Design and Construction of Steel Staircase | Industrial Staircase

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August 5, 2023

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Steel staircase structures are usually considered secondary steelworks. Primary structures comprise the critical elements necessary for the strength and stability of the overall structural frame. This usually comprises the beams, columns, walls, slabs, etc. This frame serves as the support for all other building components. Any steelwork supported by the main structure, without needing to enhance its strength or stiffness, is called secondary steelwork.

The essential elements of a staircase include treads, risers, stringers, landings, and their supports. These components can be configured in different ways to create stairs with varying levels of functionality, from simple utility to prominent architectural features. BS 5395, the code of practice governing the design, construction, and maintenance of straight stairs and winders, offers the guidelines described in the sections that follow.

**Figure 1:** Parts of a steel staircase

Geometry of Steel staircase

The geometry of a staircase structure is usually determined by building regulation requirements. The relationship between rise, tread, and pitch must be such that the stair is safe and comfortable to use. It is essential to make all rises in a flight uniform, subject to the tolerances given in Clause 5.5 of BS 5359. The relationship between the rise and going for a stair should not change along the walking line, subject to the same tolerances.

The minimum clear width should be 600 mm for occasional one-way traffic, 800 mm for regular one-way traffic and occasional two-way traffic and 1000 mm for regular two-way traffic. Stairs that are often used by large numbers of people at the same time (assembly stairs in public buildings) should be designed with a large going and a small rise to achieve a maximum pitch of 33 degrees. Stairs that are used as means of escape may require a clear width greater than 1000mm.

All stairs are required to have a minimum of three and a maximum of 16 rises per flight and the clear width of all landings should never be less than the stair clear width. The length of a landing should be not less than the clear width of the stair or 850 mm, whichever is greater.

**Figure 2:** Industrial Steel Staircase

For steel staircases in industrial structures, there should be a change of line or direction of not less than 30° after 32 risers, for straight stairs, or 44 risers, for helical or spiral stairs. Landings at the head of a stair should be designed so that it is not possible to step from a platform or walkway onto the stair without a change in direction.

Typical dimensions for public stairs are:

Rise: 100 – 190 mm
Going: 250 – 350 mm
Pitch: maximum 38 degrees
Clear width: minimum 1000 mm.

The minimum pitch for straight stairs should be 30°
The maximum pitch for occasional access should be 42°
The maximum pitch for regular two-way traffic should be 38°

Treads

Treads should comply with the requirements for strength given in BS 4592 and should be slip-resistant or at least have a slip-resistant nosing not less than 25 mm wide. Treads on open riser stairs should overlap not less than 16 mm and have a nosing depth in the range of 25 mm to 50 mm to aid visibility.

Strings

Strings should be sufficiently robust to minimize lateral flexing of the structure and should not project more than 50 mm beyond the nosing of the bottom tread.

Loads and robustness

Industrial staircases need to be designed with consideration for accidental loads, particularly when they serve as emergency escape routes. It is important to ensure that these stairs can withstand potential damage caused by accidental loads without collapsing.

To achieve this, the connections between the stairs and the primary structure must be strong and well-designed, providing enough bearing area and tie resistance. When using individual treads, their design should account for the dynamic impact of repeated foot loading, and it is advisable to opt for a cautious and conservative approach to the design.

The dynamic response can be critical as steel stairs tend to have little inherent damping.

Other criteria – safety, slip resistance, durability, acoustic requirements and lighting requirements all influence stair design and are addressed in BS 5395.

external escape steel staircase — **Figure 3:** External escape steel structure

Dynamics of Steel Staircase Structures

Footfall excitation is the primary dynamic load that significantly affects the behaviour of a staircase. Staircases can experience different types of footfall excitation, including the impact of a single person walking, a group of individuals going up or down the stairs together, and the impulse load generated when someone jumps from a height to a lower step.

The limitations in the design geometry of steel staircases lead to various approaches for different individuals when ascending or descending. Some people may choose to increase their step frequency to maintain their speed, while others may stick to the typical 25 step frequency.

Additionally, some individuals may take two or more steps at once, resulting in a higher impact load but reducing the step frequency. Due to these variations, it becomes challenging to provide a single or specific set of instructions for ascending or descending a staircase.

Slender staircases are characterized by their lightweight, leading to a low stiffness-to-mass ratio. As a result, these staircases have low natural frequencies, making the vibration serviceability criteria the primary design consideration. It is important to simulate the dynamic behaviour of a staircase using finite element analysis before construction to ensure that it meets the necessary dynamic and comfort requirements for users.

Design of Steel Staircase

Structural steel is the material commonly used in the design of industrial steel staircases. Grade S275 or S355 is commonly used. After the selection of the proper material, the next step is to design the individual components of the staircase. This includes the treads, risers, stringers, and landings.

The stringers are the beams that support the treads, risers, and landings, and they must be designed to carry the loads of the staircase. They are usually designed using I-beam sections, even though channel and rectangular hollow sections can also be used. They are usually subjected to bending moment, shear, axial, and torsional stresses.

The load from the tread can be transferred to the stringers as a series of concentrated loads or uniformly distributed loads depending on the manner of connection adopted. The stringer can be bolted or welded to a base plate or the primary structure.

The treads and risers are the parts of the staircase that people will step on, and they must be designed to provide a safe and comfortable walking surface. The treads are commonly designed using chequered structural steel plates to provide slip-resistant surfaces. Angle or channel sections can be used to enhance the rigidity of the plates.

The landings are the platforms that people will use to rest and change direction, and they must be designed to be level and stable.

Forms of Construction

Stair flights, consisting of treads and risers, are supported by stringers to create a staircase. Typically, two flights are required per storey height, arranged at 180 degrees to each other, and should occupy a footprint not exceeding 6m x 3m (although larger stairs are allowed in assembly buildings). Each end of the stair flight connects to a landing.

**Figure 4:** Forms of composite steel staircase construction

The most straightforward stair construction involves placing the staircase internally, within an opening in the primary floor structure. In this case, both the floor level and half-level landings can be directly supported by the primary structure, allowing the stair flight to span between landings. The floor level landing can be designed as part of the staircase or as part of the floor structure. Stair treads can be positioned above or in the plane of the stringers.

When the treads are located in the plane of the stringers, the stringer depth resulting from minimum planning dimensions will be structurally sufficient. Additionally, if folded steel plates are used for both the treads and risers, the staircase will inherently have enough rigidity to respond adequately to dynamic forces. This construction method proves to be highly efficient.

However, if a staircase is placed at the edge of a floor slab, the support of landings, especially the half-landings, becomes critical.

Conclusion

Steel staircases are important structural elements used for providing vertical circulation in a building. Steel offers several advantages, such as high strength, durability, and versatility. The design process involves considering various factors, including the intended use, building regulations, and safety standards.

Key considerations in the design include the geometry and arrangement of treads, risers, and stringers. The configuration of the staircase should provide a safe and efficient means of vertical circulation. Landings are essential for connecting stair flights and offering resting points for users. Structural engineers must account for dynamic loads caused by footfalls and other factors that can affect the staircase’s performance. Ensuring sufficient structural integrity to withstand accidental loading and to meet vibration serviceability criteria is crucial.

Proper connections to the primary structure are vital for ensuring stability and load-bearing capacity. The use of folded steel plates for treads and risers can enhance the staircase’s rigidity and dynamic response.

Summarily, the structural design of steel staircases requires careful planning, analysis, and adherence to building codes and safety regulations. By considering the specific requirements of each project, designers can create safe, efficient, and aesthetically pleasing staircases that meet the needs of users while enhancing the overall architectural design of the building.

Pylons in Cable-Stayed Bridges

By

Ubani Obinna

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August 2, 2023

Table of Contents

In cable-stayed bridges, the main purpose of the pylon is to transfer the forces resulting from anchoring the cable stays to the foundation. As a result, these forces will significantly influence the design of the pylon. The tensile cable forces in cable-stayed bridges are part of a closed force system that balances these forces with the compression that occurred within the deck and the pylon. Ideally, the pylon should resist these forces through axial compression whenever feasible to minimize any uneven loading.

The pylon serves as the central element that defines the visual appearance of a cable-stayed bridge, offering a chance to impart a unique style to the overall design. Additionally, the pylon’s design must be adaptable to different stay cable layouts, accommodate the bridge site’s topography and geology, and support the forces efficiently and cost-effectively. The stability of cable-stayed bridges is dependent on the stability and stiffness of the pylons.

Pylons for cable-stayed bridges are predominantly constructed using structural steel, reinforced concrete, or composite sections.

Steel Pylons

Early designs of cable-stayed bridge pylons mostly involved steel boxes, like the Stromsmund Bridge (opened in 1956). The pylons resembled steel portal frames meant to offer transverse restraint to the stay system. However, it was subsequently observed that this restraint was unnecessary as the stay system itself could provide sufficient transverse restraint.

Stromsund bridge — **Figure 1:** Stromsmund Bridge

When a single mast supports each stay plane, any lateral displacement at the top of the mast results in a rotation of the stay plane. This rotation ensures that the resultant reaction from the main span and back span stay cables passes through the foot of the pylon. The weight of the pylon remains vertical, but the reaction from the stays dominates. Thus, the effective length of the mast in buckling is not twice the height (2H) of a simple cantilever, but equal to the height (H).

In the longitudinal direction, the main and back stay cables restrain the pylon against buckling as long as the deck, to which the stays are anchored, is properly restrained against longitudinal movement. If the deck is unrestrained, the pylon will behave as a cantilever with maximum bending at the base, resulting in an effective length of twice the height (2H) in buckling.

**Figure 2:** Longitudinal restraint of the pylon by the anchor stays (Farquhar, 2008)

Effective pylon restraint can be achieved when the deck is adequately connected to an abutment, another pylon, or an independent gravity anchorage. Earlier designs used a pin at the pylon foot to prevent large bending moments on the mast. Modern designs prefer a fixed-end cantilever mast, which is simpler and more stable during erection. The use of a frictionless bearing with a fixed-end mast is possible when the member is slender enough, causing the axial load to approach the buckling capacity of the mast in a free cantilever condition.

For single mast pylons supporting a single plane of stays, two methods have been used to connect the mast at its base:

(1) encastre construction into a transverse girder forming part of the deck, requiring bearings at the pylon foundation, and
(2) passing the mast directly through the deck to sit upon the pylon foundation, needing bearings only at each end of the transverse girder.

The second method (Method 2) is more efficient and has been widely adopted in recent designs.

Concrete Pylons

Concrete has become increasingly competitive for pylon construction due to advancements in concrete construction and formwork technology, despite its higher self-weight compared to steel. Concrete has proven to be particularly adaptable to complex pylon forms.

