Expansion Joints in Buildings

By

-

September 24, 2023

Table of Contents

In the design of reinforced concrete buildings, it is essential to consider how changes in moisture and temperature can affect the volume of the structure. The magnitude of the stresses generated and the extent of the movement resulting from these volume alterations are directly related to the length of the building. To mitigate the effects of moisture or temperature-induced changes and prevent cracking, expansion joints are employed to divide buildings into distinct sections.

Expansion joints (also known as movement joints) are gaps in structures that allow different parts of the structure to move independently. They represent a disruption in both reinforcement and concrete, making them effective for accommodating both shrinkage and temperature variations. This is important because all materials expand and contract when their temperature changes. Without expansion joints, this movement could cause the structure to crack or fail.

This is especially true for building materials, such as concrete and steel, which can experience significant temperature changes throughout the day and year. Without expansion joints, these temperature changes would cause buildings to crack.

Joints in a building can serve as weak points to control crack locations (contraction joints) or create complete separation between segments (expansion joints). Currently, there is no universally agreed-upon design approach for accommodating building movements due to temperature or moisture variations. Many designers rely on “rule of thumb” guidelines that specify the maximum permissible distance between building joints.

Expansion joints are typically made of flexible materials, such as rubber or metal, which can compress and expand to absorb the movement of the structure. They are often sealed to prevent water and other elements from entering the structure.

The Need for Joints in Buildings

Expansion joints allow thermal expansions to occur in a building with minimal stress buildup. The greater the spacing between these joints, the higher the stresses they can accommodate. Typically, expansion joints divide a structure into segments, offering sufficient joint width to accommodate the building’s expansion as temperatures rise. In addition to mitigating contraction-induced cracking, expansion joints serve a dual purpose by providing relief from such cracking.

Controlling cracks in reinforced concrete structures is motivated by two main factors. Firstly, aesthetics are a significant consideration; noticeable cracks can mar the appearance, especially when the concrete is meant to be the final surface.

Cracks in crucial structural components like beams and columns can also lead to questions about the overall structural soundness, even if they don’t inherently jeopardize the building’s stability. Secondly, large crack widths can create pathways for air and moisture to infiltrate the structural framework, potentially leading to durability problems.

As a result, there is a genuine need for crack control in reinforced concrete structures. The main questions revolve around how to manage the extent of cracking, achieved through contraction joints, and how to restrict stresses in members to an acceptable level, accomplished through expansion joints.

Expansion Joints

Temperature changes induce stress within a structure, but this only occurs when the structure is restrained. In the absence of constraints, there are no resulting stresses. For instance, temperature difference has no effect on statically determinate structures.

In reality, almost all buildings have some level of restraint. The magnitude of temperature-induced stresses varies with the extent of temperature change; substantial temperature fluctuations can lead to significant stresses that must be considered during the design process, while minor temperature changes may result in negligible stresses.

These temperature-induced stresses occur due to changes in the volume of a structure between points where it is restrained. To estimate the amount of elongation caused by temperature increases, one can roughly multiply the coefficient of concrete expansion (approximately 12 x 10^-6 /℃) by the length of the structure and the temperature change.

For example, a 200-foot-long building exposed to a temperature rise of 25 degrees Fahrenheit (14 degrees Celsius) will elongate by about 3/8 inch (9.5 millimetres). Expansion joints are employed to mitigate the forces imposed by thermally induced volume changes.

Expansion joints allow distinct sections of a building to expand or contract independently without negatively impacting its structural integrity or functionality. These joints should have sufficient width to prevent contact between portions of the building on either side of the joint when the structure experiences the maximum expected temperature rise.

The width of expansion joints can range from 1 to 6 inches or more, with 2 inches being the typical width. Wider joints are used to accommodate additional differential movement resulting from settlement or seismic forces. These joints should extend throughout the entire structure above the foundation level and can be either covered or filled. Filled joints are mandatory for fire-rated structures.

Spacing of Expansion Joints

There can be some debate about whether expansion joints should be included in building design and, if so, what spacing they should have. The spacing of expansion joints depends on the acceptable level of movement, as well as the allowable stresses and/or capacity of the structural elements. It also depends on the length and stiffness of frame members and the seasonal temperature fluctuations experienced at the construction site.

The design temperature change is calculated based on the difference between the extreme values of the daily maximum and minimum temperatures. In addition to general guidelines, various methods have been developed to calculate the appropriate spacing for expansion joints.

Author	Spacing of expansion joint
Lewerenz (1907)	75 ft (23 m) for walls.
Hunter (1953)	80 ft (25 m) for walls and insulated roofs, 30 to 40 ft (9 to 12 m) for uninsulated roofs.
Billig (1960)	100 ft (30 m) maximum building length without joints. Recommends joint placement at abrupt changes in plan and at changes in building height to account for potential stress concentrations
Wood (1981)	100 to 120 ft (30 to 35 m) for walls.
Indian Standards Institution (1964)	45 m (≈ 148 ft) maximum building length between joints
PCA (1982)	200 ft (60 m) maximum building length without joints
ACI 350R-83	120 ft (36 m) in sanitary structures partially filled with liquid (closer spacings required when no liquid present).

Table 1 — Expansion joint spacings

Similar to contraction joints, practical guidelines have been established, as outlined in Table 1. These guidelines vary depending on the type of structure and span a range of 30 to 400 feet (9 to 122 meters). In addition to these rule-of-thumb recommendations, several methodologies have been devised to determine the appropriate spacing for expansion joints. This section introduces three such methods, all rooted in the research conducted by Martin and Acosta in 1970, Varyani and Radhaji in 1978, and the National Academy of Sciences in 1974.

Some recommendations propose placing movement joints in masonry structures at approximately 7 meters apart, matching the spacing of the frame elements. For concrete floor slabs, the suggested spacing is approximately 20 to 30 meters, according to Deacon (1986), Bussell and Cather (1995), and the Concrete Society (2003). This implies that continuous multi-bay frames should also incorporate movement joints at similar intervals.

Consequently, a decision must be made: either incorporate movement joints throughout the entire height of the structure, necessitating full wind bracing in each portion of the structure or design the structure to withstand the forces generated by such movements.

Calculation of Expansion Joint Spacing (Single Storey Buildings)

In 1970, Martin and Acosta introduced a technique for determining the maximum allowable spacing between expansion joints in single-story frames with spans that are approximately equal. Their approach assumes that, with appropriate joint spacing, the load factors related to gravity loads will offer sufficient safety margins against the impact of temperature variations.

Martin and Acosta derived a unified formula to calculate the expansion joint spacing, denoted as “L_j,” which relies on the structural stiffness characteristics of the frame and the designated temperature change, ∆T. This equation was developed through a study of frame structures designed in accordance with ACI 318-63 standards. The formula for expansion joint spacing is as follows:

L_j = 112000/R∆T (inches)
∆T in Fahrenheit, or

L_j = 12.24/R∆T (metres)
∆T in degrees Celsius

In the above expressions:

R = 144 × (I_c/h²) × [(1 + r)/(1 + 2r)]
∆T = 2/3 (T_max – T_min) – T_s

where:
r = ratio of stiffness factor of column to stiffness factor of beam = K_c/K_b;
K_c = column stiffness factor = I_c/h, in.³(m³)
K_b= beam stiffness factor = I_b/L, in.³ (m³)
h = column height, in. (m)
L = beam length, in. (m)
I_c = moment of inertia of the column, in.⁴(m⁴)
I_b = moment of inertia of the beam, in.⁴ (m⁴)
T_s = 30 F (17 C)

Values for T_max and T_min can be obtained from the Environmental Data Service for a particular location. The design temperature change ∆T is based on the difference between the extreme values of the normal daily maximum and minimum temperatures. An additional drop in temperature of about 30 F (17 C) is then added to account for drying shrinkage.

Length between expansion joints versus design temperature change, ∆T (Martin & Acosta 1970)

Conclusion

In the construction industry, expansion joints play a critical role in ensuring the longevity, safety, and functionality of the building structures. Their design and placement require careful consideration of various factors, including temperature variations, structural movement, and material characteristics. By providing controlled gaps to accommodate movement and stresses, expansion joints can be used to create robust and resilient structures in the face of dynamic forces and environmental challenges.

