What is prestressed concrete. Figure 5.6-9 shows schematically the variation in haunch thickness. Set the UDL Intensity Start and End as 2.5kN/m then click OK to generate the load effects. Roughing the concrete surface of the beam, Providing reinforcement as extension form the beam into the slab, Shear keys could also be constructed in the interface, P = 1140 kN (prestressing force after all the losers), = 289 mm depth to the neutral axis from the soffit. The cracking moment, Mcr, is calculated as the total moment acting on the beam when the maximum tensile stress equals the modulus of rupture. = 24kN/m 3 Deflection due to initial prestressing is computed as: P/S = -(PtesL2)/(8EciIg) (for straight bonded strands), P/S = -Ptes[L2 - (Lt + 2Lx)2]/(8EciIg) (for debonded strands). On the Pre-tensioned Beam Analysis form set Time Considered: to t = and the Fibre Stress: field to Minimum top. 2) Zlevel 2 gives : P >= A (20 Zlevel 1 - 1.0 Zlevel 2) / (Zlevel 1 + Zlevel 2), P = 449.22 103 ( 20 116.02 - 89.066) / ( 116.02 + 89.066) 10-3 = 4888 kN, Allow 10% for loss of force before and during transfer, then the initial force Po = 4888 / 0.9 = 5431kN, Using 15.2mm class 2 relaxation standard strand at maximum initial force of 174kN (0.75 Pu) <>/Pattern<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 17. Click the Generate button and then click on Yes on the confirmation form that appears. F = -200 10-6 34 1000 150 0.43 = -439 kN Maximum service stress in the steel = 33.74 ksi < 36 ksi OK. For jurisdictions that consider creep and shrinkage in the design, it is likely that positive moment will develop at intermediate piers under the effect of prestressing, permanent loads and creep and shrinkage. Also, in the Surface Condition: field, for Interface shear, change the value from Smooth to Rough, to determine the correct cohesion and friction factors, and then change it to User Defined to activate these factors before closing the form with the OK button. The optimum design is posed as single-objective optimization problem in presence of constraints formulated in accordance with the current European building code. A composite pre-tensioned pre-cast beam and concrete slab is shown below. Girder top stress after losses under sum of all loads (Service I): Girder top stress under prestressing and dead load after losses: Girder top stress under LL + (PS + DL) after losses: Girder bottom stress under all loads (Service III): Notice that the gross concrete composite section properties are typically used for the stress calculations due to all load components. Knowledge regarding the degradation processes of concrete structures is essential for the design of optimized projects and the execution of more-durable structures. xTMk@(04pQvl:VK,3oF3OLAx:_y&@B -ll4[vujmbR^*O NN(= /$(X"E$HPUYWyf9 'j'5zJkrCb2, d! Stage 4. This example elaborates on the method of calculating the stressing in the beam and the composite section. Finally it is necessary to remove the temporary construction loads. Volume 2 of this re port contains these examples. 0.408 ( 300 250 1.5 + 750 200 1.25 ) 10-3 = - 0.408 300 ( 200 0.45 270 - 150 0.45 283 ) 10-6 The beam is pre-tensioned with 14 nos 15.7mm diameter 7-wire super strands (A ps Figs 2.16-2.19 show concrete sheet pile wall examples and details of the pile cross-section and pile installation that have traditionally been used in South Africa. If a warning message appears dismiss it because we will set the limit state to SLS Frequent anyway as it is a prestressed beam. This is often preferable where durability is a concern. of designing the beam (See BS 5400 Pt2, or DB 37/01 for full The stiffness of the overall section can be taken into account in composite design. There are several methods that can be adopted to ensure proper bonding of the beam with the slab. Though the new concrete shrink, concrete in the prestress beam will not shrink. 5655 = 2400 + ( -2.8762 + 8722.84X - 1243717) 10-3 Civil Engineering Design (1) Example. The definition of the variables in the above equation and their values for this example are as follows: The second, third and fourth terms in Eq. concrete has cured then any further loading (superimposed and live Determine the deck steel at the intermediate pier. Click OK on the warning message and click OK to close the Tendon Optimisation form. Deflection values are computed based on prestressing, girder self-weight, slab, formwork, exterior diaphragm weight, and superimposed dead load weight. As a result, beam bending and shear capacity increases. Prestressed concrete is structural concrete in which internal stresses have been introduced to reduce potential tensile