Various types of pylons have been developed to support both vertical and inclined stay layouts, including H-frame, A-frame, and inverted Y-frame pylons (shown in Figure 3).

**Figure 3:** H-frame, A-frame and inverted Y-frame pylons (Farquhar, 2008)

In the case of H-frame pylons, the stay anchors are usually located above a crossbeam. For modified fan arrangements of stays, this crossbeam would be positioned between mid-height and two-thirds of the pylon height above the deck. However, when adopting the harp arrangement of stays, the anchors are distributed over the full height of the pylon above the deck. In such cases, a crossbeam can only be practically provided below the deck level, as seen in the Øresund Bridge between Denmark and Sweden.

Oresund Bridge — **Figure 4:** Øresund Bridge

The deck section located at the pylon is typically subjected to the highest stresses, combining maximum negative moment and axial load. Connecting the stay directly between the pylon leg and an edge stiffening girder within the deck requires the pylon legs to be inset into the deck.

This creates a practical detailing problem and results in a zone of concentrated stress in an already highly stressed section. Several geometrical configurations can overcome this problem: widening the pylon and connecting the stays to the deck using out-stand brackets, or sloping the pylon leg outwards at its base.

The pylon leg can be inclined over its entire height, in which case the pylon must be designed to accommodate a small eccentricity arising from the stay cable reactions. Another approach is to maintain the upper section of the leg in a vertical plane and incline the pylon only from below the level of the bottom anchorage.

By locating the crossbeam at this change of direction, the stay force reaction can be efficiently transmitted as a direct thrust. Examples of this pylon geometry can be observed in the Annacis Bridge over the Fraser River, Canada (see Figure 5), and the Vasco da Gama Bridge (Capra and Leveille, 1998) over the Tagus River, Portugal.

alex fraser bridge — **Figure 5:** Annacis Bridge

Pylon Geometry

The A-frame pylon is well-suited for inclined stay arrangements and was first used in the Severins Bridge. Another variation is the inverted Y-frame, where the vertical leg, containing the stay anchors, extends above the bifurcation point. Examples of the inverted Y-frame can be seen in the Normandy Bridge over the River Seine, France, and the Rama VIII Bridge in Bangkok, Thailand.

However, the wide footprint of the inverted Y-frame can lead to excessive land usage when a high navigation clearance to the deck is necessary. To address this, some designs break the pylon legs at or just below the deck, creating inward-leaning legs to the foundation, forming a diamond configuration (Figure 6).

**Figure 6:** Diamond shape pylon geometry (Farquhar, 2008)

This modification reduces land usage but makes the pylon less stiff against transverse wind or seismic forces, resulting in increased deflection. To counteract this deflection, a substantial increase in stiffness is required in the lower section of the pylon leg below the deck.

Nevertheless, this diamond configuration was favoured for the pylons of the Tatara Bridge in Japan, currently the world’s longest cable-stayed span at 890m, and the Industrial Ring Road Bridges in Bangkok. The same configuration was also used for the twin cable-stayed crossing of the Houston Ship Channel, where the twin diamonds were connected and tied together at the deck level to form a strong truss, transmitting transverse wind loads to the foundations.

Another architectural feature includes inclining the pylon in the longitudinal direction, resulting in visually exciting structures. However, this design introduces inclined thrust from the pylon that must be carried by the foundation, generating a significant horizontal component. In rock foundations, these horizontal reactions are easily resisted with only minor foundation displacement. In contrast, in typical estuarine soil conditions, foundation costs may represent a significant portion of the overall project cost.

Cable Stay Connection to the Pylons

In early designs, the connection between the stays and the pylon resembled that of suspension bridges, where the cables were laid in a deviator saddle and carried through the pylon. However, this method had limitations. As an alternative, modified fan and harp arrangements were introduced, with stays anchored over the upper section of the pylon leg. This led to the use of separate stays for the main span and back span.

The most straightforward anchoring method involves attaching the stay socket or anchorage plate directly to the pylon wall. In concrete pylons, the horizontal component of the cable forces can cause the shaft to split vertically, requiring transverse pre-stressing to resist these forces. Different layouts were developed to address this, as seen in Figures 8 and 9.

**Figure 8:** Pre-stressing layout for stay connection to concrete pylon (Farquhar, 2008)

**Figure 9:** Alternative layout for stay connection to concrete pylon (Farquhar, 2008)

To simplify pylon construction and ensure accurate placement of steel formers, anchor pre-stress, and reinforcement within the concrete walls, steel fabricated anchorage modules have been utilized. These modules define the required stay anchorage geometry and are incorporated into the concrete shaft during construction.

Adequate shear connection, typically in the form of shear studs, allows the anchorage forces in the fabrication to be transferred to the concrete shaft. Examples of this construction method, with the fabricated anchorage module centrally located within the concrete shaft, can be seen in the Normandy Bridge and the Stonecutters Bridge. The Ting Kau Bridge in Hong Kong also used a similar concept but connected the fabricated anchor modules on the outside of the concrete core.

It is very important to accurately model any eccentricity of the stay anchor within the pylon during structural analysis. The inclination of the back span stays and main span stays are usually different, requiring the anchors to be located at different levels to maintain the same intersection line on the pylon centerline.

Alternatively, keeping the levels of the two anchors the same may slightly eccentrically place the vertical resultant of the stay forces to the pylon. This approach simplifies the anchor zone detailing but requires careful consideration of the pylon moments arising from this small eccentricity (Figure 10).

**Figure 10:** Stay anchor pylon geometry (Farquhar, 2008)

Conclusion

In conclusion, pylons play a crucial role in the structural integrity and aesthetic appeal of cable-stayed bridges. The use of pylons in these bridges has evolved over time, with advancements in concrete construction and formwork technology making concrete pylons increasingly competitive, despite their higher self-weight compared to steel alternatives.

Various types of pylons have been developed to accommodate different stay arrangements, including H-frame, A-frame, and inverted Y-frame pylons. The modified fan and harp arrangements have allowed for separate stays for the main span and back span, enabling more adaptable and efficient designs.

Pylon geometry has been a subject of innovation and consideration in recent designs. Solutions such as breaking the pylon legs to create inward-leaning legs or using steel-fabricated anchorage modules have been employed to reduce land usage and simplify construction processes. However, these modifications must be carefully designed to maintain sufficient stiffness and resist transverse wind or seismic forces.

The design of pylons in cable-stayed bridges must take into account various factors, such as the inclination of the back span and main span stays, the connection between the stays and the pylon, and the accurate modelling of stay anchor eccentricities. These considerations are critical to ensuring the stability and performance of the cable-stayed bridge.

In summary, pylons in cable-stayed bridges continue to undergo refinement and innovation, striving to achieve optimal efficiency, safety, and aesthetics. The choice of pylon type, arrangement, geometry, and design are essential elements in the successful construction of cable-stayed bridges, contributing to their functionality, longevity, and architectural distinctiveness in modern infrastructure projects.

References:
Farquhar, D. J. (2008). Cable-stayed bridges. ICE Manual of Bridge Engineering. Published by the Institution of Civil Engineers (ICE) UK

Implementing AI and Machine Learning in Bridge Inspections

By

Ubani Obinna

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August 1, 2023

Table of Contents

All over the world, there is growing concern that environmental degradation, overloading, initial construction defects/imperfections, natural and man-made hazards, and other factors have contributed to structural deterioration and deficiencies in highway bridges. The deterioration of bridges usually occurs in response to external loads and environmental disturbance, and various maintenance plans are usually adopted in various states, countries, and jurisdictions to prolong the service life of bridges.

This article will comprehensively explore the implementation of Artificial Intelligence (AI) and Machine Learning (ML) in bridge inspections. As technological advancements continue to reshape various industries, these innovative technologies have revolutionized how we assess and maintain bridges. By leveraging the power of AI and ML, drone bridge inspection has become more efficient, cost-effective, and safer for both inspectors and the public.

According to Xia et al. (2021), the primary components of highway bridge inspection include;

geometric parameter inspection,
mechanical performance assessment,
interior inspection, and
appearance inspection.

The Transformation of Bridge Inspections

AI and Machine Learning technologies have brought about a profound transformation in bridge inspections. The traditional methods, often labour-intensive and time-consuming, have given way to automation, enabling faster and more accurate assessments of bridge conditions. This transformation has paved the way for a new era of infrastructure management, where data-driven decision-making and AI-driven analytics play a pivotal role.

It is important to note that other recently developed technologies have substantially improved the precision and effectiveness of bridge inspection work. The location of damages in bridges in three-dimensional space has been determined using a variety of technologies, including point cloud techniques, unmanned aerial vehicles (UAV), and terrestrial laser scanning techniques. Ground-penetrating radar has also been used to locate the spatial and temporal variations of concrete bridges. Infrared thermography techniques have also been utilized to inspect thermal abnormalities using thermal cameras on UAVs.

The structural state of bridges can also be evaluated using satellite-based remote sensing techniques. Persistent Scatterer Interferometry (PSI), a satellite remote sensing technique, has been used to assess the displacement of bridges. The long-term displacements of the Hong Kong-Zhuhai-Macao Bridge (HZMB) have been studied utilizing PSI and InSAR technology.

Automated Image and Data Collection

One of the key advantages of implementing AI and Machine Learning in bridge inspections is the ability to automate image and data collection. Inspectors can efficiently gather detailed images and data points without the need for risky and time-consuming under-bridge walks or expensive snooper trucks by employing drones equipped with high-definition cameras and AI algorithms. The automated process accelerates the inspection timeline and enhances the reliability and accuracy of the data collected.

Typical model for bridge inspection with an unmanned airborne vehicle (Karim et al., 2020)

AI-Driven Defect Detection

AI and ML techniques have found extensive application in diverse areas concerning structural safety, including predicting conditions and detecting damages. For instance, the neural network (NN) is well-suited for addressing large-scale data challenges as it can effectively extract multidimensional features and recognize non-linear relationships within the input data.

AI and ML algorithms analyze vast amounts of data swiftly and accurately. In bridge inspections, these algorithms can detect even the most subtle signs of wear, corrosion, cracks, and other defects that might not be readily noticeable to the human eye. Early identification of potential issues enables proactive maintenance decisions, reducing the risk of sudden and catastrophic failures. Moreover, AI-driven defect detection enhances the inspector’s ability to prioritize and focus on critical areas that require immediate attention.

Enhanced Structural Analysis

AI and Machine Learning have revolutionized structural analysis in bridge inspections. By leveraging the data collected during inspections, advanced analytics can provide a comprehensive assessment of a bridge’s overall health and performance. This includes evaluating stress distributions, load-bearing capacities and predicting the bridge’s response to different environmental conditions over time.

By gaining deeper insights into the structural integrity of bridges, engineers can make more informed and data-driven decisions about maintenance and repairs, which empowers them to ensure the safety of the bridges.