References

ACI Committee 350, “Concrete Structures (ACI 350R83),” American Concrete Institute, Detroit, 1983, 20 pp
Billig, Kurt, “Expansion Joints,” Structural Concrete, London, McMillan and Co., Ltd., 1960, pp. 962-965.
Code of Practice for Plain and Reinforced Concrete, IS 456-1964, 2nd Revision, Indian Standards Institution, New Delhi, 1964
Hunter, L.E., “Construction and Expansion Joints for Concrete,” Civil Engineering and Public Works Review, V. 48, No. 560, Feb. 1953, pp. 157-158, and V. 48, No. 561, Mar. 1953, pp. 263-265.
Lewerenz, A.C., “Notes on Expansion and Contraction of Concrete Structures,” Engineering News, V. 57, No. 19, May 9, 1907, pp. 512-514
Wood, Roger H., “Joints in Sanitary Engineering Structures,” Concrete International, V. 3, No. 4, April 1981, pp. 53-56.

Contraction Joints in Construction Works

By

Ubani Obinna

-

September 24, 2023

Table of Contents

Due to the poor tensile strength of concrete, some degree of cracking in reinforced concrete is inevitable. Contraction joints are designed to create predetermined weak points where cracks can develop. The weakened section at a contraction joint can be created through forming or sawing, either with no reinforcement or by allowing a portion of the total reinforcement to pass through the joint. Through careful architectural planning, these joints can be strategically placed to ensure that any resulting cracks are less noticeable within a building and ideally out of plain view.

Crack forming through a contraction joint

There are two primary reasons for controlling cracks in reinforced concrete buildings. Firstly, aesthetics play a significant role; visible cracks are unsightly, particularly when the concrete is intended to be the final finished product. Cracks in major structural elements like girders and columns can raise concerns about the structure’s structural integrity, even if they don’t necessarily pose a structural risk. Secondly, cracks of significant width can allow air and moisture to penetrate the structure’s framework, potentially causing durability issues.

As a result, there is a genuine need for crack control in reinforced concrete structures. The main questions revolve around how to manage the extent of cracking, achieved through contraction joints, and how to restrict stresses in members to an acceptable level, accomplished through expansion joints.

The following sections offer recommendations for contraction joint spacing. Once the joint locations are chosen, it’s crucial to construct the joint in a manner that fulfils its intended purpose.

Contraction Joints

Drying shrinkage and variations in temperature result in tensile stresses within a concrete mass, especially when the material is restrained. Cracks will develop when these tensile stresses exceed the tensile strength of the concrete, which is relatively low.

Given this inherent limitation of concrete, cracking of concrete sections is usually quite likely. Contraction joints serve as predetermined weak points where cracks can form without adversely affecting the overall appearance of a structure. Typically, contraction joints are primarily employed in walls and slabs-on-grade.

It’s important to note that the greater the spacing between contraction joints, the more significant the forces generated within a structure due to volume changes. To withstand these forces and minimize the extent of cracking in the concrete, additional reinforcement is needed.

Joint Configuration

Contraction joints are normally constructed as concrete sections with reduced cross-sectional area and reinforcement. To ensure the weakness of the section is sufficient for crack formation, it is recommended that the concrete cross-section be reduced by at least 25 percent. In terms of reinforcement, there are currently two types of contraction joints in use, referred to as “full” and “partial” contraction joints according to ACI 350R guidelines.

Full contraction joints, the preferred choice for most building construction, are established with a complete disruption in reinforcement at the joint. All reinforcement is terminated approximately 2 inches (51 mm) away from the joint, and if the joint serves as a construction joint, a bond breaker is placed between successive placements.

Partial contraction joints, on the other hand, are constructed with no more than 50 percent of the reinforcement passing through the joint. Partial contraction joints find application in liquid containment structures. In both types of joints, water stops may be employed to ensure water tightness.

Joint Location

Once the decision to employ contraction joints is made, the next consideration is determining the necessary spacing to control the extent of cracking between these joints. As detailed in Table 1, various recommendations are provided for contraction joint spacing. The suggested spacings range from 15 to 30 feet (approximately 0.6 to 9.2 meters) and from one to three times the height of the wall.

Author	Recommended contraction joint spacing
Merrill (1943)	20 ft (6 m) for walls with frequent openings, 25 ft (7.5 m) in solid walls.
Fintel (1974)	15 to 20 ft (4.5 to 6 m) for walls and slabs on grade. Recommends joint placement at abrupt changes in plan and at changes in building height to account for potential stress concentrations.
Wood (1981)	20 to 30 ft (6 to 9 m) for walls
PCA (1982)	20 to 25 ft (6 to 7.5 m) for walls depending on number of openings.
ACI 302.1R	15 to 20 ft (4.5 to 6 m) recommended until 302.1R-89, then changed to 24 to 36 times slab thickness.
ACI 350R-83	30 ft (9 m) in sanitary structures.
ACI 350R	Joint spacing varies with amount and grade of shrinkage and temperature reinforcement.
ACI 224R-92	One to three times the height of the wall in solid walls

Table 1 – Contraction joint spacings

For sanitary structures, Rice (1984) offers contraction joint spacings based on specific reinforcement percentages (as outlined in Table 2).

Contraction joint spacing in ft.	Minimum percentage of shrinkage and temperature reinforcement (f_y = 276 MPa)	Minimum percentage of shrinkage and temperature reinforcement (f_y = 413 MPa)
less than 30	0.30	0.25
30 – 40	0.40	0.30
40 – 50	0.50	0.38
greater than 50	0.60	0.45

Table 2 – Contraction joint spacings for sanitary engineering structures based on reinforcement percentage (Rice 1984)

It’s important to note that the limits specified by Rice in Table 2 extend the recommendations outlined in ACI 350R, taking into account factors such as reinforcement grade and minimum bar size. It’s worth mentioning that when employing a “partial” contraction joint, the spacing should be roughly two-thirds of that used for a full contraction joint, as per ACI 350R guidelines.

Additionally, Wood (1981) suggests that any joint within a structure should traverse the entire structure in a single plane. Misalignment of joints may result in movement at one joint causing cracking in an unjointed portion of the structure until the crack intersects another joint.

For slabs-on-grade and concrete pavements, contraction joints are usually placed at depths ranging from 1/4 to 1/3 of the slab’s thickness and are commonly spaced at intervals of 3.1 to 15 meters (approximately 12 to 50 feet). Thinner slabs tend to have more closely spaced joints. According to the Portland Cement Association (PCA), contraction joints are spaced at intervals ranging from 24 to 30 times the thickness of the slab. When the spacing between joints exceeds 15 feet (4.5m), the inclusion of load transfer mechanisms such as dowels or diamond plates becomes necessary.

contraction joint cracking — Contraction joint cracking

It is also common to have, a semi-random pattern for joint spacing in pavements to reduce their impact on vehicle resonance. Such patterns often involve a recurring sequence of joint spacings, such as 2.7 meters (9 feet), followed by 3.0 meters (10 feet), then 4.3 meters (14 feet), and subsequently 4.0 meters (13 feet).

Conclusion

In conclusion, contraction joints play an important role in the construction of concrete structures. These strategically placed joints serve as planned weak points, allowing for controlled cracking in response to factors like temperature variations and drying shrinkage. Properly designed and spaced contraction joints are essential for maintaining the structural integrity and aesthetic appeal of buildings and other concrete structures.

The choice of joint type, spacing, and reinforcement is crucial, as it directly impacts the extent of cracking and the overall durability of the structure. By adhering to recommended guidelines and considering the specific needs of the project, engineers and builders can effectively manage and control cracking, ensuring that the structure remains safe, functional, and visually pleasing for years to come.

