To reduce soil heave under a foundation or subgrade, expansive soils can be overexcavated and replaced with nonexpansive or treated soils. In this approach, the expansive soil is excavated to an adequate depth to reduce heave, and then replaced with properly treated and compacted fill up to grade.
The required depth of removal, as well as the volume, location, and cost of the fill, must all be considered. The depth of soil that must be removed is determined by the overall soil profile, the nature of the fill material, and the amount of heave that may be tolerated. A stiff layer of compacted low to nonexpansive fill has the added benefit of tending to even out variations in the heave of the underlying native soil, thereby eliminating differential heave.
In the absence of suitable nonexpansive fill around the area, moisture-conditioning and compaction control can be used to change the swell properties of the expansive soils on-site. Compacting the material to a lower density at the wet side of the optimum moisture content will minimize the expansion potential, but care must be taken to ensure that the recompacted soil is densified well enough to avoid settlement. Chemical additives can be utilized in conjunction with moisture-conditioning in some cases.
Typical behaviour of an expansive soil
However, if the expansive soil layer extends to a depth that makes total removal and replacement prohibitively expensive, appropriate soil tests and studies should be carried out to design the overexcavation and assess the projected potential heave after the overexcavation and recompaction procedure. The expected heave must be factored into the depth of overexcavation design.
Chen (1988) suggested a maximum overexcavation depth of 3 to 4 feet (1 to 1.3 meters), but these depths have been oberved to be ineffective for sites with highly expansive soils. Thompson (1992a and 1992b) studied some insurance claims and found that if there was 10 feet (3 meters) or more of nonexpansive soil beneath the footings, the frequency of claims was lower than at shallower depths. Overexcavation depths of 10 ft (3 m) or more have been specified regularly in Thompson’s works. In certain situations, the top 20 feet (6 meters) of soil have been excavated, moisture-conditioned, and recompacted in place.
Water content changes in the underlying expansive soil layers can be controlled by overexcavation and replacement. The majority of the seasonal water content variation will occur in the top few feet of soil. However, if the underlying soil has a high potential for expansion, the overexcavated zone may not be enough to prevent surface heave or shrinkage. If the underlying expansive soil gets wet, it might cause uncontrollable movement. Some of the potential water sources are impossible to forecast or control. As a result, the design engineer must consider that such events might occur during the structure’s lifetime and make appropriate design decisions.
Overexcavation and Replacement of an expansive soil
Furthermore, water collection in the overexcavation zone must be avoided at all costs. The use of permeable granular fill as a replacement fill is not suggested. Highly permeable fill will allow water to flow freely and create a reservoir for it to collect in. The ‘bathtub effect‘ is a term used to describe this phenomenon. Seepage into expansive subgrades or foundation soils will occur as a result of this situation. Any fill material that is impermeable and nonexpansive is therefore more preferable. If granular material is required, permanent, positive drainage and moisture barriers, such as geomembranes, should be installed to prevent moisture from infiltrating this zone.
The removed and recompacted material is expected to have a higher hydraulic conductivity than the underlying in situ soils and bedrock, even without granular soil. Groundwater can be intercepted using an underdrain system installed at the bottom of the overexcavation zone. Care must be taken to ensure that the drain has positive drainage and that it does not just concentrate water in an area where it would cause increased soil wetting and heave.
Advantages of Overexcavation and Replacement
The following are some of the benefits of overexcavation and replacement treatment:
• Because soil replacement does not require special construction equipment, it might be less expensive than other treatment options. • Soil treatment additives can be mixed in a more equal manner, resulting in some soil improvement. • Overexcavation and replacement may cause construction to be delayed less than other processes that need a curing period.
Disadvatantages of Overexcavation and Replacement
The following are some of the disadvantages of overexcavation and replacement methods:
• The expense of nonexpansive fill with low permeability can be high if the fill must be imported. • If the recompacted on-site soils demonstrate intolerable expansion potential, removing and recompacting the on-site expansive soils may not be enough to limit the danger of foundation movement. • The recompacted backfill material’s needed thickness may be too considerable to be practicable or cost-effective. • If the backfill material is overly permeable, the overexcavation zone could act as a reservoir, storing water for the foundation soils and bedrock over time.
If overexcavation and replacement are ineffective on their own, they can be combined with other foundation options. It may be conceivable to employ a rigid mat foundation instead of a more expensive deep foundation if the potential heave can be suitably mitigated. The needed length of the piers may also be lowered when used in conjunction with a deep foundation.
References [1] Chen, F. H. 1988. Foundations on Expansive Soils. New York: Elsevier Science. [2] Thompson, R. W. 1992a. “Swell Testing as a Predictor of Structural Performance.” Proceedings of the 7th International Conference on Expansive Soils, Dallas, TX, 1, 84–88. [3] Thompson, R. W. 1992b. “Performance of Foundations on Steeply Dipping Claystone.” Proceedings of the 7th International Conference on Expansive Soils, Dallas, TX, 1, 438–442
Recent research carried out at the Zhengzhou University of Technology, China has offered more insight into the improvement of interlayer mechanical properties of mass concrete. The study was published in the International Journal of Concrete Structures and Materials.
During the construction of mass concrete structures such as gravity dams, concrete is poured in layers. This can be as a result of a lapse in mixing and placement time, ease of construction, possible re-use of formworks, etc. As a result, the interlayer of the concrete (joint between the new and old concrete) becomes a potential weak point that is very susceptible to cracking. A structure’s durability and stability will be severely affected if interlayer bonding characteristics deteriorate. Hence, to maintain the structure’s safety, the interlayer bonding quality of mass concrete must be closely controlled.
The chemical bonding force of cementitious materials and the degree of mutual embedding of aggregates determine the interlayer bonding strength of concrete. According to research, the interlayer bonding strength of concrete can be ensured by pouring the upper layer of concrete before the initial setting time of the lower layer (substrate).
The interlayer bonding characteristics of mass concrete are therefore heavily influenced by the interval time between the placement of new concrete on old concrete. Parameters such as compressive strength, interlayer splitting tensile strength, shear strength, and impermeability of concrete reduce with an increase in interval time according to many research works. Temperature, relative humidity, and wind speed are additional important parameters that influence the quality of mass concrete construction.
As a result, researchers (Song, Wang, and Lui, 2022), carried out research focusing on the effect of harsh environmental conditions on the quality of mass concrete construction, with emphasis on the interlayer properties and cracking. The concrete layer condition and interlayer splitting tensile strength were tested in harsh situations (high temperature, strong wind, steep temperature decline, and short-term heavy rainfall).
Fig. 1: Cracks in a concrete wall
Secondly, the cracking risks of concrete in extreme weather were evaluated (coupling of high winds and dry heat, strong winds and cold waves, and short-term heavy rainfall). Finally, effective strategies to deal with construction risks during harsh weather conditions were proposed by the authors. The strategies considered were covering the concrete with an insulation quilt, artificial introduction of grooves on the old concrete, and addition of Polyvinyl alcohol (PVA) fibres.
From the study, it was observed that under harsh weather conditions, the interlayer mechanical characteristics of concrete reduced significantly (high temperature, strong wind, a steep descent in temperature, and short-time heavy rainfall).
For instance, under high temperatures (40 deg celsius), the water content of the cement mortar decreased gradually with time, while the penetration resistance increased continuously. However, when the concrete sample was covered with an insulation quilt, the water content was closer to the designed water content of 133 kg/m3. Generally, the results showed that in a high-temperature setting, covering an insulating quilt can reduce mortar water loss and lower penetration resistance of concrete specimens to a degree.
