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
Statically determinate frames are usually two-dimensional planar structures whose unknown external reactions or internal member forces can be determined using only the three equations of equilibrium. Statically determinate frames are the basic functional frames of structural engineering, forming the backbone of countless structures from bridges to buildings. Understanding their analysis is fundamental to ensuring the stability and efficiency of most civil engineering structures.
The three equations of equilibrium sufficient for the analysis of statically determinate structures are;
∑Fx = 0; ∑Fy = 0; ∑Mi = 0
An indeterminate structure is one whose unknown forces cannot be determined by the conditions of static equilibrium alone. Additional considerations, such as compatibility conditions, are necessary for a complete analysis.
Nature of Statically Determinate Frames
As stated earlier, statically determinate frames are usually 2-dimensional structures. Three-dimensional frames are usually statically indeterminate and are more suited to computer-based finite element analysis.
The vertical members in statically determinate frames are referred to as the columns, while the horizontal members are referred to as the beams. Typically, the analysis of statically determinate frames involves the determination of the support reactions, internal stresses (bending moment, shear force, and axial force), and deflections.
Support Reactions
For simplified manual analysis, the support conditions considered in the analysis of frames are;
Fixed support (consisting of three reactions)
Pinned/hinged support (consisting of two reactions)
Roller support (consisting of one reaction)
It therefore follows that when the number of support reactions in a frame exceeds three, special conditions such as internal hinges will be required to make the frame statically determinate. Such frames with internal hinges are usually referred to as compound frames. The degree of static determinacy or indeterminacy can then be calculated as follows;
ID = R – e – s
Where; ID is the degree of static indeterminacy e is the number of equilibrium equations (typically 3) s is the number of special conditions in the structure
Alternatively,
If (3m + R = 3j + s), the structure is statically determinate.
Here: m represents the number of members. R represents the number of support reactions. J represents the number of joints. s represents the equations of condition (e.g., two equations for an internal roller and one equation for each internal pin).
Rearranging the equation above;
RD = (3m + R) – 3j – S
Where; m = number of members. r = number of support reactions. j = number of nodes S = number of special conditions
If the degree of static indeterminacy is less than 0, the frame is unstable. A structure is stable if it maintains its geometrical shape when subjected to external forces. Stability is important for ensuring the safety and functionality of a structure.
To obtain the support reactions in a statically determinate frame, it is usually sufficient to take the summation of moments about any of the supports or any point with a known condition (such as an internal hinge) and equate it to zero.
Loads and Actions on Frames
The skeletal framework of structural frames, composed of beams, columns, and trusses, bears the brunt of diverse forces and actions. Understanding and accurately analyzing these loads is paramount for ensuring the safety and functionality of the entire structure.
The types of loading found on frames are;
Point Loads: These concentrated forces act at discrete locations on a member. Columns sitting on a beam or the actions of secondary beams on primary beams are usually idealised as point loads. Their magnitude and position significantly influence the stress distribution within the frame.
Point load on a statically determinate frame
Uniformly Distributed Loads (UDLs): Imagine a blanket of snow uniformly accumulating on a roof. This scenario represents a UDL, where the load acts with constant intensity across the entire length of a member. Self-weight of members is also idealised as uniformly distributed loads. Analyzing such loads involves calculating their total force based on the area they cover and their intensity.
Uniformly distributed load on a statically determinate frame
Varied Distributed Loads: Not all distributed loads are uniform. Consider the wind pressure acting on a tall building, increasing in intensity towards the top due to aerodynamic effects. These loads can be modelled as linear (triangular loads) or non-linear (trapezoidal loads) functions of the member’s length, necessitating more complex analysis techniques like integration or employing equivalent uniform load representations.
Varied distributed load on a statically determinate frame
Concentrated Moments: Imagine a child swinging on a monkey bar; the force applied at the bar’s end creates a concentrated moment, twisting the bar. This can also come from torsion being transmitted from another structural member or machinery. These moments directly influence the bending stresses within the member.
Concentrated moment on a statically determinate frame
Beyond the fundamental loading idealisation, the world of structural loading extends beyond these fundamental categories:
Line Loads: Picture the weight of a cable hanging on a support. These act along a linear element, requiring specialized analysis techniques.
Hydrostatic and Earth Pressures: Retaining walls holding back water or soil experience continuous pressure from these fluids or packed earth, necessitating specialized analysis based on their specific intensity profiles.
Impact Loads: A sudden blow, like a hammer strike, can create dynamic forces requiring specialized analysis to evaluate potential damage and ensure structural integrity.
Analysis of Statically Determinate Frames
The analysis of statically determinate frames involves several key steps. Let’s break it down:
Identify the Frame: Begin by understanding the given frame’s geometry, member lengths, and support conditions. Clearly identify the structure and its supports (hinges, rollers, etc.). Determine the type and location of all applied loads (point loads, distributed loads, moments). Specify the material properties of the frame members (e.g., Young’s modulus, cross-sectional area). Confirm that the frame is statically determinate.
Reaction Forces: Determine the reaction forces at each support using global equilibrium equations (vertical, horizontal, and moment equilibrium). Check for the force and moment equilibrium of the structure.
Cut the Frame: Split the frame into separate members. Consider each member individually. Isolate each member by cutting it at a point of interest. Draw a free-body diagram of the isolated member. Apply the three equations of equilibrium to solve for the internal shear force, bending moment, and axial force (if applicable) at the point of interest. Repeat for other points of interest in each member.
Internal Forces: Calculate the bending moment, shear, and axial force at selected locations of interest (typically member ends, midpoints, and points of maximum moment). These values help us understand the internal forces within the frame.
Check for Deflections (Optional): Use beam deflection formulas or methods like the virtual work method to calculate deflections at specific points in the members. Compare the deflections to allowable limits specified in building codes or design criteria.
Solved Example
For the frame that is loaded as shown in the Figure below, find the support reactions and draw the internal stresses diagram. Internal hinges are located at points G1, G2, and G3 and beam JK cantilevers out at a height of 4m from column CF
Solution
RD = (3m + r) – 3n – S m = 10 (ten members) r = 6 (six reactions) n = 11(eleven nodes) S = 3 (three internal hinges) RD = 3(10) + 6 – 3(11) – 3 = 0
This shows that the structure is statically determinate and stable.