References

ACI Committee 224, “Control of Cracking in Concrete Structures,” ACI 224R-80, Concrete International, V. 2, No. 10, Oct. 1980, pp. 35-76.
ACI Committee 302, “Guide For Concrete Floor and Slab Construction (ACI 302.1R-89),” American Concrete Institute, Detroit, 1989, 45 pp.
ACI Committee 318, “ACI Standard Building Code Requirements for Reinforced Concrete (ACI 318-63),” American Concrete Institute, Detroit, 1963, 144 pp.
ACI Committee 350, “Concrete Structures (ACI 350R83),” American Concrete Institute, Detroit, 1983, 20 pp.
Fintel, M. (1974). “Joints in Buildings,” Handbook of Concrete Engineering, New York, Van Nostrand Reinhold Company, 1974, pp. 94-110.
Merril, W. S. (1943). “Prevention and Control of Cracking in Reinforced Concrete Buildings,” Engineering News-Record, V. 131, No. 23, Dec. 16, 1943, pp. 91-93
Rice, P.F. (1984). “Structural Design of Concrete Sanitary Structures,” Concrete International, V. 6, No. 10, Oct. 1984, pp. 14-16.
Wood, R. H. (1981). “Joints in Sanitary Engineering Structures,” Concrete International, V. 3, No. 4, April 1981, pp. 53-56.

Core Curriculum for Civil Engineering Undergraduate Programs

By

Ubani Obinna

-

September 26, 2023

Table of Contents

Civil engineers oversee the design, planning, construction, and maintenance of public infrastructure. Although civil engineering undergraduate programs differ from university to university, some core courses are common to all programs. These courses cover the fundamentals of engineering mathematics, structural engineering, environmental engineering, soil mechanics, foundation engineering, construction management, fluid mechanics, and highway/transportation engineering.

Civil engineering is therefore the branch of engineering that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewer systems, pipelines, and power plants.

Civil engineers play a vital role in society by designing and building the infrastructure that we all rely on every day. They work on a wide range of projects, from small-scale residential developments to large-scale public works projects. A Bachelor’s Degree is often required to be called an Engineer.

In the UK, a civil engineering undergraduate programme lasts for 3 to 4 years, while in the United States of America and Australia, it lasts for 4 years. In West African countries like Nigeria, civil engineering undergraduate programme lasts for 5 years, with a semester completely dedicated to industrial training. In South Africa, the average duration of a civil engineering undergraduate programme is 4 years.

The programmes are usually assessed through examinations, quizzes, lab work, coursework, and a final research or design project. The degrees awarded at the completion of the programme vary from university to university such as Bachelor of Engineering (B.Eng), Bachelor of Technology (B.Tech), and Bachelor of Science in Engineering (B.Sc Engineering).

A Bachelor’s degree in civil engineering is a sufficient requirement for someone to practice professional engineering, and to join professional bodies in Engineering. However, some work experience and professional examinations/interviews are usually required before someone can register as a professional or chartered engineer.

civil engineering professional in the field

A civil engineering graduate may wish to specialise in the following areas during post-graduate studies;

Structural Engineering
Geotechnical Engineering
Water Resources Engineering
Environmental Engineering
Highway and Transportation Engineering, and
Construction Management

As a result, courses from these options are usually and compulsorily offered at the undergraduate level.

Core Curriculum for Civil Engineering

In most universities across the world, civil engineering students are usually required to take some basic/foundation courses in mathematics, physics, chemistry, applied mechanics, and general engineering courses in their first and second years. The third year, fourth year, and fifth year (as the case may be) are usually dedicated to the core civil engineering disciplines.

Some of the foundation courses for civil engineering undergraduate programmes are general mathematics, general physics, general chemistry, applied mechanics (statics and dynamics), engineering thermodynamics, applied electricity, engineering mathematics, etc.

Core Courses in Civil Engineering

The following are some core courses in civil engineering;

Fluid Mechanics

Introduction to incompressible viscous flow, laminar and turbulent flows, Reynolds number; boundary layer flow, lift and drag. Laminar flow – in pipes, between parallel plates. Turbulent flows – along a plate, in ducts and pipes. Physical hydraulic models. Interconnected pipes and pipe network analysis. Potential flows and application to flow nets. steady and unsteady flow in closed conduits; water hammer, surge tanks.

Strength of Materials

Advanced topics on axial, lateral and torsional loading of shafts. Beams. Emphasis on the bending moment and shear force diagrams in beams. Theory of bending of beams. Unsymmetrical bending and shear centre. Slope and deflection of beams. Castigliano’s theorem; Continuous indeterminate beams; Clapeyron’s theorem of three moments; slope deflection method; Strength theories stress concentration spring. Creep. Fatigue. Fracture. Stress concentration. Stresses in thin and thick cylinders. Rotating disks. Biaxial and Triaxial state of stress. Multi-dimensional stress systems. Mohr’s circle. transformation of stress. Strain energy. Closed-coiled Helical springs. Other types of springs.

Structural Mechanics/Theory of Structures

Analysis of determinate structures – beams, trusses; structural analysis theorems, graphical methods; application to simple determinate trusses. Influence lines. Williot-Mohr diagram. Deflection of statically determinate structures – unit load, moment-area methods, strain energy methods. Introduction to statically indeterminate structures.

Analysis of statically indeterminate structures including continuous beams, rigid frames, arches and trusses. Force and deformation method. Elastic curve, sue of symmetry, Effects of temperature changes and movement of supports, Influence lines and their application in moving load analysis, Moment distribution.

Soil Mechanics

Introduction to Soil Mechanics. Origin and formation of soils. Soil deposits. Soil properties. Specific gravity analysis of soils. Atterberg’s limits and indices, etc. Particle size distribution. Definitions and derivation of void ratio. Porosity. Specific gravity. unit weights/density. Degree of saturation. Weight Volume Relationships. Components of soil and phase diagram. Various unit-weight relationships.

USCS soil classification system. AASHTO soil classification system. Bousinesq problems in soil mechanics; stresses under uniformly loaded areas; elastic settlement of soil masses; Terzaghi’s effective stress principle; pore pressure parameters; Concepts of compressibility and consolidation; Introduction to Compaction of Soils. Hydraulic properties of soils. The capillary rise in soils. Hydraulic conductivity (k). Darcy’s Law. Estimation of hydraulic conductivity. Falling head and constant head permeability test.

Design of Structures I

Fundamentals of design process. materials selection. building regulations and codes of practice. Design philosophy; elastic design; limit state designs in concrete. principle of modular ratio and load factor method. Analysis using the Hardy Cross moment distribution. Analysis using the Clapeyron’s method. Theory of design of basic structural reinforced concrete elements. Design of structural elements in Reinforced concrete. Design of one-way slab. Design of two-slab. Design of flat slab. Design of beams and deflection checks. Types of columns, biaxially, uniaxially and axially loaded column. Short and slender column. Design of the different types of columns. Design of foundation base. Bending schedule and design project.

Design of Structures II

Steel design

Steel as a structural material, various kinds of structural steel, their properties and admissible stresses, application of steel in buildings, design of industrial structures, portal frames, steel trusses, design of gantry cranes, electric power transmission towers, communication towers, tanks, etc. specification, floor structures, primary and secondary beams, columns typical joint details, design of members and connections and particularities of design.

Timber design

Classification of structural timber, structural properties of natural wood, glued laminated timber and plywood, fire resistance, seasoning and preservation members in tension, compression and bending economic design of beams, columns and Diaphragm, compound structural members, design of timber connectors, application of timber in buildings, electric poles, bridges, forms and framework for concrete.

Civil Engineering Materials

Concrete Technology – types of cement, aggregates and their properties; concrete mix design, properties and their determination. Steel technology – production, fabrication and properties, corrosion and its prevention. Tests on steel and quality control. Timber technology – types of wood, properties, defects, stress grading, preservation and fire protection, timber products. Rubber, plastics, asphalt, tar, glass, lime, bricks and applications to buildings, roads and bridges.

Environmental Engineering

Theory and laboratory work for the design of physical, chemical, and biological processes for water and wastewater treatment. Design of stormwater and seepage collection systems. Importance of small waterworks; economical and safe water supply and treatment methods; individual and general waste disposal systems.

Water and wastewater quality (physical, chemical, biological and radiological). Water supply and design of unit operations. Water distribution design methods. Wastewater treatment design: waste stabilization ponds, activated sludge trickling filters, oxidation ditches. Introduction to environmental impact assessment.

Highway and Transportation Engineering

Introduction, history of Road development. Elementary traffic Engineering, Highway design, Highway project, introduction to volume computation, intersection and interchanges, traffic/Highway operation and management, Highway administration, systems, organizational structure, functional characteristics and classification, highway financing and road taxes, cost-benefit Analysis, review of soil mechanism, organization of highway construction projects, introduction to production and application of aggregates pavements. Problems with soils for road construction. Quality control of soil.