The study, therefore, showed that the interlayer bonding strength of concrete can be improved by covering it with an insulation quilt. The reason for this is that an insulation quilt can lessen the impact of the external environment on concrete, resulting in less water evaporation and a slower setting rate. Artificial grooves can also help to strengthen interlayer bonding. This is due to the artificial grooves increasing the roughness of the lower layer of concrete and improving the mutual embedding degree of the upper and lower layers.
Fig. 2: Cracking of concrete surface under the coupled conditions of wind, dryness, and heat (Song, Wang, and Lui, 2022).
Furthermore, under harsh weather conditions (coupling of strong winds and dry-heat, strong winds and cold waves, and short-time heavy rainfall), mass concrete has an increased risk of cracking. Concrete cracking can be efficiently prevented by using an insulation quilt (see Figure 2). It is mostly due to the insulation quilt’s ability to prevent water evaporation, resulting in a significant reduction in water loss shrinkage stress. Furthermore, the high water content fully hydrates the cement and enhances early tensile strength, which is beneficial to the anti-cracking properties of concrete at an early stage.
Finally, the addition of Polyvinyl alcohol (PVA) fibers to the concrete can help to prevent the formation and propagation of microcracks. This is due to the fact that PVA fibers can resist some of the tensile stress induced by moisture loss and shrinkage, as well as play a role in crack resistance and bridging. As a result, PVA fiber concrete can be put into important portions of concrete dams to improve the dam’s crack resistance.
References
Song H., Wang D. and Liu WJ (2022): Research on Construction Risks and Countermeasures of Concrete. Int J Concr Struct Mater (2022) 16:13 https://doi.org/10.1186/s40069-022-00501-3
Cantilever beams are beams that are free at one end and rigidly fixed at the other end. Beams that are free at one end and continuous through the other support (beams with overhangs) are also treated as cantilever beams. The primary design of cantilever beams involves the selection of an adequate cross-section and reinforcements to resist the internal stresses due to the applied loads and to limit the deflection to an acceptable minimum.
Due to the structural system of cantilever beams, they are very sensitive to deflection and vibration. When loaded, the maximum shear force and bending moment occur at the fixed support, while the maximum deflection occurs at the free end. As a result, under normal circumstances in reinforced concrete design, the length of cantilevers is usually kept to a minimum in order not to have bulky sections and heavy reinforcements. In order to save material and to reduce the load due to self-weight, cantilever beams can be tapered, increasing linearly from the free end to the fixed support.
For cantilever beams, the tensile moment occurs at the top, therefore the main reinforcements are provided at the top. At the bottom, standard beam detailing requirements recommend that at least 50% of the reinforcement provided at the top be provided at the bottom. The anchorage length of the top reinforcement is expected to enter at least 0.25 times the effective span of the backspan or 1.25 times the effective length of the cantilever (whichever is greater).
A cantilever beam relies on the backspan or an alternative counterweight for equilibrium or structural stability.
Design Example of a Cantilever Beam
Design a two-span cantilever beam (beam with overhang with the following information provided). The beam is to support a rendered 230 mm hollow block wall up to a height of 2.7m, in addition to the load transferred by the floor slab. The ultimate design load on the slab is 12 kN/m2. fck = 25 N/mm2; fyk = 500 N/mm2; Concrete cover = 35mm; Unit weight of concrete = 25 kN/m3; Unit of block wall = 3.5 kN/m2
Load Analysis
Aspect ratio of the slab k = Ly/Lx = 6/5 = 1.2 Factored load transferred from slab to beam B1 = 0.5(12 × 5) × [1 – 0.333(1.2)2] = 15.61 kN/m Factored load transferred from slab to beam B2 (factored) = γGnlx/4 = 1.35 × (12 × 2.5)/4 = 10.125 kN/m Factored self-weight of the beam (considering the 300 mm drop) = 1.35(25 × 0.3 × 0.23) = 2.33 kN/m Factored weight of block wall = 1.35(3.5 × 2.7) = 12.76 kN/m
Nominal cover to top reinforcement; cnom_t = 35 mm Nominal cover to bottom reinforcement; cnom_b = 35 mm Nominal cover to side reinforcement; cnom_s = 35 mm
Fire resistance
Standard fire resistance period; R = 60 min Number of sides exposed to fire; 3 Minimum width of beam – EN1992-1-2 Table 5.5; bmin = 120 mm
FlexuralDesign of the Cantilever Section
Design bending moment; MEd = 78.8 kNm
Distance between points of zero moment; L0 = (0.15 × Lm1_s1) + Lm1_s2 = (0.15 × 6000) + 2500 = 3400 mm Maximum flange outstand; b1 = bf – b = 720 mm Effective flange outstand; beff,1 = min(0.2 × b1 + 0.1 × L0; 0.2 × L0; b1) = 484 mm Effective flange width; beff = beff,1 + b = 714 mm Effective depth of tension reinforcement; d = 399 mm
K = M / (beff × d2 × fck) = 0.028
K’ = (2 × η × αcc / γC) × (1 – λ × (δ – k1) / (2 × k2)) × (λ × (δ – k1) / (2 × k2)) = 0.207 Lever arm; z = min(0.5 × d × [1 + (1 – 2 × K / (η × αcc / γC)0.5], 0.95 × d) = 379 mm Depth of neutral axis; x = 2 × (d – z) / λ = 50 mm
λx < hf – Compression block wholly within the depth of flange K’ > K – No compression reinforcement is required
Area of tension reinforcement required; As,req = max(M / (fyd × z), As,min) = 478 mm2
Tension reinforcement provided;3H16 Area of tension reinforcement provided; As,prov = 603 mm2
Minimum area of reinforcement – exp.9.1N; As,min = max(0.26 × fctm / fyk, 0.0013) × b × d = 122 mm2 Maximum area of reinforcement – cl.9.2.1.1(3); As,max = 0.04 × b × h = 4140 mm2 PASS – Area of reinforcement provided is greater than area of reinforcement required
Minimum area of shear reinforcement – exp.9.5N; Asv,min = 0.08 N/mm2 × b × (fck )0.5 / fyk = 184 mm2/m
Design shear force at support ; VEd,max = 63 kN Min lever arm in shear zone; z = 379 mm Maximum design shear resistance – exp.6.9; VRd,max = αcw × b × z × v1 × fcwd / (cot(θmax) + tan(θmax)) = 392 kN PASS – Design shear force at support is less than maximum design shear resistance
Design shear force at 399mm from support; VEd = 53 kN
Design shear stress; vEd = VEd / (b × z) = 0.608 N/mm2 Angle of concrete compression strut – cl.6.2.3; θ = min(max(0.5 × Asin(min(2 × vEd / (αcw × fcwd × v1),1)), 21.8 deg), 45deg) = 21.8 deg
Area of shear reinforcement required – exp.6.8; Asv,des = vEd × b / (fyd × cot(θ)) = 129 mm2/m Area of shear reinforcement required; Asv,req = max(Asv,min, Asv,des) = 184 mm2/m
Shear reinforcement provided; 2 × 8 legs @ 200 c/c Area of shear reinforcement provided; Asv,prov = 503 mm2/m PASS – Area of shear reinforcement provided exceeds minimum required
Maximum longitudinal spacing – exp.9.6N; svl,max = 0.75 × d = 299 mm PASS – Longitudinal spacing of shear reinforcement provided is less than maximum
Foundations can be subjected to dynamic loads in addition to static loads in engineering practice. Dynamics loads can be found in pile foundations supporting machines, oil and gas facilities, buildings under seismic effect, wind turbines, etc. The design of foundations under dynamic loading is complex and involves the inputs of structural, mechanical, and geotechnical engineering, as well as the theory of vibration.
