To create hardened solid materials (also known as enhanced geomaterials), which have increased strength and stiffness, chemical agents (also known as binders) can be introduced into the ground and mixed with already-existing geomaterials such as soils and rocks. Lime, cement, silicate-based gel, and chemical solutions are examples of conventional binders.
Mixing and grouting are the two common techniques for introducing and mixing binders with soils. While the grouting method uses pipelines with high-pressure grouts, the mixing approach uses mechanical mixers or augers. Mixing can take place at depths (to form columns or walls) or at the surface (mostly for improving subgrade and base course). Deep soil mixing is the term used to describe the process of mixing binders (hardening agents) with soils at depths.
Basic Concepts of Deep Soil Mixing
The deep soil mixing (DSM) technique uses augers to mix in situ soil at depths with a binder (cement, lime, slag, or other binders). Either a wet method or a dry method can be used for deep soil mixing. Figure (a) below shows a wet method that utilises the binder as a slurry, whereas Figure (b) depicts a dry method that uses the binder as a powder.
One to eight rotary hollow shafts with cutting and mixing blades above the tip may be present in the equipment for the wet method. Each hollow shaft allows the introduction of the binder slurry into the ground, which flows from the nozzle as the shaft either sinks into the soil or is removed. To increase the consistency of the soil-binder combination, some equipment features mixing blades that rotate in opposite directions.
Single or dual rotary shafts with cutting and mixing blades above the tip may be used in the dry method equipment. By using air pressure, the nozzle and each hollow shaft, the binder powder is delivered into the soil.
Rigid inclusions (such as concrete piles or spun piles) can be used to stiffen deep mixed columns in order to increase their stiffness and vertical and horizontal load capabilities. A composite column is another name for this kind of column. Some reseachers have demonstrated that after the installation of the column, the strength of the nearby sensitive clay generally recovered or even surpassed its pre-column strength. This has been attributed the long-term property changes to thixotropic hardening, consolidation, and diffusion of ions from the hardening agent (binder), and the short-term changes to soil disturbance and fracture.
Suitability of soils for Deep Mixing
Deep soil mixing has typically been utilized to strengthen soft cohesive soils, while it has also occasionally been used to reduce permeability and prevent the liquefaction of cohesionless soils. The ideal soil characteristics for deep mixing are shown in the Table below.
Property
Favorable Soil Chemistry
pH
Should be greater than 5
Natural water content
Should be less than 200% (dry method) and less than 60% (wet method)
Organic content
Should be less than 6% (wet method)
Loss on ignition
Should be less than 10%
Humus content
Should be less than 1.0%
Electrical conductivity
Should be greater than 0.04 mS/mm
If the soil is very hard, very dense, and has rocks or other obstructions, deep soil mixing becomes challenging. Due to the massive machinery utilised in most projects, deep mixing typically requires open site access and overhead clearance. In maritime operations, deep mixing can go as deep as 70 metres, while on land it can go as deep as 30 metres.
Applications of Deep Soil Mixing
Columns from deep soil mixing have been used for many applications in soft soils:
support of superstructures, including buildings, walls, embankments, and the likes
waterfront and marine applications including quay walls, wharf structures, and breakwaters
stabilization of slopes
lateral support
containment of water and pollutant,
liquefaction mitigation, and,
vibration reduction.
Generally, deep soil mixing columns are utilised in various applications to reduce vibration, contain water and pollutant flow, improve slope stability, reduce settlement, increase bearing capacity, and provide lateral support.
As seen in the Figure below, there are commonly four distinct arrangements for DM columns. When an area replacement ratio is relatively low, such as less than 50%, individual columns are used. The main uses of individual columns have been to improve bearing capacity and reduce settlement. When a high area replacement ratio, such as more than 50%, is required, block patterns are employed to bear substantial vertical and/or horizontal loads. Large marine structures have mostly benefited from the usage of block patterns to increase stability. This design pattern has also been applied to waste containment to stop dangerous substances from leaching.
Figure 8.3 Patterns of columns: (a) individual column, (b) block, (c) wall, and (d) grid.
For retaining walls to provide lateral support, seepage walls to stop seepage, curtain walls to hold waste, and walls perpendicular to the centerline of embankments to promote stability, panel or wall patterns have been widely utilised. Between the wall pattern and the block pattern is the grid pattern. It can be utilised in applications that call for block and wall layouts. The grid layout has a special use in preventing sandy soil liquefaction. The cells of grids are where the liquefiable soils are contained.
In recent years, embankments over weak foundations have primarily been supported by columns. One of the most significant applications of column technologies is thought to be this one. Deep mixed columns have also been progressively combined with other technologies, including rigid piles, PVDs, and geosynthetic reinforcement.
The geosynthetic reinforcement placed on top of the columns serves as a bridge layer to distribute the embankment load to the columns and lessen the variance in column settlement. Geosynthetic-reinforced column-supported embankments are frequently used for the following purposes:
(1) bridge approach (2) roadway widening (3) subgrade improvement, and (4) support of storage tanks
Advantages and Limitations of deep soil mixing
The deep mixing method has the following advantages:
Applicable for most soil types
Installed at great depths
Relatively fast installation
Low noise and vibration level
Formation of a DSM wall for earth retaining and water barrier at the same location and time
Less spoil soil, especially for the dry method
However, the deep soil mixing method may have the following limitations:
To transfer structural load to a capable bearing strata, micropiles, often referred to as minipiles, needle piles, or pin piles, are employed in practically any type of ground. Micropiles are slender columns of deep foundations with relatively small diameter and low load bearing capacity that are installed relatively close to each other. They are constructed using high strength steel casing or threaded pipes, and may be filled with concrete grouts and steel reinforcement. Sometimes, micropiles are also constructed using concrete or timber.
Micropiles were initially low-capacity, small-diameter piles (2 to 4 in., or 5 to 10 cm). However, improvements in drilling technology have led to design load capacities and diameters exceeding 300 tonnes and 250 mm respectively. In sites with low headroom and restricted access, micropiles are frequently used.
Although there are many uses for micropiles, they are most frequently utilised to support new or existing foundations in places with little headroom and difficult access. Other uses of micropiles are to provide structural support, underpin foundations to eliminate settlement, improve soil and slope stability, and transfer loads to a stable soil strata.
Applicable soil types
Micropiles can be employed in almost any subsurface soil or rock since they can be inserted using drilling equipment and combined with various grouting procedures to form the bearing element. The bearing soil or rock will determine their load carrying capacity. The absence of necessary overhead or lateral site constraints that would prevent installations requiring considerably larger equipment is one of the major benefits of using micropiles.
Micropiles can offer large compressional capacity as well as good tensile capacity. According to the industry (www.rembco.com), micropiles have a working capacity of up to 2200 kN (250 tonnes). According to (www.keller.com), capacities of about 500 tonnes have also been achieved. When micropiles are pressure-grouted in place for higher capacity, the relative density and lateral pressure of the surrounding soil (if compressible) is increased, thereby leading to considerably higher shaft resistance.
Traditionally, micropiles are installed in predrilled holes that are filled with concrete.
Equipment
Typically, the micropile shaft is bored or hammered into position. A drill rig or small pile driving hammer mounted on a base unit is therefore necessary. It is necessary to have the proper grout mixing and pumping equipment since the pipe is filled with cement grout. The proper grouting equipment is also necessary if compaction grout or jet grout will be used to produce the bearing element.
Micropiles typically require compact small-sized equipment that can be used in confined spaces with limited access. The application of micropiles has a very broad range; it can be carried out in spaces with little vertical clearance, such as basements and under bridge structures. The interiors of commercial structures, tiny tunnels, mountain paths, rice fields, mountainous forested areas, steep slopes, and other places are some other examples of important sites where the micropiles can be installed. Additionally, micropiles can be inserted through existing foundations and used to support buildings as well as fix broken foundations.
Procedures for construction
Typically, the micropile shaft is either driven or drilled into position. Some sort of bearing element must be created if the specified pile capacity cannot be reached in end bearing and side friction along the pipe. This could entail drilling a rock socket, filling it with grout, and installing a full length, high-strength threaded bar if the tip is covered in rock. Compaction grouting or jet grouting can be carried out below the bottom of the pipe if it is surrounded or covered by soil. Additionally, the pipe can be partially withdrawn while being filled with grout that is pressured to produce a bond zone.
The figure above shows the micropile installation procedure. A drilling technique that is appropriate for the soil/site conditions is used to drill boreholes with casings. Following removal of the drilling rod and tools, reinforcement bars—typically corrosion-resistant steel bars—are next placed into the boreholes. Next, grouting is carried out sequentially under pressure as the casing is gradually removed.
Materials for construction of micropiles
A steel rod or pipe often makes up the micropile. The bond zone and pipe fill are frequently created using grout made of Portland cement. Another typical item is a full-length steel threaded bar made of grade 40 (275 N/mm2) to 150 ksi (1035 N/mm2) steel. The micropile may occasionally be nothing more than a reinforced concrete grout column.
Design of micropiles
Three components make up the design of micropiles;
the connection to the current or proposed structure,
the pile shaft that transmits the load to the bearing zone, and
the bearing element that sends the load to the layer of soil or rock that is carrying the load.
The piling section is designed using a typical structural analysis. In the event that a grouted friction socket is intended, the Table below can be used to determine the diameter and length of the socket. Bond lengths more than 30 feet (9.2 metres) do not improve the capacity of the piles.
