Overview on the Design of Cable Structures

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September 18, 2022

Table of Contents

Steel cables are frequently used within form-based structures in the family of designs known as lightweight tension structures. For a variety of reasons, the solutions are appealing for unique constructions like roofs and bridges. Cables have a high strength capacity that is around three times that of standard steel, and because of their low weight per unit of strength, less steel is needed to support weights.

Reduced structural sections and self-weight can result in considerable gains in overall structural efficiencies and costs because self-weight loading can make up the majority of the loading that needs to be resisted in large bridges and roofs. Due to their narrow cross-section, cables are appealing in applications that aim to optimise transparency, such as supporting glass facades, and reduce shadowing, such as supporting roofs.

moses mabhida stadium South Africa — 3D Rendering of Moses Mabhida Stadium, South Africa

The low bending stiffness of cables is not a limitation, but rather a unique property that gives engineers several design options. In order to ensure that cables withstand forces effectively under axial stress, many lightweight cable systems are purposefully form-found. However, cables can be designed to handle lateral load, ‘compression’, and tension forces.

In Eurocode 3 (Part 11), cables are categorised under group B of tension components. They usually comprise of wires which are anchored in sockets or other end terminations and are fabricated primarily in the diameter range of 5mm to 160 mm.

Spiral strand ropes are spiral rope comprising only round wires. They are normally used for stay cables for aerials, smoke stacks, masts and bridges. They are also used as hangers or suspenders for suspension bridges, stabilizing cables for cable nets and wood and steel trusses, and hand-rail cables for banisters, balconies, bridge rails and guardrails.

Fully locked coiled rope is a spiral rope having an outer layer of fully locked Z-shaped wires. They are fabricated in the diameter range of 20 mm to 180 mm and are mainly used as stay cables, suspension cables and hangers for bridge construction, suspension cables and stabilizing cables in cable trusses, edge cables for cable nets, and stay cables for pylons, masts, and aerials.

Structural strand ropes are mainly used as stay cables for masts, aerials, hangers for suspension bridges, damper / spacer tie cables between stay cables, edge cables for fabric membranes, rail cables for banister, balcony, bridge, and guide rails.

Load Resistance of Cables

The ways in which cables resist load could be by tension, compression, or lateral load resistance.

(1) Tension Load

Guy cables conveying axial load from end to end are the most frequent occurrence of axial tension in cables. The performance is characterised by elastic stiffness, and the behaviour is roughly comparable to that of any tension element, be it a beam or a rod. However, “tension stiffness” becomes important if the tensile stress is significant.

(2) Compression Load

Cables can only resist compression if prestressed by self-weight or an internal self stress. However, the net axial load must be tension.

(3) Lateral Load

The initial elastic stiffness and lateral load resistance of cables are quite low. Instead of bending to resist the load, they will shift to an equilibrium position where they can resist it by applying axial stress to the cable. The shape changes to a catenary for a cable that is uniformly loaded. Although this is a well-known form, it rarely appears in such a pure sense in actual practise. Since cables are frequently loaded at specific locations along their length, the equilibrium form develops facets.

Linear, Non-Linear and Large Displacement Behaviour of Cable Structures

The level of analysis and evaluation necessary for cable structures can be very imprecise. The following sources of non-linearity in cable systems:

Individual cable elements loaded axially or laterally experience tension stiffening.
displacements of the entire system, which are typically regarded as “large” displacements, such as cables becoming slack and leaving the main structural system.
a cable system’s overall state of equilibrium against forces

In terms of behaviour, cable-stayed structures are similar to linear elastic structures. The consequences of non-linearity can be minimal in structural systems using “straight cables” based on applied tension and compression stresses to the cable ends, allowing for extensive initial study on straightforward linear programmes. The effects of a structure’s non-linearity will typically be minimal if it is “noded out” and may be solved by hand or computer.

Velodromo Abuja Nigeria 04 1200x800 1 — Velodrome, National Sports Complex, Abuja Nigeria

Cable structural systems laterally loaded experience minimal initial elastic resistance as they assume their equilibrium shape. These require to be analysed under loads using software that can handle the geometrically non-linear behaviour and are typically referred to as cable net constructions. In this situation, the structure can’t be classified as “noded out” or statically determined, like a Warren truss, for example.

In this case, non-linear programming are necessary even though simple manual computations can help suggest a solution. These typically solve the structural equations incrementally step-by-step to advance the structure from an initial beginning state to a final equilibrium point. Dynamic relaxation is a well-known method.

To arrive at an equilibrium figure, the initial geometry of cable net structures must be form-found. The prestress forces can be introduced into a nonlinear programme as previously described using constant force elements. This procedure involves adjusting the cable stiffnesses and specified forces until the required form is obtained.

The cable lengths and tensions are determined from this geometry, which produces the final geometry. The cables must be cut to the calculated lengths for the structure, taking into account both elastic stretch and inelastic, or “building” stretch. Engineers with experience are required to carry out this operation due to its complexity.

Structural Solutions using Cables

Tension structures categorise into a number of groups, each of whose form is tied to the function of the cables—that is, how the cable is loaded and how it resists loads. Several of these functions may be included in a complex structure, but the primary groups are depicted below;

Cable Stayed Structures

cable stayed bridge — The Tappan Zee Cable Stayed Bridge

The typical characteristics of cable stayed structures are that the cables are loaded axially from one end to the other, and the cable end nodes typically support steel beams or trusses. A typical application is for cable stayed bridges, e.g. Queen Elizabeth II Bridge. Some other applications for roofs are numerous and include the Inmos, Newport and National Dartford, and the Second Severn Crossing Exhibition Centre, Birmingham..

Suspension Structures

The cables in suspension structures are loaded laterally. Suspension bridges, like the Old Severn Crossing, are the most common application, and in these constructions, a catenary or parabolic cable serves as the main support for the hangers and deck. The primary cable is stressed by the dead load of major suspension structures, where the dip to span ratio is typically more than 1:12. In this instance, the deflection is not much affected by the stretch of the cable.

suspension bridge JAP — The 1915 Canakkale Bridge, Turkey

Surface Stressed Structures

In structures using surface-stressed cable, the cables are first prestressed against the supporting members to create a state of self-stress before being loaded laterally. Nonlinear computations must be utilised to determine the deflections and forces because the cable extension is important for the deflections. Individual straight cables or a network of cables that are essentially at right angles to one another can make up the structure.

Depending on the 3D form, a cable net may be flat or prestressed. Calculations using displacements to the equilibrium position are the only way to determine the initial geometry since it is determined by the equilibrium of the tension forces under the first prestress forces. The final geometry is similarly only determined by calculations involving displacements to the equilibrium position and is determined by the equilibrium of the tension forces under the forces arising from the pre-stress and applied loading.

In numerous recent applications, facades are held against lateral wind loading by cables in a single flat plane. Typically, deflections are large, and cable nets have been successfully used to create aviary enclosures at Munich Zoo, as well as other notable examples like Calgary Olympic Saddledome and Munich Olympic Stadium, built in 1972.

2D Cable Trusses

Fully triangulating a cable truss allows the individual components to resist loads by applied tensions at the end nodes. However, the phrase “cable truss” is frequently (and possibly mistakenly) used to characterise systems where the cable resists load laterally and the system is not entirely triangulated (see figure below). They are an example of a surface-stressed structure specifically chosen for its funicular geometry to the most typical loading. This method has frequently been utilised to hold back vertical facades against wind loading.

3D Cable Net

The term “3D cable net” is used as a general name for some of those structures that may have cables working in diverse ways, although it does not fully characterise the nature of some sophisticated unique systems. Using straight cables that are all “noded-out,” certain constructions have been built in three dimensions that withstand loads by direct axial tension. The BA London Eye is one example of such application. The Millennium Dome, Greenwich is another example that use cables loaded laterally.

Analysis and Design Issues for Cable Structures

The following are analysis and design issues associated with cables and cable structures;

Codes of Practice:
In Europe, Eurocode 3 (EC3), Part 1-11, BS EN 1993-1-11, Design of structures with tension components, is the most pertinent design standard for cable structures. There are other industry manuals created for post-tensioned concrete and bridges contain information about cables.

Types of Steel Cables
According to Eurocode 3, types of steel cable includes spiral strand rope, strand rope, locked coil rope, and parallel wire strand.

Cable Stiffness:
Both the material modulus and the length changes brought on by winding the strands and ropes play a role in the stiffness of cables. Testing or manufacturing data must be used to get precise values. In contrast to strength, cables are typically sized for stiffness.

Working stress or load factor design:
Early cable design pioneers for buildings used a working stress design. Because some engineers believe that form-found structures are more suited to working stress design, cable structures have seen a slow transition to load factor design. The brand-new Eurocodes use a load factor approach.

Cable strength:
Manufacturers typically refer to cable strength as the Minimum Breaking Load (MBL). In the past, working load approaches with low utilisation factors in comparison to breaking strengths were used to design cables. In most cases, the maximum unfactored force is restricted to 50% MBL.

To make sure that various manufacturers are employing the same strategy for fatigue within their reported MBL, attention must be taken when converting the MBL to design values using either working stress or limit state approaches. The ultimate limit state approach is becoming more popular. Additionally, it is important to make sure that the connector designs are more robust than cables.

In EC3, an empirical factor used in the determination of minimum breaking force of a rope is obtained as follows:

K = πfk/4

where f is the fill factor for the rope and k is the spinning loss factor.

The minimum breaking force F_min is given by;

F_min = d²R_rK/1000

where d is the diameter of the rope in mm, K is the breaking force factor, R_r is the rope grade in N/mm²

Load factors:
The general non-linearity of lightweight tension structures necessitates the use of load factors with particular caution to produce a set of loading circumstances that is safe, effective, and realistic. In comparison to other structures, the behaviour of this structure in response to changes in components must be understood from first principles and at a higher level of understanding. For different steel parts in the same structure, such as steel cables and steel tubes, it may occasionally be necessary to use both a working load approach and an ultimate limit state approach.

Generally, load factors will be the same as for other buildings. Prestress should be taken into consideration with caution. Dead loading and its contributing components are sometimes grouped with prestress loading. However, the load components should be viewed as independent variables if these are not related (for instance, if the prestress is jacked into the system).

Maximum force in the lower cables and minimal force in the upper cables were crucial design considerations for the BA London Eye (to ensure they remained active and did not go slack). The load factors for prestress, which were distinct from the load factors for dead load as indicated below for two generic loadcases, were used to calculate the extreme values of forces in the cables:

load cases — Loading conditions from dead load, imposed load, prestress and wind load applied to the BA London Eye (Source: Davison and Owen, 2012)

For derivation of the maximum tension in the lower cables ‘B’:
γ_fmax G + γ_fmax Q + γ_fmax PS + γ_fmax W

For derivation of the minimum tension in the upper cables ‘A’:
γ_fmax G + γ_fmax Q + γ_fmin PS + γ_fmax W

Construction stretch and cable compensation:
It’s important to understand how design tolerances for cable length affect the final product. Pre-stretched cables should be used, and turnbuckles or other adjustable length connectors can be fitted.

Cable vibration:
It’s important to examine cables for the impacts of wind-induced vibration, such as vortex shedding or galloping, and rain-induced vibration.

Fatigue Loading:
Even if aeroelastic instabilities are not at their worst, cables still need to be examined for fatigue loading.

Cable end connectors:
Movements during installation and maintenance cause connections to spin and move substantially more than typical steelwork connections. Fork end connections are typical for cable systems and permit rotation about one axis; however, unique connections can be needed to accommodate larger-than-normal rotations along several axes.

Cable saddles and diverters:
Because cable end connections are expensive, it is preferred to pass a large-diameter cable through a joint using a saddle, clamp, or diverter, if it is practical to do so. These joints require evaluation of concerns such as axial cable stress reduction, friction capacity, acceptable bearing stress, and installation-related Poisson’s ratio impacts.

Reclaimed Asphalt: An Alternative Road Sub-base Material

By

Anuoluwapo Kolade

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September 16, 2022

Table of Contents

In road construction, a sub-base layer is an aggregate layer that lies directly on the subgrade, the native or improved material underneath a constructed road. Likewise, the base course lies directly on the sub-base layer. The sub-base course is vital for roads built to receive vehicular traffic because it is the main load-bearing layer of flexible pavement. However, it may be omitted when a road is constructed only to receive foot traffic.

