From Queen's University Mine Design Wiki
This article is about the application of ground support strategies and techniques to "underground mining projects". For the article on general geotechnical design see Geotechnical design.
Ground support is a set of techniques, elements and methods that enable the conservation or mobilization of a rockmass' initial strength. The rockmass is given the ability to self-support throughout the course of mining. The ultimate goal of this practice is to allow for mining to occur safely while maintaining the stability of created underground excavations.These techniques can be divided into two main categories .
Support techniques refer to the action of applying an external reactive force to a rock surface in the process of deformation, i.e. submitted to strain causing changes in the shape, size and volume of the rock . Reinforcement techniques refer to the action of adding internal support, e.g. rockbolts, to maintain or improve the rockmass' properties prior to deformation. Of course, the selection of ground support is an integral part of the underground mine design process. See Main Article: The information required for the mine design
- 1 Significant properties of support elements
- 2 Empirical support design
- 3 References
- 4 External sources
Significant properties of support elements
Uses of ground supportHistorically, the installation of ground support was confined to temporary or permanent excavations. The selection of mining methods, would have been supported with long timber members to prevent ground failures in these workings. These workings would typically have remained opened for short periods of time (1-2 weeks). As for permanent excavations such as shaft stations which can remain opened for years, permanent support and reinforcement was installed. Often times, the temporary support previously put in place was removed and replaced with more permanent forms. This is contrary to modern practice where the rock-support interactions are an important design consideration.
Active vs. passive
Unlike the distinction between temporary and permanent support, the distinction between active and passive support refers to the load existing in the chosen support prior to its installation. For example, active support forces a load onto the rock surface in order to support broken rockmass and ensure its stability. Examples of active support types are: tensioned rockbolts, cablebolts, hydraulic jacks and powered supports for longwall mining. Passive support on the other hand is reactive to the ground's movements. It develops its load as the rock deforms. Examples of passive support types are: untensioned rockbolts, meshes and screens, reinforcing bars, shotcrete, timbered sets and steel arches. A combination of active and passive supports is typically optimal for most mining situations.
Primary vs. secondary
A more modern way of relating ground support techniques and systems is to define a primary and secondary support strategy. The primary support is installed in conjunction with excavation and serves supporting and reinforcing functions. This enables simultaneous control of boundary displacements. Any support applied at a later stage will be defined as secondary support. This ground control strategy maximizes the capacities of the support selected. As the excavation size and displacements are increased, the selected support develops the required load to maintain the required internal pressure. Figure 1 below clearly demonstrates this principle.
[[Image:Support-Displacement Relationship (Daeman 1977).jpg|frame|center|Support-Displacement Relationship, (Daeman, 1977)
This design strategy is also explained through the analysis for ground support reaction curves. These analyses are necessary in the design stages of a ground support strategy in order to determine the true failure mode of an excavation.
Types of support 
Since the development of the first mechanical rockbolts in the United States, where the first rockbolting occurrence is recorded in 1936 at the St. Joseph Lead Co. in Missouri Bieniawsky. "Ground Control, Section 10.5" Cummins, Hartman, Given, Howard. SME Engineering Handbook. SME, 1992</ref>,
the types of ground support available have greatly increased and offer a range of functionalities and capacities. The types of support can be divided in the following categories:
- Rockbolts (mechanical, frictional, grouted)
- Cablebolts (plain, birdcage, bulbed, nutcaged)
- Other Rockbolts (cone bolts, yieldable bars)
- Shotcrete (covers, reinforced, arches, pillars)
- Mesh, straps and screens
Often times, rockbolts and cablebolts are categorized according to their anchor type mechanical, frictional, etc.), their permanency (grouted or not grouted) and their deformation reactions (pre-tensioned or nor, dynamic vs. static).
The use of timber supports is seldom used for mining applications as its use underground is related to many hazards such as fire and is easily replaced by other support types.