Predictive Maintenance and Lifecycle Management

One of the most significant benefits of AI and Machine Learning in bridge inspections is the implementation of predictive maintenance strategies. Through the analysis of historical data and predictive analytics, authorities can gain a thorough understanding of the deterioration patterns of bridges.

This valuable information allows for developing comprehensive maintenance plans, optimizing resources, and extending the lifespan of these critical infrastructure assets. Predictive maintenance shifts the focus from reactive repairs to proactive and strategic management, resulting in long-term cost savings and enhanced bridge performance.

Overcoming Challenges and Limitations

While AI and Machine Learning offer significant advantages in bridge inspections, there are challenges to address to ensure their successful implementation. Accurate data collection is paramount, as the data quality directly impacts the effectiveness of AI algorithms.

Additionally, training AI models requires a vast and diverse dataset to detect various bridge defects accurately. Moreover, integrating AI and Machine Learning technologies with existing inspection protocols and standards demands meticulous planning and consideration to ensure seamless adoption.

Building Trust in AI-Driven Inspections

The successful integration of AI and Machine Learning in bridge inspections relies on building trust among engineers, inspectors, and the public. Demonstrating the effectiveness and reliability of AI-driven technologies is essential to gain acceptance and confidence in automated systems.

Rigorous testing, validation, and transparency are crucial steps in proving the capabilities and accuracy of AI algorithms. Building trust will foster greater acceptance and encourage further adoption of these technologies in infrastructure management.

Advancements in AI Technology for Bridges

The future holds exciting possibilities for AI and Machine Learning in bridge inspections. Ongoing advancements in computer vision, sensor technologies, and AI-driven robotics are expected to drive further innovation. As these technologies evolve, we can anticipate even more sophisticated applications in bridge inspections, including fully autonomous systems that can operate with minimal human intervention. The potential for greater efficiency, accuracy, and safety in bridge inspections will continue to grow as AI technology progresses.

Embracing the Future of Bridge Inspections

The successful use of AI and Machine Learning in bridge inspections marks a pivotal step towards safer, more efficient, and cost-effective infrastructure management. By embracing these innovative technologies, engineers and inspectors can focus on critical analysis and decision-making, armed with comprehensive and actionable data. As AI and Machine Learning are developing and advancing, overcoming challenges, building trust, and driving further innovation will be instrumental in ensuring our bridges’ continued safety and longevity.

Conclusion

Integrating AI and Machine Learning in drone bridge inspections has ushered in a transformative era in assessing and maintaining critical infrastructure. Automation, AI-driven defect detection, enhanced structural analysis, and predictive maintenance have streamlined the inspection process, increased safety, and reduced costs. As technology advances, the potential for AI and Machine Learning in drone bridge inspections is boundless.

By addressing challenges, building trust, and leveraging data-driven decision-making, the future of drone inspections holds great promise. As these technologies continue to evolve, engineers and inspectors can embrace the opportunities presented by AI and Machine Learning to create resilient and reliable bridges that serve as vital links in connecting communities for generations to come.

References

Xia Y., Lei X., Wang P. and Sun L. (2021). Artificial Intelligence Based Structural Assessment for Regional Short- and Medium-Span Concrete Beam Bridges with Inspection Information. Remote Sens. 2021, 13, https://doi.org/10.3390/rs13183687

Karima M.M., Daglia C.H. and Qina R. (2020). Modeling and Simulation of a Robotic Bridge Inspection System. Procedia Computer Science 168 (2020) 177–185. DOI. 10.1016/j.procs.2020.02.276

Uplift Capacity of Piles

By

Ubani Obinna

-

July 12, 2023

Table of Contents

In the design of pile foundations, it is usually very common to express the load carrying capacity in terms of axial compression. However in some cases, piles are subjected to uplift forces, and must be designed to resist such forces in order to avoid the pull out of the foundation or the structure. Piles that are subjected to uplift forces are also called tension or anchor piles. Uplift forces are developed due to hydrostatic pressure or overturning moments.

Forces due to earthquake, wind, or waves, are the major actions that can induce uplift forces in piles. Structures such as transmission towers, mooring systems for ocean surface or submerged platforms, tall chimneys, jetty constructions, etc., all have their foundations subject to uplift loads.

Factors Affecting Uplift Capacity

Several factors influence the uplift capacity of piles and they are briefly described below.

Soil Characteristics: Soil properties, including the cohesion and friction angle, significantly affect uplift capacity. Clay soils will rely on the cohesion or unit adhesion of the soil with the pile material for uplift resistance, while granular soils will rely on frictional forces (dependent on the angle of internal friction) for uplift resistance.
Pile Geometry: The shape, size, and length of the pile influence its uplift capacity. Longer piles provide a larger surface area in contact with the soil, thus increasing resistance against uplift forces. Additionally, the pile diameter and shape can affect the distribution of uplift forces along the pile shaft. It is also important to note that pile cap dimensions and group effects can also influence the uplift capacity of piles.
Pile Material: The material used for pile construction plays a role in uplift capacity. Steel piles are often preferred due to their high strength and ductility, providing better resistance against uplift. However, other factors, such as corrosion potential, must also be considered. Furthermore, scholars have also determined that the angle of wall friction between the pile and the surrounding soil is dependent on the pile material.
Pile Installation Method: The uplift capacity is typically higher in driven piles than bored piles.
Groundwater Conditions: The level of groundwater significantly affects uplift capacity. In saturated soil conditions, the presence of water can reduce the soil’s effective stress, potentially reducing the uplift resistance of piles. Conversely, dewatering or densification techniques can improve uplift capacity.

Methods for Determining Uplift Capacity

Uplift capacity of piles may be assessed using theoretical analyses (classical equations developed using soil properties), field tests, and numerical modeling. The following are commonly used approaches:

Analytical Methods: Several analytical methods, such as the Terzaghi’s equation and the Vesic’s method, provide simplified solutions to estimate uplift capacity. These methods typically consider soil parameters, pile geometry, and groundwater conditions to calculate the uplift resistance.
Field Load Tests: Load tests conducted in the field help validate the design assumptions and provide valuable data on the actual uplift capacity. Common load test methods include the pile load test, plate load test, and pile uplift test. These tests involve applying controlled loads to the pile and measuring its response to determine uplift capacity.
Numerical Modeling: Finite element analysis (FEA) and other numerical modeling techniques allow engineers to simulate complex soil-pile interactions and evaluate uplift capacity. Numerical models consider soil behavior, pile-soil interaction, and other relevant factors to provide detailed insights into the uplift response.

Generally, the equation for uplift capacity of a single pile may be written as;

P_ul = W_p + A_sf_r ——– (1)

where,
P_ul = uplift capacity of pile,
W_p = weight of pile,
f_r = unit resisting force
A_s= effective surface area of the embedded length of pile.

Uplift capacity of pile in clay

For piles embedded in clay, equation (1) may be written as;

P_ul = W_p + A_sαc_u ——– (2)

where,
c_u = average undrained shear strength of clay along the pile shaft,
α = adhesion factor (= c_a/c_u),
c_a = average adhesion

**Figure 1:** Relationship between adhesion factor α and undrained shear strength c_u

Figure 1 gives the relationship between α and c_u based on pull out test results as collected by Sowa (1970). As per Sowa (1970), the values of c_a agree reasonably well with the values for piles subjected to compression loadings.

Uplift capacity of pile in sand

The ultimate uplift capacity of a vertical pile for piles embedded in sandy soil depends on the skin resistance created between the pile shaft and the soil.

According to Murthy (2012), adequate confirmatory data are not available for evaluating the uplift resistance of piles embedded in cohesionless soils. Ireland (1957) reports that the average skin friction for piles under compression loading and uplift loading are equal, but data collected by Sowa (1970) indicate lower values for upward loading as compared to downward loading especially for cast-in-situ piles. A study by Ramasamy et al. (2004) showed that the pull out shaft friction is significantly less than the push in shaft friction.

Poulos and Davis (1980) suggest that the skin friction of upward loading may be taken as two-thirds of the calculated shaft resistance for downward loading.

According to Verma and Joshi (2010), the net uplift capacity of piles embedded in sand can be given by the equation (3) as:

Q_u = ½ K_s σ_v tanδ πdZ_c + K_s σ_v tanσ π(L – Z_c) ——– (3)

Where;
K_s = coefficient of earth pressure
σ_v = effective vertical stress at a depth of Zc = γ_dZ_c
d = diameter of pile
γ_d =dry unit weight of soil
δ = soil-pile friction angle
L = Length of pile
Z_cor L_cr = critical depth of embedment

According to Verma and Doshi (2010), the value of coefficient of earth pressure in Equation (3) has a large range of 0.3 to 4.0, which implies that there are many implications to the value of K_s.

Solved Example

A 450 mm diameter pile is embedded in a homogenous medium dense sand, determine the net pullout capacity (FOS = 3.0). Given: L = 12 m, φ = 38°, K_s = 1.5, and δ = 25°, γ_(average) = 17 kN/m³
The water table is at great depth, and take the critical depth to be 15D.

Solution

Critical depth = 15 × 0.45 = 6.75 m
σ_v = 6.75 × 17 = 114.75 kN/m²

f_s = 114.75 × 1.5 × tan 25 = 80.263 kN/m²

f_s1 = ½ f_sπdZ_c = ½ × 80.263 × π × 0.45 × 6.75 = 382.9 kN
f_s2 = f_sπd(L – Z_c) = 80.263 × π × 0.45 × (12 – 6.75) = 595.71 kN

Total skin resistance = f_s1 + f_s2 = 382.9 + 595.71 = 978.61 kN

Q_a = 978.61/3 = 326.2 kN (Factor of safety of 3)

After Poulos and Davis (1980), pull out capacity = 2/3 × 326.2 = 217.46 kN

Conclusion

The uplift capacity of piles is an important factor in the design of structures that are subjected to uplift loads. Geotechnical design of piles must ensure that the uplift capacity of the piles is sufficient to resist the expected loads. There are a number of equations that can be used to estimate the uplift capacity of piles, but the final design should be based on the specific soil conditions and the design requirements.

References

Ireland, H.O. (1957). “Pulling Tests on Piles in Sand,” Proc. 4th Int. Conf. SM and FE, Vol. 2.
Murthy V.N.S (2012): Geotechnical Engineering. Marcel Decker Inc. New York
Poulos, H.G., and Davis, E.H. (1980). Pile Foundation Analysis and Design, John Wiley & Sons, New York.
Ramasamy, G., Dey, B. and Indrawan, E. (2004): “Studies on skin friction in piles under tensile and compressive load”, Indian Geotechnical Journal, Vol. 34, No. 3, pp. 276-289.
Sowa, V.A. (1970). “Pulling Capacity of Concrete cast-in-situ Bored Pile,” Can. Geotech. J., Vol. 7.
Verma A. K. and Joshi R. K. (2010): Uplift Load Carrying Capacity of Piles in Sand. Indian Geotechnical Conference – 2010, GEOtrendz pp 857 – 860

Column Splice Connection Design

By

Ubani Obinna

-

July 10, 2023

Column splice connection design involves joining two or more column sections to create a longer column or to provide additional strength. It is used when the length of a column is too long to be fabricated as a single piece. They are also used for connecting columns of different sections as a building goes higher. Similar to beam splices, column splices are typically designed to transfer axial load, shear, and moment.

