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Damp proofing of Slabs on Ground

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The slabs-on-ground does not require high protection against water penetration and moisture in arid regions that does not have soils or have any sort of drainage problems.<br />
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This precaution is not necessary if the area does not have irrigation activities going on nearby. This is the case unless the building code of that regions requires treatment.<br />
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But for all site conditions other than mentioned above, it is essential to have water proofing or damp proofing for the slabs constructed on grounds.<br />
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As per ACI 302.IR-89, there is no need for damp proofing or water proofing nor vapor retarders on sites that are well drained or those sites under the following conditions:<br />
<ol>
<li>The site has water table level very low from the ground surface</li>
<li>A substratum of coarse aggregate that is freely draining is installed</li>
<li>A floor covering is provided to the slab that is not affected by the moisture.</li>
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<h3>
<span style="color: #cc0000;">Damp Proofing of Slabs–on–Ground</span></h3>
The damp proofing of slabs constructed on ground can be done either below or above the surface. Mostly, the damp proofing is installed below the surface of the slab. Mostly plastic film of vapor retarders is employed below the slab surface as a damp proofing membrane.<br />
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The figure-1 below shows the installation of a vapor retarder over the surface of gravel substrate. The vapor retarders are sealed to the foundation wall as shown. This will provide continuity in the placement.<br />
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In order to avoid the penetration of sheet, brick chairs are employed other than the wire chairs.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-ZKyPgfyjZ_E/WiSDgImVOMI/AAAAAAAAHWk/i96sOrMySosxftn09WXNNuD7wObnyUAZwCLcBGAs/s1600/plastic-vapor-retarder-slabs-on-ground.jpg" style="margin-left: auto; margin-right: auto;"><img alt="Tamped grave substrate_ engineersdaily.com" border="0" data-original-height="326" data-original-width="386" height="270" src="https://1.bp.blogspot.com/-ZKyPgfyjZ_E/WiSDgImVOMI/AAAAAAAAHWk/i96sOrMySosxftn09WXNNuD7wObnyUAZwCLcBGAs/s320/plastic-vapor-retarder-slabs-on-ground.jpg" title="Tamped grave substrate_ engineersdaily.com" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fig.1. The plastic vapor retarders are placed above the grave substrate that is tamped.</span></td></tr>
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When wood flooring has to be provided above the slabs on ground, the damp proofing is done over the surface of the floor. The damp proofing over the slab top surface is permitted only under the following conditions, when:<br />
<ol>
<li>The water table is at least 12 inches below the slab surface</li>
<li>Installation of footing drains is carried out</li>
</ol>
The slabs-on ground with wooden flooring on the top will ask for damp proofing unless the above conditions are satisfied.<br />
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The figure-2 below shows the installation of wooden flooring over the slabs that are constructed on ground.<br />
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The wood flooring span sleepers will separate the surface from the bottom slab as shown in figure-2. The damp proofing can be applied to the slab only under the sub soil conditions mentioned above.<br />
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<tr><td style="text-align: center;"><img alt="Wooden Flooring Above Slabs-on-Ground_engineersdaily.com" border="0" data-original-height="281" data-original-width="316" src="https://2.bp.blogspot.com/-9Z8JmxbADwo/WiSER3_halI/AAAAAAAAHWs/ZN8tF2jPNpojFvwRUmkl5tt-y2wL4haCwCLcBGAs/s1600/wooden-flooring-above-slabs-on-ground.jpg" style="margin-left: auto; margin-right: auto;" title="Wooden Flooring Above Slabs-on-Ground_engineersdaily.com" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fig.2.Wooden Flooring Above Slabs-on-Ground</span></td></tr>
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In the figure-2, an air space is created between the wooden flooring and the slabs constructed. This must be vented at the junctions so that the water penetration due to water vapor migration is avoided. This will help in maintaining an equal relative humidity both above and below the surface of the wooden flooring provided.<br />
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The top surface damp proofing of the slabs constructed on ground will be interrupted by the partitions and the columns present. Vapor retarders constructed will be interrupted by these extra elements bringing a loss of integrity of the damp proofing system.<br />
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The figure -3 below shows the same. Under such situations, the best alternative is to have damp proofing or water proofing under the slab.<br />
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<tr><td style="text-align: center;"><img alt="The column interrupting the vapor retarder placed above a slab-on-ground_engineersdaily.com" border="0" data-original-height="250" data-original-width="371" height="215" src="https://2.bp.blogspot.com/-4Mr1jmLyCic/WiSE1_2ydgI/AAAAAAAAHW0/xzHPGsV7p4E1IlrXbipw-x0gr4h_as6gACLcBGAs/s320/vapor-retarder-placed-above-slabs-on-ground.jpg" style="margin-left: auto; margin-right: auto;" title="The column interrupting the vapor retarder placed above a slab-on-ground_engineersdaily.com" width="320" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fig.3. The column interrupting the vapor retarder placed above a slab-on-ground</span></td></tr>
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<h3>
<span style="color: #cc0000;">Risk in Using Vapor Retarders as a Waterproofing Solution</span></h3>
The substitution of vapor retarders instead of water proofing will welcome risks. The performance of the vapor retarder is dependent on the integrity of the film as well as the way it is seamed. The maintenance of a vapor retarder seam integrity in field condition is very difficult to attain in a slab on ground construction.<br />
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The use of wooden or vinyl coverings too make the vapor retarders into risk. Other risk parameters are the use of wall – sensitive adhesives. Under these situations, it is most preferred to have a heavy-duty panel or water proofing to be installed than waiting for the loss caused by the complete replacement of moisture damaged floor.<br />
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As shown in figure-2, the attachment of sleepers to the slabs-on-ground must be carried out with the help of water resistant adhesives instead of mechanical anchors.<br />
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The use of nails and other mechanical anchors will result in puncture of vapor retarders that is located on the top surface of the slab.</div>
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<span style="color: #cc0000;">Considerations in Damp Proofing Slabs on Ground</span></h3>
When the top surface of the slab is subjected to damp proofing, the slab should have a substratum that is of a granular material. This layer of properly graded aggregate will help in preventing the rise of moisture (mainly by the principle of capillary action).<br />
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It is advised not to have a vapor retarder below the slab surface by using suspenders and other belts along with having a top surface damp proofing. The residual moisture in the concrete slabs can result in vapor pressure that can disband the vapor retarder and result in rupture.<br />
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It is not appropriate to have too many floor finishes and coatings. This is because the concrete is moisture sensitive. Moisture sensitive adhesives can be used as a mode of moisture resistance.<br />
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Liquid applied coatings in concrete slabs on ground have resulted in moisture in concrete. The following conditions can result in high level moisture contents:<br />
<ol>
<li>For those slabs that are cast on a grade with no proper functioning of the under-slab vapor retarders.</li>
<li>Conditions when the suspended slabs are cast over the non – vented steel formworks.</li>
<li>The conditions where the suspended slabs are constructed over the occupancies that possess higher relative humidity. These includes elements like commercial kitchen and swimming pools.</li>
<li>The installation of suspended slabs over the crawl spaces that are unvented.</li>
<li>The slabs with lightweight aggregates.</li>
<li>The slabs that used a water cement ration in excess of 0.55 (w/c = 0.55).</li>
<li>The slabs that cured in a period less than 90 day.</li>
</ol>
The manufactures of the floor finishes or damp proofing coatings highly follow the requirement of testing the concrete slab before the installation of any membranes. This testing will ensure that the moisture content in the slab is within the susceptible limits and won’t result in any failure.<br />
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The Calcium Chloride Test as specified by ASTM F1869 is used to determine the Moisture Emission Rate (MVER). This is measured in pounds per thousand square feet within 24 hours. The accepted range of MVER is three to five pounds.<br />
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The internal relative humidity in the structure is obtained by means of a hygrometer by placing probes in concrete. This is as per ASTM F710 and the established rate is 75 percent.<br />
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This result can be achieved within 1 month of drying time per inch of the concrete element tested. It recommends the installation of vapor retarders in the direction of concrete pouring.</div>

Damp proofing of Slabs on Ground

The slabs-on-ground does not require high protection against water penetration and moisture in arid regions that does not have soils ...