Furthermore, typical materials for sub-base courses include granular fill, recycled concrete, manufactured aggregate, lean concrete, and crushed rock or concrete. However, this article will introduce you to an alternative sub-base material in reclaimed asphalt.

Reclaimed Asphalt Material

16628039505312 — *Reclamation of existing asphal*t layers

Reclaimed asphalt material consists of removed asphalt concretes from existing road infrastructures. Perhaps you may ask why reclaimed asphalt material. Because of its intended use, reclaimed asphalt material can ensure the sustainability of asphalt materials and associated technologies in the construction and rehabilitation of flexible road pavements. In addition, reclaiming asphalt materials for reuse contributes to construction waste reduction and the provision of a cost-effective material for constructing roads and highways.

Furthermore, with the ever-increasing amount of waste generated on road construction projects and disposal costs, it becomes imperative to recover and reuse these materials. Thus, road construction companies and highway agencies have doubled their efforts in ensuring that existing asphalt concrete materials are reused on road projects. One significant way to reuse removed asphalt concrete is as a sub-base material.

Full-depth Reclamation (FDR) Technique

16628038944232 — *Full-depth reclamation of asphalt and underlying layers*

There are four techniques for removing asphalt concrete for reuse:

cold in-place recycling,
hot in-place recycling,
hot in-plant recycling, and
full-depth reclamation.

The full-depth reclamation technique is usually used for recycling asphalt cement for reuse as a sub-base material. This FDR technique has grown in popularity over the past decade. Its benefits are environmental friendliness, reduced traffic disturbance, use of virgin material, and consumption of fuel and natural resources.

The FDR technique is an on-site recycling method for reclaiming asphalt from an existing road pavement, which is to be used as the sub-base material for new roadway pavement. It involves pulverizing and blending all layers of flexible pavement and part or all of the underlying base materials to provide a homogenous material upon which to place the new base and surface courses.

images 3 — *Typical FDR technique process*

Furthermore, in cases where increased bearing capacity is required, or sub-base failure has occurred, the FDR can be employed to treat or stabilize the sub-base layer by adding chemicals such as portland limestone cement, fly ash and lime. Thus, the treatment or stabilization increases the strength capacity of the sub-base course to cater to present and future traffic.

Process of Reclamation with the FDR Technique

The process of FDR includes the milling and pulverizing of asphalt concrete material with a cold reclaimer or recycling machine in one or multiple passes. The reclaimer consists of a milling drum with teeth, mixer, tamper, fluid injector and vibrator. The fluid used is water, which is usually applied from a separate water truck. However, the liquid may also be applied through the reclaimer’s onboard fluid additive system.

Road Machine 2 3 Meter Road Cold Recycling Machine Xlz2303 Road Cold Reclaimer — *Road reclaimer*

16628040414283 — Application of water from a water truck connected to a road reclaimer

Let’s look at the reclamation process in detail below.

Milling and Pulverizing

Reclaimed asphalt — *Milled asphalt concrete from a road surface*

Milling involves breaking the top asphalt layers of a flexible pavement without disturbing the underlying layers; conversely, pulverising consists of grinding and blending the already pulled-up and broken asphalt concrete during milling. In a single pass, the reclaimer often does milling and pulverising of exiting asphalt concrete simultaneously.

16628011983752 — Road reclaimer pulverising asphalt layers

16628039194022 — *Pulverised pavement layers*

Pulverising is essential because it helps sustain ground conditions and stabilize the new asphalt layer. Thus, milling and grinding in the FDR technique reaches the underlying materials of asphalt pavement as a road reclaimer can go up to about 250 to 300mm in depth.

Furthermore, there is a tendency to have big chunks of materials even after pulverising. In this case, the speed of the reclaimer can be closely monitored and reduced. The reclaimer operator can also check for worn-out teeth on the milling drum, replace them, and remove any visibly oversized materials before grading and compaction. The resulting textured material can either be used as a driving surface or as a sub-base layer to receive base and asphaltic layers.

Grading and Compaction

image editor output image39047608 1663322451254 — *Compaction of reclaimed material as sub-base layer*

After milling and pulverising, the blended material must be graded with a grader to restore the driving surface and drainage attributes to roads. Likewise, after grading, the layer must be compacted with a vibratory drum roller. However, final compaction is preferred to be done with a pneumatic tyre roller because it brings the fines and moisture of the material to the top. Thus, creating a sealing effect. After compaction and before laying the base course material, in-situ density and moisture content tests must be performed to ascertain proper compaction at a specific dry density and moisture content.

You can watch the processes highlighted above through this link.

Conclusion

Over the past decades, the practice was to remove and replace asphalt concrete layers. However, this practice has become impractical because of cost implications and environmental impact. Therefore, an alternative sub-base material used in flexible pavement construction today is reclaimed asphalt recycled through the full-depth reclamation (FDR) technique.

The FDR technique is preferred because it can correct all types of failures, even to the highest severity. It also eliminates ruts, rough areas, potholes, and all kinds of surface cracking and restores grade contours to allow for better surface drainage. The FDR technique is ideal for replacing the traditional remove and replace flexible pavement reconstruction.

Furthermore, three requirements must be satisfied for recycled or recovered asphalt concrete to be reused as sub-base material, according to the Federal Highway Administration (FHWA). These requirements are that a reclaimed asphalt material must perform well and be cost-effective and environmentally friendly.

Lastly, reclaimed asphalt materials should be reused as sub-base materials such that a road structure’s expected performance is not compromised. Furthermore, engineers, contractors and researchers must be aware of the properties of reclaimed asphalt materials, how best they can be used, the site conditions they are suited for, and the limitations associated with their use.

Therefore, engineering investigation and material tests such as compaction, in-situ density, deformation and resilient modulus must be carried out on reclaimed asphalt materials before use as a sub-base material.

Properties of Bamboo as a Structural Member in Construction

By

Ubani Obinna

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September 12, 2022

Table of Contents

Bamboo is a perennial, evergreen, hollow-stemmed plant that is woody, hard, and green in appearance. It is a member of the Poaceae family of true grass. In fact, with 91 genera and more than 1000 species, it is the largest member of the grass family. While some of its members are big, others are more normal. Around the world, bamboo can be found in a variety of climates, from chilly mountains to tropical areas. Bamboo and its derivatives have been used in construction, textile production, medicine, and as food.

types of bamboo plant — Types and parts of bamboo plant

It is important to note that not all species of bamboo can be used for construction purposes. Only a few species of bamboo, such as Guadua angustifolia (Guadua Bamboo) and Phyllostachys edulis (Moso Bamboo), have compression ratios that are nearly twice as high as those of concrete and steel, respectively.

According to Bornoma et al (2016), the bamboo-built homes remained standing and unaffected by the tremendous earthquake that rocked Colombia in 1999, but practically all concrete buildings were seriously affected. This article examines the numerous mechanical properties of bamboo and how they might be applied to architectural design and examples of potential domestic building construction.

Bamboo Anatomy and Structure

The structure of bamboo, which determines its ultimate mechanical qualities, is described in the anatomy of bamboo. The three fundamental parts of the bamboo culm are depicted below:

The above-ground stem, which may be straight or bent.
The stem base, which is the lower portion of the stem that reaches the ground.
The stem petiole, which is composed of several short sections and is the lowest part of the stem.

The internodes and nodes, also known as diaphragms, make up the culm’s structural components. Cells that are traverse-oriented or parallel to the nodes make up the nodes, whereas cells that are axially orientated make up the internodes. Since culms are typically hollow like tubes, the distance between the inner and outer surfaces of the stem is determined by the thickness of the wall. However, some species have solid culms.

Mechanical Properties of Bamboo

Along its fibre direction, bamboo has stronger mechanical qualities than across it. Natural bamboo is a viable renewable material for construction in high performance applications due to its distinct microstructural characteristics in relation to its mechanical capabilities.

Because of its readily available nature and established mechanical properties, bamboo can be utilised as an alternative to steel for masonry reinforcing. The yield tensile strength of bamboo has outperformed several materials in some tests, including steel. However, being a natural material, bamboo’s distinctive high performance differs from one kind to another; as a result, anytime mechanical property values of bamboo are mentioned, the name of the relevant bamboo type is required.

The hollow, tubular structure of bamboo, which it evolved over millennia to withstand wind forces in its native habitat, gives it its tensile strength. It is also simple to harvest and transport thanks to the structure’s low weight. Bamboo is also very affordable because of its incredibly quick growth cycle and the range of environments in which it may grow. Because grass grows so quickly and has to absorb so much CO₂, cultivating it as a building material would slow down the rate of climate change. The development of bamboo as reinforcement is encouraged by only these characteristics.

In spite of these advantages, there is still effort to be done to get over bamboo’s drawbacks. One such limitation, brought on by both temperature variations and water absorption, is contraction and expansion. Fungus and naturally occurring biodegradation-induced structural weakening in bamboo is another risk factor. Ironically, numerous nations that might gain from bamboo reinforcement also lack the resources necessary to develop it as a practical replacement for the steel they currently rely on.

Moisture Content

Raw bamboo’s moisture content (MC) is an important factor, particularly for uses in the building and construction industry and for the creation of composite materials. The bonding strength of bamboo fibres in composite goods and bamboo laminates may be negatively impacted by MC. The performance and service life of new bamboo composite materials are therefore anticipated to be significantly impacted by the moisture content.

The geometrical features of raw bamboo, such as dimensional stability, are also impacted by moisture content in addition to its effects on mechanical parameters, such as tensile strength and flexural strength. Despite the fact that many research works have looked at the impact of water absorption on the dimensional stability of raw bamboo and bamboo composite specimens, they haven’t looked at the relationship between green bamboo’s water absorption and its mechanical characteristics. Rapid fluctuations in moisture can cause bamboo layers to shrink or expand significantly, which could fracture layer bonds, particularly when bamboo is used in laminates or composites.

Therefore, before processing the raw bamboo fibres into composites or laminates, it is crucial to determine the moisture content of different sections of raw bamboo and classify the moisture content according to the location within the culm length.

Density of Bamboo

The density of bamboo typically increases on the outside surface and decreases toward the inner layers of the wall cross section, according to a number of studies. As a result, bamboo culms’ outer layers are thought to possess superior mechanical properties. However, no exhaustive and systematic investigations of the density and culm geometry of bamboo, including wall thickness, culm diameter, and culm height, have been discovered to date. The performance of bamboo may be significantly affected by the determination of sections with higher fibre densities and conceivably improved quality in terms of physical and mechanical qualities.

The properties of some bamboo species are shown below;

BAMBOO SPECIE	SL (m)	DBH (cm)	IL (cm)	NI (unit)	DW (kg)	BD (g/cm³)
*Bambusa beecheyan*a	8.97	7.80	28	32	10.50	0.670
B. dissimulator	9.52	4.58	41	23	5.19	0.780
B. malingensis	7.36	4.33	28	26	3.49	0.700
B. nutans	9.95	5.83	38	26	7.75	0.615
B. oldhamii	9.93	6.94	41	24	8.37	0.608
B. stenostachya	15.10	8.17	35	43	17.50	0.653
B. textilis	8.13	4.77	44	18	3.80	0.690
B. tulda	11.90	6.56	49	24	11.89	0.773
B. tuldoides	9.15	4.26	46	19	3.75	0.620
B. ventricosa	9.30	4.84	44	21	4.47	0.640
B. vulgaris	10.70	8.06	32	33	12.45	0.747
B. vulgaris var. vittata	9.30	7.22	34	27	10.27	0.730
*Dendrocalamus asper**	25.60	15.40	46	62	–	–
D. asper	14.50	12.20	34	43	36.93	0.599
D. giganteus	16.00	14.20	34	47	40.73	0.552
D. latiflorus	11.50	11.50	37	31	21.58	0.683
D. strictus	10.00	7.60	38	26	8.94	0.667
*Guadua amplexifolia*	–	–	–	–	–	0.654
G. angustifolia	–	–	–	–	–	0.451
G. spinosa	–	–	–	–	–	0.489
G. superba	–	–	–	–	–	0.559
Ochlandra travancorica	11.30	9.40	40	–	26.00	0.704

Where: SL: stem length, considering the minimum defined diameter (3 cm); DBH: diameter at breast height; IL: internodes length; NI: number of internodes; DW: dry weight; BD: basic density. ² Only useful parts of the bamboo stems, after elimination of branches, pointers and “woody material” up to its first node.
* Stem length without a minimum diameter.