Support reactions Let ∑MG1L = 0; anticlockwise negative (Ay × 2) – ((2 × 22)/2) = 0 Ay = 2.0 kN
Let ∑MG3R = 0; clockwise negative (Dy × 4) – ((2 × 42)/2) = 0 Dy = 4.0 kN
Coming from the right-hand side Section D – FR (0 ≤ x ≤ 7.0)
Moment (clockwise negative) Mx = Dy.x – ((2x2)/2) = 4x – x2 At x = 0, MA = 0 (simple hinged support) At x = 4.0m, MG3 = 4(4) – (4)2 = 0 ∂Mx/∂x = Qx = 4 – 2x When ∂Mx/∂x = 0, M = Maximum at that point Hence, 4 – 2x = 0 x = 4/2 = 2.0m Mmax = 4(2) – (2)2 = 4.0 kNm At x = 7m, MEL = 4(7) – (7)2 = -21 kNm
Shear Since the sign convention changes when we are coming from the right, we reverse the signs. ∂Mx/∂x = Qx = 4 – 2x = -4 + 2x At x = 0, QD = -4 kN At x = 7m, QFR = -4 + 2(7) = 10 kN
Axial No axial force on the section
Section C – JB(0 ≤ y ≤ 4.0) Moment My = Cx.y = 4.875y At y = 0, MC = 0 (simple hinged support) At y = 4m, MJB = 4.875(4) = 19.5 kNm
At x = 7m, MFL = -(7)2 + 21.417(7) – 114.169 = -13.25 kNm At x = 10m, MG2R = -(10)2 + 21.417(10) – 114.169 = 0 ∂Mx/∂x = Qx = – 2x + 21.417 When ∂Mx/∂x = 0, M = Maximum at that point Hence, – 2x + 21.417 = 0 x = 21.417/2 = 10.7085m Hence no point of contraflexure exists in the section.
Shear ∂Mx/∂x = Qx = – 2x + 21.417 = 2x – 21.417 At x = 7m, QFL = 2(7) – 21.417 = -7.417 kN At x = 10m, QG2R = 2(10) – 21.417 = -1.417 kN
Architectural envelopes often utilize curtain walls, a type of lightweight, non-loadbearing external cladding which are attached to a framed structure to form a complete exterior sheath. They support only their own weight and wind loads, which are transferred via connectors at floor levels to the main structure.
For precision, BS EN 13830 defines curtain walling as “an external vertical building enclosure predominantly comprised of metallic, wooden, or plastic elements.” In essence, most curtain walls consist of vertical mullions (spanning floor to floor) connected by horizontal transoms. Infill panels, either glass or opaque, fill the resulting openings. Typically, such systems are constructed using proprietary systems provided by specialized metal fabricators.
Night view of a building with curtain wall system
Objectives of Curtain Wall Systems
The primary objectives of using curtain-walling systems are to:
Enclosure and Environmental Protection: Provide a comprehensive building envelope that protects the structure against external elements like wind, rain, and temperature fluctuations.
Efficient Construction: Utilize dry construction methods, potentially streamlining the building process and minimizing disruptions at the site.
Structural Optimization: Minimize the additional load placed on the building’s primary structure by the cladding system, enhancing overall structural efficiency.
Architectural Expression: Offer a versatile design element to contribute to the building’s overall aesthetic and architectural intent.
Curtain walls are popular in highrise buildings due to their low self weight
Functional Requirements of Curtain Walls
The following are the functional requirements of curtain walls.
Weather Resistance
Curtain walls are expected to protect the interior of the building from the weather conditions of the exterior. While the materials of the curtain wall themselves typically offer excellent impermeability, joints within curtain walls present potential vulnerabilities. Careful design and implementation are crucial to ensure weather resistance. Therefore, achieving weather resistance relies on meticulous design and construction. Two approaches exist:
1) Impervious joints: utilizing sealants and gaskets to entirely prevent water entry, mimicking the material’s impermeability. 2) Drained joints: acknowledging potential water ingress but strategically channelling it away through dedicated drainage systems. Both methods require consideration of thermal expansion, structural shifts, and moisture movement, with appropriate materials and skilled installation being crucial for long-term success.
Internal Temperature Control
While large glass areas in curtain walls offer stunning aesthetics, they pose challenges in temperature control. The low heat resistance allows heat transfer and solar radiation to warm internal surfaces, creating uncomfortable heat build-up. Fixed louvres within the system offer limited heat gain reduction, primarily addressing glare. External louvres provide marginal improvement by absorbing and re-radiating heat outwards.
Effective solutions include:
Deep recessed windows: Coupled with external vertical fins, these create shading pockets to reduce solar heat gain.
Balanced HVAC systems: These actively manage internal temperature through heating and ventilation for year-round comfort.
Special solar control glass: Reflective glass with metallic or dielectric coatings deflects solar radiation, reducing heat gain. Tilting the glass further enhances its effectiveness.
Sufficient Structural Strength
While non-loadbearing, curtain walls require sufficient strength to withstand their own weight and varying wind pressures. Wind load intensity depends on three key factors: building height, exposure level, and location.
Curtain wall strength hinges on the rigidity of its vertical mullions and their secure anchorage to the building frame. Glazing beads and compressible materials further enhance resilience against wind damage by allowing panels to move independently within the system, minimizing stress on the overall frame.
Vertical mullions of a curtain wall
Fire Resistance
The high percentage of unprotected areas in curtain walling systems, as defined in Building Regulations (Approved Document B4: Section 12.7), poses a significant fire resistance challenge. To achieve compliance and ensure occupant safety, architects and engineers must carefully select cladding materials or material combinations for opaque infill panels.
These materials should possess inherent fire resistance properties or be treated with fire-retardant coatings to qualify as protected areas as defined in the regulations. For further guidance on external fire spread considerations, refer to Part 7 of the same document.
Assembly and Fixing
The mullion, typically a solid or box section member, forms the backbone of a curtain wall system. It securely connects to the building’s structural frame at floor levels using adjustable anchorages or connectors, ensuring proper load transfer and stability. The infill framing and panels can be delivered as individual components requiring on-site assembly, or as prefabricated units for faster installation. When evaluating different systems, key considerations include:
Handling ease: Can the individual components or prefabricated units be safely and efficiently manoeuvred on-site, considering their size and weight?
Site assembly: Is extensive field assembly required, potentially impacting construction time and labour costs?
Access to fixing points: Can workers readily access and secure the curtain wall to the building structure at all designated anchor points?
Assembly and fixing of curtain walls
Sound Insulation
Curtain wall systems, due to their inherent lightweight nature, present challenges in terms of sound insulation. Both structure-borne and airborne sound transmission must be addressed to ensure a comfortable and acoustically controlled indoor environment.
Structure-borne sound: Primarily originating from machinery vibrations, this type of sound can be mitigated by isolating offending equipment with resilient pads or incorporating resilient connectors within the mullion connections. Careful equipment selection and placement can further contribute to reducing vibrations at their source.