Properly designed column splice connections are important in ensuring easier buildability, transportation, handling, and maintaining the overall stability and safety of various construction projects in steel structures. The primary function of a column splice connection is to transfer axial loads and moments between the connected column sections. The design should effectively distribute the applied loads through the connection without compromising the structural integrity.

In this article, we will explore the design of bolted column splice connection.

Types of Column Splices

There are two main types of column splices: bearing splices and non-bearing splices. Bearing splices rely on full bearing contact between the two column sections to transfer the axial load. In this case, the loads from the upper column are directly transferred to the lower column through the use of division plates or direct contact between the two sections.

Non-bearing splices use bolts or welds to transfer the axial load. In this case, there is no bearing between the interconnected columns and they are usually detailed with a gap in between the column stacks.

Design of column Splices

The design of a column splice must consider the following factors:

The type of splice (bearing or non-bearing)
The size and strength of the column sections
The axial load, shear, and moment applied to the splice
The material properties of the column sections and the splice plates

Design Example

Design a column splice connection for two similar column sections (UC 254x254x89) subjected to an axial dead load of 528kN and a design moment of 178 kN. The ends are not prepared for contact in bearing.

Section Details
Upper Stanchion; UC 254x254x89 (S275)
Lower Stanchion; UC 254x254x89 (S275)
Flange splice plate; 120 mm × 690 mm × 15 mm (S275)
Flange plate bolts; M22 (Grade 8.8 Black Bolts)
Web splice plate; 137 mm × 390 mm × 15 mm (S275)
Web plate bolts; M22 (Grade 8.8 Black Bolts)

Splice Details

Flange plates
Number of bolt rows above and below splice; n_fpr = 4
Number of bolt columns above and below splice; n_fpc = 2
Dist from end of upper column to first row of bolts; e_ucfend = 60 mm
Dist from end of lower column to first row of bolts; e_lcfend = 60 mm
Bolt pitch; p_fpb = 75 mm
Distance from outer bolts to plate end; e_fpend = 60 mm

Web plates
number of bolt rows above and below splice; n_wpr = 2
number of bolt columns above and below splice; n_wpc = 2
Dist from end of upper column to first row of bolts; e_ucwend = 60 mm
Dist from end of lower column to first row of bolts; e_lcwend = 60 mm
Bolt pitch; p_wpb = 75 mm
Distance from outer bolts to plate end; e_wpend = 60 mm

Loading Details
Axial compressive force due to dead load; F_cd = 528.0 kN
Moment on splice; M = 178.0 kNm

Design Loading
Design load;
F_t = max(0 kN, abs(M) / min(D_u – 2T_u – t_fp, D_l – 2T_l – t_fp) – F_cd / 2) = 580.8 kN

Check 1 – recommended detailing requirements – column splice, flange plates on inside

Upper Column
Overall depth; D_u = 260 mm
Overall width; B_u = 256 mm
Flange thickness; T_u = 17.3 mm
Web thickness; t_u = 10.3 mm
Root radius; r_u = 12.7 mm

Lower Column
Overall depth; D_l = 260 mm
Overall width; B_l = 256 mm
Flange thickness; T_l = 17.3 mm
Web thickness; t_l = 10.3 mm
Root radius; r_l = 12.7 mm

Flange Plates
Upper projection;
L_fpu = e_ucfend + (n_fpr – 1) × p_fpb + e_fpend = 345 mm

Lower projection;
L_fpl = e_lcfend + (n_fpr – 1) × p_fpb + e_fpend = 345 mm

Detailing Requirements
The upper projection of the flange plate meets the detailing requirements
Lower projection of flange plate meets detailing requirements
The width of the flange plate meets the detailing requirements
The thickness of flange plates meets the detailing requirements
The width of web plates meets the detailing requirements

Flange plate packing;
t_fpack = abs((D_u / 2 – T_u) – (D_l/2 – T_l)) = 0.0 mm

Web plate packing;
t_wpack = abs(t_u – t_l) / 2 = 0.0 mm

Sufficient web plate bolts provided
Bearing plate not required

Check 2 – the presence of tension due to axial load and bending moment – internal

Tension Force;
F_t = M / min(D_u – 2T_u – t_fp, D_l – 2T_l – t_fp) – F_cd / 2 = 580.8 kN

Check 3 – tensile capacity of flange cover plate – internal

Grade of cover plate;
p_yfp = 275 N/mm²

Net area of flange cover plates (one flange);
A_netfp = 2(d_fp – n_fpc / 2D_hfb ) × t_fp = 2880 mm²

Net area coefficient;
K_efp = 1.2

Gross area of flange cover plates (one flange);
A_grossfp = 2d_fpt_fp = 3600 mm²

Design area of flange cover plates (one flange);
A_fp = min(K_efp × A_netfp, A_grossfp) = 3456 mm²

Tensile capacity;
P_tfp = p_yfp × A_fp = 950.4 kN

Utilisation factor;
Ucheck₃ = F_t / P_tfp = 0.611

Tension capacity of flange cover plate: PASS

Check 4 – Shear capacity of bolt group connecting flange cover plate to column flange

Grade of bolts;
p_bsfp = 460 N/mm²

Shear capacity of top pair of bolts;
P_sfb1 = min(P_sfb, 0.5 × e_fpend × t_fp × p_bsfp) = 113.6 kN

Shear capacity of other bolts; P_sfb = 113.6 kN

Joint length; L_j = (n_fpr -1) × p_fpb = 225 mm

Amended bolt capacity;
P_sfba = 113.6 kN

Reduction factor;
R_f = min(9d_fb / (8d_fb + 3t_fpack), 1) = 1.000

Shear capacity of bolt group;
P_sfbsum = R_f × n_fpc × (P_sfb1 + (n_fpr – 1) × P_sfba) = 909.0 kN

Force on splice plate; F_t = 580.8 kN

Utilisation factor;
Ucheck₄ = F_t / P_sfbsum = 0.639

Shear capacity of flange plate bolt group : PASS

Check 5 – Bearing capacity of flange cover plate connected to column flange

Bearing strength of the end plate;
p_bsfp = 460 N/mm²

Bearing capacity of the flange plate per bolt (outer);
P_bsfp1 = min(d_fb × t_fp × p_bsfp, 0.5 × e_fpend × t_fp × p_bsfp) = 151.8 kN

bearing capacity of the end plate per bolt (other);
P_bsfp = d_fb × t_fp × p_bsfp = 151.8 kN

Capacity of bolt group;
P_bsfpsum = n_fpc × (P_bsfp1 + (n_fpr – 1) × P_bsfp) = 1214.4 kN

Bearing force on bolt group;
F_t = 580.8 kN

Utilisation factor;
Ucheck₅ = F_t / P_bsfpsum = 0.478

Bearing capacity of flange plate: PASS

What is the Correct Position for Column Rebar Laps?

By

Ubani Obinna

-

June 26, 2023

Columns are compression members used for transferring superstructure loads to the foundation. In reinforced concrete detailing and construction, the lapping of reinforcements is almost unavoidable due to logistics and handling issues during construction. As a result, design codes all over the world have guidelines on how to properly lap reinforcements in columns.

Improper detailing of reinforced concrete columns can lead to concrete spalling, cracking, and other forms of failure, which may compromise the structural integrity of a column. A poorly arranged reinforcement can also lead to premature buckling and bending that can reduce the load-carrying capacity of reinforced concrete columns.

Here are some important detailing guidelines provided for column laps;

(1) When the diameter of both bars at the lap exceeds 20mm and the cover is less than 1.5 times the size of the smaller bar, transverse links shall be provided throughout the lap length.

(2) At the lap, the least link diameter should be at least one-quarter the size of the smaller bar.

(3) Link spacing shall not exceed;
(a) 12 x diameter of the smallest bar
(b) 0.6 x dimension of the smallest side of the column
(c) 240 mm

(4) Compression lap length should be at least 25% greater than the compression anchorage length.

(4) For cranked bars, the minimum slope of the crank should be maintained at 1:10. However, this value may be increased up to 1:20 for smooth load transfer.

However, the code appears to be silent on the actual location where columns should be lapped. What do you think? Kindly comment below.

Analysis of Soil Liquefaction Potential

By

Ubani Obinna

-

June 19, 2023

Table of Contents

Liquefaction refers to the process in which a granular material changes from a solid to a liquid state due to increased pore-water pressure and decreased effective stress. This phenomenon occurs during ground shaking when loose or medium-compact granular soils experience pore space shrinkage, causing the pore water to be squeezed and leading to loss of bearing capacity.

If the pore water cannot easily drain, it leads to a significant increase in pore-water pressure (u) and a reduction in effective stress (𝜎′). The effective stress (𝜎′) is related to the total stress (𝜎) by the equation;

𝜎′ = 𝜎 − u —— (1)

When the effective stress drops below a certain value, the soil loses contact between grains and starts behaving like a liquid. This is very dangerous for structures supported on such soils.

**Figure 1:** Saturated sand condition during liquefaction (Xiao, 2015)

In effect, when loose or medium-compact granular soils experience ground shaking, the pore spaces shrink and squeeze the pore water. If the pore water cannot easily drain, the pore-water pressure significantly increases, leading to a reduction in effective stress. When the effective stress drops to a certain value, the soil loses its grain-to-grain contact and behaves like a liquid.

Liquefaction can have severe consequences for structures and the surrounding environment. It can result in reduced bearing capacity, causing buildings and infrastructure to sink or collapse. Lateral spreads of liquefied soils can cause large settlements and horizontal displacements. These effects can lead to significant damage and pose risks to human safety.

Figure 2 illustrates the mechanism of liquefaction, which can result in reduced bearing capacity, significant settlement, and horizontal displacement due to lateral spreads of liquefied soils. This can manifest as sand boils or lateral spread of surface soils.

Liquefaction has been observed in various earthquakes, including the 1964 Niigata, 1964 Alaska, 1971 San Fernando, 1985 Mexico City, 1994 Northridge, 1994 Kobe, 1999 Taiwan, 1999 Turkey, 2010 Baja California, 2011 Tōhoku, and 2018 Palu Sulawesi Indonesia earthquakes.