Steel Sheet Piling Works - Workflow Procedure for Site Engineers

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This brief article explains the work flow procedure for site engineeers to execute steel sheet piling works. The procedure details various steps and checks that are recommended to be followed for such activities.</div>
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<b><span style="color: #cc0000;">Method and safety</span></b></h3>
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• Piling contractors must be requested to provide a written method statement as appropriate for the piling operations. Find out what induction training and information specific to a method statement is provided by immediate site supervisors to piling operatives.</div>
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• Note that cranes must be selected and used in accordance with CP3010 and with the Construction (Lifting Operations) Regulations 1998. A firm level base of adequate bearing value must be provided, or crane mats used.</div>
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• Check that cores of pendant/bridle ropes are not fractured.</div>
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• Any crane used for raising or lowering operatives must be fitted with a dead man’s handle and the descent must be effectively controlled; the latter may be achieved by power lowering. Properly constructed man-carrying cages, which are unable to spin or tip, must be used. The cages should be regularly and carefully inspected.</div>
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• All lifting appliances and gear must carry appropriate certificates of test and examination, and must be adequate for the job, paying particular attention to the risk of damage to gear by sharp edges.</div>
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• All personnel working on piling operations must wear safety helmets (helmets appropriate for piling work are now available with retaining strap and smaller peaks). Ear and eye protection should be provided.</div>
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• Piling machine operators must be at least 18 years of age, trained, competent, medically fit and authorised by site management to operate the machine.</div>
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• When piling from a pontoon or adjacent to water, personnel must wear life jackets. Rescue equipment (e.g. a safety boat and lifebuoys with lifelines attached) must be kept ready for immediate use and enough operatives must know how to use it.</div>
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<b><span style="color: #cc0000;">Materials handling</span></b></h3>
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• When splitting bundles of sheet piles, use chocks. If large quantities of piles are handled, the use of purpose-made strops and grips is advised.</div>
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• Piles should not be stacked too high or in a cantilever position. Use spacers and chocks where necessary. Tubular piles should not be stacked more than four high and should be properly chocked.</div>
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• When lifting piles or piling hammers, use hand lines to control the load. Give due consideration to wind speed during the operation.</div>
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• Check the dimensions and alignment of clutches. If necessary perform trial clutching of piles. This is advisable for Z-shaped pile sections where the clutch is less positive than on trough sections (e.g. Larssen piles).</div>
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<b><span style="color: #cc0000;">Gate systems</span></b></h3>
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See Fig 1.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-88ZGM0VUFbM/XHpKVouWs6I/AAAAAAAAHf4/i-h_X3HLmVM_Xkv-2WfW0B26GwN4imzqwCLcBGAs/s1600/Steel%2BSheet%2BPiling%2BWorks%2B-%2BWorkflow%2BProcedure%2Bfor%2BSite%2BEngineers%2B%2528engineersdaily.com%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Gate system using concrete bases (showing piling, the use of hanger brackets and the provision of a safety walkway)." border="0" data-original-height="527" data-original-width="666" height="506" src="https://2.bp.blogspot.com/-88ZGM0VUFbM/XHpKVouWs6I/AAAAAAAAHf4/i-h_X3HLmVM_Xkv-2WfW0B26GwN4imzqwCLcBGAs/s640/Steel%2BSheet%2BPiling%2BWorks%2B-%2BWorkflow%2BProcedure%2Bfor%2BSite%2BEngineers%2B%2528engineersdaily.com%2529.jpg" title="Gate system using concrete bases (showing piling, the use of hanger brackets and the provision of a safety walkway)." width="640" /></a></td></tr>
<tr><td class="tr-caption"><span style="font-size: small;"><b>Figure 1.</b> Gate system using concrete bases (showing piling, the use of hanger brackets and the provision of a safety walkway).</span></td></tr>
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• Positioning (pitching) and driving sheet piling is usually done by using a temporary supporting structure (gate). This is made up of heavy steel or timber H-frames supporting horizontal-heavy H-beam guides. The H-frames can be supported on heavy steel spreaders or specially cast concrete blocks. Ensure an adequate foundation under these frames and bases to prevent subsidence and overturning during piling operations. This is particularly applicable during work in rivers, etc.</div>
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• If using concrete blocks ensure that they are suitably reinforced to withstand loads from lifting and shock loading. Vertical steel columns should have a good bottom fixing. Vertical timber should not be cast into the block but should be wedged and bolted. Where doubt exists over stability use guy lines or raking steel props.</div>
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• All horizontal gates with platforms over 2m high, or over any potentially dangerous areas, must be provided with adequate guardrails, toeboards and correct ladder access.</div>
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• Ladders must be secured and extend at least lm above staging.</div>
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• If using a cantilever system, use a tie-back where possible, as well as kentledge to provide safe anchorage.</div>
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• When piling is progressing and temporary piles are used to support the gate system, use purpose-made brackets and bolt them to the piles. Any welding necessary should be carried out by competent welders.</div>
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<b><span style="color: #cc0000;">Pitching piles</span></b></h3>
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• If shackle holes have to be burned in the pile, remove sharp burrs to prevent damage to shackle pins.</div>
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• Use quick-release shackles wherever possible:</div>
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– the sheet pile must not be lifted vertically without first checking that the pin is properly engaged through the sheet</div>
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– do not use a pull rope less than 5mm diameter</div>
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– the length of rope used must be less than the length of the pile, to prevent the extra rope snagging and pulling the release for the shackle</div>
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– secure the rope around the sheet pile to prevent snagging</div>
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– if a special lifting eye is to be welded to the pile for angled pitching, the weld should have a factor of safety of at least 2.</div>
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• Pitch long sheet piles with a pile threader, following the manufacturer’s guidance for use. Where this is not possible, use a pile pitching cage. The cage is normally hung from an adjacent pile, the operatives wearing safety harnesses hooked to the adjacent pile before the crane hook is removed from the cage.</div>
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• When feeding sheet piles through the top and bottom gates, use wood blocks or a bent bar. Never use a straight pinch bar, as fingers can easily be trapped. Use a spacer block between the guides to keep the leading free clutch in its correct alignment.</div>
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• Where access and work is carried out from ladders:</div>
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– Clutching: the ladder must be placed in the valley of a previously placed pile; the ladder must be footed and when at the top of the ladder both hands are required for clutching, a safety belt must be worn and secured to the pile using a manlock.</div>
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– Wedging: the ladder must be placed against the H-beam and footed wedges should be pre-placed on the beam. A 4 lb. lump hammer must be used as this can be swung with one hand but if two hands are required, a safety belt must be used with the lanyard wrapped around the H-beam or used with a manlock.</div>
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Note: At all times safety helmets and footware must be worn. When working at height the helmet should be secured with retaining strap.</div>
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• Changes in work method:</div>
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– The work method must not be changed without consultation of the senior site representative responsible for the piling operation.</div>
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– If windy conditions (e.g. over 30 mph gusts) make the handling of the sheet piles difficult, stop work until the senior site representative responsible for the piling operation has been consulted and a safe method of continuing the work has been devised.</div>

Steel Sheet Piling Works - Workflow Procedure for Site Engineers

This brief article explains the work flow procedure for site engineeers to execute steel sheet piling works. The procedure details various ...