Soil/Rock Description
SPT N value (blows/ft)
Grout Bond with Soil/Rock (ksf)
Nonpressure grouted
Silty clay
3—6
0.5—1.0
Sandy clay
3—6
0.7—1.0
Medium clay
4-8
0.75—1.25
Firm clay or stiffer
>8
1.0—1.5
Sands Soft shales
10-30
2—4 5—15
Slate and hard shales
15—28
Sandstones
15—35
Soft limestone
15—33
Hard limestone
20—35
Pressure grouted
Medium dense sand
3.5 – 6.5
Dense sand
5.5 – 8.5
Very dense sand
8-12
1 ft = 0.308m; 1 ksf = 47.9 kPa
Micropiles can be divided into two categories based on design uses. The first category consists of micropiles that are loaded laterally or axially. This collection of micropiles distributes structural loads to the competent strata beneath the foundation (for example, through the underpinning of structures), or they can be utilised to stop the movement of failure planes (i.e. stabilisation of slopes).
The second category consists of micropiles that are utilised to create a reinforced soil composite, which strengthens the soil mass. However, based on the grouting techniques, micropiles can also be divided into four groups (Groups A, B, C, and D).
The grouting for the group A micropiles is set under gravity. In group B, grout is injected under pressure into the hole, but the pressure is constrained to prevent hydrofracturing of the nearby soil. Group C micropiles are installed in two steps: first, a primary grout is pressure-applied to hydrofracture the surrounding ground, and then, just before the main grout sets, a secondary grout is injected through a manchette tube. The primary grout is injected after the primary grout has hardened in group “D” micropiles, which are similar to group “C” micropiles.
Quality control and assurance
During the construction of the micropile, the drilling penetration rate can be monitored as an indication of the stratum being drilled. Grout should be sampled for subsequent compressive strength testing. The piles verticality and length should also be monitored and documented. A test pile is constructed at the beginning of the work and load tested to 200% of the design load in accordance with the standard specification ASTM D 1143.
Columns are the most noticeable feature of a structure and are often used to support gravity loads transmitted from the floors or roofs of buildings. Strength, economy, adaptability, good fire resistance, and robustness are all advantages of in-situ reinforced concrete columns. During the design of columns, sound engineering judgement is often needed to balance their location, size, and shape with horizontal element spans and economy.
Circular columns are often designed for the ultimate axial load, NEd, ultimate design moment, MEd, and ultimate shear force VEd. For internal columns, moments may generally be assumed to be nominal when compared with external columns.
Due to their uniform strength in all directions, circular concrete columns are frequently employed in the design of pilings and bridge piers, and are very convenient for seismically active areas. Furthermore, it is much easier to confine the concrete using special reinforcement in circular columns than in other shapes.
Theoretical Background
When the neutral axis remains within a section, the basic equations for a section’s equilibrium under combined bending and axial load are as follows:
In Equation (2), moments have been taken about the concrete section’s centroid. The summation signs represent a summation of all layers of reinforcement in the section. Tensile stresses must be considered negative when summing them up. di is the distance between the section’s compressive face and the ith layer of reinforcement.
We can substitute 0.459fck for fav and 0.416 for β by assuming that the partial safety factors for the steel and concrete are 1.15 and 1.5, respectively, and that αcc is 0.85. For cases in which the neutral axis remains within the section, the resulting equations are rigorous. More complex expressions must be resolved when the entire section is in compression for the following situations;
(1) the portion of the parabolic curve cut off by the bottom of the section and (2) the reduction in the ultimate strain at the compressive face
Additionally, for situations when the concrete strength is greater than 50 N/mm2, more complicated equations are required. Because of how complex the resulting equations are, it is inappropriate to present them here. Using design charts is an easier method.
Some design charts for circular columns are given below. Since six reinforcing bars are the minimum that can be employed in a circular section, this is the assumption made while drawing the charts. It is discovered that no specific arrangement of reinforcement in relation to the axis of bending will always result in minimal strength. As a result, the charts are produced to provide a lower bound envelope to the interaction diagrams for different bar arrangements.
Design Example of RC Circular Columns
Verify the resistance of 6H25 bars to withstand the loads in a column of a high-rise building in accordance with EN1992-1-1 incorporating Corrigendum January 2008 and the UK national annex. The design information is as follows;
Height of column = 5m fck = C25/30 fyk = 500 MPa Diameter of column = 400 mm
Design axial load; NEd = 1500.0 kN Moment about y-axis at top; Mtopy = 66.0 kNm Moment about y-axis at bottom; Mbtmy = 32.0 kNm Moment about z-axis at top; Mtopz = 25.0 kNm Moment about z-axis at bottom; Mbtmz = 5.5 kNm
Column geometry Overall diameter; h = 400 mm Clear height between restraints about y-axis; ly = 5000 mm Clear height between restraints about z-axis; lz = 5000 mm
Stability in the z direction; Braced Stability in the y direction; Braced
Concrete details Concrete strength class; C25/30 Partial safety factor for concrete (2.4.2.4(1)); γC = 1.50 Coefficient αcc (3.1.6(1)); αcc = 0.85 Maximum aggregate size; dg = 20 mm
Reinforcement details Nominal cover to links; cnom = 35 mm Longitudinal bar diameter; φ= 25 mm Link diameter; φv = 8 mm Total number of longitudinal bars; N = 6
Area of longitudinal reinforcement; As = N × (π × φ2 / 4) = 2945 mm2 Characteristic yield strength; fyk = 500 N/mm2 Partial safety factor for reinft (2.4.2.4(1)); γS = 1.15 Modulus of elasticity of reinft (3.2.7(4)); Es = 200 kN/mm2
Fire resistance details Fire resistance period; R = 60 min Exposure to fire; Exposed on more than one side Ratio of fire design axial load to design resistance; mfi = 0.70
Axial load and bending moments from frame analysis Design axial load; NEd = 1500.0 kN Moment about y axis at top; Mtopy = 66.0 kNm Moment about y axis at bottom; Mbtmy = 32.0 kNm Moment about z axis at top; Mtopz = 25.0 kNm Moment about z axis at bottom; Mbtmz = 5.5 kNm
Beam/slab concrete strength class; C25/30
Beams/slabs providing rotational restraint about y axis Depth on side A; hA1y = 500 mm Width on side A; bA1y = 300 mm Length on side A; lA1y = 4500 mm
Depth on side B; hB1y = 500 mm Width on side B; bB1y = 300 mm Length on side B; lB1y = 6000 mm
Beams providing rotational restraint about z axis Depth on side A; hA1z = 500 mm Width on side A; bA1z = 300 mm Length on side A; lA1z = 3500 mm
Depth on side B; hB1z = 500 mm Width on side B; bB1z = 300 mm Length on side B; lB1z = 3500 mm
Relative flexibility end 2 for buckling about y axis; k2y = 1000.000 Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
Check nominal cover for fire and bond requirements Min. cover reqd for bond (to links) (4.4.1.2(3)); cmin,b = max(φv, φ – φv) = 17 mm Min axis distance for fire (EN1992-1-2 T 5.2a); afi = 40 mm Allowance for deviations from min cover (4.4.1.3); Dcdev = 10 mm Min allowable nominal cover; cnom_min = max(afi – φ/2 – φv, cmin,b + Dcdev) = 27.0 mm
PASS – the nominal cover is greater than the minimum required
Effective depth and inertia of bars for bending about y axis For the purposes of determining the bending capacity and interaction diagrams in this calculation, bending about the y axis is taken to be when there are two furthest equidistant bars on each side of the column centreline. Bending about the z axis is taken to be when there is one furthest bar on each side of the column centreline.