stresses in the concrete resulting from loads. <>>>/Length 29>> Tension is taken to be positive and compression is negative, throughout. In fact you can define any custom beam cross . Remove Temporary Loads and Supports The negative sign indicates upward deflection. The interface shear requirement is the red dashed line and the interface shear resistance supplied by the links defined for direct shear is the solid blue line, so it can be seen that additional links are required only in the areas where the red line is above the blue line. curvature due to temperature strain : This behavior is due to the confinement of the diaphragm concrete in the connection zone provided by the surrounding concrete. endstream Structural loads, structural analysis and structural design are simply explained with the worked example for easiness of understanding. stream Solving for M, the additional moment required to cause cracking, in this equation: The applied factored moment, Mu, taken from Table 5.3-2 is 8,456 k-ft (Strength I). Problem. Now, we can calculate the stress in the section as follows. ), = distance from end of beam to point where bonding commences (in. 3). Article S5.5.3 states that fatigue need not be checked when the maximum tensile stress in the concrete under Service III limit state is taken according to the stress limits of Table S5.9.4.2.2-1. You will notice that the beam appears to fail at the very ends but in reality this will be well within the cast in place diaphragms so web shear cracking should not be a problem. Design Tools/ 3D Exhibits; Support Detail: eBook : Standard Plans for Road Construction - Complete eBook . Nominal tensile strength = fpu =1670 N/mm2 the beams are spaced at 1.0m intervals. In addition to the prestressed beam, there will be a concrete deck, concrete fill around the beam, voids in the concrete fill, etc. From Table S5.9.4.2.1-1, the stress limit due to the sum of the effective prestress, permanent loads, and transient loads and during shipping and handling is taken as 0.6wfc (wherew is equal to 1.0 for solid sections). In addition to the stresses in the prestressed composite beams, the stress in the in-situ concrete(calculated above) and stress in the top of the prestressed beam should be checked. It will not be discussing in this article. Using conventional beam theory to determine deflection of simple span beams under uniform load or concentrated loads and using the loads calculated in Section 5.2, using noncomposite and composite girder properties for loads applied before and after the slab is hardened, respectively, the following deflections may be calculated: All deflection from dead load is positive (downward). Concrete is strong in compression, but weak in tension, and for this reason, a plain concrete beam has little strength. Live load: 800 lb/ft. Using Gibbs Example of reflective writing in a healthcare assignment; Termodinamica - guia - ejemplos - tema 1 . Considering Figure 5.6-1, by calculating the forces acting on different areas as the volume of the stress blocks for areas A1, A2 and A3 as the volume of a wedge, prism or pyramid, as appropriate, the forces in Table 5.6-3 may be calculated. The second alternative requires adding mild reinforcement bars as shown in Figure 5.6-6. Design Step 5 - Design of Superstructure Prestressed Concrete Bridge Design Example Task Order DTFH61-02-T-63032 5-47 Design Step 5.6.1.2 Stress calculations at transfer Table 5.6-1 - Stresses at Top and Bottom of Beam at Transfer Girder Stress at transfer Location self weight F Calculate the total area of steel per unit width of slab: Calculate the center of gravity of the slab steel from the top of the slab. The hardware required to pretension and post-tension concrete structures is introduced in Chapter 3, including some construction considerations. Reinforcement bars are placed in a form and stressed by the stretching of the bars at each end, inducing tension in the bar. bearings and The next step is to define the load effects for construction stage 1. to Left Temp Support. to Temp Construction.". Notes for lectures 1-8 of Dr Luigi Di Sarno's module prestressed concrete design lecture introduction to prestressed concrete structures principles of. Once the concrete gets harder, it acts together with the prestress beam and provides additional stiffness to the section. stream Center of gravity of the deck longitudinal reinforcement from the top of the deck: Calculate the depth to the slab steel from the bottom of the beam. The graphical display is a good way to make these checks, but the graphics will display only one of four conditions at a time (i.e. The concrete then