Rockbolts and cablebolts
Rockbolts and cablebolts are the most common type of ground support in current use in underground mines. The great diversity of rockbolts and cablebolts allows for selection of the most geotechnically and economically appropriate ground support element for a specific situation. The sections below describe some of the characteristics  and cost of various rockbolts and cablebolts in greater detail:
Mechanical rockbolts are the type of ground support traditionally used. These are favourable for short term support as they are only anchored in the rockmass at both ends of the bolt. Furthermore, they are subject to blast vibrations and corrosion.These bolts come in two varieties: threaded or forged ends. The threaded end rockbolts which are inserted into the rock face and held in place by a face plate and a nut allow for adjustment to the rock face surface and the angle of the face plate. As for forged ends, the end of the bolt is forged to the nut allowing for less flexibility.
Different manufacturers offer different lengths and steel gauges (C1060 Steel, C1070, C1070M, C1055 (A29), A29 (gr75 for USA)) for mechanical rockbolts. In the United States, these manufacturing standards follow the American Standards for Material Testing ASTM F432. (Please note that these standards are accessible through Queen's Library, see External Sources) For example, Dywidag Systems International (DSI), one of the world leaders in underground support systems, offers mechanical rockbolts in diameters of 5/8" (14.2mm), 3/4" (17.3mm) and 7/8" (20.1mm) and lengths from 2.5' (0.762m) - 10' (3m).
Costs Mechanical rockbolts, due to their temporary nature, are often used in shorter lengths. A typical cost for these bolts, including the face plate, are $US 4.63 for a 3' (0.8m) bolt and $US 9.22 for a 10' (3m) bolt both of 5/8" diameter.
Installation Installing mechanical rockbolts is a straightforward process. The workers are required to drill a hole to the specified diameter, usually using a jackleg or a stoper, seeMining equipment. The bolt is then inserted in the drilled hole with the plate and nut. The bolt is then tensioned to the specified torque.
Properties The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North (MASHA) provides technical information for a typical mechanical rockbolt of 1.5m in length of comparable steel grade to the DSI products and after 85mm of displacement (C1070 grade).
Frictional rockbolts or friction bolts attribute their name to their support mechanism. The bolt is maintained in the rockmass when fricition is created along the bolt. Due to this characteristic, friction bolts can slip in the hole when ground movement occurs. This makes friction bolts very efficient in dynamic conditions although they are subject to corrosion and have a lower load bearing capacity compared to supported bolts, i.e. mechanical and grouted bolts. The two main varieties of friction bolts are SwellexTM, developed by Atlas Copco, and Split-setsTM, developed by Ingersoll-Rand and manufactured by DSI.
SwellexTM develop the frictional contact with the rock wall by inflation. The bolts are inflated by high water pressure. SwellexTM are manufactured from 1.2-3.6m (standard) and 3.0-6.0m (super)in length in a regular steel gauge or a manganese alloy for corrosion resistance. The SwellexTM rockbolt diameter is specified in terms of the required hole for installation. These hole sizes vary from 32-52mm.
Costs The cost for SwellexTM rockbolts is not specified by the Mine Cost Service Handbook (Volume 2, p.38). The Handbook only specifies the cost for "friction bolts". For a hole diameter of 32mm and 52mm respectively, the costs of 1.2m bolts are $US 5.31, $US 6.78 and and for 6.0m bolts $US 17.10, $US 22.90. It is specified that any galvanizing on the bolts, i.e. manganese coating, increases the price of the bolts by 30%.
Installation As with mechanical rockbolts, Swellex are installed by inserting the bolt into a pre-drilled hole. Instead of adding torque to the inserted bolt, high water pressure is forced into the bolt which inflates it to the proper rock surface profile. This, in combination with the anchorage of the plate and nut, creates the appropriate resistance between the bolt and rock wall.
The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North (MASHA) provides technical information for a typical Swellex of 1.8-2.1m in length of comparable steel grade (Atlas Copco) and after 150mm of displacement.
As for split sets, their split ends and slightly larger diameter than the hole diameter allows them to be squeezed inside the drilled hole to create friction along the bolt. Common sizes for split-sets are refered to as SS33, SS39, SS46 which defines the bolt diameter in mm, i.e. 33mm, 39mm and 46mm. The lengths of split-sets vary according to the manufacturer but are slightly shorter than the lengths of Swellex bolts. For a 33mm bolt, the lengths vary from 2.5' (0.762m) - 8' (2.4m). For a 46mm bolt, the lengths vary from 3' (0.91m) - 12' (3.65m).