In some cases, using deep foundations rather than shallow foundations may be required for foundations subjected to dynamic loads. Many factors influence whether a structure should be supported on a shallow or deep foundation system, including subsurface conditions and induced dynamic and static stresses.
Pile foundations are utilized to prevent bearing capacity failure, improve the system’s dynamic stiffness, and reduce dynamic oscillations. However, when a complete understanding of the dynamic interaction between the pile and the soil (pile-soil interaction) and between adjacent piles (pile-soil-pile interaction) is necessary, calculations become more difficult.
Fig 1: Construction of pile foundation
In general, applying dynamic loads to piles in cohesive soils reduces their skin friction and end-bearing value, i.e., reduces their ultimate carrying capacity, whereas applying dynamic loads to piles in granular soils reduces their skin friction but increases their end-bearing resistance at the expense of increased settlement under working load (Tomlinson, 1994).
The reduction in skin friction and end-bearing resistance of piles in cohesive soils is due to cyclic loading reducing the shearing strength of these soils. The ratio of the applied stress to the ultimate stress of the soil determines the amount of decrease for an infinite number of load repetitions.
Novak (1974) proposed an approximate method for simulating the dynamic interaction between soil and single piles. His method presupposed that the soil is made up of a series of infinitesimally thin horizontal strata that extend indefinitely. As a result, it can be seen as a generic Winkler medium with inertia and the ability to dissipate energy. Novak’s work was able to establish the value of geometric damping, in addition to being more precise than earlier attempts.
Novak and AboulElla (1978) modified this approach to include the effect of having a soil profile that changes with depth. Novak and Sheta (1982) also incorporated the effect of the weak zone around the pile, which can be used to represent either soil-pile interface slippage or the real weak zone generated around the pile during construction.
All of these investigations reveal that frequency has a considerable impact on single pile dynamic impedance characteristics. Field tests (Manna and Baidya, 2009; Elkasabgy et al, 2010) have also corroborated this effect. As a result of soil non-linearity, field investigations on large-scale piles have also revealed a non-linear dynamic pile reaction.
Dynamic Behaviour of Single Piles
Khalil et al (2019) carried out numerical and experimental modelling on the dynamic behaviour of piles. In the study, a range of excitation frequencies ranging from 10Hz to 60Hz was considered in order to verify their effects on the dynamic behaviour of single piles. Under vertical and horizontal vibrations, the finite element model from the study reveals that as the excitation frequency increases, the stiffness Ks increases and the damping Cs reduces (see Figure 2).
The study found out that stiffness increased by 64% (under vertical vibrations) and by 120% (under horizontal vibrations) when the frequency is increased from 10 Hz to 60 Hz (a 500% increase). Damping, on the other hand, is reduced by 40% under vertical vibrations and by 26% under horizontal vibrations. These findings show that the excitation frequency affects the dynamic pile-soil interaction.
Fig 2: Vertical dynamic behavior of single pile: (a) stiffness, (b) damping, (c) peak displacement (L/D = 20) (Khalil et al, 2019)
The effect of varying soil stiffness (Es) was also investigated in the study. When the value of soil stiffness was reduced by 50%, the numerical model revealed a corresponding drop in the impedance parameters of up to 33% for the stiffness and 12% for the damping (under vertical vibrations). For horizontal vibrations, this was up to 43% for stiffness and 27% for damping.
As a result, peak displacements can rise by 30 to 45% under vertical vibrations and 54 to 79% under lateral vibrations. This is to be expected, because lowering the soil stiffness lowers the soil resistance around the pile, resulting in a reduction in system stiffness and damping.
The slenderness ratio (L/D) of single piles subjected to vertical or lateral vibrations has no significant effect on their dynamic behavior. Peak displacements are reduced by less than 10% (under vertical vibrations) and 3% (under horizontal vibrations) when the pile slenderness ratio is increased from 20 to 30. This is consistent with the findings of Novat (1974) which show that raising the slenderness ratio has little effect on long flexible piles, especially when subjected to lateral motion. This happens because, regardless of the pile’s entire length, the soil mass contributing to the system’s dynamic resistance is confined to a specific depth.
Dynamic Behaviour of Piles in Group
Khalil et al. (2019) investigated the dynamic behavior of pile groups using a 3D finite element model. According to the findings, the group stiffness Kg increases at a variable rate as the frequency increases (see Figure 3). However, the group damping Cg increased significantly till it reaches f = 30 Hz to 40 Hz and decreased again after this point. Furthermore, the peak displacement reduced until it is nearly constant beyond 45 Hz. The study found that a pile group’s response is more sensitive to frequency than a single pile’s response.
The finite element model from the study showed a non-uniform drop in Kg as a result of lowering the soil stiffness (Es) by 50%. The reduction varies from as low as 4% (between 25 and 35 Hz) to as high as 39% at f = 60 Hz under vertical vibrations. Meanwhile, between 10 and 27 Hz, Cg slightly increased (by less than 5%). It however dropped by up to 39% for frequencies greater than 27 Hz.
. Fig 3: Effect of group size on vertical dynamic behavior: a) stiffness group efficiency, b) damping stiffness group efficiency, c) peak displacement (100%Es, L/D = 20, S/D = 5) (Khalil et al, 2019)
An overall rise in peak displacements was observed for the pile groups. However, this increase is inconsistent over the frequency range investigated, ranging from 8% to 52%. The reduction under lateral vibrations varies from as low as 24% at f = 35 Hz to as high as 42% at f = 60 Hz. In the meantime, the Cg drops by up to 35%. As a result, there was an overall rise in peak displacements.
Under vertical vibrations, the effect of modifying the dimensionless spacing ratio (S/D = distance between piles/pile diameter) was investigated using values of 3, 5, and 10 for a pile group of four. The phase at which the stress waves reach the adjacent vibrating piles changes as the spacing between piles increases. The stress waves become in-phase or out-of-phase with the vibrating nearby piles as a result of this change, which might cause the impedance parameters to reduce or rise.
The pile slenderness ratio (L/D) has a minor effect on the dynamic behavior of a pile group subjected to vertical or lateral vibrations, according to the research. Peak displacements are reduced by less than 5% (under vertical vibrations) and less than 7% (under horizontal vibrations) when the pile slenderness ratio is increased from 20 to 30. (under lateral vibrations).
Design of Pile Foundation under Dynamic Loading
To accommodate for dynamic load application on piles, it is common practice to double the safety factor on the combined skin friction and end bearing. The lateral loading of supporting piles can be caused by the torque of rotating machinery. The approaches can be used to determine the deflection under lateral loading in accordance with established methods. The deflections computed for the comparable static load should be doubled to account for dynamic loading.
The type of pile used, whether driven, driven-and-cast-in-place, or bored-and-cast-in-place, has no impact on the behavior of piles founded entirely in cohesive soils. Because of the development of an enlarged hole around the upper part of the shaft, lateral movements of piles with driven pre-formed shafts (e.g. precast concrete or steel H-piles) may be greater than those of cast-in-place piles (Tomlinson, 1994).
In granular soil, a pile’s skin-frictional resistance to static compressive force is quite low. When the pile is subjected to vibratory stress, this resistance is further reduced, and it is best to discard all frictional resistance on piles carrying high-frequency vibrating loads. If such piles are ended in loose to medium-dense soils, the settlement will continue to an unsatisfactory level for most machinery installations.