Introduction to pavements: design and maintenance of pavements. Highway drainage and drainage structures: culvert design and construction of channels, open ditches. Drainage requirements. Pavement of erosion and silting of side ditches. Protection of verges, side slopes, embankments against failures and erosion.

Geotechnical Engineering

Consolidation theory and settlement analysis: one-dimensional consolidation, theory, the oedometer tests, determination of coefficient of consolidation, C_v, preconsolidation pressure, normally and over-consolidated clays; analysis of total and time rate of settlement structures on soils (immediate/elastic settlement, primary settlement and secondary compression; sand drains).

Shear strength of soils: General strength consideration, state of stress at a point and Mohr stress circle, Mohr-Coulomb theory of failure, shear strength tests (direct shear test, triaxial test, unconfined compressive strength test, vane shear test), shear strength of consolidated clays, shear strength of saturated clays, shear strength of soils, residual shear strength parameters, pore pressure coefficients A and B.

Foundation design: types and choice of foundations.

-Shallow foundations; footings, rafts, design procedures.

-Deep foundations; piles, use and general characteristics of piles, piles in sand, pipe in clay, negative skin friction, pile group, bearing capacity and settlement of pile groups, efficiency of pile groups; caissons, types, loads on caissons, merit and demerits of different caissons, analysis and design of caissons.

-Special foundations.

Earth pressure theory and earth retaining structures:

lateral earth pressure theory (that is, active, passive and at rest pressures), earth pressure coefficients, computation of earth pressures using Rankine’s and Coulomb’s theories, Culmann’s graphical method, earth pressure on retaining structures, earth retaining structures: types and analysis of retaining walls; use of bracings as lateral support in open cuts; sheet piles and anchored bulkheads, fixed-earth and free-earth support methods of analysis, pressure distribution of sheetings, struts and walls; slurry trenches.

Slope stability:

types and mechanics of scope failures, theoretical and graphical solutions of scope stability problems, effect of tension cracks on slope stability, ordinary methods of slices.

Construction Management

Project management fundamentals – definitions, project environment, nature and characteristics, development practice, management by objectives, and the centrality of engineering to projects, infrastructures, national and global development. The scope of project management – organisational, financial, planning and control, personnel management, labour and public relations, wages and salary administration and resource management. Identification of project stakeholders; beneficiaries and impacted persons – functions, roles, responsibilities.

Project community relations, communication and change management. Project planning, control and timeliness;decision making, forecasting, scheduling, work breakdown structure (WBS), deliverables and timelines, logical frameworks (log frames), risk analysis, role of subject matter experts (SMEs), role conflicts; Gantt Chart, CPM and PERT. Optimisation, linear programming as an aid to decision making, transport and materials handling. Monitoring and Evaluation – key performance indices (KPis); methods of economic and technical evaluation.

Industrial psychology, ergonomics/human factors and environmental impact considerations in engineering project design and management. Project business case – financial, technical and sustainability considerations. Case studies, site visits and invited industry professional seminars. General principles of management and appraisal techniques. Breakthrough and control management theory; production and maintenance management. Training and manpower development. The manager and policy formulation, objective setting, planning, organising and controlling, motivation and appraisal of results.

Continuous Flight Auger (CFA) Piles

By

Ubani Obinna

-

September 18, 2023

Table of Contents

Continuous flight auger (CFA) piles are cast-in-situ replacement piles that are constructed by rotating and driving a hollow-stem continuous flight auger into the ground at a regulated speed to the desired pile depth.

As the auger is withdrawn, concrete is pumped into the borehole through the hollow stem of the auger under constant positive pressure. The reinforcing cage can be installed and driven to the desired depth into the freshly poured concrete once the auger has been completely removed from the borehole.

Continuous flight auger drilling belongs to the dry rotary drilling methods. Drilling fluids or temporary casings are not necessary because the hollow stem auger supports the excavated shaft continuously during the drilling process. Although CFA piles were first created to support locations with weak, sandy materials beneath the water table, their instrumentation control, low vibration, and depth/torque capacity have made them a very common foundation type today.

The possible range of diameters and depths for CFA piles has increased significantly since the development of high torque rotary heads and drilling rigs with extended masts, high crowd and extraction forces, and the ability to install CFA piles through a wide range of soil types, including clays, silts, peat, sand, and sandy gravels. With the help of innovative, automated control systems and the large crowd forces that modern drilling rigs can produce, it is feasible to construct CFA piles through hard soil layers and socket them into rock.

However, the method is most suitable for cohesive, non-granular soils:

Undrained shear strength: c_u > 15 kN/m²
No boulder presence

construction procedure for CFA pile — Construction methodology for CFA piles

Although longer piles have rarely been utilized, CFA piles are normally constructed with diameters ranging from 0.3 to 0.9 m (12 to 36 in.) and lengths up to 30 m (100 ft). Because less powerful rigs have historically been employed for commercial operations with these piles in the United States, the practice has often leaned toward smaller piles with diameters of 0.3 to 0.6 m (12 to 24 in.). In Europe, bigger diameters [up to 1.5 m (60 in.)] have been used.

The reinforcement cage of CFA piles is often confined to the upper 10 to 15 m (33 to 50 ft) of the pile for ease of installation and also due to the fact that in many cases, relatively low bending stresses are transferred below these depths. In some cases, full-length reinforcement is used, as is most common with drilled shaft foundations.

Continuous flight auger (CFA) piles can be installed as single piles or as part of a pile group. Single CFA piles are typically used for smaller structures, such as soundwalls or light poles. Pile groups are used for larger structures, such as bridges. The minimum centre-to-centre spacing between CFA piles is typically 2.5 to 4 times the diameter of the pile. However, 3 times the pile diameter spacing is commonly adopted in practice.

Construction Procedure for CFA Piles

The process of constructing CFA piles can be broken down into the following essential steps:

Preparation of site and setting up the rig
Drilling
Concrete placement
Reinforcement installation

Before starting to drill a CFA pile, a flat and stable work area must be created at the pile location to support the weight and pressure of the drilling rig. The piling positions must have been predetermined through pile setting out. The inclination of the working area should be level within 3%.

Rig — Illustration showing a typical crane-mounted CFA rig

The drilling rig is positioned so that the tip of the CFA auger is exactly at the pile location. The mast of the drilling rig is then levelled using an automatic levelling device or any other equipment available to the contractor. The bottom end of the hollow auger shaft is sealed with a disposable tip.

Once the drilling rig is in place over the pile location, the CFA drill string is rotated into the ground to the desired depth using the torque from the drilling rig’s rotary drive and the crowd pressure from the crowd winch. If necessary, the drill string can be extended using Kelly extensions.

It is important to make sure that the auger does not rotate too quickly relative to its rate of penetration. If the auger rotates too quickly, it can remove soil from the sides of the borehole and bring it to the surface, which can weaken the friction interaction between the pile and the surrounding soil.

This is especially important when the auger encounters hard layers of soil or rock, as the penetration rate will be slower. The speed of rotation of the auger should be adjusted accordingly to ensure that the penetration rate is optimal.

Once the drilling rig reaches the desired depth, the concrete pump is turned on and concrete is pumped through the swan neck and swivel into the hollow shaft of the CFA auger. A pressure sensor on the swan neck measures the concrete pressure. Once the hollow shaft is full of concrete, the auger is extracted.

During the concreting and extraction phase, the auger is not normally rotated. However, some project specifications may allow for the auger to be rotated during extraction. In this case, it is important to make sure that the auger is rotated in the same direction as it was during drilling, to avoid disturbing the soil and contaminating the concrete.

In the CFA method, unlike other piling methods, the reinforcing cage is inserted into the borehole after it has been filled with concrete. Depending on the design, this cage can cover a portion of the pile’s depth or extend to the full depth of the pile. It is important to start the installation of the reinforcement cage immediately after pouring the concrete.

Typically, the reinforcing cage will naturally sink to depths of approximately 6 to 10 meters due to its weight, but for deeper depths, a vibrator is required to push the cage down to its intended position. In such cases, it is essential to weld the sections of the rebar cage together. A minimum concrete cover of 75mm is often adopted in piles.