gets poured into molds around them and cured. The modular ratio of reinforcing to concrete should be rounded to the nearest whole number. These are entered from the analysis form. Example 1: Design of a simply supported reinforced concrete beam. The following figure indicates the different types of prestressed composite beams. MEGA FLOOR,the Prestressed slab. To eliminate the possibility of sag in the bridge under permanent loads, some jurisdictions require that the above calculations for CF be repeated assuming a further reduction in the initial P/S camber. Click the Add Load Component button and repeat the process, this time setting the Start Dimension to 19.95m, the End Dimension to 20.05m. When using pre-tensioning, steel is stretched out before the placing of the concrete. 1 + pe = The correct idealization of the actional condition should be done during the design. The calculations presented herein do not include creep and shrinkage moments. q 16 0 0 1 0 0 cm/Image6 Do Q Stresses in the tensile face and the compression face of the beam shall be checked in accordance with the relevant standards. The location of the neutral axis for a section subject to external moments causing compressive stress at the side where the prestressing force is located may be determined using a trial and error approach as follows: Notice that when additional compression is introduced into the concrete due to external applied forces, the instantaneous stress in the prestressing steel is decreased by the modular ratio multiplied by the additional compressive stress in the surrounding concrete. Including creep and shrinkage would normally result in additional tensile stress at the bottom of the beam at the midspan section. This time the tendon optimisation will complete without an error message. straight, fully bonded tendons (constant force and eccentricity). force in concrete flange : - 0.408 [ 1000 150 ( 3.6 + 2.3 ) + 300 90 ( 0.9 + 1.35 ) The first component is a rectangular stress distribution with an intensity of 1.66 ksi. In this example we have taken a prestressed beam created in a previous example and applied load to it for a series of design load cases. The haunch thickness is varied along the length of the girders to provide the required roadway elevation. Hurst 2017-12-21 Prestressed concrete is widely used in the construction industry in buildings, bridges, and other structures. Tendons and reinforcement are positioned in the beam mould. Effective depth from Level 3 = 1200 - 135 = 1065mm, Assume that the 0.408 ( 300 250 1.5 344 - 750 200 1.25 556 ) 10-6 All tension stresses and allowables use positive sign convention. Prestressed Concrete Beam Design to BS 5400 Part 4. At service limit state, the depth of the neutral axis and the transformed moment of inertia under service loads may be calculated using the same procedure used earlier in the example (Section 4). PRE-Stress | Prestressed Concrete Design Software. 4.2.2), Note: The loading has been simplified to demonstrate the method Modulus of elasticity of concrete beam = 4,696 ksi (see Section 2), Concrete stress at bottom of beam = 0.00079(4,696) = 3.71 ksi, Area of deck longitudinal reinforcement = 14.65 in2 (see Section 5.6.5.1 for calculation), Force in deck steel = 14.65(0.001046)(29,000) = 444.4 k, Force in prestressing steel = 797.2 k (see Table 5.5-1). ), Ultimate Capacity of Beam and Deck Slab (Composite Section), Ultimate Design Moment = f3 M = 1.1 2867 = 3154 kNm, Only There are no secondary temperate effects as the structure is simply supported so dismiss the confirmation notice with the Yes button. The composite action of prestressed composite beams can only be taken when the horizontal shear stress at the interface between the beam and the slab is transferred. The allowable compression stress limit for pretensioned concrete components is calculated according to S5.9.4.1.1. 1), P/A - Pe/Zlevel 2 >= - 1.0 (eqn. ), NA, = specified yield strength of compression reinforcement (ksi), NA, = distance from the extreme compression fiber to the centroid of compression reinforcement (in. Set Start Dimension to 0.95m and the End Dimension to 1.05m". Click the Add Load Component button and enter the UDL Intensity Start and End as 1410.213kN/m. The beam is an internal beam of a simply supported bridge deck of 21m span and the 2m wide concrete slab is cast in one. have discussed in addition to other aspects. Set the design section location to the left hand end (point 1) and click on the Results button. Things to Remembered in Concrete Construction, Prestressed Composite Beams [design aspects], There is a significant reduction in the construction time, Low strength concrete can be used for in situ concrete. endobj stream Distance from the bottom of the beam to the centroid of Group 1 strands = 5.375 in. ), Level 1, combination 3 : f = 17.08 - 17.67 = - 0.59 N/mm2 (> - 3.2 hence O.K. EC OQ) -PJl1"T!GHmp |O-F)_j(i%[6V3Fg@?C!Dzu(.