As a result, piles must be driven to a dense or very dense granular soil stratum, and even then, settlements can be large, especially if large end-bearing pressures are used. This is due to the soil grains’ increasing attrition at their places of contact. The slow but steady settlement of the piles is caused by the continued deterioration of the soil particles. Piles supporting vibrating machinery should, if possible, be driven completely through a granular soil stratum and terminate on bedrock or within a firm clay.
References
Elkasabgy M, El Naggar MH., and Sakr M. (2010): Full-scale vertical and horizontal dynamic testing of a double helix screw pile. Proc. of the 63rd Canadian Geotech; Conf., Calgary, Canada; 2010, pp. 352–359.
Khalil M. M., Hassan A. M., and Elmamlouk H. H. (2019): Dynamic behavior of pile foundations under vertical and lateral vibrations. HBRC Journal, 15(1):55-71, DOI: 10.1080/16874048.2019.1676022
Novak M. (1974): Dynamic stiffness and damping of piles. Can Geotech J. 11:574–598.
Novak M. and Aboul-Ella F (1978): Impedance functions for piles embedded in layered medium. J Eng Mech ASCE. 104(3):643–661.
Novak M. and Sheta M. (1982): Dynamic response of piles and pile groups. 2nd International Conference on Numerical Methods in Offshore Piling; Austin, TX; 1982.
Manna B and Baidya DK. (2009): Vertical vibration of full-scale pile—analytical and experimental study. J Geotech Geoenviron Eng. 135(10):1452–1461.
Tomlinson M. J. (1994): Pile Design and Construction Practice. E & FN SPON, London, UK
An orthotropic steel deck bridge is made up of a steel plate with welded stiffeners running in opposite directions. Longitudinal stiffeners are known as ribs, and transversal stiffeners are known as cross beams or floor beams. The entire deck is supported by main girders running longitudinally. The presence of two different members in the two orthogonal directions means that the stiffness of the deck is anisotropic (not the same in every direction). The term ‘orthotropic’ is coined from orthogonal-anisotropic.
Figure 1: Typical components on an orthotropic steel deck bridge
The major structural components of an orthotropic steel deck are;
The wearing surface
The deck plate
The transverse stiffeners
The longitudinal stiffeners (ribs), and
The main girders
Because the deck serves as a top flange for the longitudinal and transversal stiffeners, as well as the major girders, the orthotropic steel deck is a cost-effective and efficient system. This concept saves material, reduces self-weight, and increases the rigidity of the deck at the same time (Håkansson and Wallerman, 2015).
Structural Behaviour of Orthotropic Steel Deck
Almost every structure that exists is made up of several structural elements such as beams, columns, and slabs. In a sophisticated way, those elements contribute to the overall behavior of the structure, however, it is common for these members to be isolated and designed individually.
The elements of orthotropic steel deck bridges are linked in a more complicated way, and the same structural elements can perform several functions. The plate functions as a load distributer between the ribs as well as a top flange for ribs, crossbeams, and main girders, as previously stated. Due to this complex interaction, individual members should not be designed in isolation from each other. In other words, the structural elements cannot be treated individually if the true response of the bridge must be known (Håkansson and Wallerman, 2015).
The diagram below depicts the transfer of a concentrated load to the major girders. The load is applied to the deck plate, which distributes it among the ribs. The load is transferred from the ribs to the cross beams, which are then distributed between the main longitudinal girders.
Figure 2: Typical load path in an orthoptropic steel deck bridge (Karlsson and Wesley, 2015)
Subsystems for Analysis of Orthotropic Steel Deck Bridges
It has been proposed that the entire bridge deck be broken into subsystems in order to make hand computations and characterize the complex structural behavior of orthotropic steel decks. Because these subsystems are believed to work independently of one another, the impacts of the several subsystems can be combined using superposition (US Department of Transportation, 2012).
The proposed subsystems are described below;
Subsystem 1: Local Plate Deformation
In this subsystem, the deck plate should only transfer the imparted wheel load to the adjacent rib walls (US Department of Transportation, 2012). Deck plate bending is used to transfer the load. When a concentrated force is applied over a rib, the deck plate deforms as shown in Figure 3.
Figure 3: Local deformation of deck plate (Karlsson and Wesley, 2015)
Subsystem 2: Panel Deformation
Due to the fact that ribs share the same top flange, they are unable to operate independently, resulting in panel deformation. As explained in the preceding section, a concentrated force applied to the deck plate will be transferred to the neighboring ribs, but because of the shared top flange, even ribs that are not loaded will deflect. This action reduces the stresses in loaded ribs while increasing stresses in unloaded ribs (US Department of Transportation, 2012). Figure 4 shows how the panel deforms as a whole, with all ribs deflecting at the same time.
Figure 4:Panel deformation of deck plate (Karlsson and Wesley, 2015)
Subsystem 3: Longitudinal Flexure of the Ribs
Ribs are constructed in a continuous pattern over cross beams, and the fact that cross beams deflect under load must be taken into account. The ribs are treated as continuous across discrete flexible supports to account for this flexure. Cross-beams are simply supported between rigid main girders in this concept, and they deflect when loaded.
Subsystem 4: Cross Beam In-plane Bending
The ribs are built in a continuous pattern over the cross beams, as previously stated. This will result in cut-outs in the cross-section of the cross beam where the rib passes through. As a result, the geometry of the cross beam will change, making hand computations of in-plane stresses from bending and shear more difficult. According to the US Department of Transportation (2012), FE-analysis should be used to simulate the entire cross beam. The deformed shape of a cross beam subjected to in-plane forces is seen in Figure 5.
Figure 5: In-plane bending of cross beam (Karlsson and Wesley, 2015)
Subsystem 5: Cross beam distortion
Three separate effects affect the local stresses in the cross beam at the cross beam and rib intersection. Out-of-plane distortion from rib bending, distortion of rib walls due to shear stresses, and distortion of ribs due to unequal deflection are the local mechanisms at these intersections.
Subsystem 6: Rib Distortion
The rib will twist about its rotating centre if a concentrated force is applied in the mid-span between two cross beams and is eccentric about the axis of the rib (US Department of transportation, 2012). Because the rib-cross beam junction will be a fixed or partially fixed barrier, depending on how large cut-outs are employed, there will be substantial stress concentrations in the welds where twisting is inhibited. When the ribs are loaded, they distort as shown in Figure 6.
Figure 6: Distortion of ribs when loaded (Karlsson and Wesley, 2015)
Subsystem 7: Global Behaviour
When there is no consideration for local effects, the global system explains the displacement of the main girders as well as the overall behavior. It is possible to determine stresses and strains in the structure using traditional methods in this system (US Department of Transportation, 2012). Figure 7 depicts the orthotropic steel deck bridge’s global bending.
Figure 7: Global bending of the OSD (Karlsson and Wesley, 2015)
References
(1) Håkansson J. and Wallerman H. (2015): Finite Element Design of Orthotropic Steel Bridge Decks. Masters Thesis submitted toChalmers University of Technology, Göteborg, Sweden (2) Karlsson A. and Wesley C. (2015): Necessity of Advanced Fatigue Analysis for Orthotropic Steel Deck Bridges. Chalmers University of Technology, Göteborg, Sweden (3) US Department of Transportation (2012): Manual for Design, Construction, and Maintenance of Orthotropic Steel Deck Bridge. US Department of Transportation, Federal Highway Administration, Publication no. FHWA-IF-12-027. USA
In highway engineering, pavements should be constructed on subgrades with a known strength. The subgrade is the foundation or existing soil surface where the new highway will be built. Subgrade strength is normally described in terms of the CBR. The design idea for heavily trafficked roads is to improve the subgrade as needed and to establish a stable platform with the sub-base for the construction of the bound structural layer and surfacing above. In the long run, the capping and/or sub-base keep water out of the bound layers and offer a platform for compacting the bound layers.
