 600 mm in all directions Number of bamboo props along the length = (15230/600) + 1 = 27 Number of rows of bamboo along the width of the building = (11230/600) + 1 = 20 rows Total number of bamboo props required = 27 × 20 = 540 pcs of bamboo.
If it is assumed that a minimum of 2 pcs of bamboo can be obtained per supply length of natural bamboo, then 270 lengths of fully matured bamboo stem should be ordered. It is also possible to calculate the quantity of bamboo props required ”room by room”.
Step 4: Estimate Material Quantities for Concrete Mix
The next step involves determining the quantities of individual components required to produce the concrete mix for the slab. This is based on the specified concrete mix design, typically denoted as “M XX” (where XX represents the characteristic compressive strength in MPa).
Common mix designs include M20, M25, and M30. For M20 concrete, a concrete mix of 1:2:4 with a maximum water-cement ratio of 0.5 should provide a minimum compressive strength of 20 N/mm2 after 28 days of curing.
The specific quantities of cement, sand, and coarse aggregate (gravel) per unit volume of concrete depend on the mix design. However, a general guideline can be used for the initial estimation of a 1:2:4 mix ratio:
Cement: 6.5 bags of cement (50kg/bag) per 1 m3 of concrete
Sand: 1000 kg per 1 m3 of concrete
Coarse Aggregate: 1450 kg per 1 m3 of concrete
For 25.654 m3 of concrete;
Cement: (6.5 × 25.654 m3) = 167 bags of cement
Sand: (1000 x 25.654 m3) = 25654 kg of sand (25.6 tonnes of sand)
Coarse Aggregate: (1450 x 25.654 m3) = 37198 kg of granite (37.2 tonnes of granite)
Note: It is very important to consult the specific mix design for accurate material quantities. This information is typically provided by a structural engineer or obtained from ready-mix concrete suppliers.
Step 5: Quantify Reinforcement Steel
The amount of reinforcement steel required depends on the slab’s structural design. This information is typically provided on the structural drawings or by a structural engineer. The steel quantity is usually expressed in weight per unit area (kg/m²) or total weight for the entire slab (kg). It is therefore important that the accurate quantity of steel required is calculated from the structural drawing.
Common Steel Reinforcement Types:
Main bars: These primary bars resist the bending moments acting on the slab.
Distribution bars: These secondary bars distribute loads and prevent cracking.
Let us assume that for the slab above, Y12 @ 150 c/c has been recommended for the sagging and hogging areas, while Y10 @ 250 c/c has been recommended for the distribution bars. For 150 mm c/c spacing, a very rough estimate will show that 12.5 kg of 12mm bars is required per square metre of the slab, while 25% of the quantity of span reinforcement is required in the hogging areas. 15% of the span reinforcement is required as the distribution bar.
Figure 5: Typical rebar arrangement in a duplex construction
Bottom reinforcement required = 12.5 × (15.23 × 11.23) = 2137.9 kg of Y12 mm Hogging reinforcement required = (25/100) × 2137.9 = 534.475 kg of Y12 mm Distribution bar required = (15/100) × 2137.9 = 320.685 kg of Y10 mm
Alternatively;
Since the bottom reinforcement is placed at 150 mm c/c in both directions, we can calculate the total length of the rebars. We can increase the length and width of the rebars by 2m to account for the return bars. Ideally, this should extend by 0.15L into the span of the slab.
Total length of the slab = 15.23 + 2m = 17.23m Number of rows required at 150 mm spacing = (11.23/0.15) + 1 = 76 rows Total length required along the width of the slab = 17.23 × 76 = 1309.48 m
Total width of the slab = 11.23 + 2m = 13.23m Number of rows required at 150 mm spacing = (15.23/0.15) + 1 = 103 rows Total length required along the width of the slab = 13.23 × 103 = 1362.69 m
The total length of reinforcement required for the bottom rebars = 1309.48 + 1362.69 = 2672.17m
Rebars are supplied per 12m length, therefore, the total number of rebars required (in pieces)= 2671.17/12 = 223 lengths Total number of bottom rebars required (in kg) = 2671.17 × 0.888 = 2372 kg of Y12 mm (Note that the unit weight of Y12mm bars is 0.888 kg/m)
Knowing that the top reinforcements in RC slabs are supposed to extend 0.3L into the span of the slab, the quantity of the top reinforcements can also be accurately determined.
Conclusion
Accurately estimating the material quantities for an RC slab is essential for efficient project planning, cost control, and material procurement. This article has outlined a comprehensive approach to achieve this goal. By systematically considering the slab geometry, formwork influence, concrete mix design, and reinforcement steel requirements, engineers and construction professionals can effectively determine the necessary materials.
It’s important to remember that the initial calculations may require further refinement based on project specifics and the involvement of a structural engineer. However, this process provides a valuable foundation for informed decision-making throughout the reinforced concrete slab construction process.
Columns are major structural members in buildings, with the sole purpose of transferring vertical and horizontal loads from beams and slabs to the foundation. The design of columns is very important in ensuring the stability and safety of buildings. The prevalent column geometries in building construction encompass rectangular, circular, and square cross-sections.
While rectangular and square sections are very popular in building construction due to the rectangular nature of walls, instances favouring circular or other column geometries do arise. For instance, for architectural reasons, standalone columns in the middle of halls or walkways are preferably circular due to aesthetic reasons. Furthermore, circular columns exhibit superior seismic performance compared to rectangular ones. A thorough understanding of these rationales is important for structural engineers and architects, particularly during the scheme development stage.
Circular column in a building
This knowledge facilitates informed decision-making regarding column geometry, thereby reducing the risk of inadequate construction work. It is to be emphasized that the selection of column geometry holds significant importance, similar to the determination of size, orientation, and positioning of both columns and beams within the structural system. While rectangular and circular columns satisfy the same structural functions, they offer distinct advantages and disadvantages in terms of strength, design considerations, and preferred applications.
Rectangular columns in an institutional building
Selection Criteria for Column Geometry in Building Construction
The configuration of a column’s cross-section, similar to other building elements, is governed by a multitude of factors such as architectural aesthetics, ease of construction, functional requirements, and structural demands.
Aesthetic Considerations
Architectural appeal is one of the prominent factors influencing column geometry. Square and rectangular columns can be easily placed within walls and covered with plastering, such that nobody will know that the columns were there in the first place. When square columns are not feasible due to structural size requirements, rectangular columns can be employed, such that the width will be equal to the width of the wall. This leads to a smooth flow and alignment of walls without undesirable projections.
Square columns can easily be hidden in walls
On the other hand, circular sections are often favoured for their inherent visual harmony. However, their application is frequently confined to specific contexts such as luxury mansions, monumental buildings, educational institutions, verandas, and public buildings. Circular columns are preferable when the column element is standing alone since they will rarely blend into walls without projecting out of the wall lines.
Formwork Considerations and Cost Implications
There is a significant disparity between the construction of column formwork of rectangular/square and circular sections. Achieving a smooth, curved profile for circular columns demands enhanced craftsmanship and superior formwork materials, often including new plywood or aluminium systems.
This complexity translates to challenges in attaining a high-quality concrete finish. Likewise, plastering a curved surface to the desired level is considerably more intricate compared to a flat plane, leading to increased construction time and cost. Given the budgetary constraints inherent in many medium-scale projects, clients often prioritize cost-effectiveness, making rectangular/square columns more favourable.
Wooden formwork construction for circular column
Furthermore, the pressure exerted on column formwork by fresh concrete can be more complicated when compared with square or rectangular sections. Consequently, stricter quality control measures and more elaborate formwork support systems are mandatory on-site. The increased level of workmanship required for these considerations translates to a significant cost increase compared to rectangular column construction.
Circular columns in a highrise building
Functional Requirements
The intended use of a space significantly influences column selection. In office environments, columns often serve as display surfaces for artwork, signage, or bulletin boards. Rectangular sections provide inherently planar surfaces ideal for such applications. This rationale extends to basement parking areas, where rectangular or square columns offer suitable flat surfaces for traffic flow notices, warnings, and signage – commonly observed in shopping malls and other commercial establishments.
Structural Considerations
While circular columns generally exhibit superior seismic performance, specific scenarios necessitate enhanced stiffness in a particular direction. This is particularly relevant for slender buildings with a limited base width and an extended length. To achieve this, engineers may favour a rectangular column with a larger dimension oriented towards the slender direction.
Moment of Inertia
A critical factor in column strength is the moment of inertia (I), a property that reflects a section’s resistance to bending. Circular columns boast a higher and more uniform I value across all axes compared to rectangular columns. This translates to superior resistance to bending moments and deflection, making them ideal for structures subjected to high lateral loads, such as bridges.
Shapes of rectangular and circular sections
For rectangular sections, the moment of inertia (I) is given by; I = bh3/12
For circular sections, the moment of inertia (I) is given by; I = πD4/64
Let us consider a square column of dimensions 250 mm x 250 mm. This column will have an area of 0.0625 m2. A circular column that will produce a similar area will have a diameter of 282 mm.
The square section will have a moment of inertia I = bh3/12 = (0.25 × 0.253)/12 = 3.255 × 10-4 m4 The circular section will have a moment of inertia I = πD4/64 = (π × 0.2824)/64 = 3.104 × 10-4 m4
Therefore for sections of similar cross-sectional area, square sections have higher moment of inertia than circular sections.
Buckling Resistance
Another important aspect of strength consideration of columns is buckling, which is the tendency of a slender column to bend under compressive loads. Circular sections, due to their uniform distribution of material around the centroidal axis, offer superior buckling resistance compared to rectangular columns, especially when the load is not perfectly centred.
Material Efficiency
Rectangular columns, however, can be more material-efficient for specific loading conditions. By strategically orienting the rectangular section with the larger dimension towards the direction of higher bending moment, engineers can achieve optimal load-carrying capacity with less material compared to a circular column of equivalent area.
Reinforcement
Circular columns typically require more reinforcement bars due to their curved shape. While this can impact material costs, it also enhances their overall compressive strength.
Applications
Rectangular Columns:
Widely used in buildings due to their ease of construction and efficient space utilization in confined areas.
Preferred for load-bearing walls where columns can be integrated with the wall structure.
Suitable for situations where higher bending moment capacity is required in a specific direction by adjusting the rectangular section.
Circular Columns:
Ideal for bridge piers and other structures subjected to high lateral loads due to their superior bending and buckling resistance.
Used in open spaces or architectural features where their aesthetic appeal is valued.
Preferred in seismic zones due to their uniform distribution of strength across all axes.