In a study by Omaliko and Ubani (2021), the density of bamboo specimens (Guadua angustifolia) at 12% moisture content were observed to range from 712.84 to 799.70 kg/m³. It was also observed that the node region has a somewhat higher density than the internode section. This is in line with the observations made by Huang et al. (2015), who found that specimens with and without nodes varied in density. This difference is caused by a unique characteristic of node vascular bundles, which show less vascular bundle content, shorter fibre length, and wider parenchyma cell lumens than internodes.

Specific Density of Bamboo

It is important to measure both specific density (SD) and moisture content (MC) values and link them to the mechanical characteristics of raw bamboo since the specific density of raw bamboo is a potential predictor of the qualities of bamboo-based products, such as laminates and bamboo composite materials. The specific density (SD) is the weight of an equal volume of water divided by the oven-dry weight of a given volume of raw bamboo. MC values and SD values have a close relationship. To guarantee that results are comparable with those from other studies, a standardised procedure for measuring SD and MC is required.

Specific density values will vary from the outer to inner portion of the wall cross section as the fibre density varies with wall thickness. Therefore, it is necessary to know which portion of the wall cross section is processed and what the associated MC and SD of that portion are before using raw bamboo for any application. The best bamboo sections can be chosen for the creation of items made of bamboo that meet specific criteria by measuring the MC and SD values and correlating them with measurements of wall thickness and mechanical properties.

Tensile Strength

A 100 kN tensile testing machine can be used to determine the tensile strength of bamboo samples in the lab using the ASTM D143-09 standard test technique for small clear specimens of timber. Samples can be made into dog-bone shapes after being cut from the 1m sections of bamboo culms that have been selected from various radial points along the sections. The sample’s average width and length can be 25 and 50 mm, respectively, while the gauge length can be 130mm on average. The ultimate load at test failure (F_ult) is measured, and its value is divided by the cross section of the sample across the gauge length (A), to determine the tensile strength.

In a study on Dendrocalamus asper. samples along the fibre direction by Javadian et al (2019), the highest tensile strength of class 1 samples (culm diameters of 80 to 90 mm) is 295 MPa for a wall thickness of 7-8 mm. Wall thickness categories of 6-7 mm and 8-9 mm have comparable tensile strengths within the same class. The samples with a wall thickness of 7-8mm in class 2 (90-100mm culm diameter) have the highest tensile strength of 298 MPa. There is no discernible difference between the values for other types of wall thickness because they all have comparable tensile properties.

However, as culm diameter increases, the average tensile strength for class 4-7 (diameter > 110 mm) decreases. When comparing the data from SD and tensile strength test, a correlation between the culm diameter, specific density, and tensile strength is seen. As the culm diameter increases, there is no discernible change in SD and tensile strength for class 1-3 (diameter 110 mm). The tensile strength and SD for class 4-7 (diameter > 110 mm) decrease as the culm diameter increases.

The density of bamboo fibres affects the tensile strength for culm diameters more than 110mm. Larger culms are likely to have more lignin and less cellulose fibres. As a result, raw bamboo loses a significant amount of its tensile strength, which is primarily derived from the tensile capacity of the cellulose fibres. As previously stated, the fibre density has a major impact on SD; as a result, decreasing the fibre density has been found to result in decreased SD in prior studies. When choosing bamboo culms for composite processing, the relationship between SD, tensile strength, and fibre density is important.

Flexural Strength of Bamboo

The flexural strength of bamboo can be measured according to ASTM D3043-00(2011) standard test method for structural panels in flexure. two-point flexural test is generally recommended. The advantages of a two-point flexure test over a center-point flexure test is that the sample is subjected to peak stress over a greater region as opposed to the center-point flexure test, which applies the peak stress to a single, isolated place. As a result, the likelihood that any fracture or flaw exists between two loading supports will be higher and the results of a two-point flexure test will be more accurate.

schematic representation of flexural strength test of bamboo

In a study by Javadian et al (2019), the flexural strength for class 1 (culm diameters of 80 to 90 mm) samples was observed to be 209 MPa, while the flexural strength for class 7 (140 – 150 mm) samples is 121 MPa. The flexural strength decreases from 209 to 198 MPa for class 1 samples when the wall thickness is increased from 6 to 9 mm.

There is no discernible correlation between the wall thickness and the flexural strength for samples from classes 2 (90-100 mm) and 3 (100 – 110 mm). In class 4 (110 – 120 mm) samples, going from a wall thickness of 6 to 10 mm causes a 6.7% decrease in the flexural strength going from 166 MPa to 155 MPa. The lowest flexural strength for class 5 (120 – 130 mm) is 149 MPa for walls with a thickness of 10 to 11 mm.

Larger culms have thicker walls, especially at the lower parts. A higher proportion of lignin and a lower proportion of cellulose fibres are caused by the thicker wall thickness. Similar conclusions can be drawn about flexural strength as they were with regard to the tensile capacity and its connection to fibre density earlier. The upper regions of the hierarchical structure of bamboo culms, where a smaller diameter predominates, are densely packed with cellulose fibres. The flexural strength of bamboo increases as culm diameter is decreased.

This emphasises how important fibre density is to the mechanical qualities of raw bamboo. Natural bamboo has exceptional mechanical properties thanks to cellulose fibres. The outer layer of the wall sections and the top portions of the culms have a higher cellulose fibre density. As a result, the flexural strength increases with rising fibre content and with falling lignin content around the fibres.

Compressive Strength of Bamboo

Two types of compressive strength, namely compressive strength parallel to the fibre direction and compressive strength perpendicular to the fibre direction, must be tested in accordance with the ISO 22157 standard in order to comply with European regulations. Three distinct samples of each stem will be evaluated because of the natural curvature of the bamboo stem. Three different areas of the log are sampled: the bottom, the centre, and the top. This is required because a bamboo stem does not have a continuous cross-section and because the bottom section, which has a bigger diameter, and the upper section, which has a smaller diameter, have different structural characteristics.

Chung and Yu (2002) conducted compression tests on two types of bamboo, Bambusa pervariabilis and Phyllostachya pubescens. Bambusa pervariabilis has an average ultimate compressive strength of 103 MPa and an average compressive modulus of elasticity of 10.3 GPa. Phyllostachys pubescens has an average ultimate compressive strength of 134 MPa and an average compressive modulus of elasticity of 9.4 GPa. Based on their observations, they concluded that bamboo had superior mechanical properties to regular structural lumber.

According to a study by Omaliko and Ubani (2021), the constitutive relationship of bamboo culm node sections and inter-nodal sections are different. Samples from the internodes demonstrated lower compressive strength than those from the node region of the bamboo culm. As a result, it can be concluded that nodes along the bamboo culm favourably affect the compressive strength of bamboo.

The study also demonstrated that when bamboo’s density increased, so did its compressive strength. Numerous other researchers have noted this relationship between the density and compressive strength of bamboo. They discovered that the unequal distribution of specific gravity across the bamboo culm’s heights and positions is the cause of the positive link between density and compressive strength.

Modulus of Elasticity in Tension

The rigidity of the bamboo matrix and its resistance to elastic deformation are both quantified by the bamboo’s modulus of elasticity. According to ASTM D143-14, the modulus of elasticity in tension of bamboo Petung (Dendrocalamus asper.) was tested by Javadian et al (2019) for various classes of bamboo Petung with variable culm diameters and wall thicknesses. Class 4 (110-120 culm diameter) samples with 9mm to 10mm wall thickness exhibit the highest modulus of elasticity (28,230 MPa), whilst class 7 samples (140 – 150 mm culm diameters) with 19mm to 20mm wall thickness exhibited the lowest modulus of elasticity (18,140 MPa).

The wall thickness of bamboo similarly increases as the culm diameter increases. As has been seen in earlier investigations, the volumetric ratio of cellulose fibres to lignin decreases as wall thickness increases in larger culms. As a result, thicker wall sections are anticipated to contain a higher percentage of lignin than cellulose fibres. As a result, larger bamboo culms have a lower modulus of elasticity than smaller culms, which have a higher volumetric ratio of cellulose fibres to lignin.

Shear Strength of Bamboo

The same machine that is used for a compression test can also be used to shear test bamboo culms parallel to the fibre. Additionally, the test was conducted in compliance with ISO-22157-2 (2004) procedure. The specimens can be made in the same way as a specimen for a compression test, with the exception that they were taken from the bottom, middle, and top of the bamboo culm and their length was equal to the outer diameter of the bamboo.

At each of the four shear zones, all measurements, including the specimen’s height, L, and thickness, t, should be taken. The specimens should be positioned in the middle of the moveable head, vertically. Additionally, the specimen needs to be centred in relation to the loading and supporting plate. The maximum load, F_ult, shall be measured at the end of the continuous application of the load at a constant rate of 0.01 mm/s. Then, the equation below is used to determine the ultimate shear strength.

τ = F_ult / ∑(t × L)

Where;

τ = Ultimate shear strength, in N/mm²
F_ult = Maximum load at which the specimen fails, in N.
∑(t × L) = Sum of four product of t and L.

References

Bornoma A. H., Faruq M. and Samuel M. (2016): Properties and Classifications of Bamboo for Construction of Buildings. Journal of Applied Sciences & Environmental Sustainability 2(4):105 – 114
Huang, P., Chang, W., Ansell, M., Chew, Y., & Shea, A. (2015). Density distribution profile for internodes and nodes of Phyllostachysedulis (Moso bamboo) by computer tomography scanning. Construction and Building Materials, 93:197-204
Javadian A, Smith IFC, Saeidi N and Hebel DE (2019): Mechanical Properties of Bamboo Through Measurement of Culm Physical Properties for Composite Fabrication of Structural Concrete Reinforcement. Front. Mater. 6:15. doi: 10.3389/fmats.2019.00015
Omaliko I. K. and Ubani O. U. (2021): Evaluation of the Compressive Strength of Bamboo Culms under Node and Internode Conditions. Saudi Journal of Civil Engineering, Sept, 5(8): 251-258

Wing Walls in Bridges

By

Ubani Obinna

-

September 6, 2022

Table of Contents

The main purpose of wing walls on an abutment is to contain backfill material behind the abutment wall and minimize carriageway settlement. High lateral earth pressures could result from the containment and compaction of backfill materials. Wingwalls can be found in abutments of bridges and and end of culverts.

The main purpose of wing walls on an abutment is to contain backfill material behind the abutment wall and minimize carriageway settlement. High lateral earth pressures could result from the backfill material being compacted and the soil being contained.

In essence, the retaining walls next to the abutment are wing walls. The walls may be separate from or a part of the abutment wall. The wing walls, which can be splayed at various angles or at a right angle to the abutment, hold the soil and fill that supports the roadway and approach embankment. The wing walls are often built at the same time as the abutments and from the same materials.

Types of Wing Walls

Wing walls can be categorised based on where they are located in relation to banks and abutments in the plan. The classification is as follows:

Free Standing Wing Walls

The foundation for free-standing wing walls is independent from the main abutment and is designed as a nominal cantilever retaining wall. In tis case, it is very possible for the abutment and wing walls to settle and tilt independently (differential settlement). Therefore, it is important to carefully plan the construction joints between the two structures in order to both allow for and conceal the relative movements. The wing walls can be positioned parallel to the abutment wall to accommodate the local topography, which makes compacting the backfill easy and eliminates any design issues, regardless of the deck’s skew angle.

As an alternative, the wing walls can be constructed to follow the path of the over-road and support both the backfill and the parapet fencing. With this structural configuration, it will be more challenging to place the backfill material, and higher earth pressures will result from the restriction against sideways movement. As a result, building this type of design would be more expensive. Instead, wing walls that are tapered in height and spread out at 45 degrees to the abutment may be used.

Cantilevered Wing Walls

Use of horizontally cantilevered wings is a second method for creating wing walls parallel to the over-road. For lengths up to 12 m from the abutment, this type of construction is workable, although care must be used while planning the intersection of the wing and abutment wall. Although the building’s common base ensures that it settles as a single unit, it may be challenging to compact the backfill around the wings. This type of rigid construction supports high earth pressures, therefore at the very least, “at-rest” earth pressures should be taken into account when carrying out the design.

A three-dimensional structure is created using this style of abutment and wing wall arrangement. Although the typical metre-strip assumption is frequently utilised, it may not be the best foundation for a design. The existence of the wing walls greatly modifies the vertical and horizontal bending movements in the abutment, and if the wings are utilised to their full potential, an overall reduction in the steel needs is conceivable.