The theory for both composite and flexible pavements is that the thickness of the sub-base/capping layer does not fluctuate with traffic, but rather with the strength of the subgrade. The thickness is the same in both types of roads.
Subgrade of a highway development
A pre-construction geotechnical site investigation shall be carried out for all sites prior to the start of any highway design/construction in order to assess a number of design issues, including the stiffness (CBR) of the material, its moisture sensitivity, and, if necessary, its suitability for earthworks and stabilisation to form a capping layer, sub-base, or road base material.
Despite problems in measurement, particularly on mixed fine and coarse graded soils and when moisture effects are considered, the California Bearing Ratio (CBR) remains the greatest predictor of soil strength. A method based on the Portable Dynamic Plate is available for measuring the stiffness of the sub-grade under dynamic loading. This is especially useful when a road is being widened such that the foundation is at or near equilibrium, while for new roads, additional approaches will be required to calculate equilibrium CBR values.
Regardless, any site investigation can only sample the soils at discrete areas inside the site. Variability is unavoidable, and it should be factored into the work’s design. A competent Geotechnical Engineer can provide guidance on the expected range of CBR values if necessary.
Typical laboratory CBR test
Aside from determining design CBR values for both short and long-term characterization of subgrade performance, several other elements might affect subgrade performance and must be considered during the design stage. The following are examples of typical issues to be addressed:
a) Water table depth/perched water tables b) Chemical contamination risk assessment c) Control of fine-grained soil piping d) The possibility of encountering loose Made Ground. a) The requirement for foundation soils to be improved on the ground (e.g. soft Alluvium, loose made ground etc.) f) The risk of collapse settlement of dry engineered fills g) The possibility of landslides. h) The possibility of subsurface caves, deneholes, and so forth. I The effect of nearby developments on locations with soft alluvium. j) The occurrence and handling of subgrade solution characteristics. k) Solution characteristics below drainage runs are treated. l) Treatment and frequency of other subgrade soft spots. m) Frost sensitivity of the subgrade. n) Risks of differential settlement/need for ground improvement. o) Subgrade soil chemistry if in-situ lime/cement stabilisation is considered. p) The ability of over-consolidated clays to shrink and expand. (Especially where trees have been destroyed) q) The possibility of open cracks in the underlying rock. r) The possibility of soft clay layers in granular soil.
The strength of a subgrade may be defined in terms of the soaked CBR. Subgrade strength classification in terms of CBR is given in the Table below;
Soaked CBR
Strength Classification
Comments
< 1%
Extremely weak
Geotextile reinforcement and separation layer with a working platform typically required.
1% – 2%
Very weak
Geotextile reinforcement and/or separation layer and/or a working platform typically required.
2% – 3%
Weak
Geotextile separation layer and/or a working platform typically required.
3%–10%
Medium
Geotextile separation layer and/or a working platform typically required.
10% – 30%
Strong
Good subgrade to Sub – base quality material
> 30%
Very Strong
Sub – base to base quality material
Selection of Method for Determination of CBR
The method for determining CBR should be chosen depending on the scale of the scheme, the precision required, and the likely soils encountered. Special precautions are required to provide adequate foundation support for CBR less than 2%.
The strength of most soils is highly dependent on moisture content. Some soils experience a rapid loss of strength as the moisture content increases. On such soils, structure protection as described in the Specification for Highway Works is very critical, as is a conservative approach when considering the effect of subgrade drainage.
For design purposes, two scenarios must be considered: the likely CBR at the time of construction and the long-term equilibrium value. Both of these are essential for design purposes. If the ‘as found’ CBR at the time of construction is less than that determined during the site investigation, a change in foundation layer thickness may be required.
The plasticity index should be computed for cohesive soils, and the description of the soil type from a grading examination of a bulk sample, as well as some knowledge of the probability of saturation in the future, should be examined for other soils. The table below can be used to approximate the CBR based on this information.
Methods of Determination of CBR
CBR’s performed upon pot samples
Advantages (i)It enables the evaluation of a soil’s CBR at various levels of saturation (CBRs, soaked/unsoaked)
Disadvantages (i) Considerable disturbance is created during the sample operation, which has a significant impact on the test results. (ii) Requires a large trial pit.
Plastic and Liquid Limits
Advantages (i) It enables a lower bound estimate of the CBR under recompacted circumstances for a wide range of effective stresses (i.e. construction conditions)
Disadvantages (i) Unless standard graphics are utilized, the analytical approach is costly. (ii) The typical graphs are based on the worst-case scenario. (iii) Can only be utilized on soils containing cohesive material (iv) Can be difficult to evaluate on granular and cohesive material mixtures
Soil Assessment Cone Penetrometer (MEXE Probe)
Advantages (i) It is simple and affordable to carry out.
Disadvantages (i) Correlation dependant (ii) Only offers the current CBR value (iii) Insensitive to the influence of the soil’s microstructure (iv) It is not suitable for usage in stony soils.
Measurement of Shear strength (hand vane/Triaxial tests)
Advantages (i) The hand vane is a quick and low-cost method of measuring undrained shear strength. (ii) Triaxial measurements of undrained shear strength take into consideration the soil microstructure (iii) For recompacted subgrades, remolded tests provide a lower bound.
Disadvantages (i) Only offers the existing CBR value when using the hand vane (ii) Triaxial measurements are somewhat expensive to perform, and sample and testing time might be lengthy (iii) It is dependent on correlation although this has a theoretical basis (iv) can only be applied for cohesive soils.
In-situ CBR
Advantages (i) Realistic CBR measurement (ii) Takes into account the macrostructure of the soil account (iii) can be used to determine the present chalk value in chalks
Disadvantages (i) Expensive to complete (ii) Only offers the present CBR value (iii) It is difficult to perform beneath the existing ground surface (iv) Not recommended for coarse granular soils.
Laboratory compaction test
Laboratory Compaction
Advantages (i) Calculates the CBR of remoulded soils at various moisture levels.
Disadvantages (i) Insensitive to soil macrostructure impacts (ii) Expensive to do (iii) Requires a big sample (iv) variable outcomes with coarse granular soils
Conclusion
CBR measurements are used to determine the current subgrade strength and to forecast the worst-case scenario for future service inside the pavement. In actuality, the current value may underestimate the subgrade’s strength at the time of construction because pessimistic conditions may not be present at the time of building, such as during summer construction. The current value, on the other hand, could have been taken in the summer and the plan built in the winter, when the subgrade may be weaker due to the moisture accumulating at that time of year.
As a result, it’s critical to think about the implications of the site investigation results in relation to those at the time of building. Unfortunately, there are no “hard and fast” guidelines, therefore field data may need to be interpreted by a professional. To develop an interpretative statement on the equilibrium CBR for design purposes, local knowledge of the effect of moisture on the relevant soil and the compaction/moisture content vs CBR connection should be combined with laboratory experiments. It will be necessary to make a request for this. Other elements impacting the performance of the subgrade, such as drainage and the possibility of foundation material settlement, must also be considered in the design.
Beams that have V-shapes (in the plan view) are commonly found in the corners of residential and commercial buildings. According to Hassoun and Al-Manaseer (2008), such beams can be analysed and designed using strain-energy principles especially when the beam is fixed at both ends.