Airborne sound: Lightweight cladding offers minimal inherent sound barrier, making glazed areas particularly vulnerable to sound transmission. Strategies to reduce airborne sound transmission include:
Minimizing glazing area: Utilizing less glazing or opting for smaller window sections can significantly reduce sound ingress.
Sealed windows with thicker glass: Implementing sealed windows with thicker glass panels increases the mass barrier, thereby enhancing soundproofing capabilities.
Double-glazing: Installing double-glazed windows with an air gap of 150-200mm between the panes creates a significant barrier for sound waves, offering superior sound insulation performance.
Typical curtain wall panel
Thermal and Structural Movements
Curtain wall systems, positioned on a building’s exterior, face heightened exposure to temperature fluctuations compared to the internal structure. This translates to significant thermal movement within the curtain wall itself, as well as potential differential settlement between the main frame and attached cladding. To accommodate these independent movements, careful design, fabrication, and fixing are crucial.
Key considerations:
Slotted bolt connections: These connections offer flexibility at attachment points between the curtain wall and the building frame, allowing for controlled thermal expansion and contraction without compromising structural integrity.
Spigot connections: Within the curtain wall system, spigot connections join components while permitting controlled movement. This flexibility mitigates stresses caused by thermal expansion and contraction within the system itself.
Mastic-sealed joints: These flexible sealant joints further accommodate movement by allowing slight shifts between individual curtain wall components while maintaining weather resistance.
Infill Panels for Curtain WallSystems
Curtain wall infill panels, responsible for opaque areas, require specific characteristics to ensure optimal performance and longevity. These include:
Lightweight construction: Minimizes overall system weight, reducing structural loads and facilitating handling.
Impermeability: Prevents water ingress and maintains weathertightness of the building envelope.
Adequate fire resistance: Complies with relevant building regulations to ensure occupant safety in case of fire.
Thermal insulation: Minimizes heat transfer and contributes to energy efficiency.
Low maintenance: Requires minimal upkeep for sustained performance and aesthetic appeal.
Panel Construction and Vapour Control:
No single material possesses all these attributes, necessitating the use of composite or sandwich panels. However, such panels pose a risk of interstitial condensation, which can be mitigated by incorporating a vapour control layer near the inner panel surface. This layer, with a vapour resistance exceeding 200 MN/g, can be formed using various materials:
Adequately lapped sheeting: Aluminium foil, waterproof building papers, or polyethylene sheet
Applied materials: Two coats of bitumen or chlorinated rubber paint
Careful placement is crucial to avoid detrimental interactions between adjacent materials, such as alkali attack on aluminium when in contact with concrete or fibre cement.
External Facing Materials:
Direct exposure to the elements necessitates careful selection of external-facing materials. Plastics and plastic-coated options are viable choices if they comply with fire regulations outlined in relevant documents. One popular choice is vitreous enamelled steel or aluminium sheets (0.7-0.8mm thickness).
This process fuses a thin glass coating onto the metal surface at high temperatures, resulting in:
High hardness and impermeability: Resisting damage from acids, corrosion, and abrasion.
Crack and craze resistance: Maintaining an attractive finish with lasting strength.
Alternatively, aluminium sheeting with a silicone polyester coating can be employed. By combining these facings with insulating materials like EPS, rockwool, polyurethane, or polyisocyanurate, lightweight infill panels achieving U-values below 0.35 W/m²K can be produced.
Furthermore, both internal and external surfaces must meet fire performance requirements outlined in building regulations, often tested according to specific standards. The insulating core must also exhibit non-combustible properties. Panel dimensions can reach up to 3000mm x 1000mm.
Glazing for Curtain Wall Systems
One critical aspect of curtain walls is glazing—the use of glass in large, uninterrupted areas to create consistent and attractive facades. While protecting the building interior from the elements remains the principal objective of facade materials, the function of glazing transcends mere weather tightness. It plays a pivotal role in orchestrating two key aspects of the built environment:
1. Daylight-Driven Illumination:
Glazing serves as a conduit for natural light, not only fulfilling the basic requirement of illuminating interior spaces but also contributing demonstrably to occupant well-being and energy conservation efforts. However, solely relying on daylight to sufficiently illuminate specific tasks necessitates meticulous consideration of several factors. Window size, placement, and calculated daylight factors all come into play in ensuring adequate and appropriate natural light distribution for dedicated work areas.
2. Fostering Visual Connection with the Exterior:
Beyond illumination, glazing fulfils a psychological need by establishing a visual connection with the surrounding environment. This connection has been demonstrably linked to enhanced occupant well-being, underlining the importance of thoughtful planning when incorporating glazed areas. Size, orientation, and the quality of the view obtained through these areas are crucial aspects to consider during the design phase.
As discussed earlier in this article, other critical considerations pertaining to glazing selection include managing solar heat gain, glare control, thermal insulation performance, and acoustic properties. Therefore, these aspects shall not be revisited here.
Cleaning and Maintenance of Curtain Walls
The use of expansive glazing in high-rise structures, particularly in curtain walling systems, presents a significant challenge: safe and cost-effective access for cleaning and maintenance. While manual cleaning with tools like swabs, chamois leathers, and squeegees remains the standard method, access becomes paramount. Neglected cleaning causes the following problems on curtain wall glazings:
Aesthetic Integrity: Accumulation of dirt distorts the intended visual appearance.
Visual Clarity: Unobstructed views are essential for occupants and aesthetics.
Material Integrity: Glazing materials are susceptible to deterioration from dirt and chemical attack.
For low- to medium-rise structures, access solutions like trestles, stepladders, and straight ladders (up to 11 meters) suffice. However, taller buildings necessitate alternative approaches:
Tower Scaffolds: While offering access, their assembly and disassembly time and cost make them impractical for frequent cleaning.
Lightweight Scaffolds: Quick-install systems can be considered for moderate heights (up to 6 meters) due to their efficiency.
High-rise curtain wall cleaning predominantly relies on suspended cradles. These come in two forms:
Temporary Cradles: These offer flexibility but must be dismantled and reassembled each time.
Permanent Systems: Integrated into the building structure, they offer readily available access but carry higher upfront costs.
The simplest permanent solution involves installing a universal beam section at roof level, extending 450 mm beyond the facade and encircling the building. A conventional cradle with castors on its lower flange runs along this beam, controlled by ropes lowered to ground level for access.
While challenges exist, a range of options ensures the cleanliness and integrity of high-rise glazed facades, contributing to both aesthetics and occupant well-being.
The efficacy of shear transfer at concrete-to-concrete interfaces is very paramount to the structural integrity of numerous reinforced concrete constructions. This is very important due to the need for shear stress transfer within reinforced concrete structures especially at horizontal construction joints. These joints become necessary due to the impracticality of single-pour of concrete in most construction works or the inherent requirements of staged construction sequences.