Comparative Design of Square and Circular Columns
Investigate the design requirements of the two column cross-sections analysed above; Square section = 250 x 250mm Circular section = 282 mm (diameter) Axial load = 1000 kN (No bending moment considered except secondary moments) The effective length of the columns about the major and minor axis = 3000 mm√ Compressive strength of concrete = C20/25 Yield strength of reinforcement = 500 MPa
Square sectiondesign
Column slenderness about y-axis Radius of gyration; iy = h/√(12) = 7.2 cm Slenderness ratio (5.8.3.2(1)); ly = l0y / iy = 41.6
Column slenderness about z-axis Radius of gyration; iz = b/√(12) = 7.2 cm Slenderness ratio (5.8.3.2(1)); lz = l0z / iz = 41.6
Min end moment about y-axis; M01y = min(abs(Mtopy), abs(Mbtmy)) + eiyNEd = 7.5 kNm Max end moment about y-axis; M02y = max(abs(Mtopy), abs(Mbtmy)) + eiyNEd = 7.5 kNm Min end moment about z-axis; M01z = min(abs(Mtopz), abs(Mbtmz)) + eizNEd = 7.5 kNm Max end moment about z-axis; M02z = max(abs(Mtopz), abs(Mbtmz)) + eizNEd = 7.5 kNm
Ratio of applied to resistance axial loads; ratioN = NEd / NRd = 0.655 Exponent a = 1.46 Biaxial bending utilisation; UF = (MEdy / MRdy)a + (MEdz / MRdz)a = 0.899
Description
Unit
Provided
Required
Utilisation
Result
Moment capacity (y)
kNm
34.23
21.84
0.64
PASS
Moment capacity (z)
kNm
40.43
20.88
0.52
PASS
Biaxial bending utilisation
0.90
PASS
Circular section design
Column slenderness about both axis Radius of gyration; iy = iz = h / 4 = 7.1 cm Slenderness ratio (5.8.3.2(1)); ly = lz = l0y / iy = 42.6
Ecc. due to geometric imperfections (y-axis); eiy = l0y /400 = 7.5 mm
Min end moment about y-axis; M01y = min(abs(Mtopy), abs(Mbtmy)) + eiyNEd = 7.5 kNm Max end moment about y-axis; M02y = max(abs(Mtopy), abs(Mbtmy)) + eiyNEd = 7.5 kNm
As can be seen from the design results, under similar axial loading and support conditions, square columns and circular columns of equal area will demand approximately the same area of reinforcement. However, once uniaxial and bi-axial bending moments are involved, we should expect a completely different behaviour in the quantity of reinforcements required.
Conclusion
The choice between rectangular and circular columns depends on a project’s specific requirements. When prioritizing strength and buckling resistance for structures like bridges or seismic zones, circular columns are often favoured. However, for ease of construction, space optimization, and cost-effectiveness in buildings, rectangular columns are the preferred choice. Understanding the strengths and limitations of each shape allows engineers to make informed decisions for optimal structural performance and aesthetics.
In conclusion, the selection of column cross-sectional geometry necessitates a comprehensive evaluation involving architectural intent, functional considerations, and structural demands. While aesthetics may favour circular columns in specific scenarios, the complexities and cost implications associated with formwork often render rectangular/square sections the more pragmatic choice for many building projects.
Piled raft foundations represent an economical and practical solution for situations where a conventional raft foundation falls short of design requirements. This type of foundation system strategically integrates a limited number of piles beneath the raft, allowing the raft itself to still contribute significantly to the load-bearing capacity.
This key distinction separates them from traditional pile foundations, where the primary responsibility for supporting the structure rests solely on the piles. Consequently, piled raft foundations occupy a unique position within the broader category of pile foundation systems, necessitating more complex analytical, design, and application considerations.
The piled raft foundation system itself comprises three key components:
Piles: These deep foundation elements transfer heavy structural loads to deeper and more stable soil layers.
Raft: This shallow foundation element distributes loads across its footprint, primarily utilizing the near-surface bearing capacity of the soil.
Supporting Soil: This plays a critical role in transmitting loads from the structure to the foundation system.
Figure 1: Load transfer in piled raft foundation systems
By combining the capabilities of piles and rafts, the piled raft foundation system offers a synergistic solution for supporting heavy structures. It leverages the deep load-bearing capacity of piles while simultaneously utilizing the shallow load-carrying capacity of the raft. This combined approach effectively resists both vertical and lateral loads, ensuring the serviceability and stability of the structure.
Load-settlement behaviour within piled raft systems is influenced by a multitude of factors. The physical and mechanical properties of the soil, raft foundation, and pile foundation all play a significant role. Furthermore, the construction sequence of the building itself can also exert an influence. While a range of simplified, approximate, and advanced methods exist for analyzing this complex system, the most realistic results are typically obtained through the use of advanced finite element analysis.
Piled raft foundations have become a prominent choice for a wide range of demanding construction projects. Their versatility and ability to handle challenging soil conditions make them ideal for high-rise buildings in urban centers, where maximizing footprint usage is crucial. Landmark structures like the Burj Khalifa in Dubai and the Shanghai Tower in China employed piled raft foundations to ensure stability and support their immense weight.
Figure 2: Burj Khalifa tower foundation was built with piled raft
Piled rafts also find application in infrastructure projects such as offshore wind turbine installations, where they provide a stable base for these towering structures amidst wind and wave loads. Furthermore, their ability to resist buoyancy is valuable for projects on sites with high water tables, such as waterfront developments or structures built on reclaimed land.
Types of Piled Raft Foundation
Piled raft foundation can be broadly categorised into two;
Piled raft for settlement control, and
Piled raft for load transfer
Piled raft for settlement reduction While raft foundations can offer adequate bearing capacity, they may still be susceptible to excessive settlement. Traditionally, this issue is addressed by incorporating a basement and a basement raft, which effectively reduces the total load acting on the foundation system. However, when this approach is not feasible, an alternative solution involves introducing a limited number of piles beneath the raft.
These piles function by transferring a portion of the overall load away from the raft itself. As the piles do not need to carry the entire load, the required number is significantly lower compared to a traditional piled foundation design. Additionally, due to this load redistribution, the settlement experienced by the raft is brought within acceptable limits.
Piled raft for load transfer The second category of piled rafts, designated as “conventional,” finds application in scenarios where the underlying soil exhibits pronounced weakness and a high water table is present. In such conditions, the adoption of a raft foundation becomes essential.
These rafts serve a dual purpose: first, resisting the buoyant forces exerted by the groundwater, and second, transmitting all net structural loads to the piles for transfer to deeper, more competent soil layers. Consequently, the number of piles necessitated in this scenario will be considerably greater compared to the previous case described.
In essence, piled raft foundations offer a synergistic approach to foundation design, leveraging the strengths of both piles and rafts. The raft’s ability to share the load and reduce differential settlements, coupled with the piles’ capacity to act as “stress reducers” and “settlement reducers” while enhancing the overall bearing capacity, paves the way for efficient and reliable foundation systems, particularly in challenging soil conditions.
Load Transfer and Sharing in Piled Raft Foundation
The load distribution in foundation systems plays a crucial role in determining the interaction between the structure and the underlying soil. While a footing or raft primarily affects the shallow soil layers (approximately 1-2 times its width), pile foundations transfer loads to deeper strata. Combining these two approaches in a combined Pile and Raft Foundation (CPRF) system creates a complex interplay influenced by several factors.
These factors include:
The rigidity of the raft: A stiffer raft tends to distribute load more evenly across the foundation, while a flexible raft allows for greater load transfer to the piles.
Soil properties: The stiffness and bearing capacity of the underlying soil layers significantly impact the load transfer mechanisms.
Pile characteristics: The number, depth, and rigidity of the piles within the raft influence how the load is shared between the piles and the raft.
The piled raft foundation system, responsible for transferring a structure’s load to the underlying soil, presents a complex interaction that have captivated researchers for years. Early notions, often overly conservative, assumed that the raft, in direct contact with the soil, offered no resistance to applied loads.
However, recent research works challenge this assumption, highlighting the raft’s significant contribution, particularly in clayey soils subjected to substantial structural loads. These studies reveal that the raft bears a portion of the load, while the piles carry the remaining portion through a creep mechanism.
The analysis and design of piled raft foundations, therefore, demand careful consideration of various critical factors, including:
Raft thickness and dimensions
Pile length, diameter, and configuration within the raft
Underlying soil properties
Stiffness characteristics of both the pile and raft
These factors collectively influence the load-sharing mechanism between the piles and the raft, ultimately impacting the stability and serviceability of the structure.
Furthermore, the success of piled raft foundation hinges on understanding the two key interaction types:
Pile-to-pile interaction: This interaction depends heavily on the soil’s elastic modulus, the pile slenderness ratio (s/d), and the pile length. Ignoring this interaction can lead to underestimating settlements and bending moments in the raft, compromising structural safety.
Pile-to-raft interaction: This interaction influences the load distribution between the piles and the raft, affecting the overall settlement behaviour of the foundation system.
Nevertheless, combined pile and raft foundation systems have challenged researchers for years due to the complexities associated with load-sharing and analysis. Several researchers have endeavoured to address this challenge, notably, by proposing simplified methods that incorporate various simplifications. However, these methods should be employed with caution due to their inherent limitations.
Quantifying the load contribution of each element within a piled raft system remains a topic of ongoing investigation. While some researchers suggest piles carry 50-80% of the total load, others provide a wider range of 30-60% for the raft’s contribution, emphasizing the dependence on factors like soil conditions, pile length, and spacing. Their research also highlights a decreasing raft contribution with denser pile spacing and increased pile length.
Further research strengthens the argument for the raft’s significant role, attributing up to 50% of the structural load to its contribution.
Classical Methods of Detemining Pile-Raft Load
Some classical methods of detemining pile-raft load sharing are discussed below.
Randolph Method In the method proposed by Randolph (1994), load sharing ratio between pile group and pile raft, pile raft stiffness and settlement of piled raft can be calculated by using Eq. 1 to Eq. 4.
Where, α = Load sharing ratio between raft and pile group, β = Load sharing ratio between pile group and pile raft, KR = Stiffness of the raft KPG = stiffness of the pile group KPR = stiffness of the piled raft S = Settlement of piled raft, Q = Design load
Poulos-Davis-Randolph (PDR) Method In the method proposed by Poulos, Davis, and Randolph, load sharing ratio between raft and piled raft (X) can be determined using Randolph (1994) method and piled raft settlement (S) can be established using Poulos and Davis (1980) method.
where; Qr = Load carried by the raft Qpr = Load carried by piled raft, kr = stiffness of the raft kpg = stiffness of the pile group kpr = Stiffness of the piled raft, αrp = Interaction factor, A = Raft area, n = Number of piles L = length of piles rm = Maximum radius from pile axis, Gl = Shear modulus of soil along pile shaft Gb = Shear modulus of soil at pile end ν = Poisson’s ratio of soil.
Design of Piled Raft
According to Poulos (2001), the design of a piled raft foundation can be effectively divided into three distinct stages. The initial stage focuses on a preliminary analysis, estimating the impact of varying pile numbers on the overall load capacity and settlement of the structure. This analysis is typically approximate in nature.
Additionally, preliminary design stages often benefit from incorporating load-sharing ratios and settlement values derived from empirical studies and case histories. The expertise of designers familiar with piled raft systems remains an important component in achieving optimal outcomes.
The second stage goes deeper, aiming to identify the specific locations where piles are necessary and providing an initial indication of the required piling specifications.
Finally, the third stage represents the detailed design phase. Here, a more refined analysis is employed to confirm the optimal number and positioning of the piles. Additionally, this stage gathers crucial information for the structural design of the entire foundation system.
Complexities inherent to piled raft systems necessitate the use of sophisticated analytical methods during the design stage. These methods, such as the finite element method (FEM), boundary element method (BEM), equivalent element method (EEM), and plate-on-spring method (POSM), account for the numerous variables influencing the system’s behaviour.
Approximate methods like the “strip on springs” approach and the “plate on springs” offer further avenues for analysis. These methods offer simplified representations of the raft and piles (as springs) to understand their interaction.
For more detailed analysis, researchers recommend resorting to numerical methods, with the Finite Element Method (FEM) being the most prevalent choice. Software like SAP2000 and PLAXIS 3D foundation are prime examples of FEM-based solutions. FEM provides approximate solutions for various nonlinear engineering problems, including those encountered in combined piled raft foundation analysis.