Since the wing walls’ self-weight significantly affects the stability and bending moments of the abutment wall, it is important to take this into account. Horizontal stresses on the wing walls are transmitted across the abutment wall and into the abutment corners. To carry the high torsional moments produced by the wing wall loading, the corner splays between the abutments and wing walls can be designed as vertical torsion blocks.

Design Considerations of Wing Walls

The following loads must be taken into account in the design of wing walls;

Earth pressures from the backfill material
Surcharge from live loading or compacting plant
Hydrostatic loads from saturated soil conditions

The structural elements of the wall are typically designed to resist “at rest” earth pressures (K₀), whereas the stability of the wall is typically designed to resist “active” earth pressures (K_a). The idea is that initial “at rest” pressures develop, and structural elements should be made to withstand these loads without failing. However, as the wall moves—either by rotating or sliding—the loads will be reduced to “active” pressure. Therefore, if the wall is built to withstand “active” earth pressures, it will stabilise if it shifts under “at rest” pressures.

Abutment of Bridges: Functions, Types, and Design

By

Ubani Obinna

-

September 2, 2022

End supports and intermediate supports are two separate categories of bridge substructures. The intermediate supports of multi-span bridges are referred to as “piers,” while the end supports are typically referred to as “abutments.” Abutments and piers of bridges are typically built from in-situ concrete. As a part of the bridge, the abutment connects the bridge to the approach roadway, gives the bridge superstructure vertical support at the bridge ends, and retains the roadway earth materials from the bridge spans.

Typically, bridges are built as part of a railway or road highway project. Although the cost of the bridges may only make up a small portion of the overall contract, the construction of the bridge substructures can significantly affect the overall contract schedule because it invariably falls on the critical path for construction and typically takes place concurrently with earthmoving and drainage operations. More than half of the costs of a bridge is frequently spent on the foundation that supports the bridge deck.

Types of Abutment

The selection of appropriate abutments for a bridge should be made at the same stage as the choice of the deck superstructure. There are many types of abutment in use all over the world. Abutments can be categorised into the following;

Solid or full height abutments
Skeletal or open abutments
Mass concrete bankseats
Integral abutments
Semi-integral abutments
Reinforced earth abutments

The criteria for the bridge’s design must be taken into account while choosing an abutment type. Bridge geometry, needs for the road and riverbanks, geotechnical conditions, right-of-way limits, requirements for the architect, and other factors might be among them. The ability to compare the benefits and drawbacks of the various types of abutments will help the bridge designer make the best choice for the bridge construction from the outset of the design process.

open spill through abutment — **Figure 2:** Spill-through or skeleton abutment

Cantilever Abutment Walls

For bridges without integral abutments, the T-section reinforced concrete cantilevered wall has remained the most popular method of construction for the solid wall type of bridge abutment. To meet various needs, the core concept has been modified in a number of ways.

For right bridge decks with spans under 12 metres, sloping abutments for aesthetic or clearance reasons, and counterfort walls for heights of 10 metres and above, propped cantilever walls are frequently employed. The overall height of a solid wall abutment is automatically in the range of 7-9 m because the minimum headroom for new highway bridges is often higher than 5.1 m. Because mass concrete retaining walls are not cost effective at this height, reinforced cantilever abutment walls are now used extensively.

The simplicity of this form of construction and the similarity with cantilever retaining walls also accounts for its economic success and popularity.

Free Cantilever Abutment Walls

For heights of 6 to 9 metres, plane cantilever abutment walls are the most popular type of construction, and despite their size, the main concrete wall is frequently poured in a single lift. The wall stem typically measures between 0.9 and 1.2 metres in width, making it possible for someone to enter the reinforcing cage while it is being constructed. The base will often be 0.4–0.6 times wider than it is tall, and the toe may extend 1.0–2.0 m in front of the wall.

The soil foundation conditions and available sliding resistance will, nevertheless, affect the base’s physical proportions and dimensions. Figure 6 shows a typical illustration of a cantilever abutment wall with horizontally cantilevered wing walls.

FREE CANTILEVER ABUTMENT — **Figure 3:** Side view of a cantilever abutment

Active earth pressure conditions are typically used for overturning, sliding, and bearing pressure calculations where an abutment wall can rotate around its base or slide horizontally. The lateral earth pressure behind the abutment wall has typically been assumed to be in the at-rest state for walls that are tightly supported, such as on a mix of vertical and raking piles.

To account for high pressures during the backfill material’s compaction, the wall stem design is typically based on at-rest conditions in all circumstances. On the assumption that the abutment wall solely functions as a vertical cantilever, the design forces are frequently estimated using a metre-wide strip. There is a compelling justification for taking the structure’s three-dimensional behaviour into account if wing walls are joined to the back of the abutment.

The main abutment wall’s need for vertical reinforcement can be decreased to a nominal proportion of the cross-sectional area when the weight of the wing wall and significant corner splays are combined. Figure 4 depicts an idealised system of forces acting vertically and horizontally on a straightforward cantilever wall. It is foolish to rely on passive pressure at the front of the wall since excavations for highway services may be introduced along the foundation’s toe, entirely removing the soil.

forces acting on abutment — **Figure 4:** Typical forces acting on a bridge abutment

Counterfort Abutment Walls

For heights more than 10 m, where the percentage reinforcement in a free cantilever becomes quite large, counterfort abutment walls become economically viable. To increase flexural stiffness and resist the lateral earth pressures created by the depth of backfill material, triangular counterforts are added to the back of the abutment wall slab.

The reinforcement and formwork surrounding the counterforts make the building more challenging, and it is more difficult to physically compact the backfill. The counterforts are vertical cantilevers that are separated at about half the height of the wall. Although the wall slab naturally spans the shorter horizontal distance between the counterforts, it can be treated as a slab clamped on three sides, allowing the wall thickness to be decreased. The heel of the base slab also spans between the counterforts.

The primary tensile reinforcement’s anchorage length at the back of the counterforts, however, is a limiting element, therefore there is typically minimal room for thickness reduction.

Propped Cantilever Abutments

Bridge decks up to a 12 m span have minimal longitudinal movement, making it possible to employ the deck as a strut for square or skew-free bridges. Although the abutments can be planned as a supported cantilever, at-rest earth forces are typically assumed for the design of reinforcement at the back of the wall and footing, as well as both stability and bearing pressure calculations, due to the inflexible character of the structure.

Since complete fixity of the foundation is improbable, it is common practise to estimate the front face reinforcement in an abutment by assuming that the wall is pinned at both the deck and base levels. The rear curtain walls at the top of the abutments are made to withstand the propping force and are typically used to separate the deck from the top of the abutments.

To prevent rotation and horizontal displacement of the abutments, it is frequently important to specify that the initial backfilling before the deck is built should be kept to a maximum of 50% of the abutment height. The deck’s completion is then postponed until the backfill behind the abutment walls is finished.

Open Abutments

The type of end supports required to extend a bridge’s central span and produce neighbouring “open side spans” are known as “open abutments,” and they are frequently used in construction terminology. In this case, abutments come in two different basic varieties; a subterranean reinforced concrete or piled skeleton or “spill-through” abutment formed at or below previously existing ground level beneath an embankment slope, or a mass concrete bankseat located at the top of the slope and includes a side span.

A three-span deck with intermediate piers and end abutment supports is an alternative to a single-span deck with solid cantilever abutments. Therefore, the prices of two intermediate piers, two end abutments, and two additional deck spans may be contrasted with the costs of two massive cantilever abutments, related wing walls, and chosen granular backfill. The choice of a three-span open structure must also take into account aesthetics, sightlines, flood relief, and pedestrian safety.

Bankseats

When the foundation level is near to the existing ground level, simple mass concrete or minimally reinforced sections may be used for abutment supports at the top of cuttings. This kind of structure is typically “stepped out” in sections to lessen foundation strain and keep the force that results on the bankseat inside the middle part of its base. To limit the immediate region of backfill behind the wall, little wing walls that hang easily from the back of the bankseat can be used.

Bankseats can also be utilised on embankments, where they can either be supported directly on pile foundations or allowed to settle with the fill. In the latter scenario, pile downdrag due to embankment settlement might lower the payload of the pile group unless isolating sleeves are utilised. Driving raking piles for a bankseat can be difficult at an embankment’s edge and is not advised if the embankment is anticipated to settle.

A solid abutment wall with substantial wing walls is usually more expensive than using a bankseat, intermediate pier, and additional deck for the side span. This is especially true for small bridges, but for wide constructions, the closed abutment is typically more cost-effective because the cost of the wing walls remains constant and decreases as the width increases.

Spill-through abutments

This type of abutment (shown below) is composed of two or more buried columns supported on a single foundation slab and topped by a cill beam to support the deck structure. To minimise long-term settlement, the backfill must be carefully compacted around the columns since it overflows between the legs.

It is frequently employed in embankment situations where a suitable foundation can be located at the original ground level. In this situation, it might be a more affordable option than a bankseat that is supported by piles pushed through the embankment fill. Figure 9 depicts a typical spill-through abutment bridge, however the completed embankment makes it impossible to see the abutment’s legs.

Since very few field tests have been conducted to ascertain the long-term movements and ground pressures on the subterranean structure, design assumptions for this sort of abutment vary substantially. Assuming full active earth pressure across the whole width of the abutment, regardless of the soil that pours between the columns, is one conservative, straightforward design strategy. While the fill between the columns may arch or experience “drag effects,” the columns and cill beams are typically thought of as being loaded by active earth pressure.

Integral Abutments

Conventional bridges typically include expansion joints and bearings inserted between the superstructure and the abutments to account for relative movement and prevent temperature-induced strains from building up between the superstructure and abutments. These expansion joints and bearings, however, may result in significant maintenance issues.

The concept of physically and structurally joining the superstructure and abutments to produce what is known as an integrated bridge has gained popularity as a result of the issues with conventional bridges that feature joints and bearings. All of the aforementioned issues with joints and bearings are prevented by integral bridges.

The abutments are however compelled to move away from the soil they hold onto when the temperature drops and the deck contracts (for example, in the winter), and towards the soil when the temperature rises and the deck expands because of the integral connection between the superstructure and the abutments (e.g. in the summer). Because of this, the soil behind the abutment experiences temperature-induced cyclic loading from the abutment, which might result in substantially higher earth pressures than originally intended.

Reinforced Earth Abutments

Modular facing panels, often made of pre-cast concrete, earth fill, and soil reinforcement make up a reinforced earth wall. The wall is constructed by repeatedly performing a series of tasks at various levels, including installing face panels, putting earth fill in place and compacting it, laying reinforcements (geotextiles), and putting more earth fill in place and compacting it. Until the necessary height is attained, the processes are repeated.

The facing panels shape the surface, enabling the construction of nearly vertical walls, and the finished wall is able to resist lateral pressure through friction along the reinforcing. When a bankseat is built on top, reinforced earth can be used as part of the abutment. To minimise any local loading effects that could result in local deformations on the face of the wall in this situation, the bankseat is often positioned back from the top of the wall.

Reinforced earth walls are widely used in conjunction with other types of abutment structures to create affordable retaining walls around bridge approaches.

Abutment Foundations

Most abutments are generally supported by either spread or piled foundations. Three issues need to be considered in the choice of foundation:

the available bearing capacity of the undisturbed natural soil at the site;
the settlement that the foundation will undergo (and impose on the superstructure); and
the tolerance of the abutments, deck, etc., to the expected differential settlements.

Most of the time, when the soil’s bearing capacity is sufficient to sustain a spread footing with minimal settlements, this will be the most cost-effective laying alternative. If rock is present at the founding level, this will necessarily result in a spread footing solution. Most dense sands, granular soils, or stiff clays will give appropriate bearing capacities for spread footings.

Abutment foundation — Types of abutment foundation

When soft compressible soils are present or the abutment is situated at the top of a steep embankment, piles are typically used. If a top-down strategy is used for building bridges in cutting, the use of piling can streamline the process.

In many cases, it might be more cost-effective to remove any soft material and replace it with well-compacted granular material or mass concrete rather than using pilings if a suitable soil or rock is present within a reasonable depth of the founding level.

Although differential settlement is difficult to predict with any degree of certainty, past experience indicates that it might be as much as two-thirds of the maximum total projected settlement. While spread foundations may be adequate for some sites based on their bearing capacity, their size frequently results in comparatively substantial overall settlements when compared to the settlements that a well-designed pile foundation is likely to encounter (typically less than 10mm at working load). The ability of the deck structure to contain the anticipated differential settlements may therefore dictate the choice of foundation method.