A prime illustration of this lies in the horizontal plane of interaction between precast concrete girders and cast-in-place concrete bridge decks. The composite behaviour exhibited by the girder and deck, which ultimately dictates the bridge’s stiffness and strength, is contingent upon the interface’s capacity to effectively transmit shear forces. In essence, the transfer of shear forces from the deck to the girders plays a crucial role in determining the structure’s load-carrying capacity.
Mechanism of Shear Transfer
The mechanisms governing shear stress transfer can be broadly categorized into three main contributors:
1. Interlock between roughened surfaces (shear – friction): Intentional surface irregularities, often achieved through sandblasting or texturing, create mechanical interlock between the concrete layers. This interlock resists relative movement under shear, contributing to stress transfer.
2. Dowel action of reinforcement: Steel bars embedded in the concrete, particularly shear connectors like headed studs, act as dowels traversing the interface. When subjected to shear, these dowels experience tension and compression, contributing to interface resistance.
3. Adhesion: The inherent bond between the concrete layers, influenced by factors like material properties, curing conditions, and surface cleanliness, also plays a role in shear transfer.
The critical mechanism of shear transfer across concrete-to-concrete interfaces in reinforced concrete (RC) structures can be elucidated through the saw-tooth model (Figure 1). This model visualizes the interaction between concrete surfaces under shear force.
Figure 1: Interface Shear Transfer, saw-tooth model
When subjected to shear, a horizontal displacement (h) occurs between the concrete layers. This relative movement triggers a vertical displacement (v) due to interlock between the roughened surfaces. This vertical displacement, in turn, induces tension in the reinforcement crossing the interface. The generated tension translates into a clamping force, enhancing frictional resistance along the interface. Additionally, cohesion, representing the intrinsic bonding force between the concrete surfaces, contributes to shear resistance.
The contribution of each mechanism varies with the applied load. At low loads, cohesion predominates, effectively resisting the shear force. However, as the load increases, cracks develop within the interface, compromising the cohesive bond. Consequently, the burden of shear resistance shifts to a combination of shear-friction and dowel action.
Shear-friction originates from the interaction between the clamping force and the frictional resistance along the interface. Essentially, the clamping force, generated by the tensioned reinforcement, presses the concrete surfaces together, creating friction that opposes the relative movement.
Dowel action stems from the direct shear resistance offered by the steel bars traversing the interface. These bars experience tension and compression under shear, contributing to the overall interface resistance.
Steel bars (stirrups) are used for shear transfer
In essence, the shear transfer mechanism in RC interfaces operates as a dynamic interplay between cohesion, shear-friction, and dowel action. Understanding the individual contributions and their interplay under varying load conditions is crucial for ensuring the structural integrity and performance of RC structures.
Factors Affecting Shear Transfer Capacity
The magnitude of shear transfer capacity is not a static value but depends on several factors, including:
Interface characteristics: Surface roughness, presence of contaminants, and potential shrinkage gaps all influence the effectiveness of mechanical interlock and adhesion.
Concrete properties: Strength, age, and moisture content of the concrete layers affect their bond characteristics and susceptibility to cracking.
Reinforcement details: Type, spacing, and embedment depth of dowel bars significantly impact their contribution to shear transfer.
Loading conditions: Sustained or cyclic loading, along with the magnitude and distribution of shear forces, influence the interface’s response.
Shear Transfer According to the Eurocodes
Section 6.2.5 of Eurocode 2 (EC2) defines the methodology for evaluating the shear capacity of interfaces between concretes cast at different times. This approach considers the combined contributions of cohesion and friction to interface resistance.
The shear stress at the interface is calculated by the difference of the longitudinal internal force ΔF (tension or compression) in the examined part of the cross-section separated by the interface. The part of the longitudinal force (compressive or tensile) that is located within the new concrete is expressed by the coefficient β.
Following a stress-based approach, the equation provided within the code expresses the shear stress capacity (VRd,i) as a function of;
where; fctd is the design tensile strength of concrete; σn is the stress per unit area caused by the minimum external normal force across the interface that can act simultaneously with the shear force, positive for compression, such that σn ≤ 0.6fcd; fyd is the design yield strength of reinforcement, not more than 600 MPa; ρ is the reinforcement ratio (As/Ac); α is the angle between concrete interface and interface reinforcement; c and μ are factors that depend on the roughness of the interface; values are listed in Table 2.
Condition
c
μ
Very smooth interface roughness condition; A surface cast against steel, plastic or specially prepared wooden molds.
0.025
0.5
Smooth interface roughness condition; A slip-formed or extruded surface, or a free surface left without further treatment after vibration.
0.2
0.6
Rough interface condition; A surface with at least 3 mm roughness at about 40 mm spacing, achieved by ranking, exposing of aggregate or other methods giving an equivalent behavior
0.4
0.7
Indented interface condition; A surface with indentations complying with more than 3 mm roughness and also depth of groove should be more than 5 mm and the width of the groove should be more than 10 times its depth
0.5
0.9
vRdi,max = 0.5 ⋅ ν ⋅ fcd
Where ν is the strength reduction factor for shear design in accordance with EN1992-1-1 §6.2.2(6). ν = 0.6 ⋅ (1 – fck / 250 MPa) fcd is the design compressive strength of the concrete fck is the characteristic compressive strength of the concrete after 28 days
Figure 3: Shear interface between concrete cast at different times
Design Example
Design the shear transfer between a girder of 600 mm width to a slab topping of 250 mm thickness. The shear force at the section is 655 kN and the interface between the old and new concrete is rough. Take the lever arm for the internal forces of composite section z = 0.9m. fck = 30 MPa, fyk = 500 MPa.
Solution
Applied shear stress at the interface
By assuming a constant lever arm of internal forces z in the examined infinitesimal segment dx then the corresponding difference of longitudinal force ΔF is:
ΔF = β(M + dM) / z – βM/z = βdM/z
Where dM is the infinitesimal change of the bending moment. In the calculation above the variation of the normal force N is not considered significant. The shear stress at the interface v is calculated by dividing the difference of longitudinal force ΔF by the width of the interface bi and the assumed infinitesimal length dx. According to fundamental mechanics, the shear force is calculated as the derivative of the bending moment V = dM / dx.
The aforementioned analysis leads to the design value of the shear stress at the interface vEdi as given by EN1992-1-1 §6.2.5(1) equation (6.24):
The coefficient for concrete cohesion c should be reduced for the case of fatigue or dynamic loads. In general according to EN1992-1-1 §6.2.5(5) under fatigue or dynamic loads, the values for c should be halved. Specifically for bridges, according to EN1992-2 §6.2.5(105) under fatigue and dynamic loads a value of 0.0 should be considered for c. Moreover when the normal stress σn is tensile (i.e. negative) then a value of 0.0 should be considered for c in accordance with EN1992-1-1 §6.2.5(1).