It is important to note that while simplified methods can provide reasonable results for preliminary assessments, numerical methods like FEM offer a superior level of accuracy and detail for complex piled raft foundation systems. Recognizing the limitations of each approach is paramount for selecting the most appropriate analytical tool for a specific project.
Summarily, understanding the load-sharing mechanisms within piled raft foundation remains a dynamic field of research. While simplified methods offer initial insights, numerical methods like FEM provide a more robust and accurate means for analyzing these complex foundation systems. Choosing the appropriate analytical approach requires careful consideration of the project’s specific needs and complexities.
Preliminary Design Example of Piled Raft Foundation System
This section considers the preliminary design of a proposed piled raft foundation system. The raft is 750 mm thick and the superstructure load distribution on the raft is shown in Fgure 3. The initial proposed distribution of the piles, comprising of 9 number of 600 mm diameter piles is shown in Figure 4.
Figure 3: Load distribution on the raft foundation system
Figure 4: Preliminary arrangement of the piled raft system
Thickness of raft = 750 mm Modulus of subgrade reaction ks = 10000 kN/m2/m Modulus of horizontal compressibility nh (medium dense wet sand) = 4000 kN/m2/m Pile diameter = 600 mm Depth of pile = 10 m
Horizontal modulus of subgrade reaction = nh(z/d) ——— (14)
The horizontal modulus of subgrade reaction was used in modelling the piles, and the spring stiffness varied with depth according to equation (14).
Figure 5: 3D render of the piled raft foundation on Staad Pro software
Figure 6: Finite element model of the piled raft foundation on Staad Pro software
Figure 7: Bending moment diagram of the piles
Figure 8: Load applied on the foundation
Total load applied on the foundation = 4(350) + 2(500) + 6(600) = 6000 kN
From the analysis results, Total load transferred to the piles = 900 kN Therefore, total load resisted by the raft = 6000 – 900 = 5100 kN
In this case, about 85% of the load is resisted by the raft foundation. If it is a piled raft foundation where the piles are to be used in load transfer, the arrangement of the piles will have to be changed. However, if it is a system where the piles are to be used for settlement control, the pile arrangement can be evaluated for acceptance or rejection.
In a different scenario when the number of piles was increased to 18 (additional piles were introduced along the column gridlines), 69% of the load was resisted by the raft. Therefore, preliminary analysis requires a careful consideration of the location and number of piles in the system.
Conclusion
Piled raft foundation systems offer a powerful solution for navigating complex soil conditions and supporting substantial loads. The design process involves a meticulous three-stage approach, starting with a preliminary analysis, then progressing to detailed location and quantity determination of piles, and finally culminating in a refined analysis for optimal pile placement and structural design of the entire foundation.
This staged approach ensures an efficient and cost-effective foundation that leverages the strengths of both raft foundations and pile foundations. Piled raft systems are a versatile solution for high-rise buildings, infrastructure projects, and construction on challenging sites, providing the stability and support necessary for a wide range of demanding applications.
Sources and Citations
Randolph M. F. (1994). Design methods for pile groups and piled rafts, 13th ICSMFE, New Delhi, India, 61-82. Poulos H.G. and Davis E.H. (1980). Pile foundation analysis and design, John Willey and Sons, New York, USA. Poulos H.G. (2001). Piled raft foundations: designs and applications. Geotechnique 51(2):95-113
Structural dynamics is a field of study that discusses the behaviour of structures subjected to dynamic loads. It encompasses the analysis, design, and evaluation of structures under the influence of various forces and vibrations. While static analysis focuses on the behaviour of structures under constant or slowly varying loads, dynamics of structures explores how structures respond to dynamic loads, which are forces that change rapidly with time.
In addition to static loads, a structural system can be subjected to variable (dynamic) loads induced by factors such as wind and wave action, earthquakes, impact, blasts, and vehicular/pedestrian traffic (which causes vibration and fatigue in bridges). Therefore, understanding the dynamic behaviour of structures is important for ensuring the safety and serviceability of structures in scenarios involving:
Earthquakes: Ground motions induced by earthquakes can cause significant dynamic forces on structures, potentially leading to failure if not properly accounted for in design.
Wind: Wind loads can create significant dynamic effects, especially on slender structures like tall buildings and suspension bridges.
Vibrations: Structures subjected to human activity, machinery operation, or traffic can experience vibrations, which can lead to fatigue, discomfort, or even damage if not managed effectively.
Blast loads: Explosions and other rapid pressure changes can create extremely dynamic forces that need to be considered in the design of structures in specific environments.
This article provides a comprehensive exploration of the key concepts and methodologies involved in the analysis and design of structures subjected to dynamic loads.
Figure 1: Typical Dynamics of buildings
Dynamic Analysis
The methods of analysis used for static loads are insufficient to analyze the ‘dynamic’ or ‘time-varying’ loads and their impacts. When compared to the values of displacement that are produced by static loading, the values that are produced by the response of structural members to time-varying loads will likewise be time-varying, and this can result in substantially larger values.
To make the concept of structural dynamics clearer, let us consider a structural element that is subjected to an externally applied load. By considering the equilibrium of applied forces and the internal forces that correspond to those forces, it is always possible to compute the internal stresses and displacements of a structure, regardless of whether the force that is being applied is “static” or “dynamic.”
Assuming that the structure is linearly elastic, the internal forces and the displacements are linearly proportional. If, on the other hand, the force is applied in a dynamic manner, two additional types of internal forces are generated as a consequence. The first of these is referred to as the “inertia forces,” and it is related to the acceleration. The second of these is referred to as the “damping forces,” and it is proportional to the velocity.
In this article, we are going to present a fundamental introduction to the principles of structural dynamics, and how it can be extended to the design of structures.
Importance of Structural Dynamics Analysis
A comprehensive dynamic analysis of structures can reveal the potential for serviceability failures that would be entirely undetectable through a purely static evaluation. For instance, there have been documented cases of oil rigs being decommissioned in relatively calm seas due to the initiation of oscillations that were unacceptably uncomfortable for the crew.
Similarly, electric transmission lines have been known to develop severe dynamic oscillations, referred to as “galloping,” to the extent that the lines made contact. While this phenomenon may not necessarily lead to structural collapse, it undoubtedly constitutes a serviceability failure from the perspective of electricity consumers.
Structures under construction are especially susceptible to dynamic effects. For example, temporary damping measures were deemed necessary for the towers of the Forth Road Bridge in Scotland to mitigate dynamic effects before the installation of the main cables. Even from a purely structural strength perspective, dynamic analysis can be crucial if fatigue is a primary concern.
In such scenarios, it becomes essential to predict not only the magnitude of stresses within the structure but also the frequency at which various stress levels occur. This is because a consistently applied low stress can have a more detrimental fatigue impact than an occasional instance of higher stress.
Characteristics of a Structural Dynamic Problem
A structural dynamic problem differs from a static loading problem in two significant ways. Firstly, the dynamic problem is characterized by its time-varying nature. Since both the loading and the response change over time, a dynamic problem does not have a single solution like a static problem does. Instead, the analyst must determine a series of solutions corresponding to different times of interest in the response history. As a result, dynamic analysis is inherently more complex and time-consuming than static analysis.
The second and more fundamental distinction between static and dynamic problems is illustrated in Figure 2. When a simple beam is subjected to a static load p (as shown in Figure 2a), its internal moments, shears, and deflected shape depend solely on this load and can be calculated using established principles of force equilibrium.
Figure 2: Basic difference between static and dynamic loads: (a) static loading; (b) dynamic loading.
However, when the load p(t) is applied dynamically (as shown in Figure 2b), the resulting beam displacements depend not only on this load but also on inertial forces that resist the accelerations causing them. Consequently, the internal moments and shears in the beam must balance not only the externally applied force p(t) but also the inertial forces resulting from the beam’s accelerations.
Inertial forces, which oppose the accelerations of the structure, are the key distinguishing characteristic of a structural dynamics problem. Generally, if the inertial forces constitute a significant portion of the total load equilibrated by the internal elastic forces of the structure, the dynamic nature of the problem must be considered in its solution.
On the other hand, if the motions are so slow that the inertial forces are negligible, the response analysis for any specific time can be conducted using static structural analysis methods, despite the load and response being time-varying.
Equations of Motion
The mass, stiffness, and damping (energy absorption capability), of a linearly elastic structural system are the basic physical parameters that define the system when it is subjected to external dynamic loading. Consider the ‘dash-pot’ model (representing a simple building with a single storey) that is presented in Figure 3. This model can be used to demonstrate the fundamental idea behind dynamic analysis.
Figure 3: Vibration modelling of a single storey structure
The structure is subjected to a time-varying force denoted by f(t), in which k is the spring constant that links the lateral storey deflection (x) to the storey shear force, and c is a damping coefficient that relates the dashpot’s damping force to the velocity. If it is assumed that all of the mass, m, is located at the beam, then the structure will be considered a single-degree-of-freedom (SDOF) system.
It is possible to write the equation of motion of the system as follows;
mẍ + cẋ + kx = f(t) ——– (1)
Types of Vibration
Free Vibration
While our initial discussion addressed the impact of time-varying loads on structural behaviour (dynamic behaviour), a foundational understanding of vibration in simple structures, independent of dynamic loads, proves most beneficial. This specific type of vibration, termed “free vibration,” arises whenever a structure experiences a disturbance from its state of static equilibrium. The initiation of free vibrations can be attributed to either impulsive events such as a collision or explosion, or to sudden movements in the structure’s support system.
In this case, the system is set to motion and allowed to vibrate in the absence of applied force f(t). Letting f(t) = 0, equation (1) becomes:
mẍ + cẋ + kx = 0 ——– (2)
Dividing equation (2) by the mass m, we have: ẍ + 2ξωẋ + ω2x = 0 ——– (3)
Where; 2ξω = c/m ——– (4) ω2 = k/m ——– (5)
The solution to the equation depends on whether the vibration is damped or undamped.
Undamped Free Vibration
In the absence of not only time-dependent forces, but also any mechanisms for energy dissipation within the vibrating system, the resulting motion can be classified as both free and undamped. Realistically, energy losses due to factors such as friction and air resistance are unavoidable. Therefore, the concept of undamped vibration, while theoretically useful, represents an idealized scenario that disregards these energy-dissipating phenomena. Nevertheless, it remains a valuable tool for theoretical analysis.
In this case, c = 0, and the solution to the equation of motion may be written as: x = Asinωt + Bcosωt ——– (6)
where ω= √(k/m) is the circular frequency. A and B are constants that can be determined by the initial boundary conditions.
Figure 4: Undamped free vibration
Damped Free Vibration
The phenomenon of damping arises from the inevitable energy loss that occurs during vibration. This lost energy is either dissipated as heat within the structure or radiated outwards, often in the form of sound waves.
Internal friction within the structural materials themselves contributes a portion to this energy loss, with frictional losses at structural joints playing an additional role. While air resistance can also contribute to energy dissipation, it is typically considered a secondary factor.
To model the effects of damping in a simplified manner, engineers often employ a theoretical element known as a “dashpot” system.
If the system is not subjected to applied force and damping is present, the corresponding solution becomes: x = A exp(λ1t) + B exp(λ2t) ——– (7)
The solution of equation (7) changes its form with the value defined as:
ξ = c/2√mk ——– (10)
Figure 5: Damped free vibration
Forced Vibration
When a structure experiences time-varying loads or continuous disturbances to its supports, the resulting motion is classified as forced vibration. The specific time-dependent influence that triggers this motion is termed excitation. The nature of the forced vibration – its frequency, amplitude, and overall behaviour – is directly tied to the characteristics of the excitation itself.