Abutment Approach Slab

One can anticipate that the embankment fill next to the deck will settle significantly (and perhaps a few per cent of the fill height). Without specific precautions, the intended vertical alignment of the highway pavement would be disrupted, which will result in a bad ride quality for vehicles on the approaches to bridge decks. There are two methods that could be used: a granular wedge next to the abutment or structural run-on (approach) slabs.

An approach slab will provide a smooth transition between the relatively flexible approach pavement and the nonflexible bridge superstructure by bridging across the settling fill immediately behind the abutment. However, for integral abutments backfilled by granular materials, the backfill will become gradually compacted under horizontal cyclic loading from the abutment and a void will form under the run-on slab, which may cause damage to the slab under traffic load if it has not been designed for this case.

Design of Abutments

The primary function of an abutment wall is to transmit all vertical and horizontal forces from a bridge deck to the ground, without causing overstress or displacements in the surrounding soil mass. The abutment wall also serves as an interface between the approach embankments and the bridge structure, so it must also function as a retaining wall.

The type of the bearing supports, if any, determines how much a bridge deck and an abutment wall interact with one another. Integral abutments are becoming more popular since they eliminate the need for additional bearings and the associated maintenance costs. It is simple to idealise the impact of bearing type, end fixity, or free supports throughout the design phase. It is more difficult to predict the impact of ground movements brought on by settlement, mining subsidence, or earth tremors, and these impacts must be taken into account specifically for a given structure.

The primary vertical loading acting on an abutment is due to the dead load and live load reactions from the bridge deck. Additional loading arises from the self-weight of the abutment, earth pressure, wall friction between the backfill and the abutment, and live loading immediately behind the abutment.

Traction and braking forces due to live loads on the deck are carried at the fixed bearings and may represent a substantial overturning moment on a tall abutment. Although these forces are applied to localised areas of the deck, they can usually be treated as a uniform load across the width of the abutment.

Loadings on Abutments

A number of actions are possible on abutments which must be thoroughly accounted for in the designs. Some of the actions are as follows;

Soil Loading

The earthfill retained at the back of abutments exert earth pressure as typical for retaining walls. This may be accompanied by water hydrostatic pressure if adequate drainage is not provided at the back of the wall. In a situation where a wall can move by tilting or sliding and the backfill is a free draining granular material, active pressures are assumed.

Vehicle loading (surcharge)

In the simplest case, for example a distributed load (q kN/m²) at the ground surface, such as an HA loading, an additional stress equal to K_aq can be added to the earth pressure assumed on the back of the abutment. For the design of highway bridges, a live load surcharge of 10 kN/m² for HA loading and 20 kN/m² for 45 units of HB is often used. For rail loading either a UDL of 150 kN/m along each track, applied over a 2.5m width, or an RU and RL surcharge of 50 kN/m² and 30 kN/m² respectively is taken over the track area.

Compaction Pressure

The application of compaction plant, such as heavy vibrating rollers, to abutment backfill in layers leads to temporary but quite large increases in both vertical and horizontal stress within the fill. Some of these stresses remain locked into the fill, and can give considerable additional lateral loading on a cantilever abutment, particularly over the depth just below the top of the wall.

Swelling Pressure

Compaction of cohesive fill produces even greater increases in lateral earth pressures than in granular fill, of the order 0.2–0.4 times the undrained shear strength. But for such clays the more significant issue is likely to be lateral swelling pressures. For clays placed relatively dry, a relaxation in lateral stress has been observed immediately after compaction.

However, as rainwater enters the fill, swelling starts to occur. In situ determinations of the average lateral stresses within a 6m high abutment backfill of London clay showed that horizontal total stresses rose up to 180 kPa near to the centre of the embankment, and up to 70 kPa close to the wing walls. Another pilot-scale experiment observed average lateral pressures on a 3m high wall of the order of 100 kPa. Given that these figures are of the order of many times higher than the commonly assumed equivalent fluid pressure, it is suggested that cohesive backfill should not be used behind abutments.

Effects of seasonal deck expansion and contraction

Longitudinal movements in the bridge deck due to creep, shrinkage and temperature changes cause forces at bearing level on non-integral abutments. The magnitude of these forces depends upon the shear characteristics or frictional resistance of the bearings. The coefficient of friction of most bearings lies in the range f_i = 0.03–0.06. The frictional force is derived from the nominal dead load and the superimposed dead loads on the deck.

Integral abutments do not have bearings, and therefore the backfill they support is subjected to seasonal increases and decreases in horizontal strain. The deck is stiff relative to the backfill and the soil provides insufficient restrain to prevent movement.

Load Combinations for Abutments

BD 30.87 – UK Standard

Case 1:
Backfill + Construction surcharge
Wall backfilled up to bearing shelf level only.

Case 2:
Backfill + HA surcharge + Deck dead load + Deck contraction

Case 3:
Backfill + HA surcharge + Braking behind abutment + Deck dead load

Case 4:
Backfill + HB surcharge + Deck dead load

Case 5:
Backfill + HA surcharge + Deck dead load + HB on deck

Case 6:
Backfill + HA surcharge + Deck dead load + HA on deck + Braking on deck
(Not applied to free abutment if sliding bearings are provided)

Load Combinations (European Standards)

Case 1:
Backfill + Construction surcharge

Case 2:
Backfill + Normal Traffic Surcharge + Deck Permanent load + Deck contraction/shrinkage

Case 3:
Backfill + Normal Traffic Surcharge + Deck Permanent load + gr1a on deck

Case 4:
Backfill + SV/100 and SV/196 Surcharge + Deck Permanent load + gr1a (frequent value) on deck

Case 5:
Backfill + Normal Traffic Surcharge (frequent value) + Deck Permanent load + gr5 on deck

Case 6:
Backfill + Normal Traffic Surcharge (frequent value) + Deck Permanent load + gr2 (ψ1LM1 with braking on deck)
(Braking not applied to free abutment if sliding bearings are provided)

Case 7:
Backfill + Deck Permanent load + gr6 (LM3 with braking on deck)
(Braking not applied to free abutment if sliding bearings are provided)

Stability of Abutments

The stability of an abutment should be checked for three basic modes of failure:

sliding;
overturning;
overall instability.

Sliding

When passive resistance in front of the toe can be relied upon, the minimum factor of safety taken in design is normally 2.0. If the passive pressure contribution is neglected, then a minimum factor of safety against sliding is usually 1.5. A shear key is sometimes provided in the base slab to mobilise greater soil resistance when otherwise the resistance to sliding is inadequate.

Overturning

Overturning is checked by taking moments about the toe when the most adverse load combination is acting on the structure. A minimum factor of safety of 2.0 is normally adopted providing the resultant reaction lies within the middle third. If there is ‘tension’ in the bearing pressure at the heel, then a higher factor of safety may be used as a further precaution against failure.

Overall instability

A slip circle analysis is essential for a bankseat form of construction and may be necessary for other types of abutment when the soil strata well below the structure is weaker than the soil layers at foundation level. Where soil strengths are based on tests, then a minimum factor of safety would be 1.5. Particular care is needed during construction if an intermediate pier foundation is being excavated at the toe of a cutting slope, when there is a bankseat positioned at the top.

Structural Design of Abutments

The structural design of abutments involves the selection of the proper thickness of the wall (stem) and base, and selection of the proper size and spacing of reinforcements to prevent ultimate and serviceability limit state failure.

Base Design

A base slab’s toe is made to withstand the highest ground forces pressing on the base, while some relief can be obtained from the toe’s self-weight and any added fill. The heel must be made to withstand upward ground pressure as well, however in this instance, fill, live load surcharge, and self-weight can generate high loading circumstances that can reverse the shears and moments that follow. The foundation slab may be supported by piles, in which case the predicted loads in each pile would take the place of the bearing pressures.

Wall Design

The stem of an abutment wall is designed to withstand the shears and bending moments caused by horizontal forces, as well as the bending imposed by the deck in the case of integral bridges. Since direct stresses from vertical loads are typically relatively minimal, they can be disregarded when designing walls. At the root of torsion blocks on horizontally cantilevered wing walls, significant in-plane strains can develop.

abutment wall construction — Construction of abutment walls

While for integral bridges the top of the wall and connection with the deck can also be crucial, the key section for moments and shear forces occurs at the root of the wall in the case of simple vertical cantilever walls. Due to traction and braking effects, concentrated horizontal stresses may exist at bearing level as well as at the back of the curtain wall. Calculating the bending moments in the wall typically involves distributing these loads vertically.

How to Design Pile Foundation using SPT and CPT Data

By

Ubani Obinna

-

August 21, 2022

Table of Contents

A lot of correlations have been proposed by researchers for relating the results from Standard Penetration Test (SPT) and Cone Penetration Test (CPT) to pile load capacity. In this article, we are going to review how to design pile foundation using SPT and CPT data. It very important that these correlations used in this article and other similar ones should be used with caution, since they are statistical relationships that may not have taken all parameters into consideration. Experience is required to successful apply them to practice.

It is common to use the results of in-situ tests to determine the ultimate bearing capacity of piles in coarse soils because it is difficult to get undisturbed samples of these soils from boreholes. Two fundamental approaches will be discussed in this article, which are SPT and CPT.

118D99DE 1A45 43A7 A34A E233C66CF3BC — **Figure 1:** CPT process in the field

In all cases, the allowable load is calculated by dividing the ultimate bearing capacity by a safety factor which usually varies between 2 and 3. The diameter of the pile and the soil’s compressibility both have an impact on the allowable settlement at the working load. Experience has shown that a safety factor of 2.5 will guarantee that an isolated pile driven into coarse soil with a shaft diameter of no more than 600 mm won’t settle by more than 15 mm.

As an alternative, partial safety factors can be used in accordance with the steps outlined in EC7, and the serviceability limit state can be verified through calculation or experience, and if necessary, by performing loading tests. If the “global” safety factor of 2.5 is utilised, these tests are still required unless experience offers a more reliable indicator of settlement behaviour.

Standard Penetration Test (SPT)

For driven piles in coarse-grained soils (sands), Meyerhof (1956) proposed the following relationship between the skin friction (f_s) of the pile and the standard penetration number;

Skin friction

The skin friction in piles can be obtained from SPT data using the relationships in Equations (1-3);

Q_f = f_s × perimeter × length ——– (1)
For Displacement piles: f_s = 1.9N₆₀; f_s ≤ 100 kPa ——– (2)
For Non-displacement piles: f_s = 0.95N₆₀; f_s ≤ 50 kPa ——– (3)

End bearing

The end bearing in piles can be obtained from SPT data using the relationships in Equations (4-6);
Q_b= f_bA_b ——– (4)
f_b = CN₆₀ (kPa) ——– (5)
C = 38(L_s/D) ≤ 380 ——– (6)

where L_s is the length of pile driven in sand, and D is the diameter of the pile.

Design of Pile Foundations using SPT and CPT Data — **Figure 2**: Relationship between standard penetration number and angle of shearing resistance

Alternatively, the standard penetration number can be used to estimate the angle of internal friction of the soil (using Figure 2), which is then used to compute the allowable load on the pile.

Cone Penetration Test (CPT)

The cone penetrometer was originally developed to estimate the end bearing capacity of piles. The cone resistance, q_c, is a measure of the end bearing capacity and the sleeve resistance, q_s1, is a measure of the skin or shaft friction.

44119BCC 12F8 4BA5 A7FA BF9196161061 — **Figure 3:** Cone penetration test

End Bearing

The ultimate end bearing capacity of a single pile (Xu and Lehane, 2005) is estimated from;

Q_b = C_bq_c-avA_b ——– (7)

where C_b= 0.6 for closed-ended driven pipe piles in sand and C_b = 0.9 for jacked piles in sand; q_c–av is the average cone tip resistance over a distance 1.5 times the pile diameter above and the same distance below the pile base, and A_b is the area of the pile base. For open-ended pipe piles in siliceous sand (Lehane and Randolph, 2002);

C_b = 0.15[1 + 3(D*/D)²] ——– (8)

and D is the external diameter, D* is the effective diameter.

The maximum expected settlement from the equation above is about 10% of the pile diameter.