For the examined case the adjustment factor applied to the value of c is 0.40. The adjusted value of the coefficient is c = 0.40 × 0.400 = 0.160.
Maximum shear strength that can be transferred at the interface
The maximum value of the design shear resistance vRdi,max of the interface is limited by the compressive strength of the concrete struts as specified in EN1992-1-1 §6.2.5(1):
Therefore the maximum value of the design shear resistance vRdi,max is calculated as: vRdi,max = 0.5νfcd = (0.5 × 0.528 × 20.00 MPa) = 5.280 MPa
For the examined case the applied shear stress on the interface vEdi = 1.213 MPa does not exceed the maximum shear stress capacity of concrete vRdi,max = 5.280 MPa. The corresponding utilization factor is u = 0.23 ≤ 1.0 ⇒ ok.
Calculation of required shear connection reinforcement
The calculation of the required shear connection reinforcement ratio ρ can be performed by solving EN1992-1-1 equation (6.25) for ρ. The equation that defines the design shear resistance of the interface is:
The values of the trigonometric functions when the shear connection reinforcement forms angle α = 90.0 ° with the interface plane are sinα = 1.0 and cosα = 0. The value of the design tensile strength of concrete fctd is calculated as specified in EN1992-1-1 §3.1.6(2)P:
where fctk,0.05 = 0.7 × fctm = 0.7 × 2.90 MPa = 2.03 MPa is the 5% fractile of the tensile strength of concrete as specified in EN1992-1-1 Table 3.1.
The value of the design yield strength of reinforcement steel fyd is calculated as specified in EN1992-1-1 §3.2:
fyd = fyk / γS = 500/1.15 = 434.8 MPa
The required shear connection reinforcement is calculated when vEdi = vRdi. Provided that vRdi ≤ vRdi,max the aforementioned equation can be solved for the required ratio ρ of the shear connection reinforcement: σn = 0
The corresponding required shear connection reinforcement per m length of the interface area is: Width of area = 600 mm Length of area (per metre run) = 1000 mm
As = ρ × 1000 mm × 600 mm = 1965 mm2/m
Therefore provide 4legs of H12 @200 mm c/c spacing (Asprov = 2260 mm2/m)
Conclusion
In conclusion, shear transfer in the interface of RC members serves as a critical mechanism for structural integrity. Recognizing the contributing factors, their interactions, and the limitations of current design approaches is essential for ensuring the safety and reliability of such structures. Ongoing research efforts aimed at refining analytical models and leveraging advanced experimental techniques hold promise for advancing our understanding and design capabilities, ultimately leading to safer and more efficient RC structures
Cantilever steel carports have become increasingly popular due to their clean aesthetics, simplicity, minimal space requirements, and ability to span large distances without obstructing parking space. However, the unique structural demands of this design system necessitate careful consideration during the design process. The design of cantilever steel carports is consistent with the design of an open monopitch canopy roof according to EN 1991-1-4.
The design of steel carports involves the selection of adequate steel columns and beams that will be able to withstand the dead, live, and environmental loads that the structure will be subjected to without undergoing excessive deflection, vibration, or failure.
Construction of steel carport
This article discusses the structural design for cantilever steel carports, exploring key principles, considerations, and design approaches.
Structural System of Cantilever Carports
Cantilever steel beams are structural systems that project outwards like outstretched arms. Technically, most steel carport frame structures fall under monopitch canopy roof systems for their wind load analysis and design. This structural system offers elegance, efficiency, and expansive coverage, finding diverse applications in bridges, balconies, and yes, even carports. But beneath their deceptively simple appearance lies a complex interplay of forces, internal stresses, and deformations.
Cantilever beams project outward from support columns without additional support at the free end. This creates a significant bending moment force at the fixed end, necessitating robust column and foundation design.
Bending Moment
Imagine a cantilever beam of a carport structure bearing a load at its free end. The beam tries to resist this bending, leading to the development of internal stresses. The top fibres experience tension, stretching as the beam deflects downwards. Conversely, the bottom fibres are compressed, pushing inwards. This stress distribution is not uniform but varies parabolically across the beam’s depth, with the maximum values occurring at the top and bottom surfaces.
Shear force
While bending usually governs overall behaviour of carport frames, shear forces also play a critical role. Imagine slicing the beam at any section. The internal forces acting across this imaginary cut represent the shear force, responsible for balancing the applied load. This force varies along the beam length, reaching a maximum value at the support and decreasing towards the free end. Understanding shear distribution is critical for selecting appropriate beam sections and preventing shear failure.
Deflection
As the beam of a carport frame bends, the free end undergoes deflection, a measure of its vertical displacement. While deflection is inevitable, excessive movement can be detrimental. Factors like beam length, material properties, load magnitude, and support conditions all influence deflection. Engineers utilize engineering mechanics principles and advanced beam theory to calculate deflections and ensure they stay within acceptable limits.
Buckling
While bending and shear are often the primary concerns, slender beams face an additional problem – buckling. Imagine pushing a long, thin ruler sideways; it bends easily. Likewise, slender beams under compression can buckle, losing their load-carrying capacity abruptly. Engineers carefully assess the risk of buckling based on beam geometry, material properties, and loading conditions, employing design techniques like increasing section depth or adding lateral supports to mitigate the risk.
Connection Details
The design doesn’t end with the beam and column structures of the carport. The connections between the structural elements play a vital role in overall behaviour. Welded, bolted, or a combination of connections transfer internal forces between the beam and the support. Improperly designed or executed connections can lead to premature failure, highlighting the importance of careful design, fabrication, and quality control during construction.
Typical steel carport structure
Load Analysis
Several loads and load combinations must be accounted for in the design of carports and they typically include:
Dead Loads: Weight of the steel structure, roof covering, and any attachments such as solar panels, electrical/mechanical services, and insulations (though rarely included).
Live Loads: Human access due to erection or maintenance, snow accumulation, and wind pressures. Wind pressure appears to be the most critical load in the design of carport structural systems.
Seismic Loads: Relevant in seismically active regions.
Load Path and Equilibrium: The design ensures a clear and efficient load path from the roof to the columns, foundation, and ultimately the soil. Counterbalancing is often required to achieve equilibrium, achieved through structural elements or anchor design.