Costs As with the Swellex bolt, the only specified cost is for a general "friction" bolt, refer to the costs of a Swellex bolt.
Installation The installation procedure for split-sets is simple. The bolt is inserted in a pre-drilled hole of a specified diameter. The bolt is then hydraulically placed into the hole. This creates resistance along the walls of the bolt. The bolt is then anchored with a plate and nut.
Properties The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North (MASHA) provides technical information for a typical split-set (39mm) of comparable steel grade to the DSI standards and after 150mm of displacement.
Grouted rockbolts refer to the use of reinforcement bars (rebar) or threadbars in combination with a grouting agent for creation of a bond along the rebar's entire length or a selected length.
The bonds are most often created using plain cement or a set of resins; fast acting at the toe, and slow acting along the bar. The required length of the bond is easily determined from strength factors of the bolt and diameter of the bolt.
Since the development of resins, the use of cement is less common in mining applications. Just as in mechanical rockbolts, rebars come with forged or threaded ends. Furthermore, their chamfered end allows the rebar to break through the resin or cement cartridges .
Resin grouted rebar is the most commly used grouted support. When installed appropriately, see Installation methods, its full length bond allows for efficient long-term support in static conditions. Furthermore, the resin used allows for corrosion protection as only the tip of the rockbolt is exposed.
Rebar is typically manufactured in four sizes #5 (15M - 16mm), #6 (20M), #7 (22M), and #8 (25M) which refer to the bar's diameter in mm or the thread size. Thread sizes are also refered to in imperial measurements with the following naming convention 5/8”- 11 UNC, 3/4”- 10 UNC, 7/8”- 9 UNC, 1”- 8 UNC. Rebars can be cut to specific lengths for the application up to 10' (3m). Of course, as with other ground support elements, their design follows manufacturing standards. In Canada they are manufactured to ASTM F432, Canadian Standards Association's CSA M430 and CSA G30.18M specifications. (Please note that these standards are accessible through Queen's Library, see External sources).
As for the manufactured resins, they come in various set times, from 15 seconds to 7 minutes, at a specified temperature. In order to create a quick bond at the end of the rockbolt a combination of fast set and the appropriate spin rate is used. These resins come in two compartment cartridges when the resin and the activator are kept separate until installation. The cartridges come in various diameters to accomodate the selected rebar/hole size (23 - 40mm) and various lengths, 12"- 60" (30.4 - 152.4cm). Most commonly, because various set times are desired at the bottom and top of hole, 12" cartridges are used. The following figures refer to appropraite spin times and temperatures for the different products.
Costs The costs for this type of support depends on the selected bolt and resin. The Mine Service Cost Handbook assigns costs of $US 4.63 for a 3' rebard and $US 9.22 for an 8' rebar. As for the resin cartridges, the price for one cartridge, regardless of its set-time, is estimated at $US 0.55 for a 17" cartridge and $US 3.07 for a 49" cartridge.
Installation The installation of resin grouted rebars require more fine tuning that other bolts. First, a hole needs to be drilled to the specified diameter and flushed with air or water to ensure a clean surface contact. Then the first resin cartridge is inserted. This cartridge usually has a fast setting time a requires the bar to be inserted the hole with an appropriate spion (usually above 100RPM). Once the bottom of the rebar is set, torque can be added as the slow-setting cartridges are inserted. Once the resin is set, the bolt is completely tensioned and cannot be tensioned further.
Properties The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North (MASHA) provides technical information for a typical resin grouted rebar (1.5m long) of comparable steel grade to the DSI standards and after 25mm of displacement.
Cement grouted rebar
Cement grouted rebars follow the same principles as resin grouted rebars. As the name implies, the only difference is in the bonding agent; cement cartridges instead of resin cartridges. For lengths and dimensions of typical rebars see the section on resin grounted rebars.Contrarily to resin cartridges, cement cartridges have a fixed set time. The cartridges, which contain dry cement material, need to be submerged in water for approximately 1.5 minutes (no longer than 5) prior to installation. The set-time is fixed all along the selected bond length of the bar at approximately 20 minutes and full yield strength is typically obtained after 24 hours of curing. Diameters for these cartriges vary from 25-38mm in lengths of 305mm.
Costs Due to the less common usage of cement cartridges, the cost of these cartridges can be inferred from the typical cost of Portland cement($CAN 273.00/ton).