Area per bar; Abar = π × φ2 / 4 = 491 mm2 Radial dist from column centre to longitudinal bar; rl = h/2 – cnom – φv – φ/2 = 144.5 mm Subtended angle between adjacent bars; α = (360 deg) / N = 60.0 deg
Layer 1; dy1 = h/2 + rl × cos(α/2) = 325.1 mm 2nd moment of area of reinft about y axis; Iy1 = 2 × Abar × (dy1 – h/2)2 = 1537 cm4
Layer 2; dy2 = h / 2 + rl × cos[(2 – 1) × a + a/2] = 200.0 mm 2nd moment of area of reinft about y axis; Iy2 = 2 × Abar × (dy2 – h/2)2 = 0 cm4
Layer 3; dy3 = h / 2 + rl × cos[(3 – 1) × a + a/2] = 74.9 mm 2nd moment of area of reinft about y axis; Iy3 = 2 × Abar × (dy3 – h/2)2 = 1537 cm4
Total 2nd moment of area of reinft about y axis; Isy = 3075 cm4
Radius of gyration of reinft about y axis; isy = √(Isy / As) = 102 mm Effective depth about y axis (5.8.8.3(2)); dy = h / 2 + isy = 302 mm
Effective depth of bars for bending about z axis Layer 1 (tension face); dz1 = h / 2 + rl = 344.5 mm 2nd moment of area of reinft about z axis; Iz1 = Abar × (dz1 – h / 2)2 = 1025 cm4
Layer 2; dz2 = h / 2 + rl × cos[(2 – 1) × a] = 272.3 mm 2nd moment of area of reinft about z axis; Iz2 = 2 × Abar × (dz2 – h/2)2 = 512 cm4
Layer 3; dz3 = h / 2 + rl × cos[(3 – 1) × a] = 127.8 mm 2nd moment of area of reinft about z axis; Iz3 = 2 × Abar × (dz3 – h/2)2 = 512 cm4
Layer 4; dz4 = h / 2 + rl × cos[(4 – 1) × a] = 55.5 mm 2nd moment of area of reinft about z axis; Iz4 = 1 × Abar × (dz4 – h/2)2 = 1025 cm4
Total 2nd moment of area of reinft about z axis; Isz = 3075 cm4
Radius of gyration of reinforcement about z axis; isz = √(Isz / As) = 102 mm Effective depth about z axis (5.8.8.3(2)); dz = b / 2 + isz = 302 mm
Relative flexibility at end 1 for buckling about y axis Second moment of area of column; Iy = π × h4 / 64 = 125664 cm4 Second moment of area of beam on side A; IA1y = bA1y × hA1y3 / 12 = 312500 cm4 Second moment of area of beam on side B; IB1y = bB1y × hB1y3 / 12 = 312500 cm4 Relative flexibility (PD6687 cl. 2.10); k1y = max(0.1, (Ecm × Iy / ly) / [2 × Ecm_b × (IA1y/lA1y + IB1y/lB1y)]) = 0.103 Relative flexibility end 2 for buckling about y axis; k2y = 1000.000
Relative flexibility at end 1 for buckling about z axis Second moment of area of column; Iz = π × h4 / 64 = 125664 cm4 Second moment of area of beam on side A; IA1z = bA1z × hA1z3 / 12 = 312500 cm4 Second moment of area of beam on side B; IB1z = bB1z × hB1z3 / 12 = 312500 cm4 Relative flexibility (PD6687 cl. 2.10); k1z = max(0.1, (Ecm × Iz / lz) / [2 × Ecm_b × (IA1z/lA1z + IB1z/lB1z)]) = 0.100 Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
Calculated effective length (cl. 5.8.3.2)
Eff. length about y axis (braced) (5.8.3.2(3)); l0y = 0.5 × ly × [(1 + k1y/(0.45+k1y)) × (1 + k2y/(0.45+k2y))]0.5 = 3851 mm
Eff. length about z axis (braced) (5.8.3.2(3)); l0z = 0.5 × lz × [(1 + k1z/(0.45+k1z)) × (1 + k2z/(0.45+k2z))]0.5 = 3843 mm
Column slenderness about y axis Radius of gyration; iy = h / 4 = 10.0 cm Slenderness ratio (5.8.3.2(1)); ly = l0y / iy = 38.5
Column slenderness about z axis Radius of gyration; iz = h / 4 = 10.0 cm Slenderness ratio (5.8.3.2(1)); lz = l0z / iz = 38.4
Design bending moments Frame analysis moments about y axis combined with moments due to imperfections (cl. 5.2 & 6.1(4)) Ecc. due to geometric imperfections (y axis); eiy = l0y /400 = 9.6 mm Min end moment about y axis; M01y = min(abs(Mtopy), abs(Mbtmy)) + eiy × NEd = 46.4 kNm Max end moment about y axis; M02y = max(abs(Mtopy), abs(Mbtmy)) + eiy × NEd = 80.4 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1) Factor A; A = 0.7 Mechanical reinforcement ratio; w = As × fyd / (Ac × fcd) = 0.719 Factor B; B = √(1 + 2 × w) = 1.562 Moment ratio; rmy = M01y / M02y = 0.577 Factor C; Cy = 1.7 – rmy = 1.123 Relative normal force; n = NEd / (Ac × fcd) = 0.843 Slenderness limit; llimy = 20 × A × B × Cy / √(n) = 26.7
ly > llimy – Therefore, second order effects must be considered
Frame analysis moments about z axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))
Ecc. due to geometric imperfections (z axis); eiz = l0z /400 = 9.6 mm
Min end moment about z axis; M01z = min(abs(Mtopz), abs(Mbtmz)) + eiz × NEd = 19.9 kNm
Max end moment about z axis; M02z = max(abs(Mtopz), abs(Mbtmz)) + eiz × NEd = 39.4 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1) Factor A; A = 0.7 Mechanical reinforcement ratio; w = As × fyd / (Ac × fcd) = 0.719 Factor B; B = √(1 + 2 × w) = 1.562 Moment ratio; rmz = M01z / M02z = 0.505 Factor C; Cz = 1.7 – rmz = 1.195 Relative normal force; n = NEd / (Ac × fcd) = 0.843 Slenderness limit; llimz = 20 × A × B × Cz / √(n) = 28.5 lz > llimz – Second order effects must be considered
Local second order bending moment about y axis (cl. 5.8.8.2 & 5.8.8.3)
Relative humidity of ambient environment; RH = 50 % Column perimeter in contact with atmosphere; u = 1257 mm Age of concrete at loading; t0 = 28 day Parameter nu; nu = 1 + w = 1.719 Approx value of n at max moment of resistance; nbal = 0.4 Axial load correction factor; Kr = min(1.0 , (nu – n) / (nu – nbal)) = 0.665 Reinforcement design strain; eyd = fyd / Es = 0.00217
Resultant design bending moment for a circular column Resultant design moment; MEd = √(MEdy2 + MEdz2) = 121.0 kNm
Moment capacity about y axis with axial load NEd
Moment of resistance of concrete By iteration:- Position of neutral axis; y = 289.8 mm Depth of stress block; dsby = min(lsb × y , h) = 231.8 mm Area of concrete in compression; Asby = 75498 mm2 Concrete compression force (3.1.7(3));Fyc = h × fcd × Asby = 962.6 kN Centroid of concrete compression from column cl; ysby = 68.0 mm Moment of resistance; MRdyc = Fyc × ysby = 65.4 kNm
Moment of resistance of reinforcement Strain in layer 1; εy1 = εcu3 × (1 – dy1 / y) = -0.00043 Stress in layer 1; σy1 = max(-1×fyd, Es × εy1) = -85.5 N/mm2 Force in layer 1;Fy1 = 2 × Abar × sy1 = -83.9 kN MRdy1 = Fy1 × (h / 2 – dy1) = 10.5 kNm
Strain in layer 2; εy2 = εcu3 × (1 – dy2 / y) = 0.00108 Stress in layer 2; σy2 = min(fyd, Es × εy2) – h × fcd = 204.1 N/mm2 Force in layer 2; Fy2 = 2 × Abar × sy2 = 200.4 kN Moment of resistance of layer 2; MRdy2 = Fy2 × (h/2 – dy2) = 0.0 kNm
Strain in layer 3; εy3 = εcu3 × (1 – dy3 / y) = 0.00260 Stress in layer 3; σy3 = min(fyd, Es × εy3) – h × fcd = 422.0 N/mm2 Force in layer 3; Fy3 = 2 × Abar × sy3 = 414.3 kN Moment of resistance of layer 3; MRdy3 = Fy3 × (h/2 – dy3) = 51.8 kNm
Resultant concrete/steel force; Fy = 1493.3 kN
PASS – This is within half of one percent of the applied axial load
Combined moment of resistance Moment of resistance about y axis; MRdy = 127.8 kNm
Moment capacity about z axis with axial load NEd Moment of resistance of concrete By iteration:- Position of neutral axis; z = 287.0 mm Depth of stress block; dsbz = min(lsb × z , h) = 229.6 mm Area of concrete in compression; Asbz = 74628 mm2 Concrete compression force (3.1.7(3)); Fzc = h × fcd × Asbz = 951.5 kN Centroid of concrete compression from column cl; ysbz = 69.1 mm Moment of resistance; MRdzc = Fzc × ysbz = 65.8 kNm
Moment of resistance of reinforcement Strain in layer 1; εz1 = εcu3 × (1 – dz1 / z) = -0.00070 Stress in layer 1; σz1 = max(-1×fyd, Es × εz1) = -140.2 N/mm2 Force in layer 1; Fz1 = 1 × Abar × sz1 = -68.8 kN Moment of resistance of layer 1; MRdz1 = Fz1 × (h / 2 – dz1) = 9.9 kNm
Strain in layer 2; εz2 = εcu3 × (1 – dz2 / z) = 0.00018 Stress in layer 2; σz2 = min(fyd, Es × εz2) = 36.0 N/mm2 Force in layer 2; Fz2 = 2 × Abar × sz2 = 35.3 kN Moment of resistance of layer 2; MRdz2 = Fz2 × (h / 2 – dz2) = -2.6 kNm
Strain in layer 3; εz3 = εcu3 × (1 – dz3 / z) = 0.00194 Stress in layer 3; σz3 = min(fyd, Es × εz3) – h × fcd = 375.7 N/mm2 Force in layer 3; Fz3 = 2 × Abar × sz3 = 368.8 kN Moment of resistance of layer 3; MRdz3 = Fz3 × (h/2 – dz3) = 26.6 kNm
Strain in layer 4; εz4 = εcu3 × (1 – dz4/z) = 0.00282 Stress in layer 4; σz4 = min(fyd, Es × εz4) – h × fcd = 422.0 N/mm2 Force in layer 4; Fz4 = 1 × Abar × sz4 = 207.2 kN Moment of resistance of layer 4; MRdz4 = Fz4 × (h/2 – dz4) = 29.9 kNm Resultant concrete/steel force; Fz = 1494.0 kN
PASS – This is within half of one percent of the applied axial load
Combined moment of resistance Moment of resistance about z axis; MRdz = 129.8 kNm
Minimum moment capacity with axial load NEd Minimum moment capacity; MRd = min(MRdz, MRdy) = 127.8 kNm
PASS – The moment capacity exceeds the resultant design bending moment
In civil engineering design and construction works, professional engineers (fully registered/chartered engineers) are often asked to review the work or documents prepared by another professional engineer. In all professional engineering bodies, there are existing policies or guidelines on how engineers should professionally relate with fellow engineers. The aim of this article is to highlight some well established and globally accepted guidelines for reviewing the work of a fellow professional engineer.