Structural Analysis
For complex structural configurations or demanding loading scenarios, advanced analysis techniques like Finite Element Analysis (FEA) become invaluable. FEA software creates a digital model of the structure, discretizing it into smaller elements and applying loads. By solving complex mathematical equations, the software calculates stresses, deflections, and buckling potential at various points within the beam, providing valuable insights beyond analytical solutions.
Structural Designof Carport Structures
Each structural member in the carport frame is individually designed to resist the anticipated loads. This involves:
Beam Design: Selecting appropriate beam sections (e.g., universal beam sections) and checking for bending stress, shear stress, and deflection within allowable limits as per design codes.
Column Design: Designing columns to resist axial loads, bending moments, and potential buckling. Steel column design tables or specific software tools can be employed.
Connection Design: Designing connections between members to ensure adequate strength and stiffness. Welded, bolted, or a combination of connections are used, following code-specified design procedures.
Member Design Example
It is desired to design a monopitch canopy steel carport structure with the details provided below;
Structural model of a carport structure
Structure data Height of column = 2.5m Length of beam = 3.027m Spacing of frame members = 3.0 m c/c Spacing of purlins = 0.605m Angle of inclination of roof = 7.59 degrees
Dead Load Unit weight of sheeting material = 0.02 kN/m2 Self-weight of members (calculated automatically) Services (assume) = 0.1 kN/m2
Live Load Imposed live load = 0.6 kN/m2
Wind Load Analysis of carport Monopitch Canopy Structures
Wind speed = 40 m/s Basic wind velocity (Exp. 4.1); v = cdir × cseason × vb,0 × cprob = 40.8 m/s Degree of blockage under the canopy roof: φ = 0 Reference mean velocity pressure; qb = 0.5 × ρ × vb2 = 1.020 kN/m2 Reference height (at which q is sought); z = 2900 mm Displacement height (sheltering effects excluded); hdis = 0 mm Aref = bd / cos(α) = 9.000 m ⋅ 3.000 m / 0.991 = 27.239 m2
Pressure zones for monopitch canopy roofs, reproduced from EN1991-1-4 Table 7.6 and Figure 7.16
Mean wind velocity The mean wind velocity vm(ze) at reference height ze depends on the terrain roughness, terrain orography and the basic wind velocity vb. It is determined using EN1991-1-4 equation (4.3):
vm(ze) = cr(ze) ⋅ c0(ze) ⋅ vb = 0.7715 × 1.000 × 40.00 m/s = 30.86 m/s
Wind turbulence The turbulence intensity Iv(ze) at reference height ze is defined as the standard deviation of the turbulence divided by the mean wind velocity. It is calculated in accordance with EN1991-1-4 equation 4.7. For the examined case ze ≥ zmin.
Iv(ze) = kI / [ c0(ze) ⋅ ln(max{ze, zmin} / z0) ] = 1.000 / [ 1.000 ⋅ ln(max{2.900 m, 2.0 m} / 0.050 m) ] = 0.2463
Basic velocity pressure The basic velocity pressure qb is the pressure corresponding to the wind momentum determined at the basic wind velocity vb. The basic velocity pressure is calculated according to the fundamental relation specified in EN1991-14 §4.5(1):
where ρ is the density of the air in accordance with EN1991-1-4 §4.5(1). In this calculation the following value is considered: ρ = 1.25 kg/m3. Note that by definition 1 N = 1 kg⋅m/s2.
Peak velocity pressure The peak velocity pressure qp(ze) at reference height ze includes mean and short-term velocity fluctuations. It is determined according to EN1991-1-4 equation 4.8:
Calculation of local wind pressure on the canopy roof
Net pressure coefficients The net pressure coefficients cp,net represent the maximum local pressure for all wind directions and they should be used in the design of local elements such as roofing elements and fixings. Net pressure coefficients are given for three zones A, B, C as defined in the figure included in EN1991-1-4 Table 7.6 that is reproduced above. Zones B, C extend at the sides of the canopy and Zone A at the central region:
The inclined length of the monopitch canopy roof parallel to the wind direction is: d’ = d / cos(α) = 3.000 m / 0.991 = 3.027 m
Zone C corresponds to the regions parallel to the windward and leeward edges having width d’/10 = 0.303 m. Zone B corresponds to the regions parallel to the side edges having width b/10 = 0.900 m, where b is the width of the canopy transverse to the wind direction. Zone A corresponds to the remaining central region.
The net pressure coefficient cp,net for each of the zones A, B, C are defined in EN1991-1-4 Table 7.6 as a function of the roof angle α and the blockage factor φ. For the examined case: α = 7.59 ° and φ = 0.000. Therefore according to EN1991-1-4 Table 7.6 the following net pressure coefficients and overall force coefficient are obtained, using linear interpolation where appropriate:
For zone A: cp,net,A = -1.307 or +1.007 For zone B: cp,net,B = -1.855 or +2.255 For zone C: cp,net,C = -1.955 or +1.455
Negative values for the external pressure coefficient correspond to suction directed away from the upper surface inducing uplift forces on the roof. Both positive and negative values should be considered for each zone.
Net wind pressure on pressure zones
The net wind pressure on the surfaces of the structure wnet corresponds to the combined effects of external wind pressure and internal wind pressure. For structural surfaces consisting of only one skin the net pressure effect is determined as:
wnet = cp,net ⋅ qp(ze)
For structural surfaces consisting of more than one skin EN1991-1-4 §7.2.10 is applicable. For the different pressure zones on the canopy roof the following net pressures are obtained:
– For zone A: wnet,A = -2.119 kN/m2 or +1.633 kN/m2 (zones A is the remaining central region located more than d’/10 = 0.303 m or b/10 = 0.900 m from the edges)
– For zone B: wnet,B = -3.008 kN/m2 or +3.657 kN/m2 (zone B extends up to b/10 = 0.900 m from the side edges)
– For zone C: wnet,C = -3.170 kN/m2 or +2.360 kN/m2 (zone C extends up to d’/10 = 0.303 m from the windward and leeward edges)
Negative net pressure values correspond to suction directed away from the external surface inducing uplift forces on the canopy roof. Both positive and negative values should be considered.
Calculation of overall wind force on the canopy roof
Overall pressure coefficient The overall pressure coefficient cf represents the overall wind force and it should be used in the design of the overall load bearing structure. The overall pressure coefficient cf is defined in EN1991-1-4 Table 7.6 as a function of the roof angle α and the blockage factor φ. For the examined case: α = 7.59 ° and φ = 0.000. Therefore according to EN1991-1-4 Table 7.6 the following overall pressure coefficient is obtained, using linear interpolation where appropriate:
cf = -0.804 or 0.452
Negative values for the overall pressure coefficient correspond to suction directed away from the upper surface inducing uplift forces on the roof. Both positive and negative values should be considered.