Several other empirical equations are used in practice. For example, Fleming and Thorburn (1983) suggested that for Equation (7), C_b = 1 and q_c–avis the average cone value over an influence zone of 8 pile diameters above the pile base and 2 pile diameters below the pile base, calculated as follows:

q_c-av = (q_c1 + q_c2 + 2q_c3)/4 ——– (9)

where q_c1 is the arithmetic average of cone resistance values over 2 pile diameters below the pile base, q_c2 is the minimum cone resistance value over 2 pile diameters below the pile base, and q_c3is the arithmetic average of minimum cone resistance values below q_c2 over 8 pile diameters above the pile base.

Shaft Resistance

The shaft or skin friction is calculated where the sleeve resistance is determined using either an arithmetic or geometric mean value of cone resistance over the buried pile depth. Cone sleeve friction is influenced by soil compressibility and relative density, whereas skin friction on a pile is influenced by pile geometry, roughness, relative density, installation technique, soil compressibility, and pile geometry.

In the case of fine-grained soils, soil consolidation around the sleeve has a significant impact on the cone sleeve friction value. As a result, utilising the results from the cone penetrometer, significant discrepancies between the short-term and long-term load capacity can be anticipated.

As evidenced by the results of the pile tests, the cone penetrometer estimates for the short-term load capacity can be as low as 20% of the long-term load capacity. One of many equations suggested in the literature can be used to predict the cone sleeve resistance if it is not measured. Some of these are as follows:

For both open-ended and closed-ended driven pipe piles, the skin frictional stress (Lehane et al., 2005) is given as;

f_s = C_sq_cA_rs × [max(2, h/D)]^-0.5 × tan (δ_cv) ——– (10)

where C_s is a constant (0.03 for compression piles and 0.0225 for tension piles), h is the distance of the pile section under consideration above the pile base, δ_cv is the soil–pile interface friction angle correlated to the mean particle size (≈23° for D₅₀ = 1 mm, increasing to 28.88 for D₅₀= 2 mm for sand on steel) and A_rs is the effective area ratio of the pile shaft given as;

Closed-ended pipe piles: A_rs = 1
Open ended piles: A_rs= 1 – min{1, (D_i/1.5)^0.2} (D_i/D)²

Other relationships that have been developed by several other authors are as follows;

Eslami and Fellenius (1997):
fs = C_sq_cs ——– (11)

where q_cs is the cone resistance after adjustments for porewater pressure measured at the cone shoulder, and C_s is a coefficient that depends on soil type, as shown in the Table below;

Type of soil	C_s
Soft, sensitive soils	0.08
Clay	0.05
Stiff clay and mixture of clay and silt	0.025
Mixture of silt and sand	0.01
Sand	0.004

Vesic (1977) —coarse-grained soils:
f_s = 0.11 exp(-3 tan ϕ’_cs)q_c ——– (12)

Jardine et al. (1998) —coarse-grained soils:
f_s = σ’_rctan ϕ_i ——– (13)

where σ’_rcis the radial effective stress on the shaft and is empirically related to the cone resistance.

Tumay and Fakhroo (1984) —stiff clays:
f_s = 0.5q_c ——– (14)

The ultimate skin friction is;
Q_f = f_s × perimeter × length

You have to exercise caution in using these empirical equations, as they were derived from pile load tests and cone penetrometer data in particular soil types and locations.

Worked Example: Pile Load Capacity Using SPT Data

A 350 x 350 mm closed-ended square pile is driven into a sand profile to a depth of 10 m. The SPT results are shown in the table below. Estimate the allowable load capacity for a factor of safety of 3.

Depth (m)	1	3	5	6	8	10	11	13
N₆₀ (blows/300 mm)	22	18	25	20	30	36	39	45

Use Meyerhof (1956) equations for displacement piles since the pipe pile is closed-ended.

Solution

Step 1: Determine the skin friction
N₆₀ = average N₆₀ = (22 + 18 + 25 + 20 + 30)/5 = 23
Displacement pile: f_s = 1.9N₆₀ = 1.9 × 23 = 44 kPa < 100 kPa; use fs = 44 kPa
q_f= f_s × perimeter × length = 44 × 4(0.35) × 10 = 616 kN

Step 2: Determine the end bearing and allowable load capacity.
f_b = CN₆₀ (kPa);
C = 38(L_s/D) = 38(10/0.35) = 1085 > 380
Use C = 380
N₆₀ = 36 (this is the N value at the base)
Q_b = f_bA_b= 380 × 36 × 0.35 × 0.35 = 1675.8 kN

Q_ult = Q_f+ Q_b = 616 + 1675.8 = 2291.8 kN
Q_a = Q_ult/FS = 2291.8/3 = 763.93kN

Lateral-Torsional Buckling Strength of Corrugated Web Girders

By

Charity Mmuo

-

August 20, 2022

Table of Contents

Corrugated web girders are being utilized more commonly in structural engineering due to their many beneficial qualities, such as lower dead load, increased shear buckling strength, and a special structural behavior known as “accordion effect.” Because of this, designing girders is simpler than it would be for those with flat web.

For the design of these girders, the stability of the local and global members is essential. The effect of local stability on cross-sectional resistances, specifically the bending moment resistance, shear buckling resistance, and resistance against transverse force, has been well studied in the past. These resistances can now be calculated using precise design models.

According to Jager et al (2022), several research works have shown that girders with corrugated web have a higher elastic critical moment than those with flat web. This implies that the lateral-torsional buckling strength of beams increases when the web is corrugated.

However, the increment has been viewed in several ways by being associated with the cross-sectional characteristics. The majority of studies concur that the web contribution should not be taken into account when calculating inertias about the strong and weak axis, although there are discrepancies when taking the enhanced elastic critical moment into account.

corrugated web girder — **Figure 1:** Corrugated web girders in application

The elastic critical moment of a conventional flat web girder subjected to uniform bending moment can be calculated by Eq. (1) according to EN1993-1-1 as;

M_cr = π/kL √EI_z [(π/k_wL)² EI_w + GI_t] ——– (1)

Where L is the span of the girder, E is the elastic modulus, G is the shear modulus, I_z is the moment of inertia about the minor axis, I_tis the torsional constant, I_w is the warping constant, k is the effective length factor about the weak axis rotation and k_wis the effective length factor with respect to warping.

To account for the critical elastic moment of corrugated web girders, previous research work by Lindner (1990) suggested an additional term with a correction factor c_w in the warping constant given by Eqs. 2–4 for double symmetric sections in order to consider the greater performance (c₁ = 8, c₂ = 25); where I_w,flatis the warping constant of flat web girder.

I_w = I_w,flat+ c_w (L²/Eπ²) ——– (2)

c_w = a₃² (h_w + t_f)²/[c₁⋅u_x⋅(a₁ + a₄) ——– (3)

u_x = (h_w + t_f)/2⋅G⋅a₁⋅t_w + (h_w+ t_f)²⋅(a₁ + a₄)³/c₂⋅a₁²⋅E⋅b_f ⋅t_f³ ——– (4)

Larsson and Persson (2013) performed a notable FE study and found that the proposal of Lindner (1990) gives the best approximation to the numerical results. However, this additional term depends on the girder length which is not possible for a sectional constant. Therefore, they substituted the Lindner’s proposal into Eq. (1) in order to rearrange the additional term to the torsional constant according to Eq. (5).

I_t= I_t,flat + c_w/G ——– (5)

The appropriateness of Eq. (5) was confirmed by Lopes et al. (2017) and they proposed a slightly modified correction factor cw for trapezoidally and sinusoidally corrugated web girders (c₁ = 22, c₂ = 300 in Eqs. 3–4) based on FE analysis.

According to EN1993-1-1 [2] the reduction factor (χ_LT) for the lateral-torsional buckling strength for rolled sections or equivalent welded sections with flat web may be calculated by Eqs. 6–8, where α_LT is the imperfection factor (for different buckling curves: a – 0.21, b – 0.34, c – 0.49, d – 0.76), λ_LT is the relative slenderness, β is the multiplication factor and λ_LT,0 is the relative slenderness limit. The standard suggests to use buckling curve d if the depth-to-width ratio of the section is greater than 2; otherwise the buckling curve c shall be used. In Eq. (6) M_y is the cross-sectional bending moment resistance considering the local flange buckling.

λ_LT = √[M_y/M_cr] ——– (6)

λ_LT,0 = 0.4, and β = 0.75
ϕ_LT = 0.5[1+ α_LT (λ_LT – λ_LT,0) + βλ_LT²] ——– (7)

χ_LT = 1/[ϕ_LT + √(ϕ_LT² – βλ_LT²)] but χ ≤ 1.0 ——– (8)

In the past, nonlinear FE (finite element) analysis was mostly used to explore the ultimate lateral-torsional buckling strength; hence, there aren’t many test data available. Only a small number of experimental tests and some non-linear FE analysis performed by various researchers have been used to study the ultimate lateral-torsional buckling strength of corrugated web girders.

Researchers (Jager et al, 2022) from the Department of Structural Engineering at Budapest University of Technology and Economics, Hungary, recently worked on an experimental study using 11 large-scale test specimens to examine the lateral torsional buckling resistance of corrugated web girders.

The study was published in the journal, Structures (Elsevier). In the research work, the prior design recommendations for trapezoidal corrugated web girders’ lateral-torsional buckling strength were compared and evaluated based on the test results, and a preliminary design buckling curve was provided.

Test Setup and Experimental Study

11 large-scale test specimens were examined under four-point-bending condition as part of the research program by Jager et al (2022). Investigations were conducted on six distinct girder geometries with the same trapezoidal corrugation profile but varied flange sizes. Five more specimens were employed in test replications to check the accuracy of the findings. The widths of the parallel and inclined web folds are the same for all specimens (a₁ = a₂ = 98 mm), as they are often employed in bridges with a corrugation angle of 45°.

notation 1 — **Figure 2**: Notations used on the study (Jager et al, 2022)

Notation 2 — **Figure 3:** Cross-sectional layout of specimen’s geometry (Jager et al, 2022)

The six specimen types with varying flange sizes were depicted in scaled drawings as shown above, and the girder numbers were assigned in accordance with the rising flange diameters. The nominal flange thickness (t_f) of specimen types #1, #2, and #3 is 14 mm, whereas specimen types #4, #5, and #6 have a 16 mm flange thickness. There are five different nominal flange widths (b_f): 140, 160, 180, 220, 250, and 300 mm.

With a nominal web depth (h_w) of 520 mm, all specimens have a web thickness (t_w) of 6 mm. Vertical stiffeners with a nominal thickness (t_s) of 10 to 16 mm were installed at the load introduction and support positions. To analyze the lateral-torsional buckling behavior of corrugated web girders, a wide range of varied LTB slenderness ratios were covered by the specimens.

S355 steel grade was used for the flanges, while S235 steel grade was used for the web, with nominal yield strengths of 355 MPa and 235 MPa, respectively. Coupon tests in accordance with ISO6892-1 were used to assess the material’s characteristics.

test set up — **Figure 4:** Test setup and location of measuring devices (Jager et al, 2022)

Prior to testing, the rigid frame measuring system’s spatial coordinates were calculated using geodetic triangulation from three places using a total station theodolite to achieve high precision. Each specimen was subjected to a static load of around 0.1 kN/s]. To assess the elastic response of the structure and the stiffness of the investigated girders in the elastic domain, loops were run five times by equal loading steps during the loading and unloading process until achieving about 60% of the projected ultimate load bearing capacity.

The hydraulic jacks that were being used were coordinated and attached to the same hydraulic system. In order to assess the results and compare them using FE models, the test specimens’ observed load-displacement curves, buckling forms, and ultimate failure modes were documented on photos. Displacement control was used during the experiments, and the post-buckling ranges were also investigated. Following the testing, portions of steel plate were removed from the intact flange and web parts of each specimen for material testing.

Overall Results and Failure Modes

According to the findings of the study, girders with compact flanges experienced pure lateral-torsional buckling failure, whereas girders with slender flanges experienced flange buckling failure in conjunction with lateral-torsional buckling failure. Furthermore, because of the rigid cross-sectional movement failure modes, no distortional web failure developed.

Moreover, it was observed that after unloading, slender specimens can regain proportionately bigger displacements owing to elastic buckling, while heavier flanged samples can experience inelastic buckling. The study also showed that initial imperfections have significant resistance reduction effect on the lateral-torsional buckling strength.

Comparison with Design Proposals

The authors compared the lateral-torsional buckling curves of EN 1993-1-1 (β =0.75) to various reduction factors estimated from the test findings (χ_LT,test). By the calculation of the relative slenderness three different proposals for the elastic critical moment are used:

(i) without any modification in the torsional or warping constants,
(ii) with an additional term in the torsional constant proposed by Larsson and Persson (2013) using the correction factor of Lindner (1990) presented by Eq. (5), and
(iii) with the slightly modified correction factor of Lindner according to Lopes et al. (2017).