{ i\'gx}&]YuwI#1G{#fF^F36k*B*&"##%D\R=8>%N[Q).(/\Mp:_5,P&Hku:QcH:EPTn]@.e"*Bo6. If the above values are within the acceptable limits, the section is acceptable. The next step will be to import some results from a separate live load analysis by using a text file that is formatted in a certain way. In the graphics window click on the slab in the small section to display the slab stresses and if the shift key is held down at the same time then reinforcement or tendon stresses are displayed. <> In addition, there has been no consideration of any enhancements that could be obtained, for example, by considering the concrete being cured at a higher temperature. In these tests, the failure always occurred in the girder. reinforced-concrete-cantilever-beam-design-example 2/8 Downloaded from engineering2.utsa.edu on November 2, 2022 by guest shown in Figure 9 and 10 below. Stage 1. (e) Flexural design (bending moment resistance) (f) Curtailment and anchorage. Subject topics: Permissible compressive stress at transfer for prestressed concrete beams Subject layout: In CP 115 it is recommended that the compressive stress in the concrete at transfer should . Pre-stressing is the application of an initial load on. Shear link spacing in the beam also needs to be determined to resist both transverse and longitudinal shear forces. Privacy | Do not sell my personal information | Cookie preferences | Report noncompliance | Terms of use| 2022 Autodesk Inc. All rights reserved. @ Level 1 = - 776.2 / 116.02 = - 6.69 N/mm2 See Figure 2-3 for girder dimensions. = Initial prestressing force taken from Table 5.5-1 (kips), = Distance between the neutral axis of the noncomposite girder and the center of gravity of the prestressing steel (in. 381 * 0.0035 / 659 + 0.0047 = 0.0067, pb2 = Set Start Dimension to 0.95m and the End Dimension to 1.05m. 1200 New Jersey Avenue, SEWashington, DC 20590 Simply put, it is concrete formed under stress. Composite beams are widely used in construction. endstream and concrete specific creep ct = 1.03 48 10-6 per N/mm2 Girder bottom stress under prestressing and dead load after losses: Girder top stress after losses under prestress and permanent loads: Notice that the stresses are calculated without including creep and shrinkage. Hence 32 tendons required. Design Although the stresses dont appear to change much in this example the differences become more marked when the structure is continuous where secondary effects become more significant. 1.3 Advantages of Prestressed Concrete. Lets calculate the tensile stress at the bottom of the cast-in-situ concrete. Take note of the warning message but the prestress is adjusted automatically anyway to satisfy this. The width is 300 mm and the eective depth is 600 mm. endobj of 10.0 kN/m2 and kel of 33kN/m . U.S. Department of Transportation Now change the Limit State: field to ULS Persistent/Transient to carry out the calculations for vertical shear where we will determine the requirement for shear links. Once the supports are removed after concrete gets hardened, composite action will carry the dead with the composite beam. Set the Results Point of Interest to 20 and Note the stresses and repeat for the other three Fibre Stress: conditions. Instantaneous deflections are computed using the modulus of elasticity for concrete as specified in S5.4.2.4 and taking the gross moment of inertia, Ig,as allowed by S5.7.3.6.2. Change the navigation window to Materials and select the 1st material. @ Level 2 = 776.2 / 89.066 = 8.71 N/mm2 Typically, these calculations are conducted using a computer program. Total shrinkage of insitu concrete = 300 10-6 to Rm Left Temp Sup. Close the Define Pre-Tensioned Beam Load form with the OK button. Downloads: 248. Furthermore, you can find the "Troubleshooting Login Issues" section which can answer your . / Es = 932 / 200 103 = 0.0047, Determine depth to In the User Name: field enter Rm temp const Load to assist with identification in the navigation window before closing the Beam Load form with the OK button. Click in the Analyse for: field and select Differential temperature primary stress to open the Differential Temperature Analysis form. 5.4.6 - Coefficient of thermal expansion = 12 10-6 per C. All symbols are defined in the text where they first appear. Further, you may refer to the article bridge beam design for further information on the ultimate limit state design of the post-tensioned beam. From BS 5400 Pt4 Table 3 : Ec = 34 kN/mm2 for fcu = 50N/mm2 <>>>/Length 29>> Jurisdictions that do not include creep and shrinkage typically design the girders for a reduced tensile stress limit or for zero tension at final condition. 