Properties The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North(MASHA) provides technical information for a typical cement grouted rebar.
Threadbars are simple dywidags very similar in design to rebars. Their entire length is threaded with a simple nut that ties on to one end. The end is also chamfered for breakage of cartridges. The use of simple threadbars, not to confuse with threaded rebars, see Threaded-end rebars, is the least common in the mining industry due to their lack of adjustability to variable rock surface, i.e. no head. Their length and diameter are similar to those of manufactured rebar: #6 (19mm), #7 (22mm), #8 (25mm), #10 (32mm), #11 (35mm), #14 (44mm) at lengths up to 10' (3m).
Costs Costs for threadbars are not readily available.
Properties The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North(MASHA) provides technical information for a typical cement or resin grouted threadbar of 2.2m in lenght and 0.5m bond at 65mm displacement.
Cablebolts are also commonly used in underground mining applications. Their development, which occured in South African and Australian cut-and-fill(Clifford, 1974, Brown, 1999b), seeMining method, led to the modern cablebolt configuration. Due to their greater capacities, in comparison with standard bolt-type support, cablebolts are most often used in large span applications such as in hanging wall support and open stoping support designs. The bolts can be used as pre or post reinforcement with pre or post tensioning.
Cablebolts are manufactured as 7-wire cables with various strand diameters: 0.5", 0.6", 0.7"  and, as they are purchased in rolls, can be cut to any specified lengths, typically 5' (1.52m) - 50' (15.2m).
The wires are layed using one of the defined types: plain, birdcaged, bulbed and nutcaged. All of these bolt types are grouted in cement along their entire length. The selected lay impacts the cement grout/rockmass/cable contact. The bulbed or birdcaged lays offer the best frictional resistance. Furthermore, the wires of the cable can be galvanized for corrosion protection. Also, in dynamic conditions cablebolts can be partially covered in order to prevent bonding of the cable with the grout. This allows the bolt to extend with rock deformation.
Costs The cost for a birdcaged cablebolt of 0.6" diameter, excluding the cement, anchor grip and bearing plate, is estimated at $US 1.29 per foot plus $US 5.28 for the anchor and $US 7.55 for the plate. The cost can also said to increase by 30% for galvanizing.
Installation Cablebolts are first taken out of their rolled transport position. A hole is then drilled to the required diameter, larger than the cable. The cable is inserted along with an air-out line and a grout line. The grout is pumped into the larger line as the air is released through the smaller air-out line. The cable is maintained in the hole by a wooden wedge at the collar of the hole. When grouting is complete, the cable is anchored to the rock face.
The 2008 report on dynamic behaviour of rock support tensors provided by CANMET and Workplace Safety North(MASHA) provides technical information for cemented plain and birdcaged cablebolts.
As the mining industry is evolving, new technologies in ground support are allowing for the testing and implementation of new ground support elements. In combination with a deep underground mining trend (in Canada), the new elements presented by manufacturers are often dynamic elements that perform well in rockbursting conditions, see Rockbursting. Similarly to friction bolts, these new bolts use created friction and yield strength to accomodate for greater ground movemements. Cone bolts (threaded, shepperd's hook) and yieldable bars and tendons have been recently tested for rockbursting conditions. For example, for a cone bolt of comparable dimensions to a typical friction bolt, the obtained yield energies (kJ) are twice as large in dynamic loading (40 kJ).
The comparison for the strengths (yield and break) of various ground support elements is useful for the design of a support system.
Shotcrete, and its historical predecessor gunite, is applied in order to passively support rockmass. For the last 20 years, shotcrete has proven to be one of the most useful ground support elements in underground mining. The combination of cement, various additives (retarders, activators, reinforcing fibres etc.) and a mix of fine and coarse particles create a powerful tool for the mining industry. Shotcrete can be used as standard ground support in combination with mesh or in light rockbursting conditions as strain bursting protection, see Rockbursting. It can also be used to create shotcrete arches and pillars.
Shotcrete and mesh Although shotcrete is used in light rockbursting conditions, its nature makes it poorly resistant to rock deformation. In order to increase its "flexibility" it can be sprayed over steel mesh and mixed with steel / polymer reinforcing fibres. Of course, these fibres increase the cost and wear and tear applied on the applicators.