Structural factor The structural factor cscd takes into account the structure size effects from the non-simultaneous occurrence of peak wind pressures on the surface and the dynamic effects of structural vibrations due to turbulence. The structural factor cscd is determined in accordance with EN1991-1-4 Section 6. A value of cscd = 1.0 is generally conservative for small structures not-susceptible to wind turbulence effects such as buildings with heights less than 15 m.
In the following calculations, the structural factor is considered as cscd = 1.000.
Overall wind force (for total roof surface)
The wind force Fw corresponding to the overall wind effect on the canopy roof is calculated in accordance with EN1991-1-4 equation 5.3: Fw = cscd ⋅ cf ⋅ Aref ⋅ qp(ze)
where Aref = 27.239 m2 is the reference wind area of the canopy roof as calculated above.
For the examined case: – Maximum overall wind force (acting downwards): Fw = 1.000 ⋅ (+0.452) ⋅ 27.239 m2 ⋅ 1.621 kN/m2 = +19.95 kN
Negative values correspond to suction directed away from the external surface inducing uplift forces on the canopy roof. Both positive and negative values should be considered, as explained below.
Direction and eccentricity of the overall wind force According to EN1991-1-4 §7.3(6) and the National Annex the location of the centre of pressure is defined at an eccentricity e from the windward edge. In this calculation, the centre of pressure is considered at an eccentricity e = 0.250⋅d’ = 0.757 m, where d’ = 3.027 m is the inclined length of the canopy roof parallel to the wind direction. Two cases should be examined for the overall effect of the wind force on the canopy roof:
Maximum force Fw = +19.95 kN (i.e. acting downwards) located at a distance e = 0.757 m from the windward edge.
Minimum force Fw = -35.49 kN (i.e. acting upwards) located at a distance e = 0.757 m from the windward edge.
Structural Analysis and Results
Finite Element Analysis (FEA) software (Staad Pro) was used to model the structure and evaluate stresses, deflections, and buckling potential under various load combinations.
Structural Modelling and Loading
Some of the images from the structural model are shown below.
3D render of the carport model
Finite element model of the carport structure/canopy roof
Gravity load on the carport structure
Negative wind load (suction) on the canopy roof
Support Reactions
The support reactions from the various load combinations are shown below.
Support Reactions (1.35gk + 1.5wk) – Suction
Support Reactions (1.35gk + 1.5wk) – Gravity
The summary of the maximum and minimum support reactions under various load combinations are shown in the Table below.
Bending Momentand shear force diagrams
The typical bending moment and shear force diagrams from the various load combinations are shown below.
Typical bending moment diagram under gravity load
Typical bending moment diagram under wind suction
Typical shear force diagram under gravity load
Design of the Cantilever Beams
The summary of the maximum stresses occurring on the beams is shown below. An abridged design calculations are presented afterwards.
Section type; UB 254x146x37 (BS4-1) Steel grade – EN 10025-2:2004; S275 Nominal thickness of element; tnom = max(tf, tw) = 10.9 mm Nominal yield strength; fy = 275 N/mm2 Nominal ultimate tensile strength; fu = 410 N/mm2 Modulus of elasticity; E = 210000 N/mm2
The section is Class 1
Check shear Height of web; hw = h – 2tf = 234.2 mm; h = 1.000 hw / tw = 37.2 = 40.2ε/ h < 72ε / h Shear buckling resistance can be ignored
Understanding soil properties is critical for foundation design. Geotechnical investigations determine soil-bearing capacity and potential for settlement. The design of the foundation should pay good attention to uplift, sliding and overturning moment from the wind load.
Depending on soil conditions and design loads, foundations can be:
Spread Footings: Individual concrete pads for each column. Continuous Footings: A continuous concrete strip supporting multiple columns. Mat Foundation: A concrete slab supporting the entire structure.
Anchor Design: Anchors embedded in the foundation resist uplift forces generated by wind and seismic loads. Anchor selection and embedment depth are critical for structural stability.
Fabrication and Construction Considerations
Shop Drawings and Fabrication: Detailed shop drawings ensure accurate fabrication of steel components. Quality control during fabrication is paramount.
Erection and Field Welding: Proper erection procedures and qualified welders are necessary to ensure structural integrity and safety.
Inspection and Quality Control: On-site inspections at various stages of construction verify adherence to design specifications and ensure construction quality.
Conclusion
Cantilever steel carports offer an aesthetically pleasing and practical solution for vehicle protection. However, due to their inherent structural challenges, their design requires meticulous attention to detail. A clear understanding of the load paths, material properties, design codes, and analysis methods is essential for a safe and reliable structure. Consulting with qualified structural engineers throughout the design and construction process is crucial to ensure a successful and long-lasting cantilever steel carport.
Signboards, with their captivating visuals and strategic placements, are very popular elements for advertisement in our towns, streets, and highways. However, the structural stability of signboards hinges on their ability to withstand the dynamic forces of wind. This requires a detailed wind load analysis from the design engineer.
Billboard advertising, despite facing competition from digital alternatives, remains a significant player in the marketing landscape. To understand its economic impact, global billboard advertising spending reached $36.8 billion in 2022, with predictions of a steady rise to $44.2 billion by 2027. The United States accounts for the largest share (around 40%), followed by China and Europe.
Signboard/Billboard structure
Wind Loadson Signboards
Wind force is the most critical action on billboards. Their cantilevered design, supported by a single column, exposes them to wind-induced stresses. Failure due to wind and hurricanes has been reported, necessitating rigorous analysis and design. Other effects, such as imperfections and the p-delta phenomenon, also impact structural performance under wind load. Wind exerts pressure on objects, generating a force proportional to the wind speed squared. This force, known as wind load, varies with factors like:
Location: Geographic location determines wind speeds within established design wind speed maps.
Terrain: Topography influences wind turbulence and local wind speeds.
Exposure category: Building codes categorize zones based on surrounding obstructions, impacting wind pressures.
Signboard geometry: Size, shape, and orientation of the signboard directly influence the wind load experienced.
Methods and Toolsfor Wind Load Analysis
Several methods are employed for wind load analysis of signboards:
Simplified methods: Building codes often provide simplified equations based on specific geometries and exposure categories. However, these methods may not always be suitable for complex designs.
Wind tunnel testing: Physical scale models of the signboard are subjected to simulated wind conditions in a wind tunnel, providing accurate pressure data. This method is expensive but precise, especially for unique designs.
Computational Fluid Dynamics (CFD) simulations: Numerical simulations model wind flow around the signboard using specialized software. This is a cost-effective alternative to wind tunnel testing, offering valuable insights into complex geometries.