Shallow Foundations - An Overview

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A shallow foundation is often selected when the structural load will not cause excessive settlement of the underlying soil layers. <br />
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In general, shallow foundations are more economical to construct than deep foundations. Common types of shallow foundations are listed in Table 1 and described later:<br />
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<b>Table 1. Types of shallow foundations</b></div>
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    <th class="tg-73oq"><span style="font-family: inherit;">Category</span></th>
    <th class="tg-73oq"><span style="font-family: inherit;">Common Types</span></th>
    <th class="tg-73oq"><span style="font-family: inherit;">Comments</span></th>
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    <td class="tg-73oq" rowspan="7"><span style="font-family: inherit;">Shallow foundations</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">Spread footings</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">Spread footings (also called pad footings) are often square in plan view, are of uniform reinforced concrete thickness, </span><br />
<span style="font-family: inherit;">and are used to support a single column load located directly in the center of the footing.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Strip footings</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">Strip footings (also called wall footings) are often used for load-bearing walls. They are usually long reinforced concrete</span><br />
<span style="font-family: inherit;">members of uniform width and shallow depth.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Combined footings</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">Reinforced-concrete combined footings are often rectangular or trapezoidal in plan view, and carry more than one column load.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Conventional slab-on-grade</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">A continuous reinforced-concrete foundation consisting of bearing wall footings and a slab-on-grade.</span><br />
<span style="font-family: inherit;">Concrete reinforcement often consists of steel rebar in the footings and wire mesh in the concrete slab.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Posttensioned slab-on-grade</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">A continuous posttensioned concrete foundation. The posttensioning effect is created by tensioning steel tendons or cables</span><br />
<span style="font-family: inherit;">embedded within the concrete. Common posttensioned foundations are the ribbed foundation, California slab, and PTI foundation.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Raised wood floor</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">Perimeter footings that support wood beams and a floor system. Interior support is provided by pad or strip footings. There is a</span><br />
<span style="font-family: inherit;">crawl space below the wood floor.</span></td>
  </tr>
<tr>
    <td class="tg-73oq"><span style="font-family: inherit;">Mat foundation</span></td>
    <td class="tg-73oq"><span style="font-family: inherit;">A large and thick reinforced-concrete foundation, often of uniform thickness, that is continuous and supports the entire structure.</span><br />
<span style="font-family: inherit;">A mat foundation is considered to be a shallow foundation if it is constructed at or near ground surface.</span></td>
  </tr>
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<b><span style="color: #cc0000;"><br /></span></b></h3>
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<b><span style="color: #cc0000;">1. Spread Footings, Combined Footings, and Strip Footings</span></b></h3>
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These types of shallow foundations are probably the most common types of building foundations. Figure 1 shows various types of shallow foundations.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-oMFGyDWJN5g/XHoqGBq7fTI/AAAAAAAAHfY/sNgRc4arZLoq77vClC7JDGiiuEq-hUe-wCLcBGAs/s1600/Examples_of_shallow_foundations%2528engineersdaily.com%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Figure 1. Examples of shallow foundations. (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)" border="0" data-original-height="277" data-original-width="340" height="520" src="https://2.bp.blogspot.com/-oMFGyDWJN5g/XHoqGBq7fTI/AAAAAAAAHfY/sNgRc4arZLoq77vClC7JDGiiuEq-hUe-wCLcBGAs/s640/Examples_of_shallow_foundations%2528engineersdaily.com%2529.jpg" title="Figure 1. Examples of shallow foundations. (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: justify;"><b>Figure 1.</b> Examples of shallow foundations. (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)<br />
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<span style="color: #cc0000;"><b>2. Mat Foundation</b></span></h3>
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Figure 2 shows various types of mat foundations. Based on economic considerations, mat foundations are often constructed for the following reasons (NAVFAC DM-7.2, 1982):</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-J7aGgSnZ9nU/XHoq9KoHC8I/AAAAAAAAHfg/QDBzNK2UtqQvJ45_LdUhhk8OAzVV25LxgCLcBGAs/s1600/Examples_of_mat_foundations%2528engineersdaily.com%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Figure 2. Examples of mat foundations. (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)" border="0" data-original-height="274" data-original-width="342" height="512" src="https://2.bp.blogspot.com/-J7aGgSnZ9nU/XHoq9KoHC8I/AAAAAAAAHfg/QDBzNK2UtqQvJ45_LdUhhk8OAzVV25LxgCLcBGAs/s640/Examples_of_mat_foundations%2528engineersdaily.com%2529.jpg" title="Figure 2. Examples of mat foundations. (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figure 2.</b> Examples of mat foundations. (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)</td></tr>
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i. <i><b>Large individual footings.</b></i> A mat foundation is often constructed when the sum of individual footing areas exceeds about one-half of the total foundation area.</div>
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ii. <i><b>Cavities or compressible lenses.</b></i> A mat foundation can be used when the subsurface exploration indicates that there will be unequal settlement caused by small cavities or compressible lenses below the foundation. A mat foundation would tend to span over the small cavities or weak lenses and create a more uniform settlement condition.</div>
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iii. <i><b>Shallow settlements.</b></i> A mat foundation can be recommended when shallow settlements predominate and the mat foundation would minimize differential settlements.</div>
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iv. <i><b>Unequal distribution of loads.</b></i> For some structures, there can be a large difference in building loads acting on different areas of the foundation. Conventional spread footings could be subjected to excessive differential settlement, but a mat foundation would tend to distribute the unequal building loads and reduce the differential settlements.</div>
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v. <i><b>Hydrostatic uplift.</b></i> When the foundation will be subjected to hydrostatic uplift due to a high groundwater table, a mat foundation could be used to resist the uplift forces.<br />
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<span style="color: #cc0000;"><b>3. Posttensioned Slab-on-Grade</b></span></h3>
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Posttensioned slab-on-grade is common in southern California and other parts of the United States. The most common uses of posttensioned slab-on-grade are to resist expansive soil forces or when the projected differential settlement exceeds the tolerable value for a conventional (lightly reinforced) slab-on-grade. For example, posttensioned slabs-on-grade are frequently recommended if the projected differential settlement is expected to exceed 0.75 in. (2 cm).</div>
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The Post-Tensioning Institute (1996) has prepared installation and field inspection procedures for posttensioned slab-on-grade. Posttensioned slab-on-grade consists of concrete with embedded steel tendons that are encased in thick plastic sheaths. The plastic sheath prevents the tendon from coming in contact with the concrete and permits the tendon to slide within the hardened concrete during the tensioning operations. Usually tendons have a dead end (anchoring plate) in the perimeter (edge) beam and a stressing end at the opposite perimeter beam to enable the tendons to be stressed from one end. However, it is often recommend that the tendons in excess of 100 ft (30 m) b stressed from both ends.</div>
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Because posttensioned slab-on-grade perform better (i.e., less shrinkage related concrete cracking) than conventional slab-on-grade, they are more popular even for situations where low levels of settlement are expected. Posttensioned slab-on-grade has become common for situations where it is desirable to limit the amount and width of concrete shrinkage cracks.<br />
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<b><span style="color: #cc0000;">4. Shallow Foundation Alternatives</span></b></h3>
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If the expected settlement for a proposed shallow foundation is too large, then other options for foundation support or soil stabilization must be evaluated. Some commonly used alternatives are as follows:</div>
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i. <b><i>Grading.</i></b> Grading operations can be used to remove the compressible soil layer and replace it with structural fill. Usually the grading option is only economical if the compressible soil layer is near the ground surface and the groundwater table is below the compressible soil layer or the groundwater table can be economically lowered.</div>
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ii. <b><i>Surcharge.</i></b> If the site contains an underlying compressible cohesive soil layer, the site can be surcharged with a fill layer placed at the ground surface. Vertical drains (such as wick drains or sand drains) can be installed in the compressible soil layer to reduce the drainage paths and speedup the consolidation process. Once the compressible cohesive soil layer has had sufficient consolidation, the fill surcharge layer is removed and the building is constructed.</div>
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iii. <i><b>Densification of soil.</b></i> There are many different methods that can be used to densify loose or soft soil. For example, vibro-flotation and dynamic compaction are often effective at increasing the density of loose sand deposits. Another option is compaction grouting, which consists of intruding a mass of very thick consistency grout into the soil, which both displaces and compacts the loose soil.</div>
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iv. <b><i>Floating foundation.</i></b> A floating foundation is a special type of deep foundation where the weight of the structure is balanced by the removal of soil and construction of an underground basement.</div>

Shallow Foundations - An Overview

A shallow foundation is often selected when the structural load will not cause excessive settlement of the underlying soil layers. In ...

Selection of Foundation Type

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Selection of the most suitable and effficient type of foundation for a particular structure is a tricky step in the whole structural design process. A well designed super structure will be a waste of time, money and efforts if due attention is not give to the choice of right type of sub structure. This brief article enlists some the most important deciding factors during the process. </div>
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<a href="https://2.bp.blogspot.com/-BfmA7V0BNHc/XHkxVeyWfRI/AAAAAAAAHfM/aye7bm6ITAAaiOTLVi_5prAcEApyf2gDwCLcBGAs/s1600/Selection_of_foundation_type%2528www.engineersdaily.com%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Selection of Foundation Type" border="0" data-original-height="1196" data-original-width="1600" height="298" src="https://2.bp.blogspot.com/-BfmA7V0BNHc/XHkxVeyWfRI/AAAAAAAAHfM/aye7bm6ITAAaiOTLVi_5prAcEApyf2gDwCLcBGAs/s400/Selection_of_foundation_type%2528www.engineersdaily.com%2529.jpg" title="Selection of Foundation Type" width="400" /></a></div>
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The selection of a particular type of foundation is often based on a number of factors, such as:</div>
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1. Adequate depth. The foundation must have an adequate depth to prevent frost damage. For suchfoundations as bridge piers, the depth of the foundation must be sufficient to prevent undermining by scour.</div>
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2. Bearing capacity failure. The foundation must be safe against a bearing capacity failure.</div>
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3. Settlement. The foundation must not settle to such an extent that it damages the structure.</div>
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4. Quality. The foundation must be of adequate quality so that it is not subjected to deterioration, such as from sulfate attack.</div>
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5. Adequate strength. The foundation must be designed with sufficient strength that it does not fracture or break apart under the applied superstructure loads. The foundation must also be properly constructed in conformance with the design specifications.</div>
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6. Adverse soil changes. The foundation must be able to resist long-term adverse soil changes. An example is expansive soil, which could expand or shrink causing movement of the foundation and damage to the structure.</div>
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7. Seismic forces. The foundation must be able to support the structure during an earthquake without excessive settlement or lateral movement.</div>

Selection of Foundation Type

Selection of the most suitable and effficient type of foundation for a particular structure is a tricky step in the whole structural design...