In essence, the excitation acts as an external “driving force” that dictates the response of the structure. This response can vary significantly depending on the excitation. For instance, a harmonic excitation (a smoothly oscillating force) will lead to a harmonic vibration with the same frequency but potentially a different amplitude. Conversely, a more impulsive excitation, like a sudden impact, can induce a transient vibration with a complex frequency spectrum.
If a structure is subjected to a sinusoidal motion such as a ground acceleration of ẍ = F sinωft, it will oscillate and after some time the motion of the structure will reach a steady state. For example, the equation of motion due to the ground acceleration (from equation (3)) is:
ẍ + 2ξωẋ + ω2x = Fsinωft ——– (11)
The solution to the equation we’ve been examining can be broken down into two key components. The first, known as the complementary solution (represented by equation 6), captures the transient behaviour of the system. If the system experiences any damping, the oscillations associated with this component will gradually diminish over time.
This decay effect eventually leads the system to reach a steady state, where it vibrates with a constant amplitude and frequency. This sustained vibration, termed forced vibration, is solely described by the second part of the solution, the particular solution, expressed as:
x = C1sinωft + C2cosωft ——– (12)
A key observation here is that the forced vibration occurs at the frequency of the excitation force, denoted by ωf, rather than the natural frequency of the structure itself, ω. Essentially, the external force dictates the frequency of the vibration. The term -F/ω² within the particular solution represents the static displacement D caused by the force, essentially accounting for the inertia of the structure.
Now, let’s explore the dynamic response of the structure under varying excitation frequencies relative to its natural frequency (ω):
Low-Frequency Excitation (ωf/ω > 1): When the applied force oscillates at a frequency significantly lower than the structure’s natural frequency, the response exhibits a characteristic termed quasi-static. In this regime, the system behaves as if it were under a constant load. The response is primarily governed by the stiffness of the structure, and the resulting displacement amplitude closely resembles the static deflection that would occur under a constant force of the same magnitude.
High-Frequency Excitation (ωf/ω < 1): Conversely, when the excitation frequency is much higher than the natural frequency, the response becomes primarily dependent on the mass of the structure. The displacement amplitude in this case is generally less than the static deflection (D < 1). This is because the structure’s inertia can effectively resist the rapidly oscillating force.
Resonance (ωf/ω ≈ 1): The most critical scenario arises when the excitation frequency nears the natural frequency of the structure (ωf/ω ≈ 1). Under these conditions, a phenomenon known as resonance occurs. Resonance drastically amplifies the displacement amplitude, potentially leading to catastrophic consequences for the structure. In essence, the external force synchronizes with the structure’s natural tendency to vibrate, causing a dramatic buildup of energy within the system.
The simplest periodic motion equation can be written as;
y(t) = Asin(ωt + φ0) ——– (13)
where A is the amplitude of vibration, φ0 is the initial phase of vibration, and t is time. This case is presented in Fig. 6a. The initial displacement y0 = Asinφ0 is measured from the static equilibrium position. The number of cycles of oscillation during 2π seconds is referred to as circular (angular or natural) frequency of vibration ω = 2 π/T (radians per second or s-1), T (s) is the period of vibration. Figure 6b, c presents the damped and increased vibration with constant period.
Figure 6: Types of oscillatory motions
Degrees of Freedom
The concept of degrees of freedom (DOF) plays a crucial role in both statics and structural dynamics. While the definition remains the same – the number of independent parameters that uniquely define the spatial positions of all points in a structure – its interpretation differs subtly between these two fields.
In statics, the DOF is often associated with structures modeled as collections of absolutely rigid discs. Here, a DOF greater than or equal to one signifies a geometrically changeable system. Such a system wouldn’t typically be considered a realistic engineering structure, as real structures exhibit some level of deformation. Conversely, a DOF of zero implies a geometrically unchangeable and statically determinate system – a structure with a unique solution for its equilibrium under applied loads.
However, in structural dynamics, the focus shifts to the deformation of the structural members themselves. A DOF of zero in this context indicates an absolutely rigid body, incapable of any displacement in space. This scenario is purely theoretical, as all real structures exhibit some degree of flexibility.
Furthermore, structures can be broadly classified into two categories based on their DOF:
Structures with Concentrated Parameters: These represent structures where the distributed mass of individual members can be neglected compared to lumped masses concentrated at specific points along the members.
Structures with Distributed Parameters: These structures are characterized by a uniform or non-uniform distribution of mass throughout their components. Analyzing these structures often requires more complex mathematical tools compared to those used for concentrated parameter systems.
From mathematical point of view, the difference between the two types of systems is the following: the systems of the first class are described by ordinary differential equations, while the systems of the second class are described by partial differential equations.
Distributed Mass Systems
While the lumped mass model offers a valuable simplification for many structures, it’s important to recognize that all real structures are fundamentally distributed mass systems. This implies that they can be conceptually divided into an infinite number of infinitesimal particles. As a consequence, if a distributed mass system experiences repetitive motion, it theoretically possesses an infinite number of natural frequencies and corresponding mode shapes – unique vibration patterns associated with each frequency.
However, the seemingly overwhelming complexity of analyzing a distributed system can be effectively bridged once its natural frequencies and mode shapes are determined. At this point, the analysis becomes mathematically equivalent to that of a discrete system, where the structure’s behavior is represented by a finite number of lumped masses interconnected by springs or other idealized elements.
The key lies in recognizing that, in practical scenarios, only a limited number of modes, typically those associated with lower frequencies, significantly contribute to the overall dynamic response of the structure. By focusing on these dominant modes, engineers can effectively convert the problem of a distributed mass system into a more manageable discrete system. This approach allows for accurate analysis using computationally efficient methods, enabling engineers to assess the dynamic behavior of real-world structures without getting bogged down by the theoretical infinite nature of distributed systems.
Conclusion
Dynamics of structures considers the interplay between time-varying external forces, internal resistance, and the inherent flexibility of structures. This article has looked into the fundamental concepts of free and forced vibrations, recognizing the crucial role of natural frequencies and damping in shaping a structure’s response.
However, real-world forces and ground motions can be incredibly complex. To accurately predict a structure’s behavior under these conditions, engineers typically rely on numerical analysis techniques. One of the most prevalent methods for solving such complex problems is the finite element method.
The analysis of structures subjected to dynamic loads hinges on the ability to model their behaviour effectively. While lumped mass systems offer a practical approach for many structures, the underlying reality of distributed mass systems with infinite natural frequencies cannot be ignored. The key lies in identifying the dominant modes that significantly influence the dynamic response, allowing us to transform the seemingly intractable distributed system into a more manageable discrete one.
In essence, the lumped mass model serves as a powerful tool for approximating the behavior of complex distributed systems. By strategically selecting the most influential modes, engineers can achieve a high degree of accuracy while maintaining computational tractability. This balance between theoretical completeness and practical feasibility is crucial for ensuring the safety and performance of structures subjected to dynamic loads.
Understanding the dynamics of structures equips engineers with the knowledge to design and build resilient structures that can withstand the challenges of the real world. From earthquakes and windstorms to traffic vibrations and human activity, structures must be able to withstand the complex effects of time-dependent loads without compromising safety, functionality, or serviceability. By mastering the principles of dynamics of structures, engineers can ensure that these structures perform their intended function in harmony with the dynamic forces that surround them.
In the field of structural engineering, understanding the internal forces acting on framed structures is important for the design of such structures. Among these forces, bending moment plays a very important role in influencing the behaviour of beams and columns in framed structures under various loading conditions. This article discusses the concept of bending moment and its visualization through bending moment diagrams (BMDs) for framed structures.
Understanding Bending Moment
Imagine a beam supported at its ends and subjected to a transverse load (a load acting perpendicular to the beam’s axis). This load induces internal forces within the beam, causing it to bend. The bending moment at any point along the beam’s length represents the turning effect (rotational tendency) or moment created by the internal forces acting on that specific section. It is essentially the product of the force (F) acting at a perpendicular distance (d) from the point of interest, expressed mathematically as:
M = F × d
The bending moment tends to rotate the beam section about an axis perpendicular to its longitudinal axis. A positive bending moment signifies concavity downwards while a negative bending moment indicates concavity upwards.
Bending Moment Diagrams
A bending moment diagram (BMD) is a graphical representation of the bending moment throughout the length of a beam or a member in a framed structure. This diagram helps visualize the variation of the bending moment along the member, enabling engineers to identify critical sections where the moment is highest and assess the potential for bending failure. Bending moment diagrams are plotted in the tension zone of structures.
Determine the support reactions: This involves analyzing the entire frame to calculate the forces acting at the supports due to the applied loads. For statically determinate frames, the equations of equilibrium are sufficient for determining the support reactions but for statically indeterminate structures, methods like the force method can be used.
Cut the member: Imagine isolating a specific section of the member by making a virtual cut at a chosen point.
Treat the section as a free body: Draw a free-body diagram of the isolated section, including all external forces (support reactions and applied loads) acting on it.
Apply equilibrium equations: Utilize the principles of equilibrium (summation of forces and moments equal to zero) to solve for the internal shear force (V) and bending moment (M) at the cut section.
Repeat for different sections: Choose multiple points along the member’s length and repeat steps 2-4 to determine the shear force and bending moment at each point.
Plot the values: Plot the calculated bending moments on the vertical axis and the member’s length on the horizontal axis, connecting the points to form a smooth curve. This curve represents the bending moment diagram for the member.
Interpreting Bending Moment Diagrams
Bending moment diagrams reveal valuable information about the bending behaviour of a framed structure:
Zero bending moment: Points on the BMD where the curve crosses the horizontal axis indicate locations where the bending moment is zero. These points typically occur at supports or points of contraflexure.
Maximum and minimum bending moment: The peak positive and negative values on the BMD represent the sections experiencing the highest and lowest bending moments, respectively. These sections are often critical for design considerations.
Slope of the BMD: The slope of the BMD at any point signifies the rate of change of the bending moment. A positive slope indicates an increasing moment, while a negative slope represents a decreasing moment.
Applications of Bending Moment Diagrams
Bending moment diagrams are instrumental in various aspects of structural engineering, including:
Structural design: They aid in selecting appropriate beam sizes and materials by identifying sections with high bending moments, ensuring sufficient strength and preventing failure.
Deflection analysis: By knowing the bending moment distribution, engineers can estimate the deflection of the frame using various methods, evaluating its serviceability under load.