The web’s contribution to the moment of inertias surrounding the strong and weak axes was ignored in every case. Both effective length factors (k_w and k) were arbitrarily set to 0.5 in order to optimize the elastic critical moment and offer a safe side solution for the buckling curve because the test specimens were almost completely constrained against warping and rotation about the weak axis. It should be noted that all test results were above the previous proposal’s buckling curve band.

Comparison of test results — **Figure 5:** Comparison of the test results and previous proposals to EN1993-1-1 buckling curves (Jager et al, 2022)

The calculation methods considered in the study are in harmony with the “accordion effect” of corrugated web girders. It is to be noted all test results are above the buckling curve b and the proposal of Lopes et al. (2017) gives the larger elastic critical moment and smaller relative slenderness then Larsson and Persson’s (2013) solution.

The calculated resistances are determined according to the equation below;

M_b,R = χ_LT⋅M_y ——– (9)

Where the reduction factors (χ_LT) are obtained from Eqs. 6–8 using the above mentioned three different proposals for the elastic critical moment. It can be seen that the best fit and safe side solution is provided by the proposal of Lopes et al. (2017) using buckling curve b.

By comparing the test and computed lateral-torsional buckling resistances, The authors pointed out that the Lopes et al (2017) proposal’s suggestion offered the greatest match and safest approach to take. However, it should be highlighted that a more extensive statistical evaluation should be carried out in accordance with EN 1990 AnnexD, expanded by advanced FE analysis, in order to determine an applicable buckling curve that satisfies the safety criterion of the Eurocode.

Article Credit:
B. Jager, L. Dunai, B. Kovesdi (2022): Lateral-torsional buckling strength of corrugated web girders – Experimental study. Structures 43 (2022) 1275–1290 https://doi.org/10.1016/j.istruc.2022.07.053

The contents of the cited original article published by Cement and Concrete Research (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.

References

[1] Larsson M, Persson J, Lateral-torsional buckling of steel girders with trapezoidally corrugated webs, MSc thesis, Gothenburg, Sweden, 57, 2013.
[2] Lindner J. Lateral torsional buckling of beams with trapezoidally corrugated webs, Proceedings of the 4th International Colloquium on Stability of Steel Structures, Budapest, Hungary, 79-82, 1990.
[3] Lopes GC, Couto C, Real PV, Lopes N. Elastic critical moment of beams with sinusoidally corrugated webs. J Constr Steel Res 2017;129:185–94.

The T-shaped Civil Engineer

By

Anuoluwapo Kolade

-

August 16, 2022

T-SHAPED ENGINEER — T-shaped people are those with a depth of knowledge in at least one discipline and a breadth of knowledge about innovation and entrepreneurship that allows them to work effectively with professionals on other disciplines to bring their ideas to life — Tina Seelig

Table of Contents

Perhaps you think you have stumbled on an article you would read in a few minutes; then, I suppose you might be wrong. I expect you to devote about 10 – 15 minutes to reading and assimilating this treasure coated in words. It will be worth your time.

Shall we? Yeah.

Recently, a friend and I had a conversation where he blatantly told me that Nigeria has not been producing good graduates in recent years. Well, you can make a case for or against his opinion, but I think I agree with him. I agree with him because the decay of our education system is obvious, and you may be disappointed after engaging students or graduates in a conversation.

This malady then begs the question: Who is to be blamed? Me? You? The government or schools? Well, let me tell you about my blame-sharing formula quickly. When I was in school, I ditched 10% of the blames to the government and another 10% to my school while I took 80%.

[themoneytizer id=”98693-11″]

Do you know why I took the largest share of the blames? I did so because I believed that whatever I become or becomes of me, even within the unfavourable education system, totally depends on my choices. It depends on what I make out of my life. It also depends on how I use my time during breaks and strikes. Moreover, I do not have control over the system, government, or school. Therefore, I had no choice but to become a T-shaped student who is well prepared to take the industry by storm.

images — *Building a set of T-shaped knowledge and skills is one of the most valuable things you can do for your future career and personal development*

The T-shaped Concept

Generally, the T-shaped concept is a metaphor for an individual’s depth and breadth in their skills. The vertical bar on the “T” represents the depth of related skills and expertise in a single field. In contrast, the horizontal bar represents a breadth of skills and the ability to collaborate across disciplines.

For students, the T-shaped concept not only means possessing deep, technical skills but also having broader characteristics or qualities. I want to emphasize that developing into a T-shaped civil engineering student gives you a competitive edge and could make all the difference in attaining a stable and successful career after graduation.

In this article, I will share my model for a T-shaped student. This model is not theoretical, but one that worked for me during my undergraduate days and shaped me into who I am today.

The T-shaped Model

The T-shaped model is a tripartite model with the vertical bar on the “T” representing professional development and the horizontal bar representing academic excellence and skill acquisition/entrepreneurship/leadership on either side.

Fitting into this model and finding appropriate balance is essential for staying competitive and becoming well-rounded professionals after graduation. Below, I will tell you everything you need to know about the T-shaped model and why you must become a T-shaped student.

Academic Excellence

Perhaps you believe that school is a scam; it is not. Nigeria’s tertiary education system presently finds itself in several challenges, including underfunding of institutions, infrastructural decay and neglect, academic corruption and fraud, wastage of resources, and distasteful conditions of learning and service. I was in the system for quite a long time, maybe 6-7 years, and I know what it means to be a student in such a system. However, school is and has never been a scam, and neither is academic excellence.

By the grace of God, I was privileged to graduate with a good grade, and I can tell you that a good grade grants you access to opportunities, boosts your confidence, and helps you earn respect. Indeed, grades are not a measure of a person, nor are they even the sole measure of academic accomplishment.

However, people care about grades. Many employers also care because your grades tell them if you can successfully handle tasks and produce results with less training or close supervision. I have two stories or experiences to share about academic excellence below.

First, I got a full-time job after the first month of leaving school. How did it happen? A Quantity Surveyor who contributed to training me during my 6 months of industrial training and knew about my professional capacity recommended me for the job. Honestly, I did not meet up with the job requirements. However, the company’s principal decided to take a chance on me because of my academic grade and punctuality.

I also passed the written test on structural design and showed a willingness to learn while working for the company. It was more like I was employed straight away, though on 3 months probation. Eventually, I left the job for NYSC camp before the end of the 3 months, and I could not return to the job even though the company was willing to allow me to keep my job.

Second, twelve other corps members and I were posted to an establishment for our NYSC year, and an interview was scheduled. One of the interviewers asked for my grade, which was the end of the interview. At the end of the interview, 7 of us were admitted, and I was the first person on the list. The academic grade was the difference.

images 1 1 — Education’s purpose is to replace an empty mind with an open one **— Malcolm Forbes**

Dear reader, you cannot afford to dismiss grades as unimportant, even if you have reservations about them, as many of us do. Furthermore, without good grades, though, gaining entrance into a master’s or PhD program or winning scholarships becomes much more difficult. Therefore, I can tell you sincerely that having a good grade will result in a life with many advantages.

Skill Acquisition/Entrepreneurship/Leadership

I have often heard people ask: what if I did not or cannot graduate with a good grade? It is no big deal because it does not mean you are doomed. You can always leverage acquired technical, soft, business and leadership skills. Being successful in school is more than just earning good grades. Going to school allows you to focus on developing new skills, making new friends, and crafting a path for your future.

Talking about leadership, taking up leadership position(s) as a student is a no-brainer because becoming a student leader will help you to develop innumerable leadership skills, including conflict resolution, cultural intelligence and professional advancement. Furthermore, becoming a student leader allows you to find how to build a team, how you work with others, and where your areas of improvement might be. Lastly, you will gain valuable soft and management skills, build networks and connections, and improve your CV or resume.

Having mentioned the importance of leadership skills and experience, I would like to remind you that losing focus on your academic and career goals is easier if you get financially stressed or frustrated. Do I also need to remind you that having access to money when you need it is enough to keep you going? Therefore, you must learn a skill or venture into a business that can earn money because trying to find your feet in the AEC industry can be very frustrating and overwhelming.

Furthermore, at the start of your journey, you may have to do many unpaid jobs or internships to get the experience and exposure you desire. Therefore, having a skill or business that pulls in money for you can make your journey much easier.

For example, I am not the type that is good at business (at least for now) and am not a fan of tech, but I ensured I left school with three skills — research, writing and teaching skills. These skills are what I have been leveraging from my penultimate year in school until now. Through these skills, I have been able to keep financial stress and frustration away with the earnings.

Screenshot 20220608 191454 — **Photo credit:** LinkedIn

Furthermore, I stumbled on a post on LinkedIn some time ago highlighting that it is wrong not to have a plan B, at least. In this post, the person in question lamented how he has been searching for jobs for almost two years without getting one. He even went as far as tearing his certificate. He must have been frustrated. Thankfully, he was able to get multiple job connections through the post.

Dear reader, with income-generating, leadership, and strong entrepreneurial skills and experience, not only will you have the option of bringing your projects and dreams into existence, but you are also likely to find yourself in high demand among potential employers who look for a mix of entrepreneurial and other professional skills.

Professional Development

How can you do better in a field when you don’t know better? It is vital to be true to yourself at this point. Do I have to remind you that great engineers are not born? Truly, they are made through professional and personal development. Therefore, evolving into a better you is the only way you will reach new heights professionally and personally.

Perhaps you had the chance to ask me what topped my priority list when I was in school; then, I would tell you it was striving to be a well-versed professional with high esthetic standards and a passion for excellence. I ensured I made use of every opportunity to advance the achievement of this goal because I never joked about it.

I did talk earlier about the importance of getting a good grade. However, your certificate holds little water compared to your experience. Therefore, you should never joke about internships and strike periods as undergraduates because they are great opportunities to gather relevant work experiences.

Similarly, if you are a recent graduate, I would advise that you pursue internship and apprenticeship opportunities that would give you relevant work experiences, even with little or no pay, rather than going for jobs with little pay and offering no relevant work experiences.

For example, from my experiences, I have discovered that anything that is meant to teach and instruct you will require patience, flexibility, growth and stretching. Engineering is not that easy because most of the concepts we adopt are partially abstract and partially concrete. Therefore, most of these things require time and careful direction or mentoring to understand and apply, and this is where your patience and willingness to learn through internships come into play.

Personally, internship experiences have changed and shaped my life and charted me on a path of career realization and helping people. It seemed like I was just being used or doing too much at first, but the benefits have been enormous. Funnily, I did not even get a penny until after my first 6 months at the organization, but I ensured that I put into practice all the skills I acquired, which has built my expertise. As a result, even while I was still an undergraduate, I was able to build my expertise and empower others alongside.

Dear reader, professional and personal development do not happen overnight but over time, that is, slowly and deliberately. It is a daily practice and lifestyle — a lifelong process!

Final Words

20160704114059 shutterstock 390101425 — *You cannot afford to be ordinary; come up higher*

As I round up this article, I want to tell you that self-confidence is the most beautiful thing you can possess in this field or career path. Unfortunately, many a time, young and aspiring engineers struggle with confidence issues because of their inability to measure up with the T-shaped model. Consequently, this results in fears that affect one’s performance and productivity.

However, the great news is: that you can do many things to measure up and help boost your confidence levels. Now is the best time to work on your confidence level and the lagging areas. Sooner, you will see yourself reach the heights you desire, after hours, days, weeks, and years of constant work and dedication.

To the young and aspiring just starting in their careers, please, invest in yourself, your learning and your career; and be unapologetic about it. The process is not always fun or easy but always beneficial. You can restart from the basics and no matter how challenging it gets, never forget to show up every day. Don’t give up. It will be worth it.

Lastly, my dear colleague, dream big, develop yourself, unleash your potential, collaborate with others, play to your strengths, work on your weaknesses, enjoy the process, share your unique gifts with the world, and grow your greatness by testing yourself, expanding yourself, learning and improving.

What is the Failure Load of Pile Foundation?

By

Ubani Obinna

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August 9, 2022

In our previous articles, we defined the failure load as the load that ultimately causes a pile to fail, or the load at which the soil’s bearing capacity is fully mobilised. However, in an engineering sense, failure might have occurred long before the structure was subjected to the maximum load because of the structure’s excessive settlement.