**Figure 3:** Building failure due to liquefaction

Certain conditions must be met for liquefaction to occur:

The soil deposit consists of sandy or silty soil.
The soil is saturated or nearly saturated (usually below the groundwater table).
The soil is loose or moderately compacted.
The soil is subjected to seismic action (e.g., from an earthquake).

Soils that are relatively well-drained, such as well or poorly graded gravels (GW, GP), are less susceptible to liquefaction compared to sand or silty sand (SW, SP, or SM). Denser granular soils are less prone to liquefaction than loose soils. Liquefaction is less likely to occur in granular soils under higher initial confining effective stress (e.g., deeper soils). Based on case histories, liquefaction typically occurs within a depth of 15 meters.

Cohesive soils generally do not experience liquefaction. To qualitatively evaluate cohesive soils, the Chinese criteria defined by Seed and Idriss (1982) can be used. Liquefaction in cohesive soils can only occur if all three of the following conditions are met:

The clay content (particles smaller than 75μm) is less than 15% by weight.
The liquid limit is less than 35%.
The natural moisture content is greater than 0.9 times the liquid limit.

Screening investigations should also consider the possibility of a locally perched groundwater table, which may occur due to changes in local or regional water management practices, leading to a significant rise in the groundwater table.

Assessment of Liquefaction Hazard

Liquefaction hazard assessments are commonly conducted by employing a factor of safety (Equation 2). This factor represents the relationship between the available resistance to liquefaction, measured in terms of the cyclic stresses required to induce liquefaction, and the cyclic stresses generated by the design earthquake.

Both of these stress parameters, the resistance and the generated stresses, are typically normalized with respect to the effective overburden stress at the specific depth under consideration. They are known as the cyclic resistance ratio (CRR) and cyclic stress ratio (CSR) respectively.

FS = CRR/CSR —— (2)

The recommended guidelines provide guidance on selecting an appropriate factor of safety. For instance, the National Earthquake Hazards Reduction Program (NEHRP) Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (2004) suggest that a factor of safety ranging from 1.2 to 1.5 is generally suitable for building sites. The actual value chosen depends on factors such as the significance of the structure and the potential for ground displacement.

Other authorities also provide recommendations on acceptable levels of risk. The California Geological Survey (1997) proposes that a factor of safety greater than 1.3 can be considered an acceptable level of risk. The DOD Handbook on Soil Dynamics and Special Design Aspects (1997) specifies that a factor of safety of 1.2 is appropriate for engineering design. Empirical methods are commonly used in practice to calculate the factor of safety and are widely adopted.

Evaluation of CSR

Seed and Idriss (1971) presented the following equation for the calculation of the cyclic stress ratio (CSR), and this equation is still the most widely used empirical method:

CSR = 𝜏_av/𝜎′_vo = 0.65 (a_max/g)⋅(𝜎_vo/𝜎′_vo)⋅r_d —— (3)

where:
𝜏_av = average cyclic shear stress induced by design ground motion,
𝜎′_vo = initial vertical effective stress at the depth under consideration in static condition,
𝜎_vo = initial vertical total stress at the depth under consideration in static condition,
a_max = peak horizontal acceleration at the ground surface generated by the earthquake,
r_d = stress reduction coefficient.

The NCEER workshop (1997) recommended the following equations by Liao and Whitman (1986a) for routine practice and noncritical projects:

r_d = 1.0 − 0.00765z (for z ≤ 9.15m) ——-(4a)
r_d = 1.174 − 0.0267z (for 9.15m < z ≤ 23m) ——-(4b)

The NCEER workshop (1997) cautioned users that there is considerable variability in r_d, and the r_d calculated from Equation (4) is the mean of a wide range of possible r_d, and the range of rd increases with depth.

Evaluation of CRR

The standard penetration test (SPT), the cone penetration test (CPT), shear wave velocity measurements, and the Becker penetration test (BPT) are the four field tests that are typically utilized by empirical methods for the evaluation of the CRR.

The SPT and CPT methods are often favoured because of the more extensive database and previous experience, although the other tests may be done at sites underlain by gravelly sediment or where access to large equipment is limited. This preference is due to the fact that the SPT and CPT methods have been around longer.

SPT Method of CRR Assessment

The CRR is graphically determined from the SPT blow count as shown in Figure 4. This CRR curve – the SPT clean-sand base curve – is for fines content ≤ 5% under magnitude 7.5 earthquakes. The SPT blow count is first corrected to consider overburden stress, equipment used to conduct the SPT, and the fines content (>5%); then Figure 4 is used to derive the CRR, which in turn is corrected for other earthquake magnitudes.

**Figure 4:** SPT clean-sand (percent fines ≤ 5%) base curve for magnitude 7.5 earthquakes (Xiao, 2015)

Step 1: Corrections to overburden stress and various SPT equipment
To account for the effect of overburden stress and various equipment used for SPT, the following equation is used:

(N₁)₆₀ = N_mC_NC_EC_BC_RC_S ——– (5)

Nm = measured standard penetration blow count,
CN = correction factor based on the effective overburden stress, 𝜎′vo,
CE = correction for SPT hammer energy ratio (ER)
CB = correction factor for borehole diameter,
CR = correction factor for SPT rod length,
CS = correction factor for samplers with or without liners.

Step 2: Corrections to fines content
The corrected (N₁)₆₀ in Equation (5) is further corrected for the fines content (FC) in the soil.

(N₁)_60CS= 𝛼 + 𝛽(N₁)₆₀ ——– (6)

where:
(N₁)_60CS= the (N₁)₆₀ for equivalent clean sand; (N₁)_60CS is used in Figure 4 to find the CRR under magnitude 7.5 earthquakes,
(N₁)₆₀ = corrected SPT blow count calculated in Equation (5),
𝛼 and 𝛽 = coefficients determined from the following relationships:

𝛼 = 0 for FC ≤ 5%
𝛼 = exp[1.76 − (190∕FC²)] for 5% < FC < 35%
𝛼 = 5.0 for FC ≥ 35%

𝛽 = 1.0 for FC≤ 5%
𝛽 = [0.99 + (FC^1.5∕1000)] for 5% < FC < 35%
𝛽 = 1.2 for FC ≥ 35%

Step 3: Magnitude scaling factors (MSFs)
A magnitude scaling factor (MSF) is used to correct the factor of safety (FS) when the earthquake magnitude is not 7.5:

FS =(CRR_7.5/CSR)⋅ MSF ——- (7)

where:
CRR_7.5 = the cyclic resistance ratio for a magnitude 7.5 earthquake.
The NCEER workshop (1997) summarized the MSFs proposed by various investigators (Figure 5).

**Figure 5:** Magnitude scaling factors derived by various investigators (Xiao, 2015)

Solved Example

Liquefaction Analysis Using SPT Method (After Xiao, 2015)

It is proposed to build a new bridge across a river. The construction site contains poorly graded sandy soil with fines content (passing #200 sieve) of 18%. The soil deposit of the riverbed is fully saturated with 𝛾_sat=19.5 kN/m³. The nearby Foot Hill fault system could generate a peak (horizontal) ground acceleration, a_max, of 0.25 g at this construction site. Caissons are used as the bridge foundation.

The bottom of the caissons is at a depth of 5m below the riverbed. SPT were performed in a 10.2-cm (4-inch) diameter borehole using a safety trip hammer with a blow count of 6 for the first 15 cm (6 inches), 7 blows for the second 15cm (6 inches), and 9 blows for the third 15cm (6 inches) of driving penetration.

During the design earthquake of magnitude 6.0, will the saturated sand located at the bottom of the caisson liquefy?

Solution:

(1) Calculate CSR:
CSR = 𝜏_av/𝜎′_vo = 0.65 (a_max/g)⋅(𝜎_vo/𝜎′_vo)⋅r_d
where:
Total overburden stress: 𝜎_vo = 19.5 × 5 = 97.5 kN/m²
Effective overburden stress: 𝜎′_vo = 97.5 − 9.81 × 5 = 48.5 kN/m²
Peak horizontal acceleration: a_max = 0.25 g
As z = 5m ≤ 9.15m,
Stress reduction resistance: r_d = 1.0 − 0.00765 × 5 = 0.965

So: CSR = 0.65 × 0.25g/g × 97.5/48.5 × 0.965 = 0.304

(2) Calculate CRR using the SPT method:
First, calculate the corrected SPT blow count:
(N₁)₆₀ = N_mC_NC_EC_BC_RC_S

N_m is the measured SPT blow count, which is the total blow count of the second and third six-inch penetrations.
So N_m = 7 + 9 = 16.
The correction factor on the basis of effective stress (note: Pa = 1 atm = 101.3 kN/m²):
C_N = 2.2/(1.2 + 𝜎′_vo/pa) = 2.2/(1.2 + 48.5/101.3) = 1.31

Given the automatic trip hammer, the borehole diameter of 102 mm (4 inch), and the rod length of 5m (15 ft),

the correction factor for SPT hammer energy ratio C_E =1.0,
the correction factor for borehole diameter C_B =1.0,
the correction factor for SPT rod length C_R = 0.85, and
the correction factor for samplers with liner C_S =1.0.

So ∶ (N₁)₆₀= 16 × 1.31 × 1.0 × 1.0 × 0.85 × 1.0 ≈ 18

Then calculate the equivalent clean-sand SPT blow count (N₁)₆₀:
(N₁)_60CS = 𝛼 + 𝛽(N₁)₆₀
As fines content (FC) = 18%,
𝛼 = exp[1.76 − (190∕FC²)] = exp [1.76 − (190∕18²)] = 3.234
𝛽 = [0.99 + (FC^1.5∕1000)] = [0.99 + (18^1.5∕1000)] = 1.066

(N₁)_60cs = 3.234 + 1.066 × 18 = 23

From Figure 4, find CRR_7.5 = 0.26.

(3) Calculate MSF:
From Figure 5, at M = 6.0, MSF is between 1.76 and 2.1. On the basis of the critical nature of the project (the foundation of a bridge), the MSF is chosen as the lower bound, 1.76.

(4) Factor of safety against liquefaction:
FS = (CRR_7.5/CSR) × MSF = (0.26/0.304) × 1.76 = 1.5 > 1.3

Conclusion: The SPT analysis concludes that the site will not liquefy under the design earthquake.

References:
Xiao M. (2015): Geotechnical Engineering Design (1st Edition). ISBN: 9780470632239 John Wiley & Sons, UK.

Embracing Tradition: Bringing the Traditional Style into Your Home

By

Ubani Obinna

-

June 15, 2023

In an era dominated by modern designs and contemporary aesthetics, there is a timeless charm in incorporating traditional style into your home. The traditional style embodies a sense of elegance, sophistication, and a connection to the past. By blending classic elements and rich textures, you can create a warm and inviting space that pays homage to the past while still maintaining a sense of comfort and functionality.