Dynamic Considerations
While static wind loads are vital, signboards may experience dynamic effects like flutter and vortex shedding, resulting in vibrations and potential fatigue failure. Advanced analysis methods or wind tunnel testing may be necessary to assess these dynamic effects, especially for tall and slender signboards.
Wind Load Analysis Example
Let us carry out a wind load analysis on an 8m high signboard in a city centre where the basic wind speed is 35 m/s. The calculated effective wind pressure weff, total wind force FW, and total wind overturning moment MW correspond to the total wind action effects and they are appropriate for global verifications of the element according to the force coefficient method.
For local verifications, appropriate wind pressure on local surfaces must be estimated according to the relevant external pressure coefficients, as specified in EN1991-1-4 §5.2. 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.
Input Data
Terrain category: = II
Basic wind velocity: vb = 35 m/s
Width of the signboard wind-loaded area: b = 10 m
Height of the signboard wind-loaded area: h = 3 m
Separation height of the signboard wind-loaded area from the ground: zg = 5 m
Orography factor at reference height ze: c0(ze) = 1
Structural factor: cscd = 1
Air density: ρ = 1.25 kg/m3
Additional rules defined in the National Annex for the calculation of peak velocity pressure qp(ze): = None
The horizontal eccentricity of the centre of pressure from the centre of the signboard as a fraction of the width b: e/b = 0.25
Calculation of peak velocity pressure
Reference area and height
The reference height for the wind action ze is located at the centre of the signboard, as specified in EN1991-1-4 §7.4.3(3). The reference area for the wind action Aref is the wind-loaded area of the signboard, as specified in EN1991-1-4 §7.4.3(3). Therefore:
ze = zg + h / 2 = 5.000 m + 3.000 m / 2 = 6.500 m Aref = b ⋅ h = 10.000 m ⋅ 3.000 m = 30.00 m2
Notation for wind load on signboards
Basic wind velocity
The basic wind velocity vb is defined in EN1991-1-4 §4.2(2)P as a function of the wind direction and time of year at 10 m above ground of terrain category II. The value of vb includes the effects of the directional factor cdir and the seasonal factor cseason and it is provided in the National Annex. In the following calculations, the basic wind velocity is considered as vb = 35.00 m/s.
Terrain roughness
The roughness length z0 and the minimum height zmin are specified in EN1991-1-4 Table 4.1 as a function of the terrain category. 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):
The roughness factor cr(ze) at the reference height ze accounts for the variability of the mean wind velocity at the site. It is calculated in accordance with EN1991-1-4 equation 4.4. For the examined case ze ≥ zmin:
cr(ze) = kr ⋅ ln(max{ze, zmin} / z0) = 0.1900 ⋅ ln(max{6.500 m, 2.0 m} / 0.050 m) = 0.9248
Orography factor
Where orography (e.g. hills, cliffs etc.) is significant its effect on the wind velocities should be taken into account using an orography factor c0(ze) different than 1.0, as specified in EN1994-1-1 §4.3.3. The recommended procedure in EN1994-1-1 §4.3.3 for the calculation of the orography factor c0(ze) is described in EN1994-1-1 §A.3.
In the following calculations, the orography factor is considered as c0(ze) = 1.000.
Mean wind velocity
The mean wind velocity vm(ze) at reference height ze depends on the terrain roughness, terrain orography and the basic wind velocity vb. It is determined using EN1991-1-4 equation (4.3):
vm(ze) = cr(ze) ⋅ c0(ze) ⋅ vb = 0.9248 ⋅ 1.000 ⋅ 35.00 m/s = 32.37 m/s
Wind turbulence
The turbulence intensity Iv(ze) at reference height ze is defined as the standard deviation of the turbulence divided by the mean wind velocity. It is calculated in accordance with EN1991-1-4 equation 4.7. For the examined case ze ≥ zmin.
Iv(ze) = kI / [ c0(ze) ⋅ ln(max{ze, zmin} / z0) ] = 1.000 / [ 1.000 ⋅ ln(max{6.500 m, 2.0 m} / 0.050 m) ] = 0.2054
Basic velocity pressure
The basic velocity pressure qb is the pressure corresponding to the wind momentum determined at the basic wind velocity vb. The basic velocity pressure is calculated according to the fundamental relation specified in EN1991-14 §4.5(1):
where ρ is the density of the air in accordance with EN1991-1-4 §4.5(1). In this calculation the following value is considered: ρ = 1.25 kg/m3. Note that by definition 1 N = 1 kg⋅m/s2.
Peak velocity pressure
The peak velocity pressure qp(ze) at reference height ze includes mean and short-term velocity fluctuations. It is determined according to EN1991-1-4 equation 4.8:
The structural factor cscd is determined in accordance with EN1991-1-4 Section 6. A value of cscd = 1.0 is generally conservative for small structures not susceptible to wind turbulence effects. In the following calculations, the structural factor is considered as cscd = 1.000.
Force coefficient
The force coefficient cf is given in EN1991-1-4 Sections 7 and 8 depending on the type of structure or structural element. According to EN1991-1-4 §7.4.3, for signboards with zg ≥ h / 4 or b / h ≤ 1, the force coefficient is cf = 1.800.
Total wind force
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.
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:
This effective pressure weff = 2.874 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. For the latter case appropriate wind pressure on local surfaces must be estimated according to the relevant pressure coefficients, as specified in EN1991-1-4 §5.2.
Overturning moment
According to EN1991-1-4 §7.4.3 the resultant force normal to the signboard should be taken to act at the height of the center of the signboard. The total overturning moment Mw acting at the base of the structure is equal to:
Mw = Fw ⋅ (zg + h / 2) = 86.216 kN ⋅ (5.000 m + 3.000 m / 2) = 560.40 kNm
The overturning moment corresponds to the wind action total effect, i.e. it is the total overturning moment for all the base supports.
Horizontal eccentricity
According to EN1991-1-4 §7.4.3 and the National Annex, the resultant force normal to the signboard should be taken to act with a horizontal eccentricity e. In this calculation, the following normalized eccentricity is considered e/b = ±0.250, where b is the width of the signboard wind-loaded area. The total torsional moment Tw acting at the base of the structure is equal to:
Tw = ±0.250 ⋅ b ⋅ Fw = ±0.250 ⋅ 10.000 m ⋅ 86.216 kN = 215.54 kNm
The torsional moment corresponds to the wind action total effect, i.e. it is the total torsional moment for all the base supports.
Conclusion
Wind load analysis is a crucial step in ensuring the safety and durability of signboards. By understanding wind forces, employing appropriate analysis methods, and considering structural design principles, engineers can guarantee structurally sound signboards that stand the test of time.