Best Engineering/Scientific/Graphing Calculators

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Choosing the right calculator for your needs can be a tough job. But you can compare some of the best calculators in the industry with our brief but useful list below. The features and number of functions vary from calculator to calculator. Some have around a hundred functions while others have several hundred. Some calculators have bright, well lit screens, while others are more difficult to see but users favor the style. Depending upon your needs, you’re sure to find the calculator for you on this list.</div>
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<a href="https://amzn.to/2NaD5ys" target="_blank">1. Texas Instruments TI-84 Plus CE Plum Graphing Calculator</a></div>
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<img alt="" border="0" height="1" src="//ir-na.amazon-adsystem.com/e/ir?t=tsx09-20&l=am2&o=1&a=B078NFWPKK" style="border: none !important; margin: 0px !important;" width="1" />
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<a href="https://amzn.to/2NaD5ys" target="_blank"><img border="0" data-original-height="450" data-original-width="450" height="320" src="https://1.bp.blogspot.com/-t1EVV-JmS5Q/W66rMKEuGeI/AAAAAAAAHdw/x7sQHDosF1A6vpJS6EDDf0e0sDpGTluRgCLcBGAs/s320/TI%2B84%2BPLUS.jpg" width="320" /></a></div>
This graphing calculator has a very high resolution backlit display. It’s likely the highest quality display available on any scientific calculator. The calculator is lightweight and available in plum, red, denim, blueberry, gray, gold, silver and white. The battery may get weak quickly if you use it a lot. A huge benefit is the fast processor. It comes with a user guide and double sided cable. The only complaint that some users have is that the font is too small. It’s great for high school students taking advanced math. If you need to easily graph complicated expressions, this is the calculator for you.</div>
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<a href="https://amzn.to/2NaD5ys" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="213" data-original-width="480" height="88" src="https://2.bp.blogspot.com/-lxxmHH9LdOo/W66r9RtR_8I/AAAAAAAAHd4/HZuLcROdjVIHHRkNxNWSk7VkcSKI_gxUACLcBGAs/s200/buynow-logo-bk.png" width="200" /></a></div>
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<a href="https://amzn.to/2xM2M3v" target="_blank">2. Casio fx-9750GII Graphing Calculator</a></div>
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<a href="https://amzn.to/2xM2M3v" target="_blank"><img border="0" data-original-height="350" data-original-width="350" height="320" src="https://1.bp.blogspot.com/-hi_NjXsFdMk/W66vBA6jndI/AAAAAAAAHeM/6j3bmI23HKMYb0b9LLi9XEZ8LiXf-RdhACLcBGAs/s320/9750.jpg" width="320" /></a></div>
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Create bar graphs and pie charts with ease. The screen is easy to read in a number of different lighting situations. Enjoy a high speed RAM CPU and USB connectivity, making it easy to share files. Some users have said that it’s not the easiest to program. However, the functions are easy to understand. It comes with a well organized user manual.<br />
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<a href="https://amzn.to/2xM2M3v" target="_blank"><img border="0" data-original-height="213" data-original-width="480" height="88" src="https://2.bp.blogspot.com/-lxxmHH9LdOo/W66r9RtR_8I/AAAAAAAAHd4/HZuLcROdjVIHHRkNxNWSk7VkcSKI_gxUACLcBGAs/s200/buynow-logo-bk.png" width="200" /></a></div>
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<a href="https://amzn.to/2N9GopI" target="_blank">3. HP HP50G 50g Graphing Calculator</a></div>
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<a href="https://amzn.to/2N9GopI" target="_blank"><img border="0" data-original-height="1500" data-original-width="817" height="320" src="https://4.bp.blogspot.com/-CTvYGCyKpYs/W66vXKEiEUI/AAAAAAAAHeU/1foCNeU9s0IalMaTJbN8rkA75KmYfbv2QCLcBGAs/s320/HP50g_engineersdaily.jpg" width="174" /></a></div>
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This calculator has 30% more screen space than the previous version and most other scientific calculators for that matter. It has a better keypad than the last model and is quipped with an SD card slot. You can choose between RPN, Algebraic, and Textbook data entry. Not that this graphing calculator uses a lot of battery power. The advantages of this calculator are the high range of functions and the ease of programmability.<br />
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<a href="https://amzn.to/2N9GopI" target="_blank"><img border="0" data-original-height="213" data-original-width="480" height="88" src="https://2.bp.blogspot.com/-lxxmHH9LdOo/W66r9RtR_8I/AAAAAAAAHd4/HZuLcROdjVIHHRkNxNWSk7VkcSKI_gxUACLcBGAs/s200/buynow-logo-bk.png" width="200" /></a></div>
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<a href="https://amzn.to/2zCUaO0" target="_blank">4. Casio fx-9860 GII</a> (<b><span style="color: #cc0000;">Engineersdaily's recommendation</span></b>)<br />
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<a href="https://amzn.to/2zCUaO0" target="_blank"><img border="0" data-original-height="1500" data-original-width="1059" height="320" src="https://1.bp.blogspot.com/-nyENqKryNqM/W66ui75kzJI/AAAAAAAAHeE/oBrfl8URYIsy7LmSP5iPJ9A2A26gfVcOwCLcBGAs/s320/9862_engineersdaily.jpg" width="225" /></a></div>
This versatile programmable calculator is very suir´table for complex jobs especially in exams where lots of calculations are needed under time pressure. Formulae can also be programmed easily. It also features a USB connection and comes handy with a cable to connect to your computer. More specs can be found at the link above.<br />
<a href="https://amzn.to/2zCUaO0" target="_blank"><img border="0" data-original-height="213" data-original-width="480" height="88" src="https://2.bp.blogspot.com/-lxxmHH9LdOo/W66r9RtR_8I/AAAAAAAAHd4/HZuLcROdjVIHHRkNxNWSk7VkcSKI_gxUACLcBGAs/s200/buynow-logo-bk.png" width="200" /></a></div>

Best Engineering/Scientific/Graphing Calculators

Choosing the right calculator for your needs can be a tough job. But you can compare some of the best calculators in the industry with our ...