In this article, we will explore the key aspects and strategies to help you achieve a traditional style in your home.

Understanding Traditional Style

Traditional style draws inspiration from various historical periods, including the Georgian, Victorian, and Colonial eras. It emphasizes symmetry, classic proportions, and intricate detailing.

Architecture plays a fundamental role in setting the stage for a traditional style home. Traditional homes often boast distinct architectural features that contribute to their timeless appeal. Here are some key architectural elements to consider:

Moulding and Millwork

Crown mouldings, baseboards, and chair rails are essential elements of traditional architecture. These decorative mouldings add depth and visual interest to walls, creating a sense of elegance. Look for intricate designs and profiles that suit the overall style of your home.

Wainscoting and Paneling

Wainscoting refers to the application of wooden panels along the lower portion of walls, typically topped with a chair rail. This traditional architectural feature adds sophistication and character to a room. Raised paneling is another option, where the panels are more intricately carved or recessed.

Coffered Ceilings

Coffered ceilings are a hallmark of traditional architecture. These ceilings feature a grid-like pattern of sunken panels bordered by beams or mouldings. They add depth and visual interest to a room while creating a sense of grandeur.

Archways and Columns

Incorporating archways and columns can add a touch of classical elegance to your home. Arched doorways, either leading from room to room or as grand entrances, evoke a sense of grandeur. Columns can be used to divide spaces, frame entryways, or as decorative elements in the interiors.

Window and Door Treatments

Traditional architecture often includes windows and doors with intricate detailing. Consider incorporating window casings with decorative trim, such as pediments or keystones. Traditional-style doors may feature panelling or glass inserts with ornate designs.

Fireplaces

Fireplaces are a quintessential feature of traditional homes, serving as focal points in living rooms or bedrooms. Opt for a fireplace with a mantel that boasts ornate carvings and classic lines. Surround it with decorative tiles or a traditional-style hearth. If you need a more modern approach to heating your home, then traditional column radiators are a good option.

traditional style fireplace design — Fireplace design

Exterior Details

The exterior of a traditional home can feature elements such as dormer windows, pitched roofs with rafters, gables, and decorative accents like dentil moulding or corbels. Incorporating these elements can help establish a cohesive traditional aesthetic from the outside in.

When selecting or renovating a home, look for properties that already possess traditional architectural features. However, if your current home lacks these elements, you can work with architects or contractors to incorporate them into your space. By adding architectural details, you can create a solid foundation for achieving a traditional style throughout your home.

Remember that architectural elements can be combined and tailored to suit your personal taste and the specific period of traditional style you wish to emulate. Whether you draw inspiration from Georgian, Victorian, or Colonial architecture, paying attention to these architectural features will go a long way in creating a traditional ambience in your home.

Colours and Patterns

Colours and patterns play a crucial role in establishing the traditional style in your home. By carefully selecting a warm and inviting colour palette and incorporating classic patterns, you can create a cohesive and timeless look. Here are some key considerations:

Colour Palette

Traditional interiors often feature a rich and warm colour palette that creates a cozy and inviting atmosphere. Earth tones, deep jewel tones, and muted hues work well in this style. Consider colours such as deep reds, warm browns, olive greens, and golden yellows. These colours evoke a sense of richness and elegance.

Neutrals

Neutrals are also essential in traditional interiors. Creams, beiges, and soft grays serve as a backdrop for the bolder colors in the space. These neutral tones provide balance and allow other elements, such as furniture and patterns, to stand out.

Upholstery Fabrics

Upholstery fabrics are an excellent opportunity to introduce patterns into your traditional space. Classic patterns such as floral, damask, toile, stripes, or plaids can be incorporated into sofas, armchairs, ottomans, and throw pillows. Choose fabrics with rich textures and a sense of luxury, such as silk, velvet, or brocade.

Draperies and Curtains

Window treatments play a significant role in traditional interiors. Opt for luxurious and heavy fabrics, such as velvet or silk, in solid colours or classic patterns. Consider long and flowing curtains with decorative tiebacks and valances. These elements add elegance and frame the windows beautifully.

Wallpaper

Wallpaper can be an excellent way to infuse pattern and depth into your traditional space. Look for wallpapers with intricate designs, damasks, or subtle prints. Consider using wallpaper in a dining room, or entryway, or as an accent wall in a bedroom or living room. It can instantly transform a space and add a sense of traditional charm.

Rugs and Carpets

Traditional-style rugs and carpets are essential for grounding a room and adding warmth. Look for Oriental, Persian, or Aubusson-style rugs with intricate patterns and rich colors. These rugs can be used in living rooms, dining rooms, bedrooms, or even hallways to tie the space together and provide visual interest.

Accent Colors

In addition to the foundational colour palette, accent colours can be introduced to highlight specific elements or add pops of colour. Consider incorporating accent colours through artwork, decorative accessories, or even painted furniture. Deep blues, burgundies, or emerald greens can be used sparingly to create visual interest and depth.

Remember to strike a balance when incorporating colours and patterns. Choose a dominant colour palette and use patterns strategically to avoid overwhelming the space. Mixing solid colours with patterns can create a visually appealing contrast.

By selecting a warm and inviting colour palette and integrating classic patterns, you can successfully achieve a traditional style in your home. The careful use of colours and patterns will contribute to the overall ambience and aesthetic, creating a space that exudes timeless charm and elegance.

Creating Traditional Spaces

a) Living Room: Arrange furniture symmetrically to establish a sense of balance. Opt for a plush sofa and matching armchairs surrounding a coffee table. Add a touch of formality with a grand chandelier or a set of classic table lamps. Incorporate a fireplace, if possible, as it is a hallmark of traditional living rooms.

b) Dining Room: Set the stage for elegant dinners with a large wooden dining table, complemented by upholstered chairs. Incorporate a statement chandelier above the table and adorn the walls with framed artwork or mirrors in ornate frames.

c) Bedroom: Select a four-poster or canopy bed to establish a focal point. Use layered bedding with luxurious fabrics and intricate patterns. Add a vanity table with an antique mirror and a cozy seating area for a touch of sophistication.

d) Kitchen: Incorporate traditional cabinetry with raised panel doors and decorative moldings. Opt for a farmhouse-style sink, classic hardware, and pendant lighting. Consider adding a kitchen island with seating to create a gathering space.

Finishing Touches

a) Accessories: Display decorative items such as porcelain vases, antique clocks, and framed artwork. Incorporate collections or heirlooms to add a personal touch and enhance the traditional aesthetic.

b) Flooring: Install hardwood floors with intricate detailing or consider classic patterns like herringbone or parquet. Rugs with oriental or Persian designs can add warmth and texture to your traditional space.

c) Lighting: Choose lighting fixtures that align with the traditional style, such as crystal chandeliers, brass sconces, or Tiffany-style lamps. Proper lighting will enhance the ambiance and showcase the architectural details.

Conclusion

Embracing the traditional style in your home allows you to create an environment that exudes timeless elegance and comfort. By incorporating architectural details, selecting classic furniture pieces, and paying attention to colors, fabrics, and textures, you can create a space that embraces the traditional style.

ChatGPT and Civil Engineering Calculations

By

Ubani Obinna

-

June 7, 2023

Within the last few months, ChatGPT has caused a disruption in the way information is accessed on the internet. It appears that artificial intelligence is becoming capable of doing virtually everything, and the civil engineering/construction industry is not left out.

ChatGPT is an AI-based language model designed to engage in natural language conversations with users. It is part of the GPT (Generative Pre-trained Transformer) family of models developed by OpenAI. GPT models are trained on a vast amount of text data from the internet, allowing them to generate human-like responses to a wide range of prompts.

ChatGPT utilizes deep learning techniques, particularly Transformer architectures, to understand and generate text based on the context provided. It can process and generate coherent and contextually relevant responses by analyzing the patterns and structures of the input text.

In this article, we are going to review the response of ChatGPT to various calculations and examples relating to civil engineering.

QUESTION 1: A 4m span beam is simply supported at both ends and subjected to a uniformly distributed load of 10 kN/m at the midspan. What are the support reactions and the maximum bending moment?

CHATGPT:
To determine the support reactions and the maximum bending moment for the given beam, we can apply the principles of statics and beam analysis.

First, let’s consider the support reactions:

Vertical Reaction at Each Support: Since the beam is simply supported at both ends, each support will provide an equal and opposite vertical reaction. Let’s denote the upward reaction at each support as Rv.

The total load on the beam is the uniformly distributed load of 10 kN/m over the entire span. As the load is symmetrical, the load acting at the midspan is half of the total load, i.e., (10 kN/m) * (4 m) / 2 = 20 kN.

According to the principle of equilibrium, the sum of the vertical forces must be zero:
2Rv = 20 kN
Rv = 10 kN

Therefore, each support reaction is 10 kN vertically upward.

Next, let’s calculate the maximum bending moment:

The maximum bending moment occurs at the midspan of the beam when it is subjected to a uniformly distributed load. In this case, the maximum bending moment can be determined using the formula:

Mmax = (wL^2) / 8

Where:
Mmax is the maximum bending moment,
w is the uniformly distributed load (10 kN/m),
L is the span length (4 m).

Substituting the values into the formula, we get:

Mmax = (10 kN/m) * (4 m)^2 / 8
Mmax = 20 kNm

Therefore, the maximum bending moment in the beam is 20 kNm.

To summarize:

The support reactions at each end are 10 kN vertically upward.
The maximum bending moment in the beam is 20 kNm.

VERDICT: CHATGPT is correct with the bending moment, but wrong with the support reaction. The total load acting on the beam is not half of the total load, but simply the total area of the load (10 x 4 = 40 kN). So the total load on the beam is 40 kN, making the support reactions 20 kN at each support.

QUESTION 2: For the beam described above, what is the deflection at 1.5m from the left-hand side support?

CHATGPT Response:
To calculate the deflection at a specific point along the beam, such as 1.5m from the left-hand side support, we can use the formula for deflection of a simply supported beam under a uniformly distributed load.

The formula for the deflection at a distance x from the left support of a simply supported beam with a uniformly distributed load can be given as:

δ = (5 * w * x^4) / (384 * E * I)

Where:
δ is the deflection at the given point (1.5m in this case),
w is the uniformly distributed load (10 kN/m),
x is the distance from the left support to the point where the deflection is calculated (1.5m),
E is the modulus of elasticity of the material the beam is made of,
I is the moment of inertia of the beam’s cross-section.

The modulus of elasticity (E) and moment of inertia (I) depend on the properties and dimensions of the beam. Without that information, it is not possible to calculate the deflection accurately. The specific values for E and I would need to be known or provided to determine the deflection at a specific point on the beam.