F = Total Load IAB = ICD (the moment of inertia of the columns are equal) K =IBCh/IABL k1 = K + 2 k2 = 6K + 1 k3 = 2K + 3 k4 = 3K + 1
Rigid frame subjected to gravity uniformly distributed load on the beam
Bending moment diagram of a frame subjected to gravity uniformly distributed load on the beam (fixed supports)
FOR FIXED SUPPORTSHA = HD = Fl/4hk1
VA = VD = F/2
MA = MD = Fl/12k1
MB = MC = Fl/6k1
Bending moment diagram of a frame subjected to gravity uniformly distributed load on the beam (pinned supports)
FOR PINNED SUPPORTSHA = HD = Fl/4hk3
VA = VD = F/2
MA = MD = 0
MB = MC = HAh = Fl/4k3
Rigid frame subjected to a point load on the beam
Bending moment diagram of a frame subjected to a point load on the midspan of the beam (fixed supports)
FOR FIXED SUPPORTSHA = HD = 3Fl/8hk1
VA = VD = F/2
MA = MD = Fl/8k1
MB = MC = Fl/4k1
Bending moment diagram of a frame subjected to a point load on the midspan of the beam (pinned supports)
FOR PINNED SUPPORTSHA = HD = 3Fl/8hk3
VA = VD = F/2
MA = MD = 0
MB = MC = HAh = 3Fl/8k3
Rigid frame subjected to a horizontal uniformly distributed load on the column
Bending moment diagram of a rigid frame subjected to horizontal uniformly distributed load on the column (fixed supports)
FOR FIXED SUPPORTSHA = F - HD
HD = Fk3/8k1
VA = -FhK/lk2 = -VB
MA = Fh/4[(K + 3)/6k1 + (4K + 1)/k2]
MB = h(HA - ½F) - MAMC = HDh - MD
MD = Fh/4[(K + 3)/6k1 - (4K + 1)/k2]
Bending moment diagram of a rigid frame subjected to horizontal uniformly distributed load on the column (pinned supports)
FOR PINNED SUPPORTS
HA = F/8[(6k3 - K)/k3]
HD = F - HA
VD = -VA = Fh/2l
MA = MD = 0
MB = h(½F - HD) = 3Fhk1/8k3
MC = HDh = Fh/8[(2k3 + K)/k3]
Rigid frame subjected to a horizontal point load at the top
FOR FIXED SUPPORTSHA = HD = F/2
VA = -VD = -3FhK/Lk2
MA = MD = Fhk4/2k2
MB = MC = 3FhK/2k2
Bending moment diagram of a rigid frame subjected to horizontal point load at the top (pinned supports)
FOR PINNED SUPPORTSHA = HD = F/2
VD = -VA = Fh/l
MA = MD = 0
MB = MC = Fh/2
Conclusion
Understanding bending moments and their visualization through bending moment diagrams is fundamental for structural engineers. By mastering this concept, engineers can effectively analyze framed structures, optimize designs, and ensure the safety and serviceability of their creations under various loading conditions.
Cylindrical structures like tanks, silos, and chimneys are widely used in various industries, including oil and gas, agriculture, chemical processing, and water storage. These structures are susceptible to wind loads, which can cause significant stresses and potential failures if not properly analyzed and designed.
In industrial and agricultural settings, cylindrical above-ground vertical tank farms are commonly used for the storage of various liquids like petroleum, oil, water and fuel. These tanks are typically welded, thin-walled structures with large diameters, making them susceptible to buckling under wind loads when empty or partially filled.
The failure of such tanks can have devastating consequences, often resulting in significant financial and human losses. Additionally, these failures pose a serious threat to public safety and can have a detrimental impact on the environment.
Cylindrical structures can be affected by wind load
This article discusses the wind load analysis for tank farms and other cylindrical structures, providing a comprehensive overview of the key factors, methodologies, and considerations for engineers.
Understanding Wind Loads
Wind loads are external forces acting on a structure due to the dynamic pressure and drag exerted by moving air. The magnitude and direction of wind loads depend on various factors, including:
Basic Wind Speed (V): This is the reference wind speed, typically determined for a specific location and return period (e.g., 50-year return period). Building codes and standards like ASCE 7-16 (“Minimum Design Loads and Associated Systems for Buildings and Other Structures”) and EN 1991-1-4 provide wind speed maps for various regions.
Exposure Category: This accounts for the surrounding terrain and influences the wind speed experienced by the structure. Different exposure categories are defined in codes, ranging from open terrain to urban and suburban environments.
Topographic Effects: Local terrain features like hills and valleys can significantly influence wind speeds and turbulence intensity.
Structure Shape and Size: The shape and size of the structure play a crucial role in determining the wind pressure distribution. Cylindrical structures experience wind loads differently compared to flat or rectangular structures.
Several approaches can be adopted for wind load analysis of cylindrical structures:
Simplified Methods: Building codes often provide simplified procedures for calculating wind pressures on basic shapes like cylinders. These methods typically involve applying an equivalent static wind pressure acting on the projected area of the structure. While convenient, these methods may not be suitable for complex geometries or situations with significant topographic effects.
Analytical Methods: Analytical methods utilize established formulas based on wind tunnel experiments and theoretical principles to calculate wind pressures on cylindrical structures. These methods consider factors like wind speed, exposure category, and surface roughness. However, they may involve complex calculations and require specialized knowledge.
Computational Fluid Dynamics (CFD): This advanced method employs computational software to simulate the flow of air around the structure. CFD can generate detailed pressure distributions on the entire structure, accounting for complex geometries and local effects. However, CFD analysis requires expertise and significant computational resources.
Wind Pressure Distribution, Farm (Left) vs. Solo (Right) Tank (Source: Simscale.com)
Specific Wind Load Considerations for Tank Farms
For the calculation of wind load action effects on circular cylinder elements, the total horizontal wind force is calculated from the force coefficient corresponding to the overall effect of the wind action on the cylindrical structure or cylindrical isolated element.
The calculated effective wind pressure weff and total wind force FW correspond to the total wind action effects and they are appropriate for global verifications of the structure according to the force coefficient method. For local verifications, such as verification of the cylinder’s shell, appropriate wind pressure on local surfaces must be estimated according to the relevant external pressure coefficients, as specified in EN1991-1-4 §7.9.1.
For cylinders near a plane surface with a distance ratio zg/b < 1.5 special advice is necessary. See EN1991-1-4 §7.9.2(6) for more details. For a set of cylinders arranged in a row with normalized center-to-center distance zg/b < 30 the wind force of each cylinder in the arrangement is larger than the force of the cylinder considered as isolated. See EN1991-1-4 §7.9.3 for more details.
The calculated wind action effects are characteristic values (unfactored). Appropriate load factors should be applied to the relevant design situation. For ULS verifications the partial load factor γQ = 1.50 is applicable for variable actions.
When analyzing wind loads on tank farms, additional factors come into play:
Spacing and Interaction: The proximity of tanks within a farm can significantly influence wind pressures. Shielding effects and aerodynamic interaction between tanks need to be considered. Several empirical methods and CFD simulations are available to account for these effects.
Appurtenances: Wind loads also act on appurtenances like piping, ladders, and platforms attached to tanks. These loads can be significant and need to be included in the overall wind load analysis.
Dynamic Amplification: Tanks may experience dynamic amplification of wind loads due to their inherent dynamic properties. This can be particularly crucial for slender tanks or those with low natural frequencies.
Wind Load Analysis Example
A cylindrical structure of diameter (b) 5m and length (l) = 20 m is to be constructed in an area of terrain category II with a basic wind velocity vb of 40 m/s. The orientation of the cylindrical element is vertical and the maximum height above ground of the cylindrical element z = 20 m. The surface of the tank is made of galvanised steel. Calculate the wind force on the tank (Take Air density: ρ = 1.25 kg/m3)
Solution
Calculation of peak velocity pressure
The reference height for the wind action ze is equal to the maximum height above the ground of the section being considered, as specified in EN1991-1-4 §7.9.2(5). The reference area for the wind action Aref is the projected area of the cylinder, as specified in EN1991-1-4 §7.9.2(4). Therefore:
ze = z = 20 m Aref = bl = 5 m × 20m = 100 m2
Basic wind velocity vb = 40 m/s.
For terrain category II the corresponding values are z0 = 0.050 m and zmin = 2.0 m. The terrain factor kr depending on the roughness length z0 = 0.050 m is calculated in accordance with EN1991-1-4 equation (4.5): kr = 0.19 ⋅ (z0 / z0,II)0.07 = 0.19 × (0.050 m / 0.050 m)0.07 = 0.19
The roughness factor cr(ze) at the reference height ze accounts for the variability of the mean wind velocity at the site. cr(ze) = kr ⋅ ln(max{ze, zmin} / z0) = 0.19 × ln(max{20 m, 2 m} / 0.050 m) = 1.1384
The orography factor is considered as c0(ze) = 1.0
The mean wind velocity vm(ze) vm(ze) = cr(ze) ⋅ c0(ze) ⋅ vb = 1.1384 × 1 × 40 m/s = 45.54 m/s
The turbulence intensity Iv(ze) Iv(ze) = kI / [ c0(ze) ⋅ ln(max{ze, zmin} / z0) ] = 1.0 / [ 1.000 × ln(max{20 m, 2.0 m} / 0.050 m) ] = 0.1669
The peak wind velocity v(ze) at reference height ze v(ze) = [2 ⋅ qp(ze) / ρ ]0.5 = [2 × 2.810 kN/m2 / 1.25 kg/m3 ]0.5 = 67.05 m/s
Calculation of wind forces on the structure
The wind force on the structure Fw for the overall wind effect is estimated according to the force coefficient method as specified in EN1991-1-4 §5.3.
Fw = cscd ⋅ cf ⋅ qp(ze) ⋅ Aref
In the following calculations, the structural factor is considered as cscd = 1.000.
Reynolds number Reynolds number characterizes the airflow around the object. For airflow around cylindrical objects, Reynolds number is calculated according to EN1991-1-4 §7.9.1(1):
Re = b ⋅ v(ze) / ν = (5 m × 67.05 m/s) / 15.0 × 10-6 m2/s = 22.3505 × 106 where the kinematic viscosity of the air is considered as ν = 15.0 × 10-6 m2/s in accordance with EN1991-1-4 §7.9.1(1).
Effective slenderness The effective slenderness λ depends on the aspect ratio and the position of the structure and it is given in EN1991-1-4 §7.13(2).
For circular cylinders with length l ≤ 15 m the effective slenderness λ is equal to: λ15 = min(l / b, 70) = min(20m / 5m, 70) = 4
For circular cylinders with length l ≥ 50 m the effective slenderness λ is equal to: λ50 = min(0.7l / b, 70) = min(0.7 × 20 m / 5 m, 70) = 2.800
For circular cylinders with intermediate length 15 m < l < 50 m the effective slenderness λ is calculated using linear interpolation: λ = λ15 + (λ50 – λ15) ⋅ (l – 15 m) / (50m – 15m) = 4 + (2.8 – 4) × (20 m – 15 m) / (50m – 15m) = 3.829
End effect factor The end effect factor ψλ takes into account the reduced resistance of the structure due to the wind flow around the end (end-effect). The value of ψλ is calculated in accordance with EN1991-1-4 §7.13. For solid structures (i.e. solidity ratio φ = 1.000) the value of the end effect factor ψλ is determined from EN1991-1-4 Figure 7.36 as a function of the slenderness λ.
The estimated value for the end effect factor is ψλ = 0.658
Equivalent surface roughness The equivalent surface roughness k depends on the surface type and it is given in EN1991-1-4 §7.9.2(2). According to EN1991-1-4 Table 7.13 for surface type “galvanized steel” the corresponding equivalent surface roughness is k = 0.2000 mm.
Force coefficient without free-end flow For circular cylinders, the force coefficient without free-end flow cf,0 depends on the Reynolds number Re and the normalized equivalent surface roughness k/b. The force coefficient without free-end flow cf,0 is specified in EN1991-1-4 §7.9.2. The value cf,0 is determined according to EN1991-1-4 Figure 7.28 for the values of Re = 22.3505 ×106, k = 0.2000 mm, b = 5.000 m, k/b = 0.000040.