In some scenarios, engineers may be tempted to design v-shaped beams as two cantilevers meeting at a point, but this is not strictly the case. There will be a need to assess other internal stresses such as torsion, and to understand the actual nature of the distribution of internal forces.
For a v-shaped beam subjected to a uniformly distributed load w (kN/m), the internal forces in the members can be obtained as follows;
(The bending moment at the centre of the beam Mc is given by; Mc = (wL2)/6 × [sin2θ/(sin2θ + λcos2θ)
Where; λ = EI/GJ L = half the total length of the beam AC θ = Half the angle between the two sides of the v-shape beam.
The torsional moment at the centreline of the section is given by; TC = (MC/sinθ) × cosθ = MCCotθ
At any section N along the length of the beam at a distance x from the centreline C,
A v-shaped beam at the corner of a building has a depth of 400mm and a width of 225 mm. The plan view of the beam is shown below. It is to support an ultimate uniformly distributed load of 30 kN/m inclusive of the factored self-weight. Design the beam according to the requirements of EC2. fck = 30 MPa, fyk = 500 MPa, Concrete cover = 35 mm
Solution
For fck = 30 MPa, Modulus of elasticity Ecm = 31476 MPa Shear modulus G = Ecm/2(1 + v) = 31476/2(1 + 0.2) = 13115 MPa Moment of inertia I = bd3/12 = (225 × 4003)/12 = 12 × 108 mm4 Polar moment of inertia J = 985033091.649413 mm4 λ = EI/GJ = (31476 × 12 × 108)/(13115 × 985033091.649413) = 2.9237
Mc = [wl2sin2θ/6(sin2θ + λcos2θ) = (30 × 2.52 × 0.75)/[6 × (0.75 + 2.9237 × 0.25)] = 140.625/8.88555 = 15.755 kNm MA = MB = MC – wl2/2 = 15.755 – (30 x 2.52)/2 = -77.995 kNm Torsional moment = TA = MCcotθ = 15.755 x 0.5773 = 9.095 kNm Shear at support = VA = VB = 30 × 2.5 = 75 kN
Let us check these answers using Staad Pro software;
By implication, one can confirm that the analysis method adopted is accurate. The beam can now be designed for torsion, bending, and shear using the guidelines provided in EN 1992-1-1:2004.
References Hassoun N. M. and Al-Manaseer A. (2008): Structural Concrete Theory and Design. Wiley and Sons Inc, New Jersey, USA
In the event of a fire, the general objectives of fire protection of structures are to limit hazards to individuals and society, adjacent property, and, where necessary, the environment or immediately exposed property (EN 1993-1-2:2005). The relevant time of fire exposure during which the associated fire resistance function of a structure is maintained despite fire actions is characterized as fire resistance in terms of time. Therefore, the fire resistance design of steel beams is concerned with maintaining the load-bearing function, integrity separating function, and thermal insulating separating function of a steel beam for a given period of time.
According to the Construction Products Directive 8911 06/EEC, the following are the essential requirement for the limitation of fire risks:
“The construction works must be designed and built in such a way, that in the event of an outbreak of fire;
the load bearing resistance of the construction can be assumed for a specified period of time
the generation and spread of fire and smoke within the works are limited
the spread of fire to neighbouring construction works is limited
the occupants can leave the works or can be rescued by other means
the safety of rescue teams is taken into consideration”.
According to the European standards, three major criteria are used to define the fire resistance of structures:
R – load-bearing function E – integrity separating function I – thermal insulating separation function
It is important to note that the above criteria may be required individually or in combination: • separating only: integrity (criterion E) and, when requested, insulation (criterion I) • load bearing only: mechanical resistance (criterion R) • separating and load-bearing: criteria R, E and, when requested I
Where mechanical resistance in the case of fire is required, steel structures shall be designed and constructed in such a way that they maintain their load-bearing function the relevant fire exposure. Criterion “R” is assumed to be satisfied in steel beams where the load-bearing function is maintained during the required time of fire exposure.
For a given load level, the temperature at which failure is expected to occur in a structural steel element for a uniform temperature distribution is called the critical temperature (θcrit). The thermal action on the steel member is a result of the heat flux transferred from the fire to the steel member. This is usually regarded as an indirect action.
The load bearing function of a structure is satisfied only if during the relevant duration of fire exposure t;
Efi,d,t ≤ Rfi,d,t
where Efi,d,t: design effect of actions (Eurocodes 0 and 1) Rfi,d,t: corresponding design resistance of the structure at instant t
It is however important to note that Eurocode permits the fire resistance of steel structures to be assessed in any of these three domains;
Time; tfi,d ≤ tfi,req (this usually feasible using advanced computational models) Load Resistance; Efi,d,t ≤ Rfi,d,t (This approach is feasible by hand calculation. Find reduced resistance at required resistance time) Temperature; θcr,d ≤ θd (The most simple approach, find the critical temperature for loading, compare with design temperature)
For ordinary structural fire structural design of steel beams, simple calculation models such as critical temperature can be used.
The thermal properties of structural steel at elevated temperature is shown below. At about 600°C, the elastic modulus of elasticity of steel is reduced by about 70% while the yield strength reduces by about 50%.
Under fire situation, the design loading is given by;
Efi,d,t = ∑Gk,j + ψ2,1Qk,1 + ∑ψ2,1Qk,I
More commonly, a reduction factor ηfi is applied to the loading under ambient conditions in order to represent the loading under fire conditions. This is given by;
Efi,d,t = ηfiEd
ηfi = Efi,d,t/Rd
In ambient temperature strength design; γG = 1.35 (Permanent loads) γQ.1 = 1.50 (Combination factor; variable loads)
In structural fire design γGA = 1.0 (Permanent loads; accidental design situations) γ2.1 = 0.3 (Combination factor; variable loads, offices)
Steps in the Fire Resitance Design of Steel Beams
The following are the steps to follow when assessing the fire resistance design of steel beams;
(1) Evaluate the actions on the structuture in fire situation Efi.d. This is commonly achieved by applying a reduction factor to the ambient temperature load. (2) Classify the member under class 1, class 2, class 3 or class 4 depending the rotation capacity using EC3 guidelines (3) Evaluate the resistance of the structure at ambient temperature (20°C) by fire rules Rfi.d.20. (4) Calculate the degree of utilisation μ0 (5) Calculate the critical temperature θcr (6) Calculate the section factor Am/V and the correction factor ksh (7) Carry out step by step calculation to verify if θfi,d= θcr at the time of fire exposure tfi,d (8) Check if tfi,dis greater than the required fire resistance period of the structure treq
Design Exampleof Fire Resistance of Steel Beams
Verify the fire resistance of an intermediate secondary beam (S275) in an office block supporting a slab of 175 mm thickness. The expected fire rating is 30 minutes. The slab is to support a variable action of 3 kN/m2, and finishes of 1.5 kN/m2.