Advantages and Limitations of CFA Piles

Continuous flight auger (CFA) piles have been used more often in private and commercial construction works than in transportation projects. There are several reasons for this trend. Some are related to the technology of CFA piles themselves, while others are due to institutional perceptions.

Favourable Geotechnical Conditions for CFA Piles

CFA piles generally work well in the following types of soil conditions:

• Medium to very stiff clay soils. In these soils, the shaft friction can provide the needed capacity within a depth of approximately 25 m (80 ft) below the ground surface. The major advantage of cohesive soils for CFA pile construction is that clays are generally stable during drilling and less subject to concerns about soil mining during drilling.

• Cemented sands or weak limestone. These soils are favourable if the materials do not contain layers that are too strong to be drilled using continuous flight augers. In cemented materials, it is not so critical that the cuttings on the auger maintain the stability of the hole. In addition, CFA piles can often produce excellent side-shear resistance in cemented materials because of the high side resistance created by the rough sidewall and good bond achieved using cast-in-place concrete.

• Residual soils. Residual soils, particularly silty or clayey soils that have a small amount of cohesion, are favourable for CFA pile installation because installation can be particularly fast and economical.

• Medium dense to dense silty sands and well-graded sands. These sands, even when containing some gravel, are commonly favourable. This is especially true if the groundwater table is deeper than the pile length.

• Rock overlain by stiff or cemented deposits. CFA piles can achieve significant end-bearing capacity on rock, provided that the overlying soil deposits are sufficiently competent to allow installation to the rock without excessive flighting. Flighting is the lifting of soil on the auger as the auger turns, in the manner of an Archimedes pump. Rock that is directly overlain by strong material or a transitional zone is well suited.

Static Capacity of CFA Piles

The static capacity of a CFA pile is somewhere between that of a drilled shaft and a driven pile. This is because the changes in lateral stress during installation are different for each type of pile. For CFA piles, the stresses in the soil remain similar to the pre-construction values (like a drilled shaft). For drilled displacement piles, the stresses in the surrounding soil increase (like a driven pile).

We can estimate the static capacity of CFA piles using methods developed for driven piles and drilled shafts, because their load-settlement behavior is similar. However, some methods have been developed specifically for CFA piles, and these methods are usually modifications of methods previously developed for drilled shafts or driven piles.

Similar to other types of deep foundations, the total axial compressive resistance (R_T) of a CFA pile is calculated as the combination of the side-shear resistance (R_S), and end-bearing resistance (R_B):

R_T = R_S + R_B

To calculate the shaft resistance, the pile length must first be divided into N pile segments. The side resistance of a particular pile segment “i” (of length L_i, and diameter, D_i) is obtained by multiplying the unit shaft friction resistance (f_s,isometimes referred to as load or transfer rate) of the segment by the surface area of the pile segment (π D_i L_i). The total shaft resistance is obtained by adding the contribution of all N pile segments as:

R_S = ∑f_s,iπ D_i L_i

Some of the methods use an average unit side-shear (f_s-ave) for the entire pile length, instead of summing individual pile segments. In these cases, the total side-shear resistance is calculated as:

R_S = f_s,aveπDL

where D is the average diameter of the pile, and L is the pile total embedment length.

The total end-bearing resistance (R_B) is calculated as:

R_B = q_pA_b

where q_p is the unit end-bearing resistance, and A_b is the cross-sectional area of the pile at the base.

Conclusion

CFA piles are a versatile and widely used type of deep foundation that can be used in a variety of applications, including:

Supporting heavily loaded structures, such as bridges, buildings, and towers
Transmitting loads through soft or unstable soil layers
Providing resistance to lateral loads, such as wind and seismic loads

CFA piles are constructed using a continuous flight auger (CFA) machine, which drills a hole into the ground after which concrete is poured into the hole. The CFA machine is equipped with a hollow auger that rotates and advances into the ground. When the embedment depth is reached, concrete is pumped down the hollow auger and into the hole as the auger is withdrawn.

The design of CFA piles is similar to the design of other types of deep foundations, such as drilled shafts and driven piles. The design process takes into account the load requirements, the soil conditions, and the specific characteristics of the CFA pile. Despite some inherent challenges challenges, CFA piles have become a popular choice for a wide range of projects due to their versatility, cost-effectiveness, and reliability.

Analysis and Properties of Plastic Sections

By

Ubani Obinna

-

September 11, 2023

In structural engineering designs, plastic section properties are used to analyze and design structural members that can withstand plastic deformation (such as structural steel). Plastic deformation is a permanent, non-reversible deformation that occurs when a material reaches its yield point.

According to clause 5.6 of EN 1993-1-1:2005, class 1 steel sections may be designed using plastic global analysis. The stress distributions in the elastic and fully plastic states for the general case of a steel section that is symmetrical about the plane of bending are shown in the picture below.

development of plastic hinge — Development of plastic hinge in an I-section

Tensile and compressive forces need to be equal for normal forces to be in equilibrium. This state is attained when the bending stress varies from zero at the neutral axis to a maximum at the extreme fibres. This is true especially when the neutral axis passes through the centroid of the section.

In a fully plastic state, equilibrium is attained when the neutral axis divides the section into two equal areas, since the stress at that state is equal to the yield stress of the material. Therefore,

M_pl = (first moment of area about the plastic neutral axis)f_y

Where;
M_pl = plastic moment
f_y = yield strength of the material

Key plastic section parameters

Usually, in the design of steel structures, plastic section properties are a set of properties that describe the ability of a cross-section to resist plastic bending. These properties include the plastic section modulus, the plastic moment of inertia, and the plastic rotation capacity.

(1) Plastic Moment (M_p): The plastic moment, denoted as M_p, is the maximum moment that a structural section can resist before it undergoes plastic deformation. It is a measure of the section’s capacity to resist bending without failing. The plastic moment can be calculated using the formula:

M_p = f_yZ_p

where:
f_y is the yield strength of the material.
Z_p is the plastic section modulus, a property that quantifies the distribution of material around the section’s centroid.

(2) Plastic Section Modulus (Z_p): The plastic section modulus, Z_p, represents the ability of a structural section to resist plastic bending about a particular axis. The plastic section modulus is an important parameter in plastic design because it determines how much bending moment a section can sustain without undergoing plastic deformation.

(3) Plastic Neutral Axis (PNA): The plastic neutral axis is the location within a structural section where the moment arm is maximized, resulting in the maximum moment capacity.

(4) Plastic Section Shape Factor (α): The plastic section shape factor, denoted as α, is a dimensionless parameter that relates the plastic section modulus of a given shape to that of a reference shape (usually a rectangle). It is used to compare the plastic bending capacity of different section shapes while keeping the same material properties.

Solved Example

Determine the plastic section moduli about the y–y and z–z axes for the ‘I’ section shown in the figure below. The section is for a 457×191×98 kg/m Universal Beam with the root radius omitted.

To determine the plastic section modulus about the y–y axis divide the section into A₁ and A₂ as shown in the figure below where;

A₁ = (h/2) × t_w = (467.2/2) × 11.4 = 2663.04 mm²
A₂ = (b_f − t_w)t_f = (192.8 − 11.4) × 19.6 = 3555.44 mm²

z₁ = h/4 = 467.2/4 = 116.8 mm
z₂ = (h – t_f)/2 = (467.2 − 19.6)/2 = 223.8 mm

Plastic section modulus
W_ply = 2(A₁z₁ + A₂z₂) = 2(2663.04 × 116.8 + 3555.44 × 223.8) = 2213501.088 mm³ = 2213.5 cm³

The value obtained from Section Tables is 2230 cm³ which is slightly greater because of the additional material at the root radius.

Similarly, for the plastic section modulus about the z–z axis divide the section into areas A₃ and A₄ as shown in the Figure below where;

A₃ = [(h – 2t_f)t_w]/2 = [(467.2 – 2×19.6) × 11.4]/2 = 2439.6 mm²
A₄ = 2(b_f/2)t_f = 2(192.8/2) × 19.6 = 3778.88 mm²
y₃ = t_w/4 = 11.4/4 = 2.85 mm
y₄ = b_f/4 =192.8/4 = 48.2 mm

Plastic section modulus
W_plz = 2(A₃y₃ + A₄y₄) = 2(2439.6 × 2.85 + 3778.88 × 48.2) = 378189.752 mm³ = 378.189 cm³

The value obtained from Section Tables is 379 cm³which is slightly greater because of the additional material at the root radius.