Please note that calculating beam deflection involves additional assumptions, such as the beam being linearly elastic and having a constant cross-section throughout its length. Different beam materials and configurations may require different deflection formulas and considerations.

VERDICT: CHATGPT’s response is wrong. The AI model used a general equation for calculating the deflection at the mid-span of a simply supported beam subjected to a uniformly distributed load to calculate the deflection at a point that is not the mid-span. You cannot merely substitute any value of x into the famous deflection equation [δ = (5wx⁴) / (384EI)] if x is not the midspan.

The general equation for calculating the deflection at any point on a simply supported beam subjected to a uniformly distributed load is;

EIδ = -wLx³/12 + wx⁴/24 + (wL³/24)x

at x = L/2 (mid-span)
δ = [-wL(L/2)³/96 + w(L/2)⁴/24 + (wL³/24)L/2]/EI
δ = [-wL⁴/96+ wL⁴/384 + wL⁴/48]/EI = 5wL⁴/384EI

At x = 3L/8 (1.5m from the left-hand side), the value of the deflection can also be calculated.

QUESTION 3: Your approach to the above question is wrong. The formula is only valid for the mid-span of the beam and not anywhere else.

CHATGPT:
I apologize for the confusion caused by my previous response. You are correct, the formula I mentioned is applicable only for the deflection at the mid-span of the beam under a uniformly distributed load.

To determine the deflection at a specific point other than the mid-span, we need to use a different approach. In this case, we can calculate the deflection using the double integration method.

The deflection at a distance x from the left support can be calculated using the following steps:

Calculate the reaction forces at the supports using the total load and beam span as explained in the previous response. In this case, each support reaction is 10 kN vertically upward.
Determine the equations for the elastic curve in each segment of the beam. The beam can be divided into two segments: one from the left support to the point of interest (1.5m), and the other from the point of interest to the right support.
Integrate the equations of the elastic curve twice to obtain the deflection equation for each segment.
Apply the appropriate boundary conditions to determine the constants of integration.
Evaluate the deflection equation at the point of interest (1.5m) to obtain the deflection at that location.

Without specific information about the beam’s material, cross-section, and other relevant details, it is not possible to provide an accurate calculation of the deflection at 1.5m from the left support. To determine the deflection accurately, you would need to know the properties of the beam and use the appropriate equations and calculations based on those properties.

VERDICT: CHATGPT’s response is correct.

QUESTION 4: A rectangular reinforced concrete beam with a depth of 500mm and a width of 250mm is subjected to an ultimate bending moment of 95 kNm. What is the area of steel required if the yield strength of steel is 500 MPa, the characteristic compressive strength of concrete is 30 MPa, and the concrete cover is 35 mm.

CHATGPT:
To determine the area of steel required in a reinforced concrete beam, we need to consider the equilibrium of forces and the stress limits of both the concrete and steel.

Calculate the section modulus: The section modulus (Z) of a rectangular beam can be calculated using the formula: Z = (b * d^2) / 6 Where: b is the width of the beam (250 mm), d is the effective depth of the beam (depth – cover – steel diameter).

Given:
Depth of the beam (d) = 500 mm
Concrete cover (c) = 35 mm
Assuming the diameter of the steel reinforcement as 8 mm (commonly used size),
Effective depth (d) = Depth – Cover – Steel diameter = 500 mm – 35 mm – 8 mm = 457 mm

Now, calculate the section modulus:
Z = (250 mm * (457 mm)^2) / 6
Z = 20,610,417 mm^3

Calculate the stress in the concrete: The stress in the concrete (σ_c) can be calculated using the formula:
σ_c = M / Z
Where: M is the ultimate bending moment (95 kNm).

Given: Ultimate bending moment (M) = 95 kNm

Convert the moment to Nmm: M = 95 kNm * 10^6 Nm/kNm M = 95,000,000 Nmm

Now, calculate the stress in the concrete:
σ_c = 95,000,000 Nmm / 20,610,417 mm^3
σ_c = 4.61 MPa

Calculate the required area of steel: The required area of steel (A_s) can be determined using the formula:
A_s = (σc * Z) / σs
Where: σ_s is the yield strength of the steel reinforcement (500 MPa).

Given: Yield strength of steel (σ_s) = 500 MPa

Now, calculate the required area of steel:
A_s = (4.61 MPa * 20,610,417 mm^3) / (500 MPa)
A_s = 189.23 mm^2

Therefore, the required area of steel in the reinforced concrete beam is approximately 189.23 mm^2.

Verdict: Uhmmmmm ???

QUESTION 5: Can you carry out the calculation again according to the requirements of the Eurocode?

CHATGPT: Certainly! I apologize for the oversight. Here’s the calculation based on the requirements of the Eurocode for reinforced concrete design.

Calculate the design bending moment (M_d): The design bending moment (M_d) is calculated by dividing the ultimate bending moment by a factor of safety, typically taken as 1.5 for ultimate limit state design.
M_d = 95 kNm / 1.5 M_d = 63.33 kNm
Calculate the effective depth (d): The effective depth (d) is calculated as the overall depth minus the concrete cover and half the diameter of the reinforcement.
d = Depth – Cover – (Steel diameter / 2)
d = 500 mm – 35 mm – (8 mm / 2)
d = 457 mm
Determine the design compressive strength of concrete (f_cd): The design compressive strength of concrete (f_cd) is calculated by dividing the characteristic compressive strength of concrete (f_ck) by a factor of safety, typically taken as 1.5 for normal strength concrete.
f_ck = 30 MPa / 1.5 f_ck = 20 MPa
Calculate the design tensile strength of steel (f_td): The design tensile strength of steel (f_td) is calculated by dividing the characteristic yield strength of the reinforcement (f_yk) by a factor of safety, typically taken as 1.15.
f_yk = 500 MPa / 1.15 f_yk = 434.78 MPa
Determine the design moment capacity (M_rd): The design moment capacity (M_rd) is calculated using the following formula:
M_rd = (f_td * A_s * (d – a_s / 2)) / γ_M

Where:
A_s is the area of steel,
a_s is the distance from the centroid of the steel to the extreme compression fiber,
γ_M is the partial factor for moment resistance (taken as 1.0 for the ultimate limit state design).

Since the beam is under-reinforced according to Eurocode, the limiting value of a_s is the smaller of:
a_s = β_1 * (d – a_s / 2) or a_s = β2 * (d – xu)

For rectangular beams, β_1 = 0.5 and β_2 = 0.8.

Assuming a_s = 35 mm (same as the concrete cover), we can calculate the value of x_u (the depth of the neutral axis):
x_u = β_2 * d x_u = 0.8 * 457 mm
x_u = 365.6 mm

Now we can substitute the values into the formula:
M_rd = (f_td * A_s * (d – a_s / 2)) / γ_M
63.33 kNm = (434.78 MPa * A_s * (457 mm – 35 mm / 2)) / 1.0

Solving for A_s:
A_s = (63.33 kNm * 1.0) / (434.78 MPa * (457 mm – 35 mm / 2))
A_s ≈ 50.57 mm^2

Therefore, according to the Eurocode requirements, the required area of steel in the reinforced concrete beam is approximately 50.57 mm^2.

VERDICT: WRONG

QUESTION 6: Your solution is a bit strange. The bending moment provided was stated as an ultimate moment. Furthermore, even if the bending moment is ‘unfactored’, are you supposed to multiply or divide action effects with the partial factor of safety?

CHATGPT: I apologize for the confusion in my previous response. You are correct, for ultimate limit state design according to Eurocode, the ‘unfactored’ ultimate bending moment should be used directly in the calculations. Additionally, the action effects should be multiplied by the appropriate partial factor of safety.

Let’s recalculate the required area of steel according to the Eurocode requirements:

Calculate the effective depth (d) as before:
d = Depth – Cover – (Steel diameter / 2)
d = 500 mm – 35 mm – (8 mm / 2) d = 457 mm
Determine the design compressive strength of concrete (f_cd): The design compressive strength of concrete (f_cd) is calculated by dividing the characteristic compressive strength of concrete (f_ck) by the appropriate partial factor of safety for concrete. For normal-strength concrete, this factor is taken as 1.5.
f_cd = 30 MPa / 1.5
f_cd = 20 MPa
Calculate the design tensile strength of steel (f_td): The design tensile strength of steel (f_td) is calculated by dividing the characteristic yield strength of the reinforcement (f_yk) by the appropriate partial factor of safety for steel. For reinforcing steel, this factor is typically taken as 1.15.
f_td = 500 MPa / 1.15
f_td = 434.78 MPa
Determine the required area of steel (A_s): The required area of steel (A_s) can be calculated using the formula:
A_s = (M_d * 10^6) / (f_td * (d – a_s / 2))

Where: M_d is the ‘unfactored’ ultimate bending moment (95 kNm),
f_td is the design tensile strength of steel (434.78 MPa),
d is the effective depth of the beam (457 mm),
a_s is the distance from the centroid of the reinforcement to the extreme compression fiber.

Assuming a_s = 35 mm (same as the concrete cover), we can substitute the values into the formula:
A_s = (95 kNm * 10^6) / (434.78 MPa * (457 mm – 35 mm / 2))
A_s ≈ 515.88 mm^2

Therefore, according to the Eurocode requirements, the required area of steel in the reinforced concrete beam is approximately 515.88 mm^2.

VERDICT: This particular solution is very close to being acceptable, even though the approach used in the calculation of the lever arm is a bit crude (considering the EC2 stress block). We know that for singly reinforced sections, the approach used by ChatGPT shouldn’t make any much difference in the design results (using the effective depth of 457mm, the area of steel required is 503 mm²).

Furthermore, ChatGPT made its own assumptions (such as selecting its own diameter of reinforcement), but it didn’t consider the diameter of links in calculating the effective depth. It was also able to pick the material partial factors of safety correctly. However, it erroneously used the term ‘unfactored moment’ which it picked from the question I posed to it. It probably assumed ‘unfactored moment’ to mean ‘design moment’.

QUESTION 7: A 500 mm diameter concrete pile is driven 12m deep into a homogenous pure clay soil with an effective cohesion of 18 kPa. What is the load-carrying capacity of the pile as a result of shaft friction?

CHATGPT:

To determine the load-carrying capacity of the pile due to shaft friction, we can use the principles of soil mechanics and the formula for calculating the ultimate shaft resistance in cohesive soils. The ultimate shaft resistance can be calculated using the following equation:

Qs = π * D * L * c’

Where:
Qs is the ultimate shaft resistance,
D is the diameter of the pile,
L is the depth of penetration,
c’ is the effective cohesion of the soil.