Shotcrete arches The design of shotcrete arches is still experimental. Created arches around drifts to create rib-like structures reduces the risk of fracturing during rockbursting.
Shotcrete pillars Shotcrete pillars are used in the same manner as rock pillars, i.e. in areas where the span exceeds same mining limits. The main difference with shotcrete pillars is that they are engineered for the specific situation. The bases can be pre-fabricated on surface and the shotcrete is sprayed on a mesh frame for reinforcement. These pillars have very high-load carrying capacities.
Costs The cost of shotcrete without any additives is approximately $US 300 per cubic yard. Added steel fibres are estimated to cost $US 0.80 per pound. This cost does not include the cost of application, the capital costs of the required equipment, the sprayers and the required labour. For example, the cost of typical shotcreting rig is approximately $US 60,000 for mining production rates of 1,000 tons per day. 
Installation The installation of shotcrete is crucial. The strength developed by the shotcrete depends on the quantities of various materials mixed, the techniques used and the application process employed by the worker. Typically, shotcrete is mixed according to these proportions: cement 15–20%, coarse aggregate 30–40% (>25mm), fine aggregate or sand 40–50%, accelerator 2–5% . The selected mix depends on various factors such as shootability, short-term and long-term strenghts, durability and economics. The mix needs to answer adequately to all the specific needs of the application. This mix can be applied using two techniques: dry-mix and wet-mix.
Dry-Mix When shotcrete is applied dry, it is shipped to site in bags, brought underground and poured (dry) into a hopper onto the shotcreting rig. On the rig, the appropriate amount of water is added (ratio of 0.3-0.5 cement:water) and then sprayed through nozzles onto the desired surface . The advantages to using dry-mix are the savings in equipment capital costs and the smaller size of equipment used. The mix is more expensive itself and the dust created by the powder can be an issue but removes any equipment cleaning stages required with the wet-mix shotcrete.
Wet-Mix When shotcrete is applied wet, the pre-mixed wet shotcrete is shipped by truck or borehole from a plant to the desired underground location where only the selected additives are added. The water ratio is kept slightly higher than the ratio used in dry-mix to facilitate transportation (0.4 - 0.5 cement:water). Similarly to dry-mix, wet mix is sprayed onto the rock surface using nozzles. The advantages to using wet mix are its lower operational costs and greater production capacities.
Performing the perfect shotcrete installation is a demanding task. Typical wall covers can be 50 - 500mm thick and require multi-layered installations. Furthermore, the addition of steel reinforcing fibres or layering with mesh requires special attention to the application process.
Properties According to an article on shotcrete standards shotcrete, after a curing time of 28 days, develops strengths of 65MPa.
Lacing Another technique that can be used in combination with shotcrete, especially in high stress excavations is lacing. Cables are basically laced in a spiderweb pattern along the wall with anchorage at intersections to diffuse stresses along the cables. This is mostly used in deep South African mines.
Mesh and screens
Mesh and screens, also straps, have two main functions. The first one being the support of tumbling and bulging pieces of rock and the second one being in support to shotcreting applications. Mesh, which is the most common ground support element in underground mines, can be build from welded wires or chain-link. Typically welded-mesh is used due to its higher strength, i.e. bigger gauge, and more adequate function for shotcreting. Chain-link mesh can also be used in highly variable rock surface because its smaller gauge allows for better contouring of the asperities.
It is evident that mesh is always used in combination with rock bolts to ensure attachment of the mesh to the rock wall. Furthermore, attachment and reinforcement of the screens/mesh layers of mesh are overlapped and sometimes double with higher gauge steel straps. The main downfall with mesh is its poor resistance to equipment damage.
Welded Mesh is manufactured in sheets of 48" to 96" in width and 48" high (or rolls of 100'). The steel gauges manufactured also vary from size 4 (0.232"), 6 (0.192"), 8 (0.160"), 9 (0.144") and 10 (.0128"). The spacing of the mesh squares is typically 4" x 4".
Chain-link mesh, similarly to welded mesh, is manufcatured in rolls of 4'-10' in width and 25' - 100' in length. The steel gauges are slightly smaller than the welded mesh; 6 (0.192"), 9 (0.144"), 11 (0.120") and 12 (0.106"). As for the spacing, diagonally across the mesh, it is offered in 2" - 3" openings.