Design of Timber Shear Walls | Studs

By

Ubani Obinna

-

August 10, 2023

Timber shear (stud) walls are an essential part of the structural system of timber structures/buildings. They are typically made up of a frame of vertical timber studs sheathed with plywood or other structural sheet material.

In the design of timber frame structures, one of the significant functions of walls is to provide load-bearing support and stability for vertical actions from the floor (decking) and roof (rafters or trusses), and also to provide strength and stability against the effects of lateral actions. These walls also accommodate various architectural features such as doors, windows, and built-in shelving.

details of stud walling — **Figure 1:** Details of a typical stud wall: (a) elevation; ( b) section; (c) typical fixing of top and bottom plates to studs

A timber stud wall is a type of wall that is made up of a frame of vertical timber studs (structural wooden posts), which are spaced evenly apart and held in place by horizontal plates at the top (header plates) and bottom (sole plates) of the wall. The studs are typically made of 75mm x 50mm or 100mm x 50mm sawn timber, and the spacing between them is typically between 450mm to 600mm.

Timber shear walls provide lateral resistance to wind and seismic forces, helping to keep the structure from undergoing failure due to lateral actions. The plywood sheathing helps to transfer the lateral forces to the studs, which then resists the forces by bending and shearing.

timber stud walling construction — **Figure 2:** Timber stud wall construction

Design of Stud Walls

As stated above, the vertical components in a timber shear wall system are commonly known as studs, while the walls are typically referred to as stud walls. These studs are aligned with their stronger axis (y-y) parallel to the wall’s surface and are securely positioned by the header and sole plates. Battens or noggins are utilized for in-plane stability, preventing lateral movement through diagonal or equivalent bracing members. These battens serve a dual purpose, both during construction and in persistent design scenarios.

In situations where the wall sheathing cannot provide sufficient lateral resistance, the use of diagonal or equivalent bracing (noggins) compensates for this. In such cases, the effective length of the stud around the z-z axis is determined by the longest span of stud between the plate and batten support.

When the sheathing material can provide adequate lateral restraint, concerns about stud buckling around the z-z axis can be disregarded. The sheathing material provided it is fixed to the studs and plates as per the manufacturer’s guidelines or design requirements, offers satisfactory lateral resistance. However, if sheathing is affixed to only one side of the wall, complete lateral restraint for the studs is not achieved, necessitating the use of a reduced effective length.

Stud walls are unlikely to exhibit any form of fixity at their ends. In the case of out-of-plane buckling around the y-y axis, the studs are deemed to be securely held in place and torsionally restrained by the fastenings to the header and sole plates. Nonetheless, these studs are allowed to rotate laterally at these points. Consequently, the effective length of the stud in relation to this axis is assumed to be equivalent to the height of the stud wall.

Timber stud analysis and design example (EN1995-1-1:2004)

In accordance with EN1995-1-1:2004 + A2:2014 incorporating corrigendum June 2006 and the UK national annex.

Stud details
Description; 47 x 125 C24 timber studs
Restraint in plane of panel; Sheathing
Stud spacing; s_Stud = 600 mm
Stud height; l_Stud = 2800 mm
Panel height; l_Panel = l_Stud + 2b = 2894 mm

Forces input on Stud
Lateral wind load; H_{W_Z0_Stud} = 1.50 kN/m²
Permanent distributed load on top rail; L_{G_Stud} = 5.60 kN/m
Imposed distributed load on top rail; L_{Q_Stud} = 8.40 kN/m

Stud loading details

Lateral wind load;
p_W,h0 = H_{W_Z0_Stud} × s_Stud = 0.90 kN/m

Total vertical permanent point load (2800 mm);
P_{G_1} = L_{G_Stud} × s_Stud = 3.36 kN

Total vertical imposed point load (2800 mm);
P_{Q_1} = L_{Q_Stud} × s_Stud = 5.04 kN

Member Loads

The summary of the member loads is shown in the Table below.

Member	Load case	Load Type	Orientation	Description
Member	Permanent	Point load	GlobalZ	3.36 kN at 2.8 m
Member	Imposed	Point load	GlobalZ	5.04 kN at 2.8 m
Member	Wind	UDL	GlobalX	0.9 kN/m at 0 m to 2.8 m

Loading Combinations

The load combinations used in the analysis of the structure are shown in the Table below.

Load combination	Permanent	Imposed	Snow	Wind
1.35G + 1.5Q (Strength)	1.35	1.50	0.00	0.00
1.35G + 1.5Q + ψ_S1.5S + ψ_W1.50W (Strength)	1.35	1.50	0.75	0.75
1.0G + 1.5W (Strength)	1.00	0.00	0.00	1.50
1.00G + 1.0Q (Service)	1.00	1.00	0.00	0.00
1.00G + 1.0Q + ψ_S1.0S +ψ_W1.0W (Service)	1.00	1.00	0.50	0.50
1.0G + 1.0W (Service)	1.00	0.00	0.00	1.00

Support reactions

The support reactions from the load combinations are shown below.

Load case/combination	Fx (kN)	Fz (kN)
1.35G + 1.50Q (Strength)	0	12.2
1.35G + 1.50Q + ψ_S1.50S + ψ_W1.50W (Strength)	-1.9	12.2
1.0G + 1.50W (Strength)	-3.8	3.4
1.00G + 1.00Q (Service)	0	8.5
1.00G + 1.00Q + ψ_S1.00S + ψ_W1.00W (Service)	-1.3	8.5
1.0G + 1.00W (Service)	-2.5	3.4

Member Envelope (Strength)

Position (m)	Shear force (kN)		Moment (kNm)
0	1.9 (max abs)	0	0
1.4	0		1.3 (max)	0
2.8	0	-1.9	0

Partial factor for material properties – Table 2.3;
γ_M = 1.300

Member details
Load duration – cl.2.3.1.2; Short-term
Service class – cl.2.3.1.3; 2

Timber section details
Number of timber sections in member; N = 1
Breadth of sections; b = 47 mm
Depth of sections; h = 125 mm
Timber strength class – EN 338:2016 Table 1; C24

Bearing length; L_b = 100 mm

Modification factors
Duration of load and moisture content – Table 3.1; k_mod = 0.9
Deformation factor – Table 3.2; k_def = 0.8
Depth factor for bending – Major axis – exp.3.1; k_h,m,y = min((150 mm / h)^0.2, 1.3) = 1.037
Bending stress re-distribution factor – cl.6.1.6(2); k_m = 0.7
Crack factor for shear resistance – cl.6.1.7(2); k_cr = 0.67
Load configuration factor – cl.6.1.5(4); k_c,90 = 1
System strength factor – cl.6.6; k_sys = 1.1

Check compression parallel to the grain – cl.6.1.4

Design axial compression; P_d = 3.428 kN
Design compressive stress; σ_c,0,d = P_d / A = 0.583 N/mm²
Design compressive strength; f_c,0,d = k_mod × k_sys × f_c.0.k / γ_M = 15.992 N/mm²
σ_c,0,d / f_c,0,d = 0.036

PASS – Design parallel compression strength exceeds design parallel compression stress

Compression perpendicular to the grain – cl.6.1.5

Design perpendicular compression – major axis; F_c,y,90,d = 1.89 kN
Effective contact length; L_b,ef = L_b = 100 mm

Design perpendicular compressive stress – exp.6.4;
σ_c,y,90,d = F_c,y,90,d / (b × L_b,ef) = 0.402 N/mm²

Design perpendicular compressive strength;
f_c,y,90,d = k_mod × k_sys × f_c.90.k / γ_M = 1.904 N/mm²
σ_c,y,90,d / (k_c,90 × f_c,y,90,d) = 0.211

PASS – Design perpendicular compression strength exceeds design perpendicular compression stress

Check shear force – Section 6.1.7

Design shear force; F_y,d = 1.89 kN
Design shear stress – exp.6.60; τ_y,d = 1.5F_y,d / (k_cr bh) = 0.720 N/mm²

Design shear strength;
f_v,y,d = k_mod × k_sys × f_v.k / γ_M = 3.046 N/mm²
τ_y,d / f_v,y,d = 0.236