The estimated value for the force coefficient without free-end flow is cf,0 = 0.803
Force coefficient The force coefficient cf for finite cylinders is given in EN1991-1-4 §7.9.2(1) as: cf = cf,0 ⋅ ψλ
where cf,0 is the force coefficient without free-end flow, and ψλ the end effect factor, as calculated above. Therefore: cf = cf,0 ⋅ ψλ = 0.803 × 0.658 = 0.528
Pressure distribution for circular cylinders for different Reynolds number ranges and without end-effects
Total wind force The total wind force on the structure Fw is estimated as:. Fw = cscd ⋅ cf ⋅ qp(ze) ⋅ Aref = 1.0 × 0.528 × 2.810 kN/m2 × 100.00 m2 = 148.495 kN
The total wind force Fw takes into account the overall wind effect. The corresponding effective wind pressure weff on the reference wind area Aref is equal to: weff = Fw / Aref = 148.495 kN / 100.00 m2 = 1.485 kN/m2
Note: The effective pressure weff = 1.485 kN/m2 is appropriate for global verifications of the structure according to the force coefficient method. It is not appropriate for local verifications of structural elements, such as the shell of the cylinder. For the latter case appropriate wind pressure on local surfaces must be estimated according to the relevant external pressure coefficients, as specified in EN1991-1-4 §7.9.1.
Design Implications
The results of the wind load analysis are crucial for designing safe and efficient cylindrical structures. The wind loads are translated into equivalent static forces and moments, which are then incorporated into structural analysis software to assess the stresses and deflections in the structure. Based on these results, engineers can:
Determine the appropriate wall thickness and material properties for the tank shell.
Design roof support systems capable of withstanding wind uplift and wind-induced vibrations.
Optimize the anchorage system for the tank to ensure stability under wind loads.
Evaluate the potential need for additional bracing or wind mitigation measures.
Conclusion
Wind load analysis plays a vital role in ensuring the safety and functionality of tank farms and other cylindrical structures. Understanding the wind load characteristics, utilizing appropriate analysis methods, and considering specific complexities like tank farm interaction are crucial for engineers to design robust and wind-resistant structures. Continuous advancements in software and computational techniques are expected to further enhance the accuracy and efficiency of wind load analysis in the future.
Structural analysis and design software have revolutionized the field of civil and structural engineering. These powerful tools enable engineers to efficiently analyze, visualize, and design complex structures. They are also extensively utilised in the academia for research and development.
The ability of these software programs to model the intricacies of two and three-dimensional structures and analyse the results using finite element analysis is quite profound. A lot of analytical techniques for structures are available such as first-order linear analysis, non-linear analysis, buckling analysis, push-over analysis, time-history analysis, p-delta analysis, etc. Whether you’re designing a skyscraper, a bridge, or a residential building, having the right software can significantly impact your workflow and the safety of your designs.
In this article, we will explore the top structural analysis and design software available in 2024. These tools offer precision, speed, and compliance with a lot of international design codes. Let’s dive in:
Top 20 Structural Analysis and Design Software
1. SAP2000 (Computers & Structures Inc.) A veteran in the field, SAP2000 boasts a long history of being used for a wide range of projects, from simple buildings to complex bridges and stadiums. Its versatility stems from its ability to handle various structural materials, nonlinear analysis capabilities, and integration with other CSI software for a comprehensive workflow. However, the software can have a steeper learning curve compared to some competitors and might be less user-friendly for beginners.
Typical SAP2000 user interface
2. ETABS (Computers & Structures Inc.) Another popular offering from CSI, ETABS focuses specifically on building analysis and design. It excels at modelling multi-story buildings, including concrete, steel, and composite structures. Its user-friendly interface and comprehensive library of codes and standards make it accessible to a broader range of engineers. However, its capabilities are primarily geared towards buildings and might not be as comprehensive for other structural types like bridges or offshore structures.
Typical ETABS user interface
3. STAAD.Pro (Bentley Systems) STAAD.Pro offers a user-friendly interface and extensive analysis capabilities for various structural materials and types. STAAD.Pro is very robust for structural analysis, including static, dynamic, and finite element analysis. It integrates seamlessly with other Bentley software, allowing for efficient data transfer and collaboration within a single ecosystem. However, its licensing structure can be complex, and some users may find the interface less intuitive compared to other options.
Typical Staad Pro user interface
4.RISA-3D (RISA Tech, Inc.) RISA-3D is a powerful structural engineering software designed for analyzing and designing three-dimensional models of buildings and other structures. This software offers a range of features that streamline the structural design process. RISA-3D allows engineers to rapidly design structures of all types, including buildings, bridges, tanks, and culverts. It supports a wide range of materials, making it suitable for various projects.
Typical RISA-3D user interface
RISA-3D features an intuitive and user-friendly interface, making it accessible to both seasoned professionals and beginners. The software’s powerful analysis engine performs linear and non-linear static analysis, buckling analysis, modal analysis, harmonic analysis, and seismic analysis.
5. Tekla Structural Designer (Trimble) A powerful and versatile option, Tekla Structural Designer combines robust analysis capabilities with detailed 3D modelling tools. This allows engineers to create complex structures and visualize them realistically. However, its advanced features and steep learning curve can make it less accessible to users with less experience in BIM (Building Information Modeling) workflows.
Typical Tekla Structural Designer user interface
6. Autodesk ROBOT Structural Analysis Professional Autodesk’s ROBOT Structural Analysis Professional is a comprehensive solution for structural engineers. It offers advanced analysis capabilities, including linear and nonlinear static analysis, dynamic response, and code compliance checks. The software integrates seamlessly with other Autodesk products like Revit and AutoCAD.
Typical ROBOT Structural Analysis Professional user interface
7. MIDAS(MIDASoft) MIDAS provides a comprehensive suite of structural analysis and design tools. These include dedicated programs for building analysis (Midas Civil), bridge design (Midas GTS NX), and general FEA (Midas Gen). Its nonlinear analysis capabilities, optimization features, and seamless BIM integration make it a valuable asset for engineers. It covers various materials and structural systems.
8.Dlubal RFEM(Dlubal Software GmbH) Dlubal RFEM is a finite element analysis (FEA) software specifically designed for the analysis and design of 2D and 3D structures. RFEM can handle a wide range of structural materials, including concrete, steel, wood, masonry, and more. It also supports various structural analyses, including linear and nonlinear static, dynamic, stability, and contact analyses.
Typical RFEM user interface
RFEM operates as a modular program, allowing users to purchase and integrate additional modules based on their specific needs, offering flexibility and cost-effectiveness for smaller or less specialized projects.
9. SOFiSTiK SOFiSTiK is not just a single software program, but rather a suite of integrated software tools specifically designed for structural engineers. It caters to the entire structural engineering workflow, from initial concept design and analysis to detailing, formwork planning, and reinforcement generation. SOFiSTiK’s parametric capabilities allow users to quickly explore different design options and optimize their models iteratively.
Typical RFEM user interface
The software offers a wide range of analysis capabilities, including linear and nonlinear static, dynamic, stability, and buckling analyses. SOFiSTiK integrates seamlessly with various BIM (Building Information Modeling) software, allowing engineers to collaborate effectively with other disciplines involved in the construction project.
10. Prota Structures ProtaStructure is a structural analysis and design software specifically geared towards the needs of structural engineers. ProtaStructure combines analysis, design, detailing, and drafting capabilities within a single platform, streamlining the workflow and minimizing the need for data transfer between different software. The software offers compatibility with BIM (Building Information Modeling) workflows, allowing for data exchange with other construction software and improved collaboration.
Typical Prota Structures Model
11. Lusas (Finite Element Analysis Ltd.) Lusas is a well-established structural analysis software developed by Finite Element Analysis Ltd. It caters primarily to linear and non-linear analysis of various types of structures, making it a valuable tool for engineers tackling complex projects. Lusas boasts a long history in the structural engineering software market, earning recognition for its reliability and accuracy in analysis.
Unlike some software focused solely on linear analysis, Lusas excels in non-linear analysis, allowing engineers to consider material and geometric non-linearities for more realistic simulations. The software offers basic parametric modelling capabilities, enabling users to explore different design options efficiently. Lusas caters to a variety of structures, including buildings, bridges, offshore platforms, and other complex engineering projects.
12. Prokon Prokon is a structural analysis and design software developed by Irish company Prokon Software Limited. While offering some global reach in about 150 countries and supporting multiple languages, Prokon has traditionally held a stronger presence in the European market.
Prokon boasts a long history in the structural engineering software industry, recognized for its reliability and accuracy in analysis. Prokon handles various structural materials like concrete, steel, wood, and timber. It offers capabilities for linear and non-linear static, dynamic, stability, and buckling analyses, making it suitable for diverse projects.
13. SCIA Engineer SCIA Engineer is a robust structural analysis and design software widely recognized for its versatility, user-friendliness, and integration capabilities. It caters to engineers working on various projects, from simple buildings to complex bridges and stadiums. SCIA Engineer supports various materials, including steel, concrete, and composite structures. It handles both linear and nonlinear analysis.
The software provides an intuitive interface, allowing engineers to efficiently create 3D structural models. SCIA Engineer performs static and dynamic analyses, seismic analysis, buckling analysis, and more. It ensures accurate results for complex load conditions. SCIA Engineer integrates seamlessly with various BIM software like Tekla Structures and Archicad, enabling efficient data exchange and collaboration within a BIM workflow.
14. SimScale SimScale is a cloud-native simulation platform that provides powerful tools for structural analysis and design. Developed by SimScale GmbH, it offers engineers and designers an end-to-end solution for various engineering simulation workflows. Due to its cloud-based nature, SimScale requires a stable internet connection for full functionality. This can be a limitation in areas with unreliable internet access. SimScale’s Structural Mechanics module allows users to analyze static and dynamic behaviour of structures.
15. Ansys ANSYS Mechanical is not specifically a structural analysis software, but rather a general-purpose finite element analysis (FEA) software. However, its wide range of capabilities makes it a valuable tool for comprehensive structural analysis. Ansys Mechanical covers a wide range of structural analysis needs, including linear and nonlinear static analysis, dynamic analysis, thermal analysis, and more.
Typical Ansys Model
It supports various materials, boundary conditions, and loading scenarios. While offering an intuitive and customisable interface, Ansys Mechanical uses robust and accurate solvers to compute stress, deformation, and other structural responses. It handles complex geometries, contact interactions, and material nonlinearities.
16. ABAQUS ABAQUS is a comprehensive finite element analysis (FEA) software widely used for advanced structural analysis, particularly in non-linear and complex engineering applications. While not solely dedicated to structural analysis, its powerful capabilities make it a valuable tool for specialized engineers.
ABAQUS excels in non-linear analyses, handling complex material behaviour, large deformations, and contact scenarios, crucial for simulating real-world structural behaviour accurately. The software offers a vast library of material models, allowing engineers to accurately represent the behaviour of various materials, including metals, composites, rubber, and other specialized materials.
17. PLAXIS PLAXIS (2D and 3D) is not primarily a structural analysis software in the traditional sense. Instead, it focuses on geotechnical analysis and design, specifically for soil and rock structures and their interaction with built structures like foundations, embankments, and tunnels. PLAXIS offers dedicated tools and features tailored to analyze and design structures within the context of soil and rock mechanics. This includes considering soil behaviour, groundwater flow, and their interaction with structures.
Typical PLAXIS model
The software incorporates various advanced constitutive models that realistically simulate the non-linear and time-dependent behaviour of soils and rocks, providing a more accurate representation of real-world performance. PLAXIS allows engineers to model the construction process in stages, enabling them to analyze the impact of each construction phase on the stability and behaviour of the soil and structure.
18. Strand7 Strand7 is a finite element analysis (FEA) software used for analyzing and designing various structures across various industries. Strand7 boasts a wide range of capabilities, allowing engineers to analyze different structural types, including buildings, bridges, offshore platforms, and other complex structures.