Fire and Safety Features of High-Rise Buildings and Structures

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Fire and other safety features of high rise buildings and structures is essential. Types and concerns related to these features is discussed.<br />
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The <a href="http://www.engineersdaily.com/2014/02/book-settlement-calculation-on-highrise-buildings-xiangfuchen.html" target="_blank">high-rise building</a> construction concept when compared with other buildings, possess certain features and characteristics that makes them unique and highlighting. The high-rise buildings are considered as the product of the modern evolution. It is filled and composed of sophisticated systems and essential components.<br />
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Each of these systems carry out special roles either positive or negative. These elements have an effective role in the overall fire department’s operation.<br />
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Most of the components in the high-rise construction focus on safety during emergency or fire risk. They are more focused on fire systems to protect the occupants.<br />
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These will hence demand costlier building systems and unique fire safety codes. The fire and safety issues with different features available in the high-rise building is explained hereby.<br />
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Over years, the high-rise buildings have garnered significant attention in the fire safety throughout the world. The multiple floors present in the high-rise building makes great number of persons to travel long vertical distances by the stair during an evacuation.<br />
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The public regulations, the design of the building, the ownership, code bodies, the regional, local and federal governments are affected by the high-rise building safety.<br />
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The high rise buildings are designed to be safe at all undesirable conditions. But when there is a need for a full scale evacuation, it will be necessary to take quick responsibility for their own safety and planned action from the fire fighters.</div>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fire and Safety Features of High-Rise Buildings and Structures</span></td></tr>
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<h3>
<span style="color: #cc0000;">Construction Concerns in High-Rise Building Construction</span></h3>
When compared with other form of <a href="http://www.engineersdaily.com/2011/01/energy-efficient-design-of-buildings.html" target="_blank">building construction</a>, high rise building construction have a major focus on the building fire and emergency concerns. To understand this, the first major requirement is to study the number of floors of the building under consideration.<br />
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The number of floors both above and below the grade have to be evaluated for the same purpose. The firefighting operations is very much dependent on how these levels are identified and labeled in the building.<br />
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For example, if there is a floor which is numbered 13; it is found out whether there exist any other levels like the concourse levels or the mezzanines, or it is found that the floor 13 is where the mechanical level is located and have different mechanical levels. Or sometimes the floor has a penthouse level.<br />
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An occurrence of a high-rise fire or any other emergency will ask many questions regarding the high-rise building construction features, that are available.<br />
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Hence the Incident Commander (IC) have the role to assign different teams to conduct an ongoing reconnaissance. The team consists of group leaders and division supervisors. Most of the fire department consists of a system officer who is positioned inside the fire command center (FCC).<br />
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The system Officer is responsible in the monitor of different building systems like the fire alarm panel, the HVAC system, the elevators etc. The system officer is the important source for the incident commander to gather the data and information of the building which are considered very critical.<br />
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The quick determination of the age of high rise buildings and the generation which it falls is also identified by the IC. This is very important to know whether the building make use of any lightweight components, for example, any truss assemblies.<br />
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This idea will give us an estimate on how long the fire fighters can operate inside the buildings with reasonable safety.</div>
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<span style="color: #cc0000;">Concerns on the Structural System the Building Possess</span></h3>
The concerns or question that comes to mind during a fire operation is whether:<br />
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<li>The building is core type or not</li>
<li>If not Core type, what <a href="http://www.engineersdaily.com/2014/04/structural-systems-in-reinforced-concrete-buildings.html" target="_blank">structural system</a> do the building possess</li>
<li>If it’s a core type, is the core center or some other type</li>
<li>Does the building possess a central HVAC system?</li>
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This information will help in bringing a quality pre-fire plan. When you consider the use of high rise construction in the world, almost all countries possess high rise building to an appreciable range.<br />
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The lack of proper resources and the time constraints will affect in bringing a quality pre-fire plan for the building. But many firms work for developing these pre-fire plan which are very expensive.<br />
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It’s a matter of fact that most of the buildings do not possess a plan by themselves nor approach any other company for the same.</div>
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<span style="color: #cc0000;">Concerns on Static and Dynamic Features of Building</span></h3>
Once the pre-fire plan is considered for a high-rise building, it will stay active until the features of the building remain static. This is hence the main issue because most of the high-rise buildings are dynamic.<br />
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With demand, more and more up gradation is brought to the buildings. Any change on features of the building system will affect the plan and the considerations. Hence these plans must be updated accordingly.</div>
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<span style="color: #cc0000;">Concerns on the Materials used in High Rise Building</span></h3>
In the case of a core type structural building, emphasis is on finding out what material forms the structural components, the core, the structural frame, the floor components; whether concrete or steel or both.</div>
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Most of the modern high-rise building construction consist of floors where the concrete is poured over a metal deck. Regarding this, the questions arise on:<br />
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<li>Whether the load of the floor is taken by the structural frame?</li>
<li>Is there any I – section to support the floors?</li>
<li>Is there any fire proofing material used to protect the steel components?</li>
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Concerns regarding the roof construction of the building: The material type of the roof, the type of equipment on the roof, the load that is carried by these structural components are the concerns regarding the roof construction.<br />
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In high rise construction, the question on whether the roof have the capacity to take the load of a helicopter is raised. Other concerns are on the roof obstructions.<br />
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The roof with high parapet walls provide additional safety for the firefighters who are operating on the roof also the ones who have be evacuated. Shorter parapet won’t provide no protection in situations where the visibility is lost due to the smoke or during night operations.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Concerns with Fire Detection and The Protection Systems in High- Rise Buildings</span></h3>
It is very essential to determine and identify the fire detection and the protection system that is available in the building to bring the best fire safety plan.<br />
<br />
There may be different types of fire detection devices installed in the building. These include the smoke detectors, the heat detectors, manual pull stations, the rate of rise and etc. It is very essential to determine the location of the fire alarm in the building.<br />
<br />
If there is any indication from multiple alarms that are in different locations it fixes the probability of actual fire in the building. When multiple locations of alarms are heard it is recommended to check the lowest alarm.<br />
<br />
The sprinkler system in the building is identified if installed. The position or the location of the sprinkler system is very essential. It is also essential to determine the type of sprinkler system in the building; whether it is partial sprinkler protection, or full sprinkler protection or no sprinkler protection. A check on the operation of the sprinkler system has to be examined.</div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
<h3>
<span style="color: #cc0000;"><br /></span></h3>
<h3>
<span style="color: #cc0000;">Water Supply in High-rise construction</span></h3>
To construct a fire protection system in the high-rise building, it is very essential to have a comprehensive knowledge on the built-in fire protection systems. Water supply is an essential concern with the fire safety measure.<br />
<br />
The mode of water supply for fire protection system must be determined. Not only the source but also the water flow. The water supply equipment as a part of fire protection system will include the gravity tanks, fire pumps, the city water mains and other different components.<br />
<br />
In a situation where the primary water supply becomes insufficient or it fails to operate, a backup water supply will be served by the fire department connection (FDC) coming under the area and the locality.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Concerns with the Stairs in High-rise building during a Fire Emergency</span></h3>
Early Identification of number of stairs in the building must be considered. Most of the high-rise buildings will possess two stairs well that runs throughout the height of the building. But most probably one among the two will have the access towards the roof.<br />
<br />
In modern high-rise buildings, when the fire alarms of specific zones are activated, these primary stairwells are pressurized. In old buildings, under a fire emergency, one of the stairwell will behave like a smoke tower.<br />
<br />
Whatever be the type of stair, scissor type or return type, both are found to be critical under a fire emergency. All information regarding, which stair can be easily accessed for evacuation and which is easily occupied by the fire are very valuable during an emergency plan.<br />
<br />
Always a pre-plan during the good performance of the building itself it must be categorized that which stair is used for evacuation and which is the attack stair.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Concerns with the Elevators</span></h3>
All high-rise building will possess elevators. Large buildings will have elevators in more number that are arranged in separate banks that serves separate locations.<br />
<br />
Elevators can be considered as an essential parameter for the firefighters. They behave as valuable tools in emergency situations. Operational success is attained by accounting the number of elevators and their type, before undergoing the operation.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">The HVAC Systems in High Rise buildings</span></h3>
Most of the modern high rise buildings are equipped with well modernized and sophisticated Heating ventilation and the air conditioning system.<br />
<br />
Many buildings are equipped with ventilation system to get rid of smoke and to control the air movement because of fire within the building.<br />
<br />
The first and the second generation high-rise building make use of horizontal ventilation. Any chance of smoke found, make them to open the windows. This way blocking of smokes was avoided. This strategy is not possible in the present day modern high rise buildings.<br />
<br />
The third-generation buildings where more of sealed ones. These were referred to as windowless buildings. This is not because of the absence of the windows in the building, but the fact that they are designed to be opened or easily broken out.<br />
<br />
In a third-generation building, a smoke generated will be collected in a remote area of the building. This problem is well solved by the installation of HVAC system. Sometimes the HVAC system can result in very tragic negative problems also.<br />
<br />
The problem of ventilation in high rise buildings is a great issue. Mostly the issue is with the smoke than with the fire problems. The smoke has resulted in countless injuries and deaths during most of the fires in the high-rise building.<br />
<br />
The issue with the ventilation in high rise buildings must be considered in the initial planning stage of the buildings, to reduce additional expense.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Concerns with the Utilities in The High-Rise Buildings</span></h3>
The daily utilities in the building like the electricity, water, steam and the natural gas have a very important role in the daily operations of a given building. These operations do have an important role during a fire emergency. A control of these operations is a simple matter and are of less effort which can promote large safety.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Generalization of Fire Damage in High Rise Buildings</span></h3>
The fire damage will be categorized under three ways.<br />
<ol>
<li>The detrimental effect for the occupant’s life safety</li>
<li>Structural Damage</li>
<li>Damage to the properties-Non-structural damage</li>
</ol>
Among most of the fire incidents that have been recorded, it is observed that the injuries and the loss of life is less. What everyone wish is to bring a less effect on the property damages also.<br />
<br />
The migration of heat and the smoke within the high rise buildings is a great threat for the occupants within the building. Most of the death due to fire accidents are caused within the dwellings.<br />
<br />
The fire will result in the formation of toxic gases that is very dangerous to the human health. In such situations, the structural damages have least importance when compared with the life safety. After extinguishing the fire, it is found that the structure is subjected to water damage. The repair and the maintenance is a great economic loss.<br />
<br />
The high-rise buildings are stuffed with large equipment which are numerous are costly. Fire will bring lots of property loss due to these reasons. These reasons have resulted in the bankrupt of many companies as their production process was completely stopped and lost the market.<br />
<br />
There are many factors that affect the fire and safety concerns of a high-rise building. It is always recommended that how extreme be the fire damage, the measures and operations must bring life safety as the primary concern. This will ask for fire and building codes that will possess both passive and active fire protection systems in order to reduce the fire damages.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #cc0000;">Performance Based Design for Structural Safety Against Fire</span></h3>
Performance based design concept is the design the buildings according to the main goals. PBD is hence regarded as one of the best solution for this problem of fire issues in structural point of view.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img alt="Different Performance Levels in Performance Based Design_engineersdaily.com" border="0" data-original-height="281" data-original-width="496" src="https://3.bp.blogspot.com/-hKcjZIYRlJ0/WiSHxS8yu9I/AAAAAAAAHXE/ZJukoNdFjlM--mdO5iMWgNJY0e77i3EIgCLcBGAs/s1600/fire-safety-high-rise-buildings.jpg" style="margin-left: auto; margin-right: auto;" title="Different Performance Levels in Performance Based Design_engineersdaily.com" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fig.1. Different Performance Levels in Performance Based Design</span></td></tr>
</tbody></table>
<br />
The selection of a level from the levels, Immediate Occupancy (IO), Life Safety (LS), Collapse Prevention (CP) is the basis on which the building design. This is mainly a design concept used in earthquake resistant structures.<br />
<br />
Each level has different damage states. In fire-resistant <a href="http://www.engineersdaily.com/2014/03/book-design-and-construction-building-in-value-rickbest.html" target="_blank">design</a>, the life safety level is used, where we expected to have damages to the building with no harm to the life. It can be sometimes chosen between IO and LS also.<br />
<br />
The PBD design will provide more on the provision of hinges in more critical point of the structure making the building more ductile. This ability to provide the performance hinges will describe the ability to have fire dynamics in the spaces of the tall buildings.<br />
<br />
How severe be the fire, the structure should stand still letting all the life to be safe, this must be the output of a PBD design.<br />
<br />
Understanding and studying the fire accidents happened in a modern building will help to assess the critical components that are involved in the fire safety strategy. As this truly reflects the nature of the tall buildings.<br />
<br />
<i>[ Ref: Cowlard[2013], Fire Safety design for tall buildings, Science Direct].</i></div>

Fire and Safety Features of High-Rise Buildings and Structures

Fire and other safety features of high rise buildings and structures is essential. Types and concerns related to these features is discusse...