The guidelines in this article provide professional engineers performing reviews of work created by other practitioners with guidance on how to complete such tasks in a way acceptable to the profession. The suggestions in this article are thought to be in line with all of the practitioners’ professional obligations, and are adapted from the guidelines of the Professional Engineers Ontario (PEO).
In so many professional engineering bodies’ ethics and code of conducts (professional engineering acts), it is clearly stated that engineers should not agree to review another practitioner’s work for the same employer unless you have the other practitioner’s consent or the other practitioner’s connection to the work has been terminated.
Why should my work be reviewed?
Although fairly specific, the prohibition on reviewing another engineer’s work by several engineering acts is constrained by some factors. Professional engineers shouldn’t, however, object to having their work or that of a colleague, reviewed. It is reasonable and, in the event of legally mandated requirements, a necessary practice for another engineer to review the work of a practitioner. It is in accordance with a practitioner’s ethical requirements, the association’s duty to uphold high professional standards, and the requirement to preserve the public’s confidence in the profession as long as the practice is carried out impartially and fairly.
Giving feedback on the work of another professional engineer has wider ramifications that should be understood by all practitioners. The fact that a practitioner’s work was reviewed may occasionally have a detrimental effect on the engineer’s reputation. A negative review can permanently damage the relationship between a practitioner and a client or employer, even if the outcome is not generally publicised. Reviewing engineers must be familiar with the methods for assuring the fairness, impartiality, and thoroughness of the review process if they are to ensure reviews achieve the justifiable aims in the most professional manner.
An impartial evaluation may reveal errors or issues with the examined work that need to be disclosed. Different projects will differ in what needs to be reported and to whom, so the reviewing engineer should be given some leeway. The reviewer must understand the difference between legitimate flaws in the work and professional differences of opinion in order to correctly convey what is required. Practitioners conducting reviews must be aware of these problems and take all necessary precautions to handle them properly.
Reasons and Types of Professional Review
A practitioner’s work may be reviewed for a variety of reasons and in a variety of contexts. Colleagues inside an organisation, staff members of regulatory agencies, employees of client companies or other organisations utilising the engineer’s work, or outside engineers hired by a client to provide an unbiased evaluation of the work are all examples of reviewers. A request for a review may result from a variety of situations, including corporate quality assurance and legal action against a practitioner.
However, the Professional Engineers Ontario identified two general types of review;
Practice review, and
Technical review
In the wider context, the main objective of a practice review is to evaluate the job performed by an engineer or the service they supplied. In this case, the assessment of the practitioner’s performance is made.
Conversely, a technical review evaluates whether the information in a document or design produced by an engineer is accurate, complete, or acceptable. Technical reviews produce opinions about the output quality of the job, not the engineering process itself. In other words, a technical review evaluates a design, analysis, calculation, instruction, or opinion, but a practice review evaluates the practice of a professional engineer.
Technical Reviews
Technical reviews are conducted to evaluate a design, technical report, or other engineering service output’s acceptability and see if it complies with project criteria. Typically, these evaluations only involve randomly checking engineering documents for technical errors.
Technical reviews, however, can involve in-depth analyses of the methodology, design criteria, and calculations employed by the authoring engineer as well as the accuracy, suitability, economic viability, or other characteristics of the design decisions or study recommendations, depending on the needs of the client.
The reviewer will confirm the accuracy of computations in addition to making sure the right approach was used. Technical reviewers should also make sure that the standards, codes, and other design criteria utilised in the project under consideration are acceptable for it and that they were implemented correctly. According to the Professional Engineers Ontario, technical reviews generally aim to evaluate the following things:
whether the completed work has met the objectives;
whether the objectives set out for the work were reasonable;
whether there were other options that should have been considered by the authoring engineer;
whether the evaluation of options is comprehensive, unbiased and rigorous;
validity of any assumptions made by the authoring engineer;
validity of the conclusions or calculations;
validity of recommendations; and
fitness of the design or recommendations to the requirements.
The reviewer is free to offer feedback on whether the design is suitable for the intended use, including assessments of its effectiveness and economics. In the case of a technical report, the reviewer should state whether the analysis or facts in the report support the recommendations.
The review engineer may comment on the inventive, efficient, cost-effective, and other noteworthy parts of the design or report in addition to pointing out flaws, abuse, or lack of application of recognised industry standards, regulations, or design criteria.
A technical review wouldn’t often be as thorough as an original design or analysis. In most circumstances, random checks of the work rather than a thorough examination of every part of the writing engineer’s work would be carried out. The extent of the review, however, must be left to the reviewers’ judgement, based on what they think is required to fully complete the assignment and satisfy themselves that they have enough data to draw reliable conclusions.
The reviewing engineer may suggest to the client or employer that a more thorough examination is required if such a recommendation is justified in light of the issues found during the assessment.
Regulatory Review
Municipal building departments, building control agencies, provincial ministries and their agencies, federal government agencies, and town planning agencies are examples of regulatory authorities that carry out different types of reviews. Employees of the regulatory body in these situations examine the practitioners’ work that has been submitted for approval in order to verify that it complies with prescriptive legislation like building codes and municipal bye laws.
A professional engineer is not required to analyse regulatory compliance, with the exception of what is detailed below, as it is a legal rather than an engineering matter. In most cases, it is unlawful for those performing regulatory compliance checks to provide engineering opinions.
Only the information in the engineering papers or drawings must be compared to standards, codes, or legal requirements during the compliance check. For instance, whether the design is economical or not should not be their concern, rather it should bother on whether it meets the regulatory requirements.
A regulatory body should only notify the practitioner when performing compliance checks to identify non-compliance issues. The authoring engineer must be trusted to make the final call on how to modify the document to address non-compliant concerns.
Regulating authorities do, however, occasionally conduct more thorough evaluations to ascertain whether designs are technically adequate, to ascertain whether they fulfil performance standards, or to evaluate designs that are not subject to prescriptive rules.
For the municipality’s own due diligence, the building department, for instance, might carefully examine a proposed structural design to ensure that it is secure. A professional engineer must conduct this kind of evaluation, and it must be conducted in accordance with the guidelines for a technical review outlined in this policy.
In-house Design Review in Organisations
For a variety of reasons, professional engineers working for engineering firms or other organisations may be asked to examine their coworkers’ work. Such internal evaluations could be technical reviews for quality control or practise reviews to see if the authoring engineer is competent of completing the task at hand or for personnel performance evaluation objectives.
Because the firm will ultimately be responsible for the outcome of the engineering service, it is expected that the relationship between the practitioners will be very cooperative when reviews are conducted by a colleague within an engineering firm. The reviewer may act as a problem-solving consultant in these situations. For this reason, a practitioner with greater authority inside the company may override the authoring engineer’s judgement.
Written corporate policy notifying all practitioners that their work will be examined is sufficient notice in organisations where all drawings and documentation are scrutinised for quality before issuance or approval. Only regular reviews—including those conducted as part of employee performance audits—are subject to this regulation. The practitioner must be informed prior to the assessment of the work in situations where the review deviates from customary quality assurance because there are doubts about a person’s capacity to do the responsibilities given to them.
Pre-Construction Reviews
A professional engineer working for a contractor, fabricator, manufacturer, or other party that will use the authoring engineer’s design to build or create a product for which the reviewing engineer’s employer will then be liable is also able to examine the authoring engineer’s work. In these situations, the individual or group employing the design may be inspecting the engineering documents as part of its due diligence evaluation.
Since a company creating a product or executing a project must be able to rely on the correctness and thoroughness of the engineering work, it is reasonable for them to review the design to make sure it is error-free. In this scenario, a review is being requested by a party other than the writing engineer’s client or employer, and the review’s goal is to safeguard the general public or the design’s user rather than to evaluate the professional engineer.
Clause 77.7.ii of O. Reg. 941 (PEO) does not apply because the review was started by someone other than the authoring engineer’s employer or customer. The authoring engineer need not be made aware that a review is being conducted by the reviewing engineer.
Review or Second Opinion?
Reviewing engineers should always make it clear if the client or employer is asking for a second opinion or a review of a practitioner’s work. A second opinion is an assessment of the problem that is offered to the client in order to provide the client with more information before making a choice. An engineer offering a second opinion examines the identical problem that the first engineer was given, and without taking into account the first engineer’s work, they provide a solution, develop a concept, or offer suggestions.
For instance, a client who wishes to construct a medium rise building can contact an engineer who suggests an expensive piled-raft foundation. Due to the high cost of the suggested work, the homeowner may opt against moving forward right away in favour of seeking a second opinion. It is obvious that what is required in this case is not a review of the work of the first engineer, but rather a unique study and recommendation, which can be made without taking the work of the first engineer into account.