Design Data
Imposed variable load qk = 3.0 kN/m2 Thickness of R.C. slab = 150 mm Finishes = 1.5 kN/m2
Analysis and Design at Normal Room Temperature Permanent loads
Unit weight of reinforced concrete = 25 kN/m3 Thickness of slab = 150 mm = 0.15 m
Self weight of slab = 25 × 0.15 = 3.75 kN/m2 Weight of finishes = 1.5 kN/m2 Total permanent actions (gk) = 5.25 kN/m2
Variable Actions Imposed variable load = 3.0 kN/m2 Total live load (qk) = 3.0 kN/m2
Normal TemperatureDesign of the Secondary Beam
The load transferred from the slab to the secondary beams considering a bay width of 2.667m
At ultimate limit state (neglecting reduction factors); PEd = 1.35gk + 1.5gk PEd = 1.35(5.25) + 1.5(3) = 11.6 kN/m2
Ultimate load transferred to every secondary beam; Fd = 11.6 kN/m2 × 2.667m = 30.937 kN/m Self weight of beam = 1.35 × 0.392 = 0.528 kN/m Total design load on the beam = 30.937 + 0.528 = 31.465 kN/m
An advanced UK beam S275 is to be used for this design. fy = 275 N/mm2 γm0 = 1.0 (Clause 6.1(1) NA 2.15 BS EN 1993-1- 1:2005)
The required section is supposed to have a plastic modulus about the y-y axis that is greater than; Wpl,y = My,Ed.γm0/fy Wpl,y = (150.093 × 103 × 1.0)/275 = 545.792 cm3
From steel tables, try section UB 305 x 165 x 40 Wpl,y = 623 cm3
Properties h = 303.4 mm; b = 165 mm; d = 265.2 mm; tw = 6.0 mm; tf = 10.2 mm; r = 8.9 mm; A = 51.3 cm4; Iy = 8500 cm4; Iz = 764 cm4; Wel,y = 560 cm3;
hw = h – 2tf = 265.2 mm E (Modulus of elasticity) = 210000 N/mm2 (Clause 3.2.6(1))
Classification of section ε = √(235/fy) = √(235/275) = 0.92 (Table 5.2 BS EN 1993-1- 1:2005)
Outstand flange: flange under uniform compression c = (b – tw – 2r)/2 = [165 – 6 – 2(8.9)]/2 = 70.6 mm c/tf = 70.6/10.2 = 6.921
The limiting value for class 1 is c/tf ≤ 9ε = 9 × 0.92 5.03 < 8.28 Therefore, outstand flange in compression is class 1
Internal Compression Part (Web under pure bending) c = d = 265.2 mm c/tw = 265.2/6 = 44.2 The limiting value for class 1 is c/tw ≤ 72ε = 72 × 0.92 = 66.24 44.2 < 66.24 Therefore, the web is plastic. Therefore, the entire section is class 1 plastic.
Member Resistance Verification
Moment Resistance
For the structure under consideration, the maximum bending moment occurs where the shear force is zeo. Therefore, the bending moment does not need to be reduced for the presence of shear force (clause 6.2.8(2)).
For rolled I-section with shear parallel to the web, the shear area is; Av = A – 2btf + (tw + 2r)tf (for class 1 sections) but not less than ηhwtw Av = (51.3 × 102 – (2 × 165 × 10.2) + [6 + 2(8.9)] × 10.2 = 2006.76 mm2 η = 1.0 (conservative) ηhwtw = (1.0 × 265.2 × 6) = 1591.2 mm2 2006.76 > 1591.2 Therefore, Av = 2006.76 mm2
The shear resistance is therefore; Vc,Rd = Vpl,Rd = [2006.76 × (275/ √3)/1.0] × 10-3 = 318.6159 kN VEd/Vc,Rd = 94.395/318.62 = 0.296 < 1.0 Ok
Shear Buckling
Shear buckling of the unstiffnened web will not need to be considered if; hw/tw ≤ 72ε/η hw/tw = 265.2/6 = 44.2 72ε/η = (72 × 0.92)/1.0 = 66 44.2 < 66 Therefore shear buckling need not be considered.
Serviceability limit state
Vertical deflections are computed based on unfactored variable loads. Permanent loads need not be considered (BS EN 1993-1-1 NA 2.23)
qk = 3.0 × 2.667 = 8 kN/m w = 5ql4/384EI w = (5 × 8 × 60004)/(384 × 210000 × 8500 × 104) = 7.563 mm Span/360 = 6000/360 = 16.667 (BS EN 1993-1-1 NA 2.23)
7.563 < 16.667 Therefore, deflection is satisfactory
Fire Design of the Secondary Beam
The loading due to fire design is given by;
Efi,d,t = ∑Gk,j + ψ2,1Qk,1 + ∑ψ2,1Qk,I
As a simplification to the loading above, the fire part of EC 3 permits us to apply a reduction factor ηfito the load of normal temperature design.
ηfi = (γGAGk + ψ2,1 Qk,1)/(γGGk + γQQk,1)
For the secondary beams; Gk = 5.25 × 2.667 = 14.0 kN/m Qk = 3.0 × 2.667 = 8.0 kN/m
According to equation 4.2 of EN 1993-1-2 for fire resistance design; ε = 0.85√(235/fy) = 0.786 for S275 grade of steel Outstand flange: flange under uniform compression c = (b – tw – 2r)/2 = [165 – 6 – 2(8.9)]/2 = 70.6 mm
c/tf = 70.6/10.2 = 6.921
The limiting value for class 1 is c/tf ≤ 9ε = 9 × 0.786 (c/tf)5.03 < (9ε) 7.074 Therefore, outstand flange in compression is class 1
Internal Compression Part (Web under pure bending) c = d = 265.2 mm c/tw = 265.2/6 = 44.2
The limiting value for class 1 is c/tw ≤ 72ε = 72 × 0.786 = 56.592 44.2 < 56.592 Therefore, the web is plastic. Therefore, the entire section is class 1 plastic under fire loading.
From our calculations for normal temperature design, it can be verified that; Mc,Rd = Mpl,Rd = 171.325 kNm Vc,Rd = Vpl,Rd = = 318.6159 KN
From relation 4.24 of EN 1993-1-2; We can calculate the utilisation ratio of the unprotected steel beam;
As the beam supports the concrete slab above, the impact of the kappa factors relative to the temperature gradient over its depth have to be taken into account. However, they have an impact on bending moment alone. No rule is provided for shear.
The modified degree of utilisation for bending moment; κ1 = 1.0 κ2 = 1.0
For the unprotected beam having all four sides exposed – clause 4.1(16) of EN 1993-1-2
For the protected section due to protection of the three sides exposed to fire; κ1 = 0.85 (three sides exposed; insulated) κ2 = 1.0 (for the unprotected beam having all four sides exposed – clause 4.1(16) of EN 1993-1-2
The modified degree of utilisation factor for vertical shear μ0,v,k = μ0,v = 0.166 (no adaptation factor) μ0 = max (μ0,m,k; μ0,v,k) μ0 = max (0.393; 0.166) = 0.393
Critical temperature of the protected beam From equation 4.22 of EN 1993-1-2; θcr = 39.19In[1/(0.9674μ03.833)- 1] + 482 θcr = 39.19In[1/(0.9674 × 0.3933.833 )- 1] + 482 = 622°C
From a more accurate linear interpolation from reduction table (Table 3.1); ky,θ (0.47) = 600°C ky,θ (0.393) = ?? ky,θ (0.23) = 700°C
Section factor is the ratio of the perimeter of the beam exposed to fire to the volume of the beam section (Am/V). In other words, it is the ratio between “perimeter through which heat is transferred to steel” and “steel volume”.
From steel table; Am/V = 240 m-1 (for UKB 305 x 165 x 40) (Am/V)b = 185 m-1 (boxed value)
The correction factor for shadow effect; ksh = 0.9(Am/V)b / (Am/V) ksh = (0.9 × 185)/240 = 0.6937
Heating of the unprotected beam The heating of the beam can be obtained from relation 4.25 of EN 1993-1-2.