Antifreeze Admixtures for Concrete during Cold Weather Concreting

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</div>
Freezing reduces strength of concrete by 20 to 40 % when fresh concrete 
is subjected to freezing. Antifreeze admixtures of concrete, its 
properties and uses in cold weather concreting are discussed.<br />
<br />
The
 resistance of the fresh concrete against the freeze and thaw cycle is 
given by the durability factor which is also lowered by 40 to 60%. There
 is 70% decrease in the bond between the reinforcement and the concrete 
that is normally cured.<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img alt=" Cold Weather Concreting_engineersdaily.com" border="0" data-original-height="359" data-original-width="644" src="https://3.bp.blogspot.com/-tbgWA0k1rlc/WnSmbmiRAAI/AAAAAAAAHa4/GcoDI1ZE3FgPuwj8NKE7PC1LK428Cq0fACLcBGAs/s1600/antifreeze-admixture-for-concrete.jpg" title=" Cold Weather Concreting_engineersdaily.com" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="font-size: small;"> Cold </span></b><b><span style="font-size: small;"><b><span style="font-size: small;">Weather </span></b>Concreting</span></b></td></tr>
</tbody></table>
<div style="text-align: justify;">
<br />
Hence it is very essential during the concreting in cold weather conditions to ensure that the concrete will not undergo freezing in its plastic state.<br />
<br />
There are two methods for carrying out cold weather concreting:<br />
<ol>
<li>Provision of normal ambient temperatures for the concrete. This can be done through the heating of the concrete ingredients or bley providing heating enclosures.</li>
<li>The addition of chemical admixtures.</li>
</ol>
<br />
<h3>
<span style="font-size: large;"><span style="color: #cc0000;">Conventional Chemical Admixtures in Cold Weather Concrete</span></span></h3>
<h3>
<span style="font-size: large;"><span style="color: #cc0000;"> </span></span></h3>
Conventional concrete used calcium chloride as <a href="http://www.engineersdaily.com/2013/08/introduction-to-chemical-admixtures.html">accelerating admixtures</a> to offset the retarding effects of slow hydration of concrete in low temperatures. This admixture is not effective below the freezing temperatures.<br />
<br />
This is found to be a drawback in the conventional form of admixtures. Hence, for arctic weather conditions, special admixtures are necessary. One such is antifreeze admixtures.<br />
Antifreeze Admixtures for Concrete<br />
<br />
The antifreeze admixtures affect the physical condition of the mix water used in the concreting. These can depress the freezing point of the water to a large extent and can be used in temperatures lesser than -30 degrees Celsius. This can enable the extension of the period of the construction activity.</div>
<div style="text-align: justify;">
<br />
<h3>
<span style="color: #3d85c6;">Chemical Composition and Action of Antifreeze Admixtures</span></h3>
<br />
There are two groups of antifreeze admixtures that provide the characteristics of antifreeze and the accelerated setting and hardening properties.<br />
<br />
They are:<br />
<br />
<h3>
<span style="font-size: small;"><b>1. First Group</b></span></h3>
<br />
This includes chemicals, weak electrolytes, sodium nitrite, sodium chloride and non-electrolytic organic compounds which lower the freezing point of the water used in the concrete. But these group acts as weak accelerators to promote the setting and hardening.<br />
<br />
<h3>
<span style="font-size: small;"><b>2. Second Group</b></span></h3>
<br />
These include binary as well as ternary admixtures which contains potash and additives based on calcium chloride, sodium nitrite, calcium chloride with sodium nitrite, calcium nitrite -nitrate-urea and other chemicals.<br />
<br />
These have effective antifreeze properties and accelerating property to promote the setting and hardening. These are used in larger dosages compared to that of conventional admixtures.<br />
<br />
One such example is the use of 8% of sodium nitrite to keep the liquid at a temperature of -15-degree Celsius.<br />
<br />
These admixtures function by lowering the liquid phase freezing point and by accelerating the cement hydration at the freezing temperatures.<br />
<br />
Based on the dosage in the mixture, the non-chloride admixture enables the mix (concrete or the mortar) to be placed at sub-freezing temperatures. This hence reduces the need of protective measures required during the cold weathering works.<br />
<br />
The method improves the quality of the concrete and as it facilitates early setting, early <a href="http://www.engineersdaily.com/2016/04/considerations-for-concrete-formwork-design.html">stripping of formworks</a> can also be carried out. This helps in the reuse of the form within a small duration and hence speed up the construction.<br />
<br />
The table-1 shows the significant difference is strength gain at 3, 7 and 28 days for plain concrete and antifreeze admixture used concrete.<br />
<br />
<h3>
<span style="color: #3d85c6;">Table.1: Concrete Compressive strength with and without antifreeze admixture</span></h3>
<h3>
<span style="color: #3d85c6;"> </span></h3>
<b><span style="font-size: small;">(As per Ratinov and Rosenburg)</span></b><br />
<br />
<br />
<table align="center" style="border-collapse: collapse; border-spacing: 0px; text-align: center;"><tbody>
<tr><th style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; font-weight: bold; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">Property</th><th style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; font-weight: bold; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">Plain Concrete</th><th style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; font-weight: bold; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">Freeze-protection Admixture</th></tr>
<tr><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">Set time (-4 degree Celsius)</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">–</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">–</td></tr>
<tr><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">Compressive strength (MPa)</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;"><br /></td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;"><br /></td></tr>
<tr><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">-4 degree Celsius (3 days)</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">3.4</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">9.24</td></tr>
<tr><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">-10 degree Celsius (7 days)</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">8.3</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">39.3</td></tr>
<tr><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">-10 degree Celsius (28 days)</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">18.1</td><td style="border-style: solid; border-width: 1px; font-family: "arial",sans-serif; font-size: 14px; overflow: hidden; padding: 10px 5px; text-align: center; word-break: normal;">49.9</td></tr>
</tbody></table>
</div>
<div style="text-align: justify;">
<br />
<br />
It is possible for the incorporation of other admixtures that contains superplasticizers to be incorporated with the antifreeze admixtures. The main advantage of such combination is that in totality there will be a reduction of water.<br />
<br />
The water reduction will reduce the freezable free water content in the mix. This freezable water content is the one that serves as the heat sink for the heat liberated by the initial hydration reactions. This will hence reduce the number of antifreeze admixtures.<br />
<br />
<h3>
<span style="color: #6fa8dc;">Selection of Antifreeze admixtures</span></h3>
<br />
The factors based on which the selection of antifreeze admixtures is carried out are: <br />
<ol>
<li>The type of structure</li>
<li>The operating Conditions</li>
<li>Protecting methods employed in winter concreting</li>
<li>Cement brand and aggregate types</li>
</ol>
<br />
A laboratory test must be carried out with the operating materials and the dosage of antifreeze admixtures that are intended to be used in the field.<br />
<br />
The incorporation of other admixtures like retarders, superplasticizers with antifreeze admixtures is not restricted in cold weather concreting. The dosage of all the admixture that are used must be established experimentally.<br />
<br />
<h3>
<span style="color: #3d85c6;">Application and Advantages of Antifreeze admixtures</span></h3>
<br />
The antifreeze admixtures are technologically simple and beneficial for cold weather concreting. The admixture helps in improving the cohesiveness, cold joint minimizations, sand streaking, and plasticity. These are estimated to provide large cost saving than other methods of steam curing or concrete enclosures.<br />
<br />
The combination of antifreeze agents with water reducing agents or air-entraining agents will help in increasing the resistance of concrete towards the frost action and corrosion.<br />
<br /></div>

Antifreeze Admixtures for Concrete during Cold Weather Concreting

Freezing reduces strength of concrete by 20 to 40 % when fresh concrete is subjected to freezing. Antifreeze admixtures of concrete, its ...