PASS – Design shear strength exceeds design shear stress

Compression or combined compression and bending – cl.6.3.2

Effective length for y-axis bending;
L_e,y = 0.9 × 2800 mm = 2520 mm

Slenderness ratio;
λ_y = L_e,y / i_y = 69.836

Relative slenderness ratio – exp. 6.21;
λ_rel,y = λ_y / π × √(f_c.0.k / E_0.05) = 1.184

Effective length for z-axis bending; L_e,z = 0 mm

Slenderness ratio;
λ_z = L_e,z / i_z = 0

Relative slenderness ratio – exp. 6.22;
λ_rel,z = λ_z / π × √(f_c.0.k / E_0.05) = 0

λ_rel,y > 0.3 column stability check is required

Straightness factor; β_c = 0.2

Instability factors – exp.6.25, 6.26, 6.27 & 6.28;
k_y = 0.5 × (1 + β_c(λ_rel,y – 0.3) + λ_rel,y²) = 1.290
k_z = 0.5 × (1 + β_c(λ_rel,z – 0.3) + λ_rel,z²) = 0.470
k_c,y = 1 / (k_y + √(k_y² – l_rel,y²)) = 0.556
k_c,z = 1 / (k_z + √(k_z² – l_rel,z²)) = 1.064

Column stability checks – exp.6.23 & 6.24;
σ_c,0,d / (k_c,y f_c,0,d) = 0.066
σ_c,0,d / (k_c,zf_c,0,d) = 0.034

PASS – Column stability is acceptable

Check design 1400 mm along span (Mid-span)

Check bending moment – Section 6.1.6

Design bending moment; M_y,d = 1.323 kNm
Design bending stress; σ_m,y,d = M_y,d / W_y = 10.809 N/mm²

Design bending strength;
f_m,y,d = k_h,m,y × k_mod × k_sys × f_m.k / γ_M = 18.956 N/mm²
σ_m,y,d / f_m,y,d = 0.57

PASS – Design bending strength exceeds design bending stress

Combined bending and axial compression – Section 6.2.4

Combined loading checks – exp.6.19 & 6.20;
(σ_c,0,d / f_c,0,d)² + σ_m,y,d / f_m,y,d = 0.572
(σ_c,0,d / f_c,0,d)² + k_m × σ_m,y,d / f_m,y,d = 0.400

PASS – Combined bending and axial compression utilisation is acceptable

Compression or combined compression and bending – cl.6.3.2

Effective length for y-axis bending;
L_e,y = 0.9 × 2800 mm = 2520 mm

Slenderness ratio;
λ_y = L_e,y / i_y = 69.836

Relative slenderness ratio – exp. 6.21;
λ_rel,y = λ_y / π × √(f_c.0.k / E_0.05) = 1.184

Effective length for z-axis bending;
L_e,z = 0 mm

Slenderness ratio;
l_z = L_e,z / i_z = 0

Relative slenderness ratio – exp. 6.22;
λ_rel,z = λ_z / π × √(f_c.0.k / E_0.05)= 0

l_rel,y > 0.3 column stability check is required

Straightness factor; β_c = 0.2

Instability factors – exp.6.25, 6.26, 6.27 & 6.28;
k_y = 0.5(1 + β_c(λ_rel,y – 0.3) + λ_rel,y²) = 1.290
k_z = 0.5(1 + β_c(λ_rel,z – 0.3) + λ_rel,z²) = 0.470
k_c,y = 1 / (k_y + √(k_y² – λ_rel,y²)) = 0.556
k_c,z = 1 / (k_z + √(k_z² – λ_rel,z²)) = 1.064

Column stability checks – exp.6.23 & 6.24;
σ_c,0,d / (k_c,yf_c,0,d) + σ_m,y,d / f_m,y,d = 0.636
σ_c,0,d / (k_c,zf_c,0,d) + σ_m × s_m,y,d / f_m,y,d = 0.433
PASS – Column stability is acceptable

Check beams subjected to either bending or combined bending and compression – cl.6.3.3

Lateral buckling factor – exp.6.34; k_crit = 1.000

Beam stability check – exp.6.35;
(σ_m,y,d / (k_critf_m,y,d))² + σ_c,0,d / (k_c,zf_c,0,d) = 0.359
PASS – Beam stability is acceptable

Conclusion

Timber shear wall design in accordance with the Eurocodes involves the structural analysis and design of timber-framed walls (stud walls) to resist gravity (such as floor and roof loads) and lateral loads (such as wind or seismic forces). Timber shear walls are typically made up of a frame of vertical timber studs, which are sheathed with plywood or other structural sheet material. The plywood sheathing helps to transfer the lateral forces to the studs, which then resist the forces by bending and shearing.

The structural design of timber shear walls involves the determination of the appropriate timber stud section, grade, spacing, and sheating material that will effecively and economically resist the anticipated design loading. The design must therefore take into account a number of factors, including the wind and seismic loads that the wall will be subjected to, the height and length of the wall, the type and thickness of the plywood sheathing, the size and spacing of the timber studs, and the type of connections between the studs and the plywood sheathing.

In addition to the design standards, the structural design of timber shear walls must also consider the following factors: the moisture content of the timber, the fire resistance requirements of the wall, the insulation requirements of the wall, and the cost of the wall. By carefully considering all of these factors, the structural engineer can design timber shear walls that are strong, stable, and cost-effective.

Analysis of Coupled Shear Walls

By

Ubani Obinna Uzodimma

-

August 6, 2023

When two shear walls are connected intermittently with rigid beams or links, a coupled shear wall structure is formed. In coupled shear walls, the structural response of the two shear walls is linked to each other, influenced by the stiffness of the connecting beams. Coupled shear walls have found a variety of applications in the design of tall buildings, and other earthquake-resistant structural systems.

The effect of wind becomes more influential as a building gets taller. To effectively resist the force from wind, shear walls, frames, or a combination of both structural forms are normally employed in tall buildings. When shear walls have openings (pierced) which may serve for aesthetic, lighting or ventilation purposes, the behaviour of the shear wall is coupled to some degree.

The coupling beams, which connect the shear walls, play a crucial role in the behaviour of coupled shear walls. These beams are specifically designed to exhibit ductile inelastic behaviour, meaning they can undergo significant deformation without failure. This ductility allows them to dissipate energy during seismic events, effectively absorbing and distributing the lateral forces throughout the structure.

Furthermore, the dissipation of energy in coupled shear walls relies on the yield moment capacity and plastic rotation capacity of the coupling beams. When the yield moment capacity is excessively high, the beams experience limited rotations and dissipate minimal energy. Conversely, if the yield moment capacity is too low, the beams may undergo rotations exceeding their plastic rotation capacities.

Consequently, it is very important to design the coupling beams to have an optimal level of yield moment capacities, which are contingent upon the available plastic rotation capacity in the beams.

Advantages of Coupled Shear Walls over Planar Shear Walls

The arrangement of coupled shear walls provides several advantages over regular shear walls or other lateral load-resisting systems:

Enhanced stiffness: The coupling of multiple shear walls significantly increases the overall stiffness of the structure, reducing lateral deflections and sway during wind or seismic events.
Improved load distribution: The coupling beams ensure a more even distribution of lateral loads across the shear walls, preventing localized stress concentrations and improving the overall load-carrying capacity of the system.
Architectural flexibility: Coupled shear walls offer architectural flexibility, allowing for larger open spaces and creative designs, as the lateral stability is not solely dependent on the positioning of walls.
Seismic resilience: The ductile behaviour of the coupling beams helps dissipate seismic energy, making coupled shear walls particularly effective in earthquake-prone regions, where they can significantly enhance a building’s seismic resilience.
Cost-effectiveness: Compared to other lateral load-resisting systems like moment frames or braced frames, coupled shear walls can provide a cost-effective solution while still offering excellent performance

This aericle explores the wind load analysis of coupled shear wall structures with a fully solved example, under the following assumptions;

(i) The entire wind load is transferred to the shear walls (the contribution of the frames have been neglected)
(ii) The wind load acts as a uniformly distributed force of F/H

The two main parameters that define the behaviour of pierced shear walls are alpha(α) and beta (β), which depend on the geometrical properties of the coupling/connecting media (beams or floor slabs) and the shear wall. For fairly symmetrical arrangements as shown below, the following relationships given below can be used for the purpose of analysis.