The general cost for support mesh is estimated at $US 84.00 for a gauge 9 mesh and $70.00 for a gauge 11 mesh in rolls of 6' x 50'.
Mesh strengths can be estimated according to the table below:
Empirical support design
The selection of a support design has not always been, through mining history, a sound engineering process. Historically, observation served as the main design criteria. Often times, wood supports were added where deformation was observed and the rest of the exposed ground remained unsupported. Although the underground mines of 1900's were not comparably deep as today's, incidents related to falls of ground were common. In 1947, as the United States Mines Bureau (USBM) promoted the use of ground support for this purpose. "In under two years, it had come into general use in the US mining industry. In 1949, the method was in use at over 200 mines, and by 1952, annual consumption had reached 25 million bolts. Growth of rock bolting was rapid. In 1969, the USBM reported that 912 coal mines used 55 million roof bolts annually and 60% of underground coal production was mined under bolted roof. In 1989, the Bureau of Mines estimated that about 120 million rock bolts were used annually in American mines, and over 90% of underground coal production was mined under bolted roof." (SME Minine Engineering Handbook, Section 10.5, Bieniawsky, 1993)
In modern day mining applications, three main engineering methods are available for the selection of an appropriate ground support strategy. These methods vary from analytically analyzing the ground situation to observing the conditions and selecting an appropriate design. Empirical design falls in between these two design methods as it relies on previously registered cases and "rules of thumb" developed throughout mining history. This method is efficient, commonly used but also less precise than analytical solutions. This method is also based on various rock mass classification systems developed for the application of ground support systems to underground tunnels . Of course, ground support designs are developed to answer to common underground mining problems and safety hazards such as the development of large underground openings, rockbursting, geological rock conditions such as jointing, etc. The selected designs should be engineered to answer three main goals: provide a ground support design, provide specifications for installation of this design and provide quantitative rather than qualitative information about the design..
In Ontario, a fourth requirement is added to these three main design constraints. Under the Ontario Occupational Health and Safety Act, see external sources, otherwise known as the "green book", section 6 of article 854 provides legislation for mines and mining plants in Ontario. These laws include the development of "sound engineering design" in mine planning as well as the development of a Ground Control Management Plan (GCMP). This plan must describe the selection of the mining method, the selected ground support, the geological setting etc.
These laws were developed after the Ham report was released in 1976. This report, which intended to assess the safety of Ontario mine workers, pointed out issues in various areas of a mine including breathing quality, radiation and falls of ground. The fatality rate in underground mines in the 1970's was on average twice as high as today's rate regardless of the increase in mine production and depth. Throughout the ages, the development of new ground support techniques and stricter legislation has allowed for safe mining to occur at even great depths.
A sound ground support design answers this main question: what design is appropriate for this rock mass' specific mode of failure. With this question comes the following design considerations: type of support, length of support, spacing, time of installation, pre-tension or not. The concept of matching the ground support type to the mode of failure of the excavation is easily explained with the rock-reinforcement relationship and ground reaction curves.The design factors mentioned above can all be estimated based on a few empirical designs which account for a design factor of safety and the required legal standards. The selected support must assess safety functions such as holding, reinforcing and retaining the rock mass. These functions can be determined by observation of the rock mass, i.e. the degree of jointing, the orientation of main stresses, the depth of the excavation etc. These are all indicators to which support type is adequate for the mode of failure.
Ground reaction curves indicate the relationship between the selected support and the rock wall. As the rock mass moves, the curve predicts the required load to be applied to the walls and roof to maintain the excavation at the desired factor of safety. With rock movement, the stiffness of the support and the type of displacements performed by the rock mass balance each other to an equilibrium point where the proper support load is obtained. That being said, this can only be achieved when the selected support is appropriate. These curves are useful in determining the time at which the support shoudld be installed and if pre-tensioning is required. In most grounds, the rock mass movement is low enough that pre-tensioning is required. Furthermore, if the ground support is installed at the wrong moment, the ground reaction curve shifts up and the support becomes inefficient. Pre-tensioning the bolt can account for this difference in displacement prior to installation.
Design methods [[Image
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