Materials Used for Bridge Construction

<div style="text-align: justify;">
<h2>
<span style="color: #cc0000;"><b><span style="font-size: large;">Materials Used in Bridge Construction</span></b></span></h2>
<br />
Stones, Timber, Concrete and Steel are the traditional materials that are used to carry out bridge construction. During the initial period, timber and stones were used in the construction, as they are directly obtained from nature and easily available.<br />
<br />
Brick was used as a subgroup construction material along with stone construction. Stones as construction materials were very popular because of its durable properties. Many historic bridges made from stones are still present as a symbol of past architectural culture.<br />
<br />
But some of the timber bridge have been washed away or are in the stage of degradation due to their exposure to the environmental conditions.<br />
<br />
As time passed, the bridge construction has undergone more development in terms of materials used for construction than based on the bridge technology.<br />
<br />
The concrete and steel are manmade refined materials. The bridge construction with these artificial materials can be called the second period of the bridge engineering. This hence was the start of modern bridge engineering technology.<br />
<br />
Modern bridges make use of concrete or steel or in combination. Different other innovative materials are being developed so that they can well suit with the bridge terminologies.<br />
<br />
Incorporation of fibers which comes in the category of high strength gaining materials is now incorporated for the construction of bridges. These materials are also used in order to strengthen the existing bridges.</div>
<br />
<div style="text-align: justify;">
<h2>
<span style="font-size: large;"><span style="color: #3d85c6;">
Stones for Bridge Construction</span></span></h2>
<br />
For a long time in the history, the stone has been used in and as a single form. They are mainly used in the form of arches. This is because they possess higher compressive strength.<br />
<br />
The use of stones gave the engineers ease of constructing bridges that are aesthetically top and high in durability.<br />
<br />
When considering the history of bridge construction with stones, the Romans were the greatest builders of bridges with stones. They had a clear idea and understanding of the load over bridge, the geometry as well as the material properties. This made them construct very larger span bridges when compared with any other bridge construction during that period.<br />
<br />
The period was also competitive for Chinese. China had also developed large bridge called the famous Zhuzhou Bridge. The Zhuzhou bridge is the world’s known oldest open-spandrel, stone and segmental arch bridge. Nihonbashi is the most famous stone bridge in Japan. This is called as the Japan Bridge.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img alt="The Zhuzhou bridge, China_engineersdaily.com" border="0" data-original-height="419" data-original-width="689" height="388" src="https://2.bp.blogspot.com/-Hv2u73nDmGo/WmtWc_n32OI/AAAAAAAAHaU/xR4trNcwMxA3i72SxokvnanV1c1lRG-8gCLcBGAs/s640/zhazhou-bridge.jpg" title="The Zhuzhou bridge, China_engineersdaily.com" width="640" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>Fig.1: The Zhuzhou bridge, China</b></span></td></tr>
</tbody></table>
<br />
With time, the stone bridges have proved most efficient and economical due to the durability and low maintenance guaranty it provides throughout its life period.</div>
<div style="text-align: justify;">
<br />
<h2>
<span style="font-size: large;"><b><span style="font-weight: normal;"><span style="color: #3d85c6;">
Timber or Wood for Bridge Construction</span></span></b></span></h2>
<br />
The wood material was used highly in the construction of bridges, unlike today, where it is used for the construction of building works and related. Nowadays, steel and concrete grant a higher range of work flexibility, that the use of wood and timber for mega works diminished.<br />
<br />
But, there are innovations related to the preservation of wood, which has helped to increase the demand of wood in structures.<br />
<br />
Wood as an engineering material has the advantage of high toughness and renewable in nature. They are obtained directly from nature and hence are environmentally friendly.<br />
<br />
The low density of wood makes it gain high specific strength. They have an appreciable strength value with a lower value of density. This property makes them be transported easily.<br />
<br />
Some of the disadvantages related to wood as a construction material are that it is:</div>
<div style="text-align: justify;">
<ul>
<li>Highly Anisotropic in Nature</li>
<li>Susceptible to termites, infestations, and woodworm</li>
<li>Highly combustible</li>
<li>Susceptible to rot and disease</li>
<li>Cannot be used for High temperature</li>
</ul>
<br />
There are a variety of timber bridges around the world. Figure-2 shows the Mathematical Bridge located in Cambridge. Another bridge is the Togetsu-Kyo Bridge over the Katsura River in Kyoto.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-0RYEM4P4Zlg/WmtWcTjV0pI/AAAAAAAAHaM/L5LUhcBmDqEf7wB-PLsZSN0onLnrdhxDACLcBGAs/s1600/mathematical-bridge-cambridge.jpg" style="margin-left: auto; margin-right: auto;"><img alt="The Mathematical Bridge, Cambridge_engineersdaily.com" border="0" data-original-height="327" data-original-width="675" height="310" src="https://1.bp.blogspot.com/-0RYEM4P4Zlg/WmtWcTjV0pI/AAAAAAAAHaM/L5LUhcBmDqEf7wB-PLsZSN0onLnrdhxDACLcBGAs/s640/mathematical-bridge-cambridge.jpg" title="The Mathematical Bridge, Cambridge_engineersdaily.com" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="font-size: small;">Fig.2: The Mathematical Bridge, Cambridge</span></b></td></tr>
</tbody></table>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img alt="The Togetsu-Kyo Bridge, Japan_engineersdaily.com" border="0" data-original-height="240" data-original-width="624" height="246" src="https://2.bp.blogspot.com/--w3CfUjeHtQ/WmtWcv9rl_I/AAAAAAAAHaQ/YUz8nT3dJDAlRj10Z2ListuUfkhCG05zwCLcBGAs/s640/togetsu-kyo-bridge-japan.jpg" title="The Togetsu-Kyo Bridge, Japan_engineersdaily.com" width="640" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>Fig.3. The Togetsu-Kyo Bridge, Japan</b></span></td></tr>
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<span style="font-size: large;"><span style="color: #3d85c6;">
Steel for Bridge Construction</span></span></h2>
<h3>
 </h3>
Steel gain high strength when compared with any other material. This makes its suitable for the construction of bridges with longer span. We know that steel is a combination of alloys of iron and other elements, mainly carbon.<br />
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Based on the amount and variation of the elements, the properties of the same is altered accordingly. The properties of tensile strength, ductility and hardness are influenced by the change in its constitution.<br />
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The steel used for normal construction have several hundred Mega Pascal strength. This strength is almost 10 times greater than the compressive and the tensile strength obtained from a normal concrete mix.<br />
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The major inbuilt property of steel is the ductility property. This is the deformation capability before the final breakage tends to happen. This property of steel is an important criterion in the design of structures.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-5P-VpOp30Lk/WmtWcZwEfEI/AAAAAAAAHaI/tZUrMuAIllEv-FS1CJ4774wZVxNI1WzIACLcBGAs/s1600/hachimanbashi-bridge.jpg" style="margin-left: auto; margin-right: auto;"><img alt="The Hachimanbashi Bridge_engineersdaily.com" border="0" data-original-height="320" data-original-width="600" height="340" src="https://3.bp.blogspot.com/-5P-VpOp30Lk/WmtWcZwEfEI/AAAAAAAAHaI/tZUrMuAIllEv-FS1CJ4774wZVxNI1WzIACLcBGAs/s640/hachimanbashi-bridge.jpg" title="The Hachimanbashi Bridge_engineersdaily.com" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="font-size: small;">Fig.4. The Hachimanbashi Bridge</span></b></td></tr>
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The first iron bridge, Danjobashi Bridge which was built in 1878 in Japan. The figure-4 below shows the Danjobashi Bridge. Danjobashi Bridge was relocated to the present location and was named as Hachimanbashi Bridge in 1929.<br />
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It has great historical and technical value as a modern bridge. The bridge was honored by the American Society of Civil Engineers in the year 1989.<br />
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The chemical composition and the method of manufacture determines the properties of structural steel. The main properties that are to be specified by the bridge designers when it is required to specify the products are:<br />
<ul>
<li>Strength</li>
<li>Toughness</li>
<li>Ductility</li>
<li>Durability</li>
<li>Weldability</li>
</ul>
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When we mention the steel strength, it implies both the yield and the tensile strength. As the structures are more designed in the elastic stage, it is very essential to know the value of yield strength.<br />
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Yield strength is mostly used as it is more specified in the design codes. In Japan, the code recommended is designed for ultimate strength. For example, SS400 designated by the ultimate strength of 400MPa. This is an exception.<br />
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The property of ductility is very much relied on by designers and engineers for the design aspects related to the bolt group designs and the distribution of stress at the ultimate limit state conditions. Another important property is the corrosion resistance by the use of weathering steel.</div>
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<h2>
<span style="font-size: large;"><span style="color: #3d85c6;">
Concrete for Bridge Construction</span></span></h2>
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Most of the modern bridge construction make use of concrete as the primary material. The concrete is good in compression and weak in tensile strength. The reinforced concrete structures are the remedy put forward for this problem.<br />
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The concrete tends to have a constant value of modulus of elasticity at lower stress levels. But this value decreases at a higher stress condition. This will welcome the formation of cracks and later their propagation.<br />
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Other factors to which concrete is susceptible are the thermal expansion and shrinkage effects. Creep is formed in concrete due to long time stress on it.<br />
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The mechanical properties of concrete are determined by the compressive strength of concrete.<br />
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The reinforced or the prestressed concrete is used for the construction of bridges. The reinforcement in R.C.C provides the ductility property to the structure. Nowadays, ductility reinforcement is provided as an additional requirement mainly in the earthquake resistant construction.<br />
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RCC is nowadays made from steel, polymer or other combination of composite materials. Much sustainable materials is available that can take the role of cement. This is a new innovation in sustainable bridge construction.<br />
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When compared with RCC bridge construction, prestressed concrete is the most preferred and employed. A pre-compressive force is induced in the concrete with the help of high strength steel tendons before the actual service load.<br />
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Hence this compressive stress will resist the tensile stress that is coming during the actual load conditions. The prestress is induced in concrete either by means of post tensioning or by means of pretensioning the steel reinforcement.<br />
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Many disadvantages of normal reinforced concrete like strength limitations, heavy structures, building difficulty is solved using prestressed concrete.<br />
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Also Read: <a href="http://www.engineersdaily.com/2017/11/dutch-inaugurate-3d-printed-reinforced-concrete-bridge-designed-by-tu-eindhoven.html" target="_blank"><span style="color: blue;"><span style="font-weight: normal;"></span>Dutch inaugurate the 3D Printed Reinforced Concrete Bridge Designed by Technical University of Eindhoven </span></a><br />
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<h2>
<span style="font-size: large;"><span style="color: #3d85c6;">
Composite Materials in Bridge Construction</span></span></h2>
<h3>
 </h3>
</div>
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Composite materials are developed and used for both the construction of new bridges as well as for the rehabilitation purposes.<br />
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Fiber reinforced plastic is one such material which is a polymer matrix. This is reinforced with fibers which can be either glass or carbon. These materials are light in weight, durable, high strength giving and ductile in nature.<br />
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New solution and materials are encouraged due to the problems of deterioration the steel and concrete bridges are facing.<br />
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Another material is the reactive powder concrete (RPC ) that was developed in Korea. This material is a form of high performance concrete that is reinforced with steel fibers. This mix will help to make slender columns for bridges of a longer span. This also guarantees durability extensively.<br />
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Composite materials are used in the repair of bridge columns and any other supporting elements to improve the ductility and the resistance against the seismic force.<br />
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Epoxy impregnated fiberglass are used to cover the column (columns that are non-ductile in nature). This is an alternative for the steel jacket technique.<br />
<br /></div>