General Principles for carrying out a review
(1) The extent of the the review must be project-specific and as thorough as called for by the scope and kind of review. The extent of checking is always up to the reviewer’s reasonable discretion and judgements of the most effective approaches to complete the task. The reviewer must always be certain that the conclusions—whether favourable or unfavorable—regarding the documents’ quality or the writing engineer’s service are founded on accurate evaluations of the subjects under consideration.
(2) A review must be thorough enough to give the client or employer adequate information to answer all of their questions and to support the reviewer’s assessments of the work’s quality. This must be however done in accordance with the principle of fairness. If a review is not thorough enough, the reviewer may overlook problems that the client or employer should be made aware of. The reviewer’s service would be inadequate in this case.
(3) On the other side, a review shouldn’t go so far as to criticise unimportant, trivial issues. A reviewer shouldn’t point out spelling mistakes, poor grammar, poor drafting, or other features of a document’s form unless these issues make the document unclear, hard to understand, or provide others depending on it the chance to apply it incorrectly.
(4) Both verbally and in writing, it is important that the reviewer’s mandate be phrased neutrally and without making any assumptions about the desired outcome. The reviewing engineer should remind the client or employer that the reviewer is professionally required to stay independent and exhibit no bias in performing this service if the client or employer declares or implies that a practitioner should skew the evaluation in any way.
(5) Reviewing engineers should create a plan for conducting their technical reviews that outlines the documents to be examined, resources available to the reviewer, the methodology of the review, the format of the review report, the protocol of communications between the reviewer and other parties, considerations for confidentiality, a schedule for the review, and other pertinent factors. Such a plan, provided to the client before starting a review, will demonstrate the reviewing engineer’s independence and reduce the possibility of any conflicts of interest or misconceptions.
Basis for Review and Criticisms in Reporting
Reviewing engineers must identify both the positive and negative elements of the engineering work and draw attention to anything that is inaccurate, ambiguous, unsupported, or problematic in the original document as a standard part of the process. It is part of the reviewer’s job description to occasionally reflect negatively on elements of the work completed by another professional engineer. Reviewing engineers may, however, feel that they are also expected to be critical and to uncover things that, while not always wrong or harmful, can nonetheless be seen negatively.
Reviewers must make sure that their reporting of negative evaluations adheres to the provisions in the Code of Ethics that outline practitioners’ obligations to other professional engineers. According to article 77.7 of O. Reg. 941 (PEO), it stipulates the following:
“A practitioner shall, i. act towards other practitioners with courtesy and good faith, … iii. not maliciously injure the reputation or business of another practitioner”.
This approach should be carried out objectively and consistently performed in order to be fair to an authoring engineer. For this reason, while determining what is incorrect with an engineering job, reviewers should follow the procedure below.
Identifying the applicable assessment criteria is the first step in every review. It is obvious that in order to be objective, a practitioner’s work must be compared to the standard procedure for professional engineers performing identical work in order to assess both the technical and professional components of their job. Professional engineers are required to abide by all laws establishing standards and codes, however not all laws establishing best practices are adopted by practitioners experienced in a given industry.
The comparison of the work with instances of good engineering practice is another crucial factor for forming judgements in a review. Good engineering practice consists of widely accepted, well known, and generally acceptable standards that has been used or accepted by the majority of professionals that routinely work in that field.
Reviewing engineers shouldn’t inquire about an authoring engineer’s qualifications. Only when they are qualified to do so, licensed practitioners are expected to accept and complete engineering tasks. The authoring engineer makes this evaluation of skill. It shouldn’t be expected of reviewing engineers to assess the expertise of authoring engineers or to express an opinion on their suitability for the tasks described in the documents.
A reviewing engineer should not ask a client or an authoring engineer to disclose the fee or salary paid to the authoring engineer for the work under review. Practitioners must constantly devote enough time and effort to carrying out their tasks in a way that adheres to the standards of the engineering profession. Professionalism standards are unaffected by payment or income and are not negotiable with clients or employers.
Ethical obligations of a reviewing engineer
The obligations of a reviewing engineers are therefore as follows;
(1) Notification A practitioner should only take on the assignment with the knowledge of the other practitioner if a client or employer requests that they review the work of another engineer who is still working on a project under the terms of an employment contract or a contract for professional services. However, it is the review engineer’s duty to make sure that the client is aware of the obligation for notification and complies with it. This notification should be made by the client or employer.
Article 77.7.ii of PEO specifically indicates that it only applies when the engineer is asked by the same employer to examine the work of another practitioner. The relationship between the practitioner and the employer/client is, without a doubt, the crucial issue in this area. Only while that professional relationship is active does the responsibility apply.
(2) Confidentiality Practitioners need to always consider their interactions with clients and employers as professional ones. A professional relationship is based on trust, thus practitioners must conduct in a way that fosters both acquiring and preserving that trust. A reviewer shouldn’t speak to an authoring engineer or anybody else about the review without first asking and receiving authorization from the client or employer.
(3) Good faith Being driven by a conviction for the validity of one’s beliefs or the morality of one’s deeds is referred to as acting in good faith. The rightness of a course of action is determined by adherence to the Code of Ethics for a practitioner offering professional engineering services. Evaluations of whether one’s opinions are true or false are subjective judgments based on a person’s character. Every practitioner must be realistic about their own assessments and assured that using their knowledge and abilities consistently produces trustworthy results while accounting for human imperfection.
(4) Fairness Any person who has discretion over how to distribute burdens and advantages among group members must adhere to the idea of fairness. Practitioners are free to express their opinions about the work in a review. Depending on the nature of the opinions and the effects they have, they may help or hurt the customer, authoring engineer, or other stakeholders in different ways.
The reputation, standing in the engineering community, or financial interests of an authoring engineer should not be thought to be harmed by statements made by a reviewing engineer or the release of all or any portion of a review report. If the client or employer asks the reviewing engineer to take part in any such activity, they shall refuse unless the publishing of the report is mandated by the freedom of information act or another law.
However, a professional engineer is not prohibited by the duty of impartiality from stating facts or offering an honest opinion that could be detrimental to another professional or the client.
(5) Conflict of interest A relationship between a practitioner and one or more parties that could be seen as a conflict of interest is another issue that could occur when offering professional services. A conflict between two or more conflicting interests and a duty of the practitioner is the primary characteristic of a conflict of interest. A conflict of interest occurs when a practitioner finds it difficult to fulfil their obligations to someone whose interests may be impacted by their decisions.
Conflict arises when the practitioner or a third party both have interests that must be ignored or put aside in order for the practitioner to pursue their own. It would be against the practitioner’s obligation to disregard or put that person’s interests second. In general, the responsibility that needs to be upheld is one that the practitioner has to the client or employer; nevertheless, there are numerous additional obligations that practitioners have, including obligations to fellow practitioners, which may also be jeopardised by competing interests.
When settlements of foundation could be an issue, such as when a site has erratic deposits or lenses of compressible materials, suspended boulders, etc., mat foundations are frequently used. Settlement of mat foundations has been observed to be lower compared to spread footing.
It is impossible to completely eliminate the settlement of shallow foundations founded on natural soils. At least, the immediate (elastic) must occur, before the consolidation settlement will begin, if the foundation is founded on clay. The following methods are frequently used to control the settlement of foundations during the design of foundations:
Making use of a larger foundation to reduce soil contact stresses
Displaced volume of soil (flotation effect); in theory, the system “floats” in the soil mass and no settlement takes place if the weight of the excavation is equal to the total weight of the structure and mat (see design of bouyancy raft foundation).
Bridging effects attributable to mat rigidity and contribution of superstructure rigidity to the mat.
Allowing bigger settlements that are 50 mm instead of 25 mm larger.
Even in cases where consolidation is a challenge or piles are employed, the flotation effect through the use of buoyancy raft (or compensated foundation) ought to be able to keep most mat settlements to a maximum of 50 to 80 mm. For all types of foundations and structures, differential settlement is a problem that deserves more serious attention. However, the use of mat foundation tends to reduce this problem.
From our previous articles, we have seen that the bending moments (6EI∆/L2) and shear forces (12EI∆/L3) in frames are dependent on the relative movement ∆ between the beam ends.
In comparison to a spread footing (pad foundation), mat foundation due to its continuity produces somewhat reduced anticipated value of differential settlement compared to the total settlement.
Foundation Type
Expected Maximum Settlement (mm)
Expected Differential Settlement (mm)
Pad foundation
25
20
Mat foundation
50
20
The settlement of mat foundation depends on the rigidity of the mat, type of mat, the type of soil, the homogeneity of the soil, groundwater condition, and construction method.
To estimate both total and differential settlements, one can use computer approaches that take into account frame-foundation interaction. However, if any other than a strip from the mat is employed in a beam-on-elastic foundation type of analysis, the computing work is significant and the overall settlements will only be as accurate as the soil data.