Δθa.t = (ksh/(ca ρa) × Am/V ×hnet,d×Δt —– (1)
We will apply this relationship with the following assumptions; Δt = time interval increments = 5 seconds ρa = density of steel = 7850 kg/m3 ca = specific heat of steel = 600 J/kgK θa.t = 0.6937/(600 × 7850) × 240 × hnet,d× 5
Therefore; θa.t = (1.7664 × 10-4)hnet,d
hnet,d (heat flux) has two parts (the convective part hnet,c and the radiative part hnet,r) and varies with time as shown in the equation below. It can be easily calculated if the gas temperature θg is known.
Under standard fire situations; εres = εf × εm = 0.7 (εfis the emissivity of the fire usually taken as 1.0 while εm is the surface emissivity of the member usually taken as 0.7 for carbon steel) ϕ (view factor or configuration factor) = 1.0 αc = the coefficient of heat transfer by convection = 25 W/m2K
Therefore; hnet,r = 3.969 × 10-8[(θg + 273)4 – (θm + 273)4] hnet,c = 25(θg – θm) θg = 20 + 345log(8t + 1) (t in minutes) θm is the surface temperature of the steel member
The most relevant way to deal with hnet,d is to consider a mean value within the time interval ∆t (5 seconds in this case) between the instant ti and ti+1
When this is solved iteratively, the time at which the bare section reaches critical temperature can be obtained. The temperature development curve can also be plotted. By programming Eq. (1), it is easy to build tables or nomograms like the ones presented in Annex A ofFranssen and Real (2015)for unprotected steel profiles subjected to the ISO 834 fire curve. The use of these tables and nomograms avoids the need to solve Eq. (1). The nomograms from Annex A are reproduced in the Figure below.
kshAm/V = 166.5 m-1
For a critical temperature of 603°C (for the unprotected beam) and kshAm/V of 166.5 m-1, the time to achieve that temperature when exposed to fire is about 14 minutes. This is less than 30 minutes, therefore the beam cannot be designated as R30.
In the temperature domain; Table 4.6 gives the temperature after 30 minutes and 60 minutes of standard fire ISO 834 exposure, for different values of the modified section factor ksh[Am/V].
From Table 4.6, the critical temperature for 30 mins for ksh[Am/V] = 166.5 m-1 fire is 825.185°C. Therefore, the temperature in the section exposed on 4 sides after 30 min of standard fire ISO 834 exposure is 825.185°C. As this temperature is greater than the critical temperature, the member doesn’t fulfil the condition for temperature approach verification, because:
θd > θcr,d , at time tfi,requ
This further confirms that the member does not satisfy R30 requirements.
Maintaining an efficient HVAC system is crucial in delivering good indoor air quality in commercial establishments. Indoor Air Quality (IAQ) pertains to the air quality inside buildings and facilities. Understanding the risks involved in having air pollutants inside the facility is vital to appreciate the importance of maintaining the cleanliness of your HVAC unit.
In line with other significant building components, your HVAC system is primarily responsible for distributing heated or cooled air within the building. Having a properly functioning ventilation and air conditioning system not only promotes good IAQ but is also crucial in maintaining smooth operations for your business.
Due to its role in building operation, experts highly recommend regular inspection and cleaning of the commercial HVAC unit. With preventative maintenance, technicians can make repair and cleaning recommendations when necessary. A good inspection program is crucial in identifying minor leaks inside the ductwork, as minor issues quickly become severe and costly.
By scheduling regular maintenance, you can ensure the performance and longevity of your mechanical air conditioning system. While you can rely on technicians when it comes to assessment and repair, you can do your part by installing HVAC access doors and panels.
What is an HVAC Access Door?
A reliable commercial HVAC system needs to have its components functioning well to properly distribute conditioned air throughout the building. Its essential elements include the heat exchanger, blower motor, air ducts, combustion chamber, and thermostat. But how about the HVAC or duct access door? Can it be considered as part of the air conditioning unit?
The answer is a resounding yes. Access openings are without a doubt necessary in facilitating inspections, testings, repairs, and cleaning. These HVAC panels play a crucial role during maintenance services to ensure business operations — not only because they provide access but also because a good service ensures that the commercial AC unit is performing to expectations regarding safety and efficiency.
Ideally, contractors should install the HVAC panels near system components or either side of obstructions such as dampers and fans during installation. Purchasing a panel based on accurate measurements is also crucial for sufficient access to the air conditioning parts. Poorly constructed openings can harm the commercial HVAC unit in ways such as:
When improperly installed, the air ducts may compromise the system’s overall structural integrity.
Duct air leakage
Affect indoor air quality
Expose the mainframe to contamination and dust particles
No matter the panel used, it is vital to install the HVAC openings correctly and in a manner that facilitates proper closure. Therefore, it is highly ideal to hire professional contractors who have experience in physical installations.
Common Issues to Encounter if You Don’t Install HVAC Access Doors
There are many reasons why experienced contractors and technicians recommend using HVAC panels. The absence of a safe opening of the system’s mainframe and components presents many issues, particularly maintenance service providers. Without proper maintenance, your commercial air conditioner will inevitably affect its performance leading to poor air quality, among other things. Here are some possible issues you have to deal with if you choose not to install HVAC access panels.
Access Limitations – Technicians’ most common problem when undertaking service maintenance or repair is limited access to HVAC components. Access limitation doesn’t primarily refer to a lack of access, but it can also refer to insufficient space due to wrong measurements or improper door installation. The building owner needs to comply with standard access regulations and the request of the maintenance service provider to enable the required work to be safely accomplished.
Dust and Debris Accumulation – The absence of an entry door significantly promotes dust and debris accumulation inside the air ducts and the other components. Without proper cleaning, the dust particles can readily travel through the vents and into the interior, causing allergic reactions, dust build-ups, and poor air quality.
Animal Infestation – Without a good HVAC access point, your ductwork can quickly become a breeding ground for bacteria and mold growth. The molds can then attract small animals and insects, including rats, spiders, birds, and even snakes since your air passage has somehow become a thriving ecosystem for these animals. Having animals live in the ductwork can cause many issues, such as corrosion, destroyed wiring, blockage, and health issues due to animal wastes.
Lack of Protection – Keeping the components intact and in good condition is crucial for commercial HVAC systems to function appropriately. A duct access door offers additional protection from external elements or unauthorized access that may damage the system’s internal structure.
Reduced Aesthetic Appeal – There are residential housing properties with strict aesthetic requirements. The paint and materials used during construction must be similar on all floors, and an exposed HVAC unit can be an eyesore. Concealing the device is an excellent way of staying in line with the property’s overall appearance. In addition, there are now access door options that will allow the user to paint over the cover for the unit to blend seamlessly to the surface installation.
Delayed Repair and Maintenance – The primary purpose of an HVAC panel is to provide access. When it comes to commercial air conditioning systems, you cannot overestimate the importance of an efficient maintenance program. Technicians will undoubtedly have difficulties identifying and isolating the damage without sufficient access. Lack of repair and maintenance can cause a landslide of problems, eventually leading to either of the HVAC issues mentioned previously.
Takeaway
Maintaining good indoor air quality inside your building or facility is tremendously important, especially in residential units and office spaces. Turning a blind eye towards the significance of cleaning and maintaining your commercial air ducts could lead to a series of problems and, worse, the closure of your business due to negligence. Accepting that access doors have become an essential part of your commercial HVAC system is the key to a well-maintained ventilation system. Contact a licensed professional for more information, and remember to only purchase from a reputable store.