N/B: This is a curtailed information; kindly consult specialist textbooks/publications for full knowledge of the subject.

The value of Kv can be obtained from the table below;

Solved Example

The structural arrangement of a tall building is shown below. The building is 90m tall, with 30 storeys @3m storey height. We are to determine the internal forces induced in the shear walls due to the wind load.

Building Data:
Height of building (H) = 90m
Storey height (h) = 3m
Thickness of shear wall (t) = 0.35m
Depth of connecting beam (d) = 900mm
Width of opening (b) = 2500mm
Centreline of connected walls (L) = 8000mm
Basic wind speed = 40 m/s

Wind Load Analysis (Eurocode 1 Part 4)

(a) Basic wind velocity
The fundamental value of the basic wind velocity V_b,0 is the characteristic 10-minute mean wind velocity irrespective of wind direction and time of the year, at 10 m above ground level in open-country terrain with low vegetation such as grass, and with isolated obstacles with separations of at least 20 obstacle heights.

The basic wind velocity V_b,0 is calculated from;

V_b = C_dir .C_season .V_b,0

Where:
V_b is the basic wind velocity defined as a function of wind direction and time of the year at 10m above the ground of terrain category II
V_b,0 is the fundamental value of the basic wind velocity
C_dir is the directional factor (defined in the National Annex, but recommended value is 1.0)
C_season is the season factor (defined in the National Annex, but recommended value is 1.0)

For the area and location of the building that we are considering;

Basic wind velocity V_b,0 = 40 m/s
V_b = C_dir .C_season . V_b,0 = 1.0 × 1.0 × 40 = 40 m/s

(b) Mean Wind
The mean wind velocity V_m(z) at a height z above the terrain depends on the terrain roughness and orography, and on the basic wind velocity, V_b, and should be determined using the expression below;

V_m(z) = c_r(z). c_o(z).V_b

Where;
c_r(z) is the roughness factor (defined below)
c_o(z) is the orography factor often taken as 1.0

The terrain roughness factor accounts for the variability of the mean wind velocity at the site of the structure due to the height above the ground level and the ground roughness of the terrain upwind of the structure in the wind direction considered. Terrain categories and parameters are shown in the table below;

c_r(z) = k_r. In (z/z₀) for z_min ≤ z ≤ z_max
c_r(z) = c_r.(z_min) for z ≤ z_min

Where:
Z₀ is the roughness length
Kr is the terrain factor depending on the roughness length Z₀ calculated using
Kr = 0.19 (Z₀/Z_0,II )^0.07
Where:
Z_0,II = 0.05m (terrain category II)
Z_min is the minimum height
Z_max is to be taken as 200 m
Kr = 0.19 (0.05/0.05)^0.07 = 0.19
c_r(z) = kr. In (z/z₀) = 0.19 × In(90/0.05) = 1.424

Therefore;
V_m(90) = c_r(z).c_o(z).V_b = 1.424 × 1.0 × 40 = 56.96 m/s

(c) Wind turbulence
The turbulence intensity I_v(z) at height z is defined as the standard deviation of the turbulence divided by the mean wind velocity. The recommended rules for the determination of I_v(z) are given in the expressions below;

I_v(z) = σ_v/V_m = k₁/(c₀(z).In(z/z₀)) for z_min ≤ z ≤ z_max

I_v(z) = I_v.(z_min) for z ≤ z_min

Where:
k_I is the turbulence factor of which the value is provided in the National Annex but the recommended value is 1.0
C_o is the orography factor described above
Z₀ is the roughness length described above.
For the building that we are considering, the wind turbulence factor at 90m above the ground level;

I_v(90) = σ_v/V_m = k₁ / (c₀ (z).In (z/z₀)) = 1/(1 × In(90/0.05) ) = 0.1334

(d) Peak Velocity Pressure
The peak velocity pressure q_p(z) at height z is given by the expression below;

q_p(z) = [1 + 7I_v(z)] 0.5.ρ.V_m²(z)= c_e(z).q_b

Where:
ρ is the air density, which depends on the altitude, temperature, and barometric pressure to be expected in the region during wind storms (recommended value is 1.25kg/m³)

c_e(z) is the exposure factor given by;
c_e(z)= (q_p(z))/q_b
q_b is the basic velocity pressure given by;
q_b = 1/2.ρ.V_b²

q_p(90m) = [1 + 7(0.1334)] × 1/2 × 1.25 × 56.96² = 3921.313 N/m²
Therefore, q_p(90m) = 3.921 kN/m²

(e) Wind Pressure Coefficient

h/d = 90/22.5 = 4
Pressure coefficient for windward side (zone D) = +0.8
Pressure coefficient for leeward side (zone E) = -0.65 (from linear interpolation)

Net pressure coefficient = 0.8 – (-0.65) = 1.45

According to clause 7.2.2(2), the force generated from zone D and E simultaneously should be corrected for lack of correlation.

Since h/d = 4 in our calculation, we have to interpolate between h/d ≥ 5(1.0) and h/d ≤ 1.0 (0.85).

On interpolating;
Correction factor = 0.9625
Therefore, net wind pressure = 0.9625 × 1.45 × 3.921 = 5.472 kN/m²

IV Structural Analysis

The wind force of the structure;
F = 5.472 kN/m² × 24m × 90m = 11819.52 kN (taking structural factor as 1.0 because building is less than 100m tall, and h/d = 4)

If we assume that this load is shared equally among the two shear walls, then the load on each shear wall = 5909.76 kN

Geometrical Properties of Elements
Area of shear walls = A₁ = A₂ = 0.35 × 5.5 = 1.925 m²
Second moment of area of walls = I₁ = I₂ = (0.35 × 5.5³)/12 = 4.852 m⁴
Moment of inertia of connecting beam I_b = (0.35 × 0.9³)/12 = 0.02126 m⁴

b_e = (2b + 5d)/3 = [(2 × 2.5) + (5 × 0.9)] / 3 = 3.167

αH = 19.962
Therefore, the axial force (N) at the bottom of wall;

The bending moment at the bottom of the wall elements;

The shear force at the connecting beams;

The bending moment on the connecting beams;

These internal forces should be factored, and combined with other appropriate load cases for the purpose of design.

Thank you for reading.
Join our Facebook page for more at
www.facebook.com/structville

Design and Construction of Steel Staircase | Industrial Staircase

By

Ubani Obinna

-

August 5, 2023

Table of Contents

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

-

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

-

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

The Need for Joints in Buildings

Expansion Joints

Spacing of Expansion Joints

Calculation of Expansion Joint Spacing (Single Storey Buildings)

Conclusion

References

Contraction Joints

Joint Configuration

Joint Location

Conclusion

References

Core Curriculum for Civil Engineering

Core Courses in Civil Engineering

Fluid Mechanics

Strength of Materials

Structural Mechanics/Theory of Structures

Soil Mechanics

Design of Structures I

Design of Structures II

Civil Engineering Materials

Environmental Engineering

Highway and Transportation Engineering

Geotechnical Engineering

Construction Management

Construction Procedure for CFA Piles

Advantages and Limitations of CFA Piles

Favourable Geotechnical Conditions for CFA Piles

Static Capacity of CFA Piles

Conclusion

Key plastic section parameters

Solved Example

Design of Stud Walls

Timber stud analysis and design example (EN1995-1-1:2004)

Conclusion

Advantages of Coupled Shear Walls over Planar Shear Walls

Solved Example

Geometry of Steel staircase

Dynamics of Steel Staircase Structures

Design of Steel Staircase

Forms of Construction

Conclusion

Steel Pylons

Concrete Pylons

Pylon Geometry

Cable Stay Connection to the Pylons

Conclusion

The Transformation of Bridge Inspections

Automated Image and Data Collection

AI-Driven Defect Detection

Enhanced Structural Analysis

Predictive Maintenance and Lifecycle Management

Overcoming Challenges and Limitations

Building Trust in AI-Driven Inspections

Advancements in AI Technology for Bridges

Embracing the Future of Bridge Inspections

Conclusion

EDITOR PICKS

POPULAR POSTS

POPULAR CATEGORY

ABOUT US

FOLLOW US