The differential settlement of mat foundation may be arbitrarily taken as 20 mm (0.75 inches) if the total expected settlement ∆H is not more than 50 mm. Alternatively, it may be approximated using a rigidity factor Kr [see ACI Committee 336 (1988)] defined as;
Kr = EIb/EsB3
where: EIb = flexural rigidity of the superstructure and mat Es = modulus of elasticity of soil B = base width of foundation perpendicular to direction of interest
ACI Committee 336 suggests that mat differential settlements are related to both the total estimated foundation settlement ∆H and the structure rigidity factor Kr about as follows:
Kr
Differential Settlement Expected
0
0.5 x ∆H (for long base) 0.35 x ∆H (for square base)
0.5
0.1 x ∆H
> 0.5
Rigid Mat (no differential settlement)
However, where the net increase in pressure exceeds the current in situ pressure p’o, full settlement analyses will need to be done. Depending on the underlying soil stratification, these settlements may be immediate or consolidation settlements adjusted for OCR.
The proper design of a raft foundation should therefore strike a balance between the requirement to prevent the raft’s structure from becoming excessively rigid, and the need to limit the differential settlement of the raft and, by extension, the superstructure. Flexibility in a raft results in minimal bending moments, which saves money in the substructure.
However, this flexibility comes at the expense of relatively large differential settlement and higher costs to accommodate these movements in the superstructure, such as through joints or a flexible cladding. A raft’s stiffness reduces differential settlement but increases bending moments, which raises the cost of the raft by redistributing load.
The stiffness of the structure relative to the raft can be expressed by the following equation;
Kr = [4Ec(1 – µs2)/3Es(1 – µc2)] x (t/B)3
Where; Kr = relative stiffness Ec = Modulus of elasticity of concrete Es = Modulus of elasticity of soil µs = Poisson ratio of soil µs = Poisson ration of concrete t = Thickness of raft B = Width of raft
Heave in Mat Foundation
Expansion and/or lateral flow into the excavation base, which causes the base elevation to rise, is a significant issue, especially for deep excavations in clay. Heave is the word for this occurrence, and values between 25 and 50 mm are very typical. In literature however, values up to 200 mm (or 8 inches) have been reported. When heave has occurred, settlement calculations are challenging. Theoretically, if we restore a mat pressure q0 equal to that which was previously extant, all the heave should be recovered.
In reality, this recovery doesn’t happen, or it doesn’t happen as quickly as the heave occurs. It should be anticipated that it will be extremely difficult to forecast either the overall amount of heave or how much of this will be recovered by elastic recompression if some of the heave results from a deep-seated lateral flow.
Since there are currently no valid theories for the issue of heave, estimation of the expected soil response generally requires extensive knowledge and engineering judgement where heave is encountered. A finite element of the elastic continuum computation is said to be able to solve the problem, however this claim is speculative and based on the expectation that calculations and measurements would turn out well.
The explanation is that the accuracy of a finite-element computation depends on the input parameters soil modulus of elasticity and Poisson ratio. Even if we were able to obtain a reliable initial value Es, it would still decrease during and after excavation because of the heave that is caused by the loss of confining pressure (p’o) and expansion.
Methods of Estimating the Settlement of Mat Foundation
The method of summation of partial settlements or the method of an elastic layer of finite thickness can be used to determine the settlement of raft foundations. When using the method of summation of partial settlements, the settlement is determined at a single location without taking the stiffness of the foundation into consideration.
However, in cases involving large-scale foundations, the average settlement of the foundation must be taken into account by computing the settlement at various foundation positions. The thickness of the compressed zone, which can be influenced by the size of the foundation, the applied load of higher buildings, and the soil condition, determines the settlement results of the foundation for the method of elastic layer of finite thickness.
The settlement of mat footings can be estimated using the methods developed from the theory of elasticity, assuming that they impart stresses on the ground in a manner similar to that of spread footings. The following expression (Timoshenko and Goodier, 1951) based on the theory of elasticity can be used to estimate the corner settlement of a rectangular footing with dimensions of L′ and B′;
where q is the contact stress, B′ is the least dimension of the footing, νs is the Poisson ratio of the soil, and Es is the elastic modulus of the soil. Factors I1, I2, and IF are influence factors that can be obtained from so many geotechnical engineering textbooks, in terms of the ratios N = H/B′ (H = layer thickness), M = L′/B′ (L′ = other dimension of the footing), and D/B (the foundation depth ratio).
The same expression above can be used to estimate the settlement of the footing at any point other than the corner by approximate partitioning of the footing. It must be noted that even if the footing is considered as a combination of several partitions (B′ and L′), in determining the settlement of an intermediate (non-corner) location, the depth factor, IF, is applied for the entire footing based on the ratio D/B.
Gazetas et al. (1985) considered an arbitrarily shaped rigid footing embedded in a deep homogeneous soil and proposed the following equation for the elastic settlement:
Si = (P/EuL) × (1 – vu2) × µsµembµwall
where P is total vertical load, Eu is the undrained elastic modulus of the soil, L is one-half the length of a circumscribed rectangle, vu is Poisson’s ratio for the undrained condition, and µs, µemb, and µwallare shape, embedment (trench), and side wall factors given as;
Ab is the actual area of the base of the foundation and Aw is the actual area of the wall in contact with the embedded portion of the footing. The length and width of the circumscribed rectangle are 2L and 2B, respectively. The dimensionless shape parameter, Ab/4L2, has the values for common footing geometry shown in the Table below;
Footing Shape
Ab/4L2
Square
1
Rectangle
B/L
Circular
0.785
Strip
0
The equations proposed by Gazetas et al. (1985) apply to a foundation of arbitrary shape on a deep homogeneous soil. What is meant by “deep” is not clearly defined. When the thickness of the soil layer is such that 90% of the applied stresses are distributed within it, the author advises using the equations of Gazetas et al. The soil layer should be at least 2Br thick for a rectangle with actual width Br.
The accuracy of the elastic modulus is very important for any elastic equation for soils. It is standard laboratory procedure to calculate a secant Eu from unconfined compression tests or undrained triaxial tests with a deviatoric stress equal to 50% of the highest shear strength. However, it is preferable to determine Eu over the range of deviatoric stress relevant to the problem for better solution. One possible solution is to divide the soil into sublayers and use a weighted harmonic mean value of Eu.
Worked Example1
Determine the immediate settlement of the foundation shown below. The undrained elastic modulus varies with depth, as shown in the figure, and vu = 0.35.
Approach You have to determine the length (2L) and width (2B) of a circumscribed rectangle. The undrained elastic modulus varies with depth, so you need to consider the average value of Eu for each of the layers and then find the harmonic mean. You also need to find the shape parameter Ab/4L2.
Step 1: Determine the length and width of the circumscribed rectangle. 2L = 8 + 7 = 15 m; L = 7.5 m 2B = 6 + 4 + 10 m; B = 5 m
Step 5: Calculate the settlement Si = (P/EuL) × (1 – vu2) × µsµembµwall = (6500/17311 × 7.5) × (1 – 0.352) × 0.5678 × 0.972 × 0.856 = 0.02075 m = 20.754 mm
Worked Example 2
A medium dense sandy soil foundation layer is found under the mat shown below, which is underlain by a weathered bedrock at a depth of 6.0 m below the surface, estimate the average immediate settlement and the maximum differential settlement of the mat footing. Let us assume that in this case the sand is normally consolidated with SPT value of 15.
Depth of foundation = 1.0 m
Then, for an average SPT value of 15, Es is approximately given by 500(N + 15) = 15000 kPa or 15 MPa. A Poisson’s ratio of 0.30 can also be assumed in normally consolidated sand.
The footing has been arranged such that a uniform pressure will be obtained at the base.
P = 350 + 800 + 350 + 800 + 1200 + 800 + 350 + 800 + 350 = 5800 kN Area of base = 10 × 10 = 100 m2
Then the uniformly distributed contact stress = 5800/100 = 58 kPa D/B for the entire footing = 1/10 = 0.1 From the chart below, for L/B = 1 and D/B = 0.1, IF = 0.85.
Therefore, the immediate settlement expression can be simplified to:
For the corner settlement M = L/B = 1.0, N = H/B = 5/10 = 0.50 From Table above, I1 = 0.049, I2 = 0.074 Si = 0.00299B'(I1 × 0.571I2) si = 0.00299 × 10 × [0.049 + 0.571(0.074)] = 0.0027284 m = 2.72 mm
For the center settlement M = L/B = 5/5 = 1.0, N = H/B = 5/5 = 1.0 From Table above, I1 = 0.142, I2 = 0.083 si = {0.00299 × 5 × [0.142 + 0.571(0.083)]} × 4 = 0.01132 m = 11.325 mm
The number “4” indicates the four equal partitions required to model the center by superposition of four corners of the partitions.
Differential Settlement Differential settlement = 11.325 – 2.712mm = 8.613 mm Maximum angular distortion within the footing = (23.0 – 5.471)/5000 = 0.0017226 < 1/3000 Therefore, the foundation is safe from any architectural/structural damage.
Finite Element Modelling
The foundation was modelled on Staad Pro software. The soil was modelled with solid elements with the following properties;
Es = 15000 kPa Poisson’s ratio = 0.3
The raft slab was modelled as a thin flexible plate with a full pressure of 58 kPa applied in the global vertical direction. A fixed support was applied at the base of the ground model to represent the bedrock. It should be noted that the thickness of the selected plate affects the settlement values.
The vertical pressure distribution as a result of the loading is shown below;
The observed settlements are shown below;
The observed corner displacements was 3.914 mm and the centre displacement was 15.546 mm.
Deflection is the movement of a point on a structure or structural element, usually measured as a linear displacement or succession displacements transverse to a reference line or axis. Thus, deflection can be said to be a deformation that occurs over time on a structure or structural element under a load. The primary material parameters influencing concrete deflection are temperature, modulus of elasticity, shrinkage, modulus of rupture, and creep.