Engineers generally agree with Terzaghi’s assertion that, for practical purposes, the ultimate load can be defined as the load that results in a settlement of one-tenth of the pile’s diameter or width. However, the settlement at the working load may be excessive if this criterion is applied to piles with a large diameter and a nominal safety factor of 2.

The allowable load is almost always determined purely by tolerable settlement at the working load in situations when piles are serving as structural foundations. For every given type and size of pile in any soil or rock conditions, the engineer should be able to predict the load—settlement relationship up to the point of failure when calculating the allowable loads on piles.

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Failure Load and Settlement

In most cases a simple procedure is to calculate the ultimate bearing capacity of the isolated pile and to divide this value by a safety factor which experience has shown will limit the settlement at the working load to a value which is tolerable to the structural designer. But where settlements are critical it is necessary to evaluate separately the proportions of the applied load carried in shalt friction and end-bearing and then to calculate the settlement of the pile head from the interaction of the elastic compression of the pile shaft with the elasto-plastic deformation of the soil around the shaft and the compression of the soil beneath the pile base.

In all cases where piles are supported wholly by soil and are arranged in groups, the steps in calculating allowable pile loads are as follows;

Determine the base level of the piles which is required to avoid excessive settlement of the pile group. The practicability of attaining this level with the available methods of installing the piles must be kept in mind.
Calculate the required diameter or width of the piles such that settlement of the individual pile at the predetermined working load will not result in excessive settlement of the pile group.
Examine the economics of varying the numbers and diameters of the piles in the group to support the total load on the group.

The overall goal should be to adopt the highest working load on each individual pile while keeping the number of piles in each group as small as possible. As a result, pile caps will be smaller and less expensive, and the group settlement will be at a minimum. However, excessive settlement that causes intolerable differential settlements between neighbouring piles or pile groups may occur if the safety factor on the individual pile is too low.

The diameter and length of the piles in the case of isolated piles or piles arranged in very small groups will be determined only by taking into account the settlement of the isolated pile at the working load. Installation methods significantly impact the carrying capacity of piles. The interaction between the pile and the soil is influenced by a number of variables, including whether a pile is driven or cast in situ in a bored hole, whether it is straight-sided or tapered, and whether it is made of steel, concrete, or timber.

Engineers shouldn’t have very high expectations for formulas used to determine the carrying capacity of piles and shouldn’t be upset if the calculations show failure loads that are off by plus or minus 60% of the failure load determined by test loading. It should be kept in mind that a full-scale foundation is being evaluated when a pile is subjected to test loading.

It is not surprising that there could be relatively large differences in failure loads on any given site given the typical variability in ground conditions and the influence of installation techniques on ultimate resistance. If full-scale pad or strip foundations were loaded to failure, engineers would not be surprised to see such huge differences.

The alternative is to calculate allowable loads or design bearing capacities by dynamic formulae. These will give even wider variations than soil mechanics’ methods and, in any case, these dynamic formulae are largely discredited by experienced foundation engineers, unless they are used in conjunction with dynamic testing and analysis using standard equipment.

Digital Fabrication with Concrete and Sustainable Designs

By

Charity Mmuo

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August 6, 2022

Table of Contents

Over the past few years, the subject of digital fabrication with concrete has advanced significantly, with numerous alternative techniques having been created and numerous large-scale models having been built.

A recent assessment indicates that 3D concrete printing, the most extensively researched and commercially available of these technologies, is at a technology readiness level (TRL) of 6-7, comparable to polymer fused deposition modelling technology, putting it on the verge of becoming widely used. However, according to Flatt and Wangler (2022), the viability of such processes is still under discussion, which frequently results in divisive and pointless conversations.

Pioneers created these procedures with the goal of resolving productivity challenges in the building industry. However, in recent years, the need to expand architects’ creative areas and make it more cost-effective to build increasingly complex buildings made feasible by computer-aided design has been a major driving force behind digital fabrication in construction. With this capability, digital fabrication is being pushed more and more as a way to increase efficiency while also lowering the environmental impact of the building industry.

The fact that digitally fabricated structures would only use material where it was necessary, allowing for significant material savings, is a major defense of this claim. This reasoning encounters difficulties with concrete, too, because digitally created concrete frequently has a substantially larger environmental footprint per unit volume than regular concrete.

Additionally, the printing process itself may have some additional negative effects on the environment due to the manufacturing of the printing cell or the energy used to run it. It has been demonstrated that printing factors like printhead velocity and resolution have a significant impact on these process-related effects.

These well-known and currently investigated issues, as well as the fact that previous digital fabrication demonstrations have frequently focused more on “production prowess” than material savings, might result in dry and fruitless discussions of the technology’s sustainability.

Flatt and Wangler (2022) of the Institute for Building Materials, ETH Zurich, Zurich, Switzerland, recently published a paper in the journal, Cement and Concrete Research to highlight the real opportunities and challenges with regard to sustainability in digital fabrication with concrete, hopefully sparking fruitful discussions on the topic as the technology becomes more widely used.

Their article outlined a straightforward equation that incorporates the primary issues with regard to a structure’s environmental footprint. Three things come into play: Shape efficiency (or material utilized), Material footprint, and Service life (durability). The material itself was then further discussed in the context of concrete extrusion (3D printing), the technology that is most commonly used in many industries like cars, home improvement, computers, and PCB manufacturing. It was emphasized that in many cases, printed concrete is overdesigned and that well-chosen accelerators can address that issue quite effectively.

Main Factors of Concern

According to Flatt and Wangler (2022), three factors primarily determine a concrete structure’s environmental impact:

The total amount of materials used
The material’s embodied carbon dioxide, and
The durability.

According to the equation, it would be the product of the volume of material used and the environmental impact of that substance per unit volume, divided by the service life. It was highlighted that this first-order estimation does not account for variations in this and is only appropriate for comparing structures with equivalent load-bearing capacity. Additionally, the environmental effects of related changes in concrete production, such as formwork use or the aforementioned operating energy, are not expressly taken into account in this relationship.

2 6 — Schematic illustration of the main factors affecting the environmental impact of a structural element with a given load-bearing capacity per year of service life (Flatt and Wangler, 2022).

The primary benefit of digital fabrication is that it can require less material. Although the effect on durability is still being researched, this typically accompanies an increase in the material’s environmental imprint and a potential reduction in service life.

Such conflicts mean that the results of environmental balancing will typically not be trivial and will undoubtedly depend on the circumstances. According to Flatt and Wangler (2022), this necessitates a more thorough consideration of the issue, taking into account the true potential for material savings while keeping in mind the limitations of material composition and durability.

Shape Efficiency

The cost of constructing buildings that use less material to provide a certain load-bearing capacity is one of the key defenses for digital fabrication. Thus, it could facilitate structural design methods that are very successful but are all too frequently overlooked. In this context, it is worthwhile to reflect on Pier Luigi Nervi’s ribbed floor designs.

Although labour was inexpensive at the time these constructions were made, concrete was expensive. Today, the situation is the opposite, making it less expensive to create consistent floor slabs by utilizing a lot more concrete than is actually necessary. This is a particularly instructive example because it is simple to visualize the savings since floors are a significant consumer of concrete in structures.

2 7 — Ribbed floor system by Per Luigi Nervi at the Gatti Wool Factor

Material Footprint

Despite the potential for material savings, digital concrete frequently has a larger environmental impact than regular concrete, at least for the most popular kind of concrete extrusion. This can be reduced by using recycled components in place of new ones, looking into using different, lower-CO₂binders, or cutting the amount of paste in the cement (increasing aggregate content).

However, none of these approaches are specifically applicable to digital concrete and are instead investigated for concrete in general. The greater level of processing, particularly pumping, which normally increases paste volume, is principally responsible for digital concrete’s higher environmental impact.

In fact, given that mix designs often do not include coarse (>4 mm) aggregate, digital “concrete” is more appropriately referred to as digital “mortar” even though coarse aggregates are beginning to emerge in both academic and industrial settings. Whatever the case, the lower maximum aggregate size restricts the maximum packing fraction of aggregates, increasing the paste volume and, consequently, cement contents and carbon footprints that are larger.

Also keep in mind that while digital concretes have water-to-binder ratios that are more in line with infrastructure and high-performance concrete, their primary use has been in non-load bearing capacities, such as replacing concrete masonry or serving as a lost formwork for cast reinforced concrete. As a result, given their current utilization, digital concrete mixes frequently have twice as much cement content than is really required.

Durability

The durability of digital concrete is a crucial final aspect to take into account when talking about its sustainability. Concerningly, the prevalent technology of extrusion printing in this context can result in cold joints between the layers. However, in general, it depends on the material qualities, state of the extruded material and the previously deposited layer.

The formation of cold joints in 3D-printed concrete is still an active area of research. Therefore, it is influenced by the time interval (contour length and printing speed), and it also seems to be significantly influenced by the substrate’s surface drying throughout the layer time interval. If created, cold joints can weaken the bond between layers, but more significantly for durability, they open up channels for faster ingression of water and/or CO₂.

Investigations are now being done to determine how digital concrete reacts to freezing and thawing cycles, although early results show that it performs poorly when compared to conventional concretes. Digital concrete faces the added challenge of curing in full exposure, thus losing the formwork as a “skin,” which increases the likelihood of shrinkage cracking and opens channels for aggressive chemicals.

Only recently have shrinkage issues specific to digital concrete been studied, but future research on these issues will undoubtedly need to be expanded. Noting that lowering the paste content is an easy technique to reduce shrinkage, raising the maximum aggregate size is beneficial for lowering the material footprint as well as boosting durability.

Similar to regular concrete, durability describes a material’s performance under particular exposure conditions and for a particular use. In this situation, it is important to distinguish between structural applications—where reinforcement is required—and other situations because the majority of—but not all—concerns regarding the influx of aggressive species are caused by the presence of reinforcement.

Another noteworthy achievement is the Pantheon, a non-reinforced concrete building whose performance is dependent on sound structural planning. Digital manufacturing can therefore help with important design-related issues of durability.

Determining the appropriate applications for digital manufacturing technologies and whether steel reinforcing is necessary is then crucial. One choice is to largely abandon structural concrete in favour of competing with masonry, or to simply use printed concrete as a substitute for lost formwork.

This eliminates the challenging task of strengthening digital concrete. The problem of reinforcing, on the other hand, must be addressed if structural applications are the focus, and this involves a significant amount of continuing research. Despite this, significant advancements are still required before the majority of reinforcement schemes can be widely accepted and approved in practice.

Conclusions

The fundamental argument made in the study by Flatt and Wangler (2022) is that, in addition to being situation-specific, the subject of the environmental impact of digital fabrication is complex and has a difficult answer. Examples that highlight potential significant material savings were given, however they are now more expensive to build than bulkier pieces with simpler designs.

In fact, the potential for material efficiency is what sets digital concrete construction apart from conventional construction in terms of sustainability, a distinction that should not be lost on those who aim to promote the technology to this end.

This is especially important because adoption of the technology based solely on cost-related factors would entail accepting a higher carbon footprint in exchange for lower labour costs. The current incentives for the implementation of digital concrete processes appear to be primarily cost-driven, related to formwork and masonry labour. These technologies may still have other social advantages (or problems), but those are outside the focus of this research, which is just looking at the environmental aspect of these technologies.

For a variety of reasons, the footprint of digital concrete is bigger than that of traditional concrete. One has to do with using a stronger paste volume, and is a problem that can be solved by increasing the maximum aggregate size through material advancements, which may also have additional advantages like reduced shrinking and greater incentive to use local materials.

The use of high clinker cements and overly strong final designs appear to be another factor contributing to the high carbon footprint. Both are the outcome of ineffectively attempting to meet the needs for gaining strength. Instead, utilizing accelerators based on aluminum can increase strength when it is needed, preventing overdesign of final strength and allowing the use of carbon-lean cements. Therefore, such compounds could be taken into account for quick vertical building rates of thin (and more shape-efficient) structures as well as a way to perhaps reduce the environmental impact of digital concrete.

However, extra caution must be used while employing such compounds because doing so could result in the formation of cold joints, which could reduce durability. In fact, the effect of digital fabrication techniques on the durability of concrete must be further examined in light of durability’s relationship to environmental impact.

References:
Flatt R. J., Wangler T. (2022): On sustainability and digital fabrication with concrete. Cement and Concrete Research, Volume 158, 2022, 106837 https://doi.org/10.1016/j.cemconres.2022.106837

The contents of the cited original article published by Cement and Concrete Research (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.