Typical Strand7 model
It supports various materials like concrete, steel, wood, and composites. Beyond linear static analysis, Strand7 offers advanced features for non-linear analysis, enabling consideration of material and geometric non-linearities for more realistic simulations of complex structural behaviour.
19. Skyciv SkyCiv is a cloud-based structural engineering software platform offering analysis and design tools for various structures. SkyCiv provides online structural analysis capabilities, including frame analysis, section builder, buckling analysis, cable analysis, plate analysis, frequency analysis, response spectrum analysis, and non-linear analysis. The software integrates a wide range of steel, wood, and concrete design codes from organizations such as AISC, EN, AISI, NDS, AS, and CSA.
20. Oasys GSA Oasys GSA is a comprehensive software suite catering to the structural analysis and design needs of engineers. GSA allows you to create structural models using 1D, 2D, and 3D finite elements, regardless of the structure’s size or complexity. It includes routines for form-finding in lightweight structures such as arches, cable nets, grid shells, and fabric structures.
You can assign linear and nonlinear materials to various element types, including beams, slabs, and custom shapes for static, dynamic, prestress, or thermal loads. You can evaluate buckling capacities, including tension-only fabric material models and lateral torsional buckling of plate girders. GSA offers various solvers for modal vibration, seismic response, harmonic vibrations, and more.
The summary of the software discussed above is presented in the Table below;
Software
User Friendliness and Learning Curve
Analytical Capabilities
Pricing/Subscription
BIM Integration
SAP2000
Moderate – Interface can be complex for beginners, but extensive documentation and tutorials are available.
Extensive – Suitable for static, dynamic, non-linear, and time-history analysis of various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Integration with Revit and other BIM platforms requires additional tools or APIs.
ETABS
Similar to SAP2000
Similar to SAP2000, with a focus on building analysis.
Similar to SAP2000
Similar to SAP2000
STAAD.Pro
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
RISA-3D
Relatively user-friendly – Good for beginners due to its intuitive interface.
Primarily focused on linear static analysis of buildings, but offers some non-linear capabilities.
More affordable compared to some options, with various subscription models.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
Tekla Structural Designer
User-friendly – Designed for ease of use with BIM workflows.
Primarily focused on building analysis, with some non-linear capabilities.
Subscription-based pricing. May be expensive for smaller firms.
Excellent – Native integration with Tekla BIM software.
Autodesk ROBOT Structural Analysis Professional
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Included in the Autodesk AEC Collection subscription.
Good – Integrates with other Autodesk BIM software.
MIDAS
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
Dlubal RFEM
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
SOFiSTiK
Less user-friendly – More advanced software geared towards experienced users.
Highly advanced – Offers powerful analysis capabilities for complex projects.
Varies based on modules and project needs. Can be expensive for smaller firms.
Good – Offers various interfaces and plugins for BIM integration.
Prota Structures
Moderate – Similar to SAP2000 in complexity.
Primarily focused on building analysis, with some non-linear capabilities.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
Lusas
Less user-friendly – More advanced software geared towards experienced users.
Highly capable – Offers advanced analysis options for complex structures and materials.
Varies based on modules and project needs. Can be expensive for smaller firms.
Limited – Primarily intended for stand-alone analysis, but some BIM integration options are available through third-party tools.
Prokon
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Limited – Similar to SAP2000, requires additional tools or APIs for BIM integration.
SCIA Engineer
Moderate – Similar to SAP2000 in complexity.
Extensive – Offers a wide range of analysis capabilities for various structures.
Varies based on version and modules. Can be expensive for smaller firms.
Good – Integrates with various BIM platforms like Revit and ArchiCAD.
SimScale
Relatively user-friendly – Cloud-based platform with a web interface.
Primarily focused on linear static and dynamic analysis.
Cloud-based subscription model.
Limited – Offers basic integration with some BIM platforms through APIs.
Ansys
Less user-friendly – Highly advanced software for complex engineering simulations.
Extremely powerful – Offers a wide range of capabilities for various engineering
Disclaimer: This is a general overview, and specific features and pricing may vary depending on the version and chosen modules. It is recommended to consult the respective software websites for detailed information.
Bottomline
This article presented a snapshot of the top 20 options in structural analysis and design software, but the best choice for your specific project depends on its complexity, budget, and BIM workflow needs. It’s crucial to research and compare features, pricing models, and user reviews before making a decision. Remember, the most powerful software isn’t always the best fit. Consider factors like your team’s skill level, project requirements, and budget to find the ideal partner in creating safe and sustainable structures.
Plastering is the process of covering block or brick walls with cement mortar for decorative or protection purposes. Sometimes, plastering is also referred to as rendering. As an aspect of the finishing works of a building, it is a specialised item of work that must be executed with care using quality workmanship and materials. The cost of plastering a house in Nigeria depends mainly on the price of materials in the market and the labour rate in the area.
Typically, the materials that are used in plastering works are cement (grade 32.5 or grade 42.5N), plaster sand, water, and additives (where recommended). The additives could be colouring, waterproofing, bonding admixtures, etc. It is important to note that the selection of the wrong type of cement can ruin plastering works. Cement with high early strength gain is more susceptible to shrinkage cracking, and in a high-temperature zone like Nigeria, early thermal cracking can adversely affect the plastering works. The process of plastering a house must guarantee straightness and perfection.
To obtain the correct cost of plastering a house, the homeowner, quantity surveyor, and/or contractor must evaluate some important details which can affect the cost of plastering works. It is very common to express the cost of plastering per meter square (m2) of a wall. Some of the details to be evaluated are;
(1) The thickness of the rendering: Typically, the standard thickness of rendering specified by architects is usually 12 mm – 15 mm. When the thickness of the rendering exceeds 15 mm, chicken wire mesh is usually required to stop shrinkage cracking from taking place. It should also be noted that the cost of a 12 mm thick plaster is different from the cost of a 15 mm thick plaster.
(2) The mix ratio of the plaster: Mix ratios are often recommended for different reasons. Some mix ratios that can be specified are 1:1, 1:2, 1:3, or 1:4. The mix ratio of 1:3 is the commonest and it means one part of cement to three parts of plaster sand. In this case, one bag of 50kg cement will be mixed with 6 headpans of plaster sand.
(3) The area of walls to be plastered: The net area of walls to be plastered should be determined by the quantity surveyor. This is usually given by the total area of walls less the area of openings. It is important to note that the dressing of doors, windows, and other surfaces such as columns, cornices, copings, etc are usually priced separately.
Dressing of doors in a building
(4) Location: In Nigeria, the labour rate for interior plastering is usually different from the labour rate for exterior plastering. Therefore, the allowance should be made as appropriate during the costing.
(5) Other ancillaries: During the plastering of framed structures, it is typical to put wire mesh at the block-column joints in order to prevent vertical cracks from occurring there in the future. Furthermore, materials like angle beads, edge trimmers, etc may be needed at the edges in order to obtain perfect straightness. All these costs should be factored in.
How to build up rate for plastering work
Let us build up the rate for plastering a wall with 15 mm thick 1:4 mix ratio plaster. In a 1:4 mix ratio plaster, 9 bags of cement and 2035 kg of plaster sand are required to produce 1m3 of mortar.
Cement (basic cost) – ₦9,000 per 50 kg bag : ₦81,000/m3 of mortar Plaster sand – ₦10,500 per 1000 kg: ₦21,368/m3 of mortar Water (allow): ₦500/m3 of mortar Labour – Production of mortar: ₦18,000/m3 of mortar Labour – Placement: ₦18,000/m3 of mortar Total cost = ₦138,868/m3 of mortar
Therefore, for a rendering of 15 mm thickness, the cost per square metre is (0.015 x 138,868) = ₦ 2083/m2
Allow 20% for contractor’s profit and overhead = 1.2 x 2083 = ₦2500/m2
Therefore, the cost of plastering a square metre (m2) of a wall in Nigeria using a 1:4 mix ratio plaster is about ₦2,500/m2 (Two thousand five hundred Naira per square metre wall).
For a four-bedroom duplex building in Nigeria, the cost of the internal and external plastering of the walls (say 1200 m2 of wall) is about ₦3,000,000.
In Nigeria, duplexes are the most preferred choice for private residential building construction. Duplexes normally consist of a ground floor and one suspended reinforced concrete floor with a living room (sitting room/parlour), en-suite bedrooms, dining room, kitchen, lounges, and other spaces as may be desired. Lobbies are used to connect the spaces in a duplex building, and a staircase is used for vertical circulation. Residential buildings with more than one suspended floor should not be described as duplexes.
In most duplex designs, it is very typical for the living room, dining, kitchen, laundry room, and storeroom to be on the ground floor. The living room may be double volume (with no reinforced concrete slab over it), or it can be covered with a reinforced concrete slab to create more spaces upstairs.
The former alternative is usually for aesthetics and gives a sense of a freer atmosphere in the living room. Furthermore, it reduces the cost of construction due to the void over the sitting room, however, this comes at the expense of the loss of potentially useful space on the first floor.
A traditional townhouse duplex design by Structville Integrated Services Limited
The ground floor of most duplexes in Nigeria also houses the ante-room, visitor’s toilet, and the visitor’s bedroom which is usually provided with its own convenience (en-suite with toilet and bathroom). Depending on the desire of the client or homeowner, additional bedrooms and facilities may be provided on the ground floor. While this is usually very applicable to moderate duplexes, luxury duplexes can considerably vary in arrangement.
The first floor of a moderate duplex usually contains the majority of the bedrooms. A private family lounge can be provided on the first floor with a kitchenette that can serve as a coffee room. In modern construction, all the bedrooms should be en-suite.
Luxury duplexes can contain additional spaces such as exclusive wine cellars, study rooms/private offices, gyms, saunas, library rooms, theatres/cinemas, games rooms, bigger walk-in closets, kids’ play area, exclusive pantry rooms, elevator, panic room, mechanical/electrical panel rooms, internet server rooms, indoor swimming pool, etc. Modern luxury apartments should be smart buildings with most of the facilities fully automated.
The cost of constructing a duplex building in Nigeria depends on a number of factors such as;
Size: The size of the building will significantly increase the cost of materials and labour needed to construct the building. The bigger the building, the bigger the cost of execution.
Type of land: Buildings that are founded on soft/weak soils will cost considerably more than buildings that are founded on stiff non-problematic soils. Also, the effects of the depth groundwater table can influence the cost of construction. Duplex buildings on marginal soils can be supported on a raft or pile foundation, while duplexes on good soils can be supported on pad foundations. Buildings on pad foundations are cheaper than buildings supported on a raft or pile foundation.
Method of Construction: The construction method you choose might have a big impact on the cost of your building project. Before installing the block walls and partitions, contractors can build the structural parts of duplexes as pure reinforced concrete frames consisting of beams, columns, slabs, and staircases.
On the other hand, the partition walls and the structural frames can be constructed simultaneously, an approach that is more common in low- to medium-budget duplex construction projects. The latter has the advantage of being faster while saving a significant amount of money on materials and labor. The former, however, is of higher quality due to more stringent quality control throughout the construction of the structural elements.
Construction of a building as a pure framed structure (Supervised by Engr. O. U. Ubani)
Location of the project: The cost of a project can also be influenced by its location. Sites that are close to sand and gravel supplies will have lower material costs than sites that are further away. Additionally, if the site is not accessible by truck, significant labour expenditures will be incurred in transloading the items into your site before they are used. Labour costs can also be a factor since the average cost of labour varies from location to location.