Deflection is a vital serviceability limit state criterion in the design of reinforced concrete structures. Therefore, structural designers must always consider deflection and ensure compliance with acceptance criteria for deflection as stated in RC design codes such as BS 8110, EC 2 and IS 456.
This article will discuss the theory of deflection of slabs and thin plates, the effects of deflection on the performance and functionality of RC buildings, factors affecting the deflection of RC slabs, methods of assessing the deflection of slabs, how to control deflection during design, and how to remedy a building failing in deflection.
Beam theory of slab deflection
Slabs are common structural elements of RC building structures, taking up nearly 50% of the total weight of buildings. Slabs are usually analyzed under transverse loading, and the slab thickness governs the serviceability requirement for deflection. Therefore, structural designers need to properly analyze slabs to choose the minimum slab thickness satisfying the deflection criterion and minimizing the building’s weight.
The deflection theory of slabs is similar to that of beams. However, it is more complex. Consequently, we will adopt a simplified approach for one-way and two-way spanning slabs.
One-way slabs
(a) One-way slab (b) Two-way slab
Given the figures above, the slabs are analyzed as a beam with the bending moments per unit strip. As shown in (a), one-way slabs are supported on two opposite sides. The load transfer and structural action are usually in one direction along the slab’s shorter span (la) or perpendicular to the supporting beams. Thus, we can say that the slab consists of a single parallel strip.
To derive the deflection equation, we assume the strip acts like a simply supported beam uniformly loaded across its length (l). Thus, the general slope and deflection equations can be derived using the double integration method, as shown below.
General slope equation:dy(EI/dx) = wlx2/4 – wx3/6 – wl3/24 General deflection equation:yEI = wlx3/12 – wx4/24 – wl3x/24
Since maximum deflection occurs at the mid-span of the strip, that is, where x = l/2
Then, substituting x = l/2 into the deflection equation gives the resulting equation below.
Maximum deflection at mid-span:y = 5wl4/384EI
Two-way slabs
Similarly, the two-way slab in (b) is essentially supported on all four sides, and the load transfer and structural action are in two directions resulting in biaxial bending moments. Thus, we can say that the slab consists of a parallel strip in each direction (la and lb), and they intersect each other. Consequently, the load supported by the slab is shared between the two strips though dominant in the direction of the shorter span (la).
Furthermore, it is proper to assume that the mid-span deflections in the two-way slab at the point of intersection are equal since the strips are part of the same slab. Therefore, under a uniformly distributed load (w) per square metre, each strip takes its share of w as wa and wb, and the deflection equations are given below.
5wala4/384EI in the shorter direction 5wblb4/384EI in the longer direction
It must be noted that the maximum deflection equations above hold for simply supported end conditions. Thus, the maximum mid-span deflection is wl4/192EI for hinged-fixed end conditions and wl4/384EI for fixed-fixed end conditions.
Deflection of thin plates
Plates are defined as plane structural elements with a small thickness compared to other dimensions of the plate. As a result, plates resist applied loads employing bending in two directions and twisting moment. Thus, the plate theory takes advantage of the disparity in length scale to reduce the entire 3-D solid mechanics problem to a 2-D problem.
Furthermore, plates are categorized into thick, thin, and membranes depending on thickness to width ratio. For example, if a plate’s thickness to width ratio is less than 0.1 and the maximum deflection is less than one-tenth of the thickness, then the plate is classified as a thin plate structure.
Several plate theories are associated with geometric assumptions, such as the Kirchhoff plate theory, the Reissner-Mindlin plate theory, the von Karman plate theory, and the Timoshenko plate theory. Below, the Timoshenko plate theory is briefly discussed.
One-way slabs
Timoshenko’s plate theory for cylindrical bending of uniformly loaded rectangular plates with simply supported edges can be used for one-way slabs because the bending nature of such slabs can be simulated as thin plates with small deflections. Thus, the governing differential equation for the deflection curve is given below:
–M = D(d2w/dx2) and, D = Eh3/12(1-v2)
Where D is the Flexural rigidity of the plate, E is the modulus of elasticity of the plate material, v is the Poison’s ratio, h is the thickness of the plate, and the variable quantity ‘w’ is the transverse deflection of the middle plane of the plate.
Thus, the maximum deflection for simply supported conditions is at the center, and it is given by: w = 5ql4/348D
Where q is the UDL loading intensity on the plate and l is the length of the plate along supported edges.
Two-way slabs
For a two-way, rectangular plate with sides a and b, as shown above, the derivation of the maximum deflection at the center of the plate involves rigorous analysis. Thus, it would not be considered in this article. However, if we assume that the plate is instead square such that sides a and b are equal, then the maximum central deflection is given below.
w(max) = 4qa4/π6D = 0.00416qa4/D
Effects of deflection on building performance and functionality
It is true that buildings move and experience vibrations. However, designing a building aims to achieve a state of static equilibrium. The state of equilibrium is to be among the parts of the constructed building and the forces acting on it. Therefore, deflection is one of the movements in buildings affecting performance and functionality.
Excessive deflection of flexural members above those the structural designer allows can result in several difficulties for building occupants. These difficulties include cracking of wall, floor and ceiling finishes, unsightly and unacceptable appearance or visual effects, impaired functionality, alarm and discomfort to building occupants, and damaged roof membranes and supported partitions.
Deflection of cantilever slab leading to cracking to masonry walls
Additional potential problems associated with slab deflection include jamming doors and windows, gaps between partitions and floors and between columns and floors, and visual perception of sagging floors and ceilings. Furthermore, deflection can worsen over time and lead to additional maintenance costs and structural problems.
Moreover, a suspended floor slab must be serviceable during the life of a building. Therefore, it is expected that the top profile of a slab does not show any sign of deflection. However, occupants of a building can decide to change the use of a building or space if they perceive any deflection on a floor slab surface under sustained loading. For example, an occupant can convert a building or space from an office, institutional, educational or industrial use to general domestic use.
Factors affecting the deflection of RC slabs
Several factors affect the deflection of RC slabs, and a holistic and accurate assessment of slab deflections can only be achieved if consideration is given to these factors. Furthermore, the factors affecting slab deflections vary intrinsically and may change with time. For example, factors such as elastic modulus, creep coefficient, and tensile strength of concrete significantly influence the final slab deflections.
Furthermore, some factors are influenced by others. Consequently, deflection calculations remain an estimate because of the variability of several factors. Therefore, the technical report (TR58) of a joint project of the British Cement Association, The Concrete Centre, and The Concrete Society advises that actual deflection may vary from calculated deflections in a range of -30% to +15%. The report also discusses the rigorous method of estimating slab deflections and the factors influencing deflection.
Some of the factors affecting slab deflections are discussed below.
Boundary Conditions
The boundary conditions of a slab have a profound effect on the deflection behaviour of the slab. Fully fixed supports will have less deflection compared to simple supports. Monolithic and/or continuous supports also have a more positive effect on deflection compared to corners that are free to lift.
Concrete Tensile Strength
Generally, slab designs are closer to the cracking load, and small property or loading variation can cause a slab to crack and thus deflect more. Therefore, the tensile strength of concrete is an essential property because a slab will crack once the tensile stress in the extreme fibre is exceeded. To reduce slab deflection, then tensile strength must be increased. This can be achieved by increasing concrete compressive strength because tensile strength is proportional to the square root of compressive strength.
Aggregate properties
Fine and coarse aggregates comprise about 70% of a typical volume of concrete. Thus, aggregates significantly influence the elastic modulus of concrete. Therefore, slab deflection will increase substantially if poor-quality aggregates are used.
Material properties have a profound effect on the deflection of slabs
Relative humidity (RH)
According to TR58, it is reported that predicted deflection will decrease with increasing RH. For example, an RC slab in an outdoor environment with RH between 80 – 85% is likely to have deflections about 20% lower than another slab in an indoor environment with RH between 45 – 50%.
Ambient Temperature
The hydration of cement is usually slower at a lower temperature. Therefore, a concrete slab cast under low ambient temperature will experience low strength gain and, consequently, more likely to deflect even under its self-weight.
Time of loading
The effect of early-age loading or overloading of slabs has pronounced effects on deflection, especially when the age of the slab is less than 5 days. However, the further difference in deflection is minimal.
BS 8110 methods of assessing slab deflections
Two methods can check the deflection of slabs according to BS 8110. It is important to know that in the design of RC slabs, deflections are checked in the shorter span, which is more critically loaded. The two methods of checking the deflection of slabs are discussed below.
The first method is guided by the maximum limits of deflections based on slab spans given by the code. For example, BS 8110-2:1985 states that the sag in a concrete member will become visible once deflection exceeds span/250. Therefore, if a structural designer knows the maximum slab deflection for the relevant load case, he can check whether it is within the limit given in Section 3 of BS 8120-2:1985.
Conversely, the second method limits the basic span–effective depth ratio to specific values given in Table 3.9 of BS 8110-1:1997 depending on the slab boundary condition type.
Support Condition
Rectangular Section
Flanged beam with bw/b ≤ 0.3
Cantilever
7
5.6
Simply supported
20
16.0
Continuous
26
20.8
Table 3.9 of BS 8110-1:1997: Basic span/effective depth ratio for rectangular or flanged beams
Furthermore, structural designers should modify the values given in Table 3.9 by multiplying them with the factors for tension and compression reinforcements given in Tables 3.10 and 3.11, respectively.