Materials Used for Bridge Construction

Materials Used in Bridge Construction Stones, Timber, Concrete and Steel are the traditional materials that are used to carry out bridge...

Principle of Least Squares Applied to Surveying

<b><span style="color: #cc0000; font-size: large;">1. Introduction</span></b><br />
<b><span style="color: #cc0000; font-size: large;"><br /></span></b>
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‘<i><b>Least squares</b></i>’ is a powerful statistical technique that may be used for ‘<b><i>adjusting</i></b>’ or estimating the coordinates in <a href="http://www.engineersdaily.com/2014/03/book-engineering-surveying-5th-edition-schofield.html" target="_blank">survey</a> control networks. The term adjustment is one in popular usage but it does not have any proper statistical meaning. A better term is ‘least squares estimation’ since nothing, especially observations, are actually adjusted. Rather, coordinates are estimated from the evidence provided by the observations.</div>
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The great advantage of least squares over all the methods of estimation, such as traverse adjustments, is that least squares is mathematically and statistically justifiable and, as such, is a fully rigorous method.</div>
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It can be applied to any over determined network, but has the further advantage that it can be used on one-, two- and three-dimensional networks.A by-product of the least squares solution is a set of statistical statements about the quality of the solution. These statistical statements may take the form of standard errors of the computed coordinates, error ellipses or ellipsoids describing the uncertainty of a position in two or three dimensions, standard errors of observations derived from the computed coordinates and other meaningful statistics described later.</div>
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The major practical drawback with least squares is that unless the network has only a small number of unknown points, or has very few redundant observations, the amount of arithmetic manipulation makes the method impractical without the aid of a computer and appropriate software.</div>
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The examples and exercises in this material use very small networks in order to minimize the computational effort for the reader, while demonstrating the principles. Real survey networks are usually very much larger.</div>
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A‘<b><i>residual</i></b>’ may be thought of as the difference between a computed and an observed value. For example, if in the observation and estimation of a network, a particular angle was observed to be 30°0' 0'' and after adjustment of the network the same angle computed from the adjusted coordinates was 30° 0' 20'', then the residual associated with that observation would be 20''. In other words:</div>
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<b>computed value − observed value = residual</b></div>
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Any estimation of an over determined network is going to involve some change to the observations to make them fit the adjusted coordinates of the control points. The best estimation technique is the one where the observations are in best agreement with the coordinates computed from them. In least squares, at its simplest, the best agreement is achieved by minimizing the sum of the squares of the weighted residuals of all the observations.</div>
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<h2>
<b><span style="color: #cc0000; font-size: large;">2. Least squares applied to engineering</span></b></h2>
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In practical <a href="http://www.engineersdaily.com/2017/11/what-is-surveying.html" target="_blank">survey</a> networks, it is usual to observe more than the strict minimum number of observations required to solve for the coordinates of the unknown points. The extra observations are ‘<b><i>redundant</i></b>’ and can be used to provide an ‘<b><i>independent check</i></b>’ but all the observations can be incorporated into the solution of the network if the solution is by least squares.</div>
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All observations have errors so any practical set of observations will not perfectly fit any chosen set of coordinates for the unknown points.</div>
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Some observations will be of a better quality than others. For example, an angle observed with a 1'' theodolite should be more precise than one observed with a 20'' instrument. The weight applied to an observation, and hence to its residual, is a function of the previously assessed quality of the observation.</div>
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In the above example the angle observed with a 1" theodolite would have a much greater weight than one observed with a 20" theodolite. How weights are calculated and used will be described later.</div>
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If all the observations are to be used, then they will have to be ‘<b><i>adjusted</i></b>’ so that they fit with the computed network. The principle of least squares applied to surveying is that the sum of the squares of the weighted residuals must be a minimum.</div>
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<b><i>2.1 A simple illustration</i></b></h3>
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A locus line is the line that a point may lie on and may be defined by a single observation. Figure1(a), (b) and (c) show the locus lines associated with an angle observed at a known point to an unknown point, a distance measured between a known point and an unknown point and an angle observed at an unknown point between two known points respectively. In each case the locus line is the dotted line. In each case all that can be concluded from the individual observation is that the unknown point lies somewhere on the dotted line, but not where it lies.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-zNvrj5fstLM/WmMkSia6OwI/AAAAAAAAHZg/VbkY1eGcjug5jWIG3ffIM2YbKNkfcY_yACLcBGAs/s1600/least_squares%2528www.engineersdaily.com%25291.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Principle of Least Squares applied to Surveying" border="0" data-original-height="455" data-original-width="1417" height="204" src="https://4.bp.blogspot.com/-zNvrj5fstLM/WmMkSia6OwI/AAAAAAAAHZg/VbkY1eGcjug5jWIG3ffIM2YbKNkfcY_yACLcBGAs/s640/least_squares%2528www.engineersdaily.com%25291.png" title="Principle of Least Squares applied to Surveying" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>Figure 1 Locus lines</b></span></td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Nufiy5KdsP0/WmMkg3S3jZI/AAAAAAAAHZk/GkY4mwh30b4sGtDi6TulQLdmvq2TJZKVgCLcBGAs/s1600/least_squares%2528www.engineersdaily.com%25292.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Principle of Least Squares applied to Surveying" border="0" data-original-height="635" data-original-width="645" height="315" src="https://1.bp.blogspot.com/-Nufiy5KdsP0/WmMkg3S3jZI/AAAAAAAAHZk/GkY4mwh30b4sGtDi6TulQLdmvq2TJZKVgCLcBGAs/s320/least_squares%2528www.engineersdaily.com%25292.png" title="Principle of Least Squares applied to Surveying" width="320" /></a></td></tr>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-size: small;"><b>Figure 2 Intersection of locus lines</b></span></td></tr>
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<div style="text-align: justify;">
In the following, the coordinates of new point P are to be determined from horizontal angles observed at known points A, B, C and D as in Figure 2(a). Each observation may be thought of as defining a locus line. For example, if only the horizontal angle at A had been observed then all that could be said about P would be that it lies somewhere on the locus line from A towards P and there could be no solution for the coordinates of P. With the horizontal angles at A and B there are two locus lines, from A towards P and from B towards P. The two lines cross at a unique point and if the observations had been perfect then the unique point would be exactly at P. But since observations are never perfect when the <a href="http://www.engineersdaily.com/2014/04/azimuths-and-bearings-in-surveying.html" target="_blank">horizontal angles</a> observed at C and D are added to the solution the four locus lines do not all cross at the same point and the mismatch gives a measure of the overall quality of the observations. Figure 2(b) shows the detail at point P where the four lines intersect at six different points. The cross is at the unique point where the sum of the squares of the residuals is a minimum.</div>
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<h3 style="text-align: justify;">
<b><i>2.2 The mathematical tools</i></b></h3>
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By far the easiest way to handle the enormous amounts of data associated with least squares estimation is to use matrix algebra. In least squares it is necessary to create a system of equations with one equation for each observation and each ‘observation equation’ contains terms for each of the coordinates of each of the unknown points connected by the observation. So, for example, in a two-dimensional network of 10 points where there are a total of 50 observations there would be a set of 50 simultaneous equations in 20 unknowns. Although this represents only a small network, the mathematical problem it presents would be too difficult to solve by simple algebraic or arithmetic methods.</div>

Principle of Least Squares Applied to Surveying

1. Introduction ‘ Least squares ’ is a powerful statistical technique that may be used for ‘ adjusting ’ or estimating the coordinates in...

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