Taste of the client: While the cost of constructing the frames and carcass of a duplex should be relatively consistent among buildings of similar size and volume, the cost of finishing a duplex might vary significantly because of the wide range of alternatives available to clients. A building’s finishes might be either high-end or low-cost. This can include everything from roofing sheets to doors, windows, tiles, sanitary fittings, electrical fittings, painting, among other things. A homeowner can choose between the cheapest choice and the most expensive luxury option. The price difference can be as much as 500%.
Getting Started in Duplex Construction
Land Acquisition As should be expected, the first step in the construction of a duplex should be the acquisition of land. In the villages or rural areas, family or communal lands can be conveniently obtained depending on the family agreements. In the towns of Nigeria, landed properties can be purchased from individuals, corporate bodies, or real estate firms.
In all cases, the land to be used for the construction should be properly surveyed by a registered surveyor, and the title of the land clearly defined. The land should be properly registered and all legal documents for ownership properly verified. All laws for property ownership in the state should be fulfilled by the client.
ArchitecturalDesign After you have secured your plot of land for the proposed construction, the design of the building can commence. The architect designs your preferred building while also satisfying the local building regulation codes/requirements, taking into account the nature, size, and shape of your site.
The airspace and setbacks between the property lines and the building line should adhere to the local building code. Septic tanks, soakaway pits, boreholes, gatehouses, generator houses, outdoor swimming pools, and other structures should all be clearly mapped out on the site layout.
Civil Engineering Designs The geotechnical and structural engineering designs should be carried out for the ultimate safety of the proposed building. Site investigation and sub-surface exploration should be carried out to determine the engineering properties of the sub-surface soils. This information will inform the type of foundation to be used for the duplex. At the initial stage, a cue should be taken from the type of foundation used for supporting the surrounding buildings if any.
A structural design will identify the location and design of the columns, beams, slabs, staircase, and foundation. The structural design should be carried out, checked, and sealed by a COREN-registered civil engineer. A letter of structural stability and supervision should also be issued to you by the structural engineer.
Mechanical and Electrical Designs The mechanical design should include the building’s plumbing, HVAC, and water sprinkler systems, among other things. The design should be in harmony with the building’s architectural and structural design so that the route of pipes, ducts, and other utilities can be clearly specified during the design stage, to avoid chiselling of structural components after construction.
The arrangement of electrical pipes and light fittings, security cameras, alarm systems, internet and television cables, cable tray routes, the position of distribution boards/panels, and so on should all be included in the electrical designs. COREN-registered mechanical and electrical engineers shall design and stamp the services drawing.
Approval Having obtained all the necessary drawings, the complete set of drawings comprising the architectural, structural, mechanical, electrical, and soil test report should be submitted to the Physical Planning Board/Agency of the locality for approval. Other documents as may be required should be submitted too. Once the drawings are approved, the construction can commence.
Cost of Constructing a Duplex in Nigeria
For the sake of convenience in costing and project management, duplex construction in Nigeria can be conveniently broken into the following stages;
Substructure (foundation)
Ground floor to overhead level
First-floor decking
First floor to roof overhead level
Parapet and roofing
Finishes
These stages are consistent with projects where the block walls and the frames are to be built up together. For buildings that are to be constructed as pure frame structures, the above breakdown will not be very adequate.
Let us now survey the cost of constructing each phase of a duplex using the four-bedroom duplex building plan below as a case study. The building is to be constructed in a semi-urban region in south-eastern Nigeria, on lateritic soil with a bearing capacity of 175 kN/m2 at a depth of 1 m. Groundwater is at a great depth from the ground surface.
Ground floor plan of the proposed duplex
First floor plan of the proposed duplex
Substructure (Foundation)
The activities usually carried out under substructure works are setting out, excavation, concrete works (blinding, column bases, strip foundation, column stubs, and ground floor slab), reinforcement works, carpentry works, and filling.
Foundation layout of the proposed duplex
Setting out 3 bundles of pegs @ ₦2500 = ₦7500 20 pcs of 2″ x 3″ softwood @ ₦750 = ₦15000 1 bag of 3″ and 2″ nails each @ ₦48,000 each = ₦96,000 6 rolls of twin ropes @ ₦500 = ₦3000 Labour and supervision (allow) = ₦100,000 Total for setting out = ₦221,500
Excavation works Excavation of 82 m3 of earthwork for the column bases and the strip foundation @ ₦1,800/m3 = ₦147,600 Supervision = ₦60,500 Total cost for excavation works = ₦208,100
Substructure works of a duplex by Structville Integrated Services Limited
Concrete Works(foundation) Blinding and casting of column base and strip foundation = 26.5 m3 of grade 25 concrete @ ₦108,600/m3 = ₦2,877,900 Labour and supervision cost = ₦425,000 Total cost for concrete works = ₦3,302,900
Reinforcement Works Column base mat reinforcements = 384 kg of Y12 @ ₦1005/kg = ₦385,920 Column starter bars reinforcements = 455 kg of Y16 @ ₦1005/kg = ₦457,275 Column base links = 50 kg of Y8 @ ₦1005/kg = ₦50,250 Binding wire 1 roll @ ₦34,000 = ₦34,000 Labour and supervision cost = ₦100,000 Total cost for reinforcement works = ₦1,027,445
Block work 170 m2 of 9″ hollow block work @ ₦10,150/m2 = ₦1,725,500 Labour and supervision = ₦254,000 Total for block work = ₦1,979,500
Carpentry Works Column stubs – 13.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦47,590 Slab edge formwork- 50 m length of 1″ x 9″ plank @ ₦780/m= ₦39,000 20 pcs of 2″ x 3″ bracings @ ₦750 = ₦15,000 Labour and supervision costs = ₦40,000 Total cost for carpentry works = ₦141,590
Backfilling and Compaction 150 tonnes of lateritic earth fill @ ₦6000/tonne = ₦900,000 Labour cost (allow) = ₦150,000 Total cost for backfilling and compaction = ₦1,050,000
Backfilling and Compaction of a Duplex Substructure by Structville Integrated Services Limited
BRC Mesh 160 m2 of A142 BRC mesh @ ₦1400/m2 =₦224,000 Cost of installation = ₦25,000 Total cost of BRC mesh works = ₦249,000
Damp Proof Membrane Allow ₦75,000 for purchase and installation = ₦75,000
Casting of ground floor slab Blinding and casting of column base and strip foundation = 22.5 m3 of concrete @ ₦108,600/m3 = ₦2,443,500 Labour and supervision = ₦365,000 Total cost for concreting ground floor slab = ₦2,808,500
Total cost of substructure (foundation to DPC) = ₦11,063,535
Ground Floor to Overhead Level
Block work 212 m2 of 9″ hollow block work @ ₦10,150/m2 = ₦2,151,800 Labour and supervision = ₦304,400 Total cost for block work = ₦2,456,200
Concrete Works (Lintel and Columns) 9m3 of concrete @ ₦108,600/m3 = ₦977,400 Labour and supervision = ₦146,000 Total cost for concrete works = ₦1,123,400
Construction of a duplex (ground floor to overhead level) by Structville
Reinforcement Works Y16 for columns – 512 kg @ ₦1005/kg = ₦514,560 Y12 for lintels – 405 kg @ ₦1005/kg = ₦407,025 Y8 for lintel and column links – 232 kg @ ₦1005/kg = ₦233,160 1 roll of binding wire = ₦34,000 Labour and supervision cost = ₦120,000 Total cost for reinforcement works = ₦1,308,745
Carpentry Works Column formwork = 31.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦111,040 Lintel formwork (sides) = 46.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦163,915 Lintel formwork (bottom) = 12m2 of sawn 1″ x 9″ plank @ ₦3525/m2 = ₦42,300 Labour and supervision cost = ₦120,000 Total cost of carpentry works = ₦437,255
Total cost from ground floor to overhead level = ₦5,325,600
First Floor Decking
Formwork 1” x 9” x 12’ plank as soffit to slab and staircase = 155 m2 @ ₦3525/m2 = ₦546,375 1” x 9” x 12’ plank as sides to beam = 46.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦163,915 1” x 6” x 12’ plank as sides to beam and riser to staircase = 45 pcs @ ₦1200/pcs = ₦54,000 2” x 3” x 12 softwood = 120 pcs @ ₦750/pcs = ₦90,000 Bamboo props = 275 pcs @ ₦600/pcs = ₦165,000 2 bags of 2″ and 3″ nails each = ₦192,000 Labour and supervision cost = ₦300,000 Total cost of carpentry works = ₦1,511,290
Reinforcement Works Y16 for beams – 855 kg @ ₦1005/kg = ₦859,275 Y12 for slab – 2425 kg @ ₦1005/kg = ₦2,437,125 Y10 for slab – 295 kg @ ₦1005/kg = ₦296,475 Y8 for links of beams – 190 kg @ ₦1005/kg = ₦190,950 2 rolls of binding wire @ ₦34,000 = ₦68,000 Labour and supervision cost = ₦300,000 Total cost of reinforcement works = ₦4,151,825
Typical reinforcement works on the decking of a Duplex by Structville
Electrical and Mechanical Piping Works Allow – ₦800,000
Concreting of the slab, beams, and staircase 33m3 of concrete @ ₦108,600/m3 = ₦3,583,800 Labour and supervision cost = ₦512,000 Total cost of concreting = ₦4,095,800
Total cost of first floor decking = ₦10,558,915
First Floor to Roof Overhead Level
Block work 223 m2 of 9″ hollow block work @ ₦10,150/m2 = ₦2,263,500 Labour and supervision = ₦429,100 Total cost for block work = ₦2,692,600
Concrete Works (Lintel and Columns) 9m3 of concrete @ ₦108,600/m3 = ₦977,400 Labour and supervision = ₦157,500 Total cost for concrete works = ₦1,134,900
Reinforcement Works Y16 for columns – 512 kg @ ₦1005/kg = ₦514,560 Y12 for lintels – 405 kg @ ₦1005/kg = ₦407,025 Y8 for lintel and column links – 232 kg @ ₦1005/kg = ₦233,160 1 roll of binding wire = ₦34,000 Labour and supervision cost = ₦150,000 Total cost for reinforcement works = ₦1,338,745
Carpentry Works Column formwork = 31.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦111,040 Lintel formwork (sides) = 46.5 m2 of 1″ x 10″ plank @ ₦3525/m2 = ₦169,915 Lintel formwork (bottom) = 12m2 of sawn 1″ x 9″ plank @ ₦3525/m2 = ₦42,300 Labour and supervision cost = ₦150,000 Total cost of carpentry works = ₦473,255
Total Cost from the first floor to roofing level = ₦5,639,500
Cost Summary
Total cost of substructure (foundation to DPC) =₦11,063,535 Total cost from ground floor to overhead level =₦5,325,600 Total cost of first floor decking =₦10,558,915 Total Cost from the first floor to the roofing level = ₦5,639,500 Total cost = ₦32,587,550
Allow 25% for contractor’s profit and overhead = ₦8,146,890
Therefore, the total cost of constructing a 4-bedroom duplex from the foundation to the roofing level should range between ₦32,587,550 to ₦40,734,437. Note that different professionals and contractors may have their own scale of fees or rates for executing every item of work which may vary from what is presented here.
Residential Duplex under Construction by Structville Integrated Services Limited
For your building design and construction services, contact; Structville Integrated Services Limited Phone/WhatsApp: +2348060307054, +2347053638996 E-mail: info@structville.com