Eurocode 2 (EN 1992-1-1) Methods of Assessing Deflection
In Eurocode 2, the deflection of a structure may be assessed using the span-to-effective depth ratio approach, which is the widely used method. It is also allowed to carry out rigorous calculations in order to determine the deflection of a reinforced concrete structure, which is then compared with a limiting value.
According to clause 7.4.1(4) of EN 1992-1-1:2004, the appearance of a structure (beam, slab, or cantilever) may be impaired when the calculated sag exceeds span/250 under quasi-permanent loads. However, span/500 is considered an appropriate limit for good performance.
Using the span-to-effective depth approach, the deflection of a structure must satisfy the requirement below;
Allowable l/d = N × K × F1 × F2 × F3 ≥ Actual l/d
Where; N is the basic span-to-effective depth ratio which depends on the reinforcement ratio, characteristic strength of the concrete, and the type of structural system. The expressions for calculating the limiting value of l/d are found in exp(7.16) of EN 1992-1-1:2004. The expressions are given as follows;
Where: l/d is the limit span/depth ratio K is the factor to take into account the different structural systems ρ0 is the reference reinforcement ratio = √fck /1000 ρ is the required tension reinforcement ratio at midspan to resist the moment due to the design loads (at supports for cantilevers) ρ’ is the required compression reinforcement ratio at midspan to resist the moment due to the design loads (at supports for cantilevers) fck is the characteristic compressive strength of the concrete in N/mm2
The values of K for different structural systems are given in the Table below;
Structural System
K
Simply supported beam, one or two way spanning simply supported slab
1.0
End span of continuous beam or one-way continuous slab or two-way spanning slab continuous over one long side
1.3
Interior span of beam or one way or two-way spanning slab
1.5
Slab supported on columns without beams (flat slab)
1.2
Cantilever
0.4
F1 = factor to account for flanged sections (not applicable to slabs) = 1.0
F2 = factor to account for brittle partition in long spans. In flat slab where the longer span is greater than 8.5m, F2 = 8.5/leff In beams and slabs with span in excess of 7.0m, F2 = 7.0/leff
F3 = factor to account for service stress in tensile reinforcement = 310/σs ≤ 1.5 Conservatively, if a service stress of 310 MPa is assumed for the designed reinforcement As,req, then F3 = As,prov/As,req ≤ 1.5
More accurately, the serviceability stress in the reinforcement may be estimated as follows;
σs = σsu[As,req/As,prov]((1/δ)
Where; σsu is the unmodified SLS steel stress taking account γM for reinforcement and of going from ultimate actions to serviceability actions. σsu = fyk/γs(Gk + ψ2Qk)/(1.25Gk + 1.5Qk) As,req/As,prov = Area of steel required divided by the area of steel provided.
How to control slab deflection during design
Deflection control is a vital serviceability requirement in the design of RC building structures because slabs will crack due to excessive deflections if deflection control is not adequately considered. Although providing an adequate safety level against collapse is the primary design consideration, structural designers must consider the possible adverse effects of excessive deflections on the performance and functionality of a structure at service load levels.
Furthermore, design codes guide how to control slab deflection, which will be perfectly adequate and provide economical solutions for most building designs. However, such methods are semi-empirical, and while approximate deflection estimates may be made, they are not intended to predict how much a member will deflect over time.
Deflection in reinforced concrete slabs can be reduced or controlled by increasing the thickness of slab, increasing the area of steel provided, modifying the structural scheme by reducing the span, or reducing the dead load on the slab. Sometimes, two or more of these solutions are required in order to keep the deflection of slab to a minimum.
Increase slab depth
Stiffness plays an essential role in the design of RC slabs because it indicates the ability of the slab to return to its original shape or form after an applied load is removed. Thus, stiffness directly influences slab deflection. Consequently, if stiffness increases, the less the slab deflects under a load because stiffness is inversely related to deflection.
For example, stiffness is EI/L, and the moment of inertia (I) is bh3/12 for a regular, uncracked rectangular section. Therefore, increasing the dimension b or h of a slab would result in a reduced value for the deflection. However, it must be noted that the effect of increasing depth (h) is much more dominant than that of increasing width (b), especially in slabs.
Increase the area of steel provided
By increasing the area of steel, the service stress in the reinforcement reduces, and increases the modification factor for deflection control. However, there is a limit to which increment of area of steel can go.
Reduce slab span
Reducing a slab’s shorter span helps reduce deflection since deflection is also a function of the basic span–effective depth ratio (lx/d). Thus, if lx is reduced, then deflection reduces, and vice-versa. However, it is essential to note that reducing slab spans may not be possible in all cases as it involves introducing new columns and beams and depends on floor layout and architectural requirements for spaces.
Reduce additional dead loads
Additional dead loads on slabs include loads from partition walls and floor finishes. Therefore, alternative, lightweight materials for partition walls and floor finishes will help reduce long-term dead load application on slabs.
Remediation of deflected slabs
The overlay method of fixing a deflected slab
Since deflection control is a serviceability consideration, thus, small slab deflections may necessarily not lead to collapse. However, large deflections may lead to slab collapse if necessary actions are not taken to remedy the slab. Let’s look at the overlay method of fixing an existing deflected slab.
The overlay method seems to be the most practical way of remedying a slab after deflection. It involves increasing the stiffness of the slab while reducing deflection. However, the process must be carried out by experts. The steps of the overlay method are listed below.
1. Design and install lifting system. 2. Start lifting of slab from the soffit according to the recommended force. 3. Inject the cracks formed at the top of the slab due to adverse lifting force. 4. Lightly chip the surfaces of the slab and supporting columns. 5. Drill holes in the slab and supporting columns to receive new dowels. 6. Clean the drilled holes with pressurized air. 7. Fill the holes with epoxy materials to aid bonding between steel dowel bars and anchors with the concrete. 8. Insert anchors and main steel in the drilled holes. 9. Apply bonding materials on the anchor and main steel bars. 10. Cast the new concrete material on the existing slab. 11. Allow curing for at least 14 days. 12. Remove lifting system.
Perhaps you are interested in a visual aid for the overlay method; then you can click this link.
Worked Exampleon Deflection of Slab(BS 8110)
Conduct the deflection check for a continuous slab with the data given below.
Effective depth (d) = 124 mm Area of steel required = 681.48 mm2 per m run Area of steel provided = 754 mm2 per m run
Slab span = 3900 mm Steel strength (fy) = 380 N/mm2 Allowable span/depth ratio = 26
Bending moment (M) = 27.15 kNm
Solution
Service stress (fs) = (2fyAs req)/(3As prov) × (1/δb), Where δb = 1
fs = (2 x 380 x 681.48) / (3 x 754) x (1/1) = 229 N/mm2
Taking the distance between supports as the effective span, L = 3625 mm The allowable span/depth ratio = βs × 30.838 = 2.0 × 190.327 = 280.645 Actual deflection L/d = 3625/119 = 30.462 Since 280.645< 30.462 Therefore, deflection is ok.
Conclusion
Structural designers and building contractors continue to employ reinforced concrete for suspended floor slabs in building structures because of its durability and economic benefits. However, short and long-term deflection remains a concern. Therefore, structural engineers and other professionals in the building construction industry must understand the implications of slab deflection and make adequate design allowances to accommodate it.
References
[1] TR58 (2005), Technical Report No. 58: Deflections in Concrete Slabs and Beams, The Concrete Society, Camberley, UK.
[2] BS 8110 (1997), Structural Use of Concrete – Part 1: Code of Practice for Design and Construction, British Standards Institution, London.
[3] BS 8110 (1985), Structural Use of Concrete – Part 2: Code of Practice for Special Circumstances, British Standards Institution, London.
[4] Priyanka, M. D. and Ramesh, V (2022), Comparative Study on Slab Deflections, IOP Conference Series: Earth and Environmental Science, Vol. 982, available at: https://iopscience.iop.org/article/10.1088/1755-1315/982/1/012081
[5] RC Design II: One-way and Two-way slabs, University of Asia Pacific, Dhaka, Bangladesh, available at: https://www.uap-bd.edu/ce/anam/Anam_files/RC%20Design%20II.pdf
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.
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 arespiral 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.
Spiral Strand Ropes
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.
Fully locked coil ropes
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.
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
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.
Parts of a suspension bridge
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.
Calgary Olympic Saddledome
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.
Cable truss (Source: Davison and Owen, 2012)
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.
The Millenium Dome
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 Fmin is given by;
Fmin = d2RrK/1000
where d is the diameter of the rope in mm, K is the breaking force factor, Rr 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.
The London Eye
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:
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’: γfmax G + γfmax Q + γfmax PS + γfmax W
For derivation of the minimum tension in the upper cables ‘A’: γfmax G + γfmax Q + γfmin PS + γfmax 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.
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
Reclamation of existing asphalt 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
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.
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 reclaimer
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
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.
Road reclaimer pulverising asphalt layers
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
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.
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 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 beecheyana
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 (Fult) 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.
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, Fult, 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 = Fult / ∑(t × L)
Where;
τ = Ultimate shear strength, in N/mm2 Fult = 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
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 (Ka). 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.