Given: Diameter of the pile (D) = 500 mm Depth of penetration (L) = 12 m Effective cohesion of the soil (c’) = 18 kPa

Converting the diameter to meters: D = 500 mm / 1000 D = 0.5 m
Converting the effective cohesion to kN/m²: c’ = 18 kPa * 1 kN/m² / 1000 Pa
c’ = 0.018 kN/m²

Substituting the values into the formula: Qs = π * 0.5 m * 12 m * 0.018 kN/m²
Qs ≈ 3.83 kN

Therefore, the load carrying capacity of the pile due to shaft friction is approximately 3.83 kN.

VERDICT: WRONG

QUESTION 8: But kPa is the same thing as kN/m^2

ChatGPT: You’re absolutely right, I apologize for the confusion in my response. kPa (kilopascal) is indeed equivalent to kN/m² (kilonewton per square meter), representing the unit of pressure or stress.

Given that the effective cohesion (c’) is already in kPa, we can directly substitute the values into the formula:

Qs = π * D * L * c’
Qs = π * 0.5 m * 12 m * 18 kPa
Qs ≈ 34.56 kN

Therefore, the load-carrying capacity of the pile due to shaft friction is approximately 34.56 kN.

VERDICT: This particular solution is correct. But out of curiosity, it is important to find out if the AI model picked the right equation.

QUESTION 9: Did you consider the adhesion factor (α) in your calculation?

I apologize for not considering the adhesion factor (α) in the calculation. The adhesion factor takes into account the reduction in the effective cohesion along the pile shaft due to factors such as pile installation method and soil characteristics.

The equation to calculate the ultimate shaft resistance considering the adhesion factor is:

Qs = α * π * D * L * c’

The adhesion factor (α) typically ranges between 0.5 and 1.0, depending on the soil conditions and installation method. Without specific information regarding the adhesion factor for your case, it is challenging to provide an accurate value. However, for a conservative estimate, let’s assume α = 0.5.

Using this assumption, we can calculate the load-carrying capacity of the pile due to shaft friction:

Qs = 0.5 * π * 0.5 m * 12 m * 18 kPa
Qs ≈ 8.14 kN

Therefore, considering an adhesion factor (α) of 0.5, the load carrying capacity of the pile due to shaft friction is approximately 8.14 kN.

VERDICT: For driven piles in clay soils with effective cohesion less than 40 kPa, the recommended value of the adhesion factor is 1.0. I guess we can forgive ChatGPT.

Conclusion

In conclusion, ChatGPT can be a useful tool for carrying out civil engineering calculations. However, it can only get better. As can be seen from this article, it can quickly perform calculations, especially for problems involving popular equations and well-known theories. For other advanced calculations, extreme caution should be used.

It is important to note that ChatGPT is an AI language model and does not have access to specific project details or real-time data. Therefore, its responses are based solely on the information provided and the knowledge it has been trained on.

While ChatGPT can provide valuable assistance in performing calculations, it is essential to exercise caution and independently verify the results as can be seen in this article. It appears that it is heavily influenced by the input data, and the expertise of the engineer is required to drive it in the right direction.

Engineering calculations often require careful consideration of various factors, including applicable codes, standards, material properties, and site-specific conditions. Therefore, it is always recommended to consult with qualified engineers and professionals to ensure accurate and reliable results.

Critical Depth for Skin Friction in Piles

By

Ubani Obinna

-

June 2, 2023

Table of Contents

Skin friction is the resistance developed along the sides of the pile shaft due to the interaction between the pile and the surrounding soil. It is one of the primary mechanisms by which piles transfer load to the soil. The magnitude of skin friction is influenced by various factors, including soil type, pile geometry, installation method, and load conditions.

In geotechnical engineering, the vertical effective stress, denoted by σ’, normally increases with depth. As a result, it should be logical that the magnitude of skin friction in piles should increase infinitely with increasing depth. In reality, the magnitude of skin friction will not continue to increase infinitely with increasing depth. It was formerly thought that at a certain depth, the value of skin friction in piles would become constant. This particular depth is called the ‘critical depth’.

The critical depth for skin friction is the depth below the ground surface at which the increase in pile diameter does not contribute significantly to the overall capacity of the pile. In other words, beyond this critical depth, the additional skin friction developed due to an increase in pile diameter becomes negligible. Determining the critical depth is crucial because it helps optimize the design and construction of piles, considering both cost-effectiveness and structural efficiency.

**Figure 1:** The theory of critical depth (Rajapakse, 2008)

As shown in Figure 1, skin friction was assumed to increase up to the critical depth and then maintain a constant value.

d_c = critical depth
S_c= skin friction at the critical depth (K.σ’_c.tanδ)
σ’_c= effective stress at critical depth

The following approximations were assumed for the critical depth

Critical depth for loose sand = 10d (d is the pile diameter or the width)
Critical depth for medium-dense sand = 15d
Critical depth for dense sand = 20d

However, this theory does not explain recent observations made from precise pile load test data. According to recent experiments, skin friction will not become absolutely constant as was once believed.

Experimental Evidence of Critical Depth

A typical variation in skin friction that occurs with increasing pile depth is shown in Figure 2. As can be seen in Figure 2, the assumption proposing constant skin friction below the critical depth is not supported by the results obtained from the experiments.

**Figure 2:** Variation of skin friction. (Source: Randolph et al., 1994)

The skin friction has a tendency to increase with depth, and it reaches its maximum value right above the tip of the pile. After then, there would be a significant reduction in skin friction. At the moment, there is no theory that can adequately explain the observations made in the field. The critical depth theory is still widely used in engineering today because there is no more advanced alternative.

Reasons for limiting skin friction in Piles

In order to explain why the skin friction does not increase infinitely with depth as the skin friction equation suggested, the following explanations have been presented.

Unit Skin Friction = K∙σ’∙tanδ
σ’ = γd

The value of K presented above is determined by the soil angle of friction, denoted by φ’. As one goes deeper, the angle of internal friction angle typically reduces. As a result, the K value reduces as depth increases (Kulhawy 1983).
The aforementioned equation for skin friction does not hold true at high-stress levels because the sand particles have to adjust their orientation.
A reduction in the magnitude of friction is experienced by the shaft as the pile depth increases. (See Figure 3) (Randolph et al. 1994).

**Figure 3:** Variation of skin friction in relation to depth (Rajapakse, 2008)

Let’s assume a pile was driven to a depth of 3m (10 ft), and the unit skin friction was measured at a depth of 1.5m (5 ft). If we also assume that the pile was driven further to a depth of 4.5m (15 ft) and that the unit skin friction was measured at the same depth of 1.5m( 5 ft). It has been reported that the second scenario has a lower unit skin friction at a distance of 1.5m.

Figure 3 demonstrates that as the pile is driven further into the earth, the local skin friction experiences a reduction. According to NAVFAC DM 7.2, the maximum value of skin friction and end bearing capacity is attained after 20 diameters within the bearing zone. This is the case regardless of the bearing material.

Solved Example on Critical Depth

(Calculation after Rajapakse, 2008)

Find the skin friction and end-bearing capacity of the pile shown. Assume that critical depth is achieved at 20 ft into the bearing layer. The pile diameter is 1 ft, and other soil parameters are as shown in the figure.

Solution
The skin friction is calculated in the overburden soil. In this case, skin friction is calculated in the soft clay. Then the skin friction is calculated in the bearing layer (medium sand) assuming the skin friction attains a limiting value after 20 diameters (critical depth).

STEP 1: Find the skin friction from A to B.
Skin friction in soft clay = α × c × perimeter surface area
= 0.4 × 700 × πdL = 0.4 × 700 × π × 1 × 12 = 10,560 lbs = 46.9 kN

STEP 2: Find the skin friction from B to C.
Skin friction in sandy soils S = K∙σ’∙tanδ × A_p

S = skin friction of the pile
σ’ = average effective stress along the pile shaft
Average effective stress along pile shaft from B to C = (σ_B + σ_C)/2
σ_B = effective stress at B
σ_C = effective stress at C

To obtain the average effective stress from B to C, find the effective stresses at B and C and obtain the average of those two values.
σ_B = 100 × 4 (100 – 62.4) × 8 = 700.8 lb/ft² (33.6 kPa)
σ_C = 100 × 4 (100 – 62.4) × 8 + (110 – 62.4) × 20 = 1452.8 lb/ft² (69.5 kPa)
Average effective stress along pile shaft from B to C = (700.8 + 1452.8)/2 = 1076.8 lb/ft²

Skin friction from B to C = K∙σ’∙tanδ × A_p = 0.9 × 1076.8 × tan 25 × (π × 1 × 20) = 28,407 lbs

STEP 3: Find the skin friction from C to D.
Skin friction reaches a constant value at point C, 20 diameters into the bearing layer.
Skin friction at point C = K∙σ’_v∙tanδ × A_p

σ’_v at point C = 100 × 4 (100 – 62.4) × 8 (110 – 62.4) × 20 = 1,452.8 lb/ft²
Unit skin friction at point C = 0.9 × 1,452.8 × tan 25 = 609.7 lb/ft² (29 kPa)
Unit skin friction is constant from C to D. This is because skin friction does not increase after the critical depth.
Skin friction from C to D = 609.7 × surface perimeter area = 609.7 × (π × 1 × 8) = 15,323.4 lbs (68.2 kN)

Summary
Skin friction in soft clay (A to B) = 10,560 lbs
Skin friction in sand (B to C) = 28,407 lbs
Skin friction in sand (C to D) = 15,323 lbs
Total = 54,290 lbs (241 kN)

STEP 4: Compute the end bearing capacity.
End bearing capacity also reaches a constant value below the critical depth.
End bearing capacity = q × N_q × A

q = effective stress at pile tip
N_q = bearing capacity factor (given to be 15)
A = cross-sectional area of the pile

If the pile tip is below the critical depth, q should be taken at critical depth. In this example, the pile tip is below the critical depth, which is 20 diameters into the bearing layer. Hence, q is equal to the effective stress at the critical depth (point C).

Effective stress σ’_v at point C = 100 × 4 (100 – 62.4) × 8 (110 – 62.4) × 20 = 1,452.8 lb/ft²
End bearing capacity = qN_qA = 1,452.8 × 15 × (πd²/4) = 17,115 lbs

Total ultimate capacity of the pile = total skin friction + end bearing = 54,290 + 17,115 = 71,405 lbs (317.6 kN)

Conclusion

The critical depth for skin friction in piles is a crucial parameter for the design of piles in sand. It is believed to depend on factors such as soil type, pile diameter, and installation techniques. The determination of the critical depth is very important to ensure that the shaft friction of the pile is not overestimated, thereby ensuring the stability and safety of structures supported by piles. Ongoing research and advancements in geotechnical engineering continue to enhance our understanding of the critical depth and its significance in pile foundation design.

Reference

Rajapakse R. (2008): Pile Design for Structural and Geotechnical Engineers. ISBN: 978-0-08-055916-2 Butterworth-Heinemann

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