5 0 obj Pre-tensioning This is the most common form for precast sections. Maximum compression is checked under Service I limit state and maximum tension is checked under Service III limit state. Recall that the centers of gravity of a wedge, a prism with all rectangular faces, a prism with a triangular vertical face and a pyramid are at one-third, one-half, one-third and one-quarter the height, respectively. The design of structures in general, and prestressed concrete structures in particular, requires considerably more information than is contained in building codes. Fc > Ft therefore reduce depth to neutral axis and repeat the calculations. When the deck slab ", Click the Add Load Component button and repeat the process (remembering to make ULS and SLS Load Factors negative), this time setting the Start Dimension to 19.95m, the End Dimension to 20.05m and the Component Ref. 2 0 obj Stress at transfer = ( 17.67 - 3.2 ) / 0.8 = 18.1 N/mm2 (use allowable stress of 20 N/mm2). Apply temperature differences given in BS 5400 Pt2 Fig.9 (Group 4)to a simplified beam section. The main advantages of prestressed concrete (PSC) are: In any span, the max cable sag, zd depends on the concrete cover requirements and the tendon dimensions. Compression (1.25 Table 22) Set the file name to My EU Example 5_2.sam and click the Save button. prestressed concrete bridges, but have used either AASHTO Specification to design other types of bridges may be able to follow the design example, however, they will first need to familiarize themselves with the basic concepts of prestressed concrete design. As a result, the number of equations greatly . The precast pre-stressed bridge system offered two principal advantages: it is economical and it provides minimum downtime for construction. Slab C32/40 fcu = 40 N/mm2. DESIGN OF PRESTRESSED CONCRETE. 11 0 obj = width of the effective flange, = web width taken equal to the section width "b" for a rectangular section (in. Change the ULS and SLS Load Factors to -1.35 and -1 respectively to make this an upward load and set the Component Ref. ), NA, = stress block factor specified in S5.7.2.2, NA, = compression flange depth of an I or T member (in. Tensile force in tendons Fp = 0.87 28 139 1670 10-3 = 5655 Detailed example showing sample calculations for design of typical Interior AASHTO Type-IV prestressed concrete Beam supporting single span bridge. This suggests that there is no need for the positive moment connection. MI y / Ic = 337.5 x 106 x 422.5 / 2.514 x 1010 = 5.67 N/mm2. During construction the beam is initially supported on temporary supports at 1m from the beam ends. min top stress, min bottom stress, max top stress or max bottom stress). We can calculate the allowable stress in the section based on the relevant design class of the relevant standards. maximum design stress is developed in the tendons, then : 9 0 obj Assume maximum concrete compressive strain = 0.00079 in./in. Example of bridges where prestressed concrete is used can be seen in figure 4,5,6,7. In the Increments section, set Beam span equally divided by to 50 then click OK to close the Generate Beam Loads form. All compression stresses and allowables use negative sign convention. Set the value in the Exposure: field to XD1. For prestressed concrete beams (fc = 6.0 ksi). Generally, the water content of the cast-in-situ concrete is lower than the beam as it has low strength. %PDF-1.5 Allow for 20% loss of prestress after transfer. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet draws a handy diagram showing the designer the tendons chosen profile. = factor for the effect of the volume-to-surface area ratio of the component as specified in Figure S5.4.2.3.2-1. Assume neutral axis at 32.5 inches from the bottom of beam. It depends on the design consideration. stress corrosion is characterized by the coupling between the conventional corrosion (pitting attacks in chloride environment) and the steel micro-cracking; the latter induced by the high-stress. Click the Analyse for: drop down and select Bending for gr 1b-gr5 1. In addition, the Bridge Beam Design article elaborates on the procedure to be followed when designing the method for a non-composite beam. ), = area of nonprestressed tension reinforcement (in, = specified yield strength of reinforcing bars (ksi), = distance from extreme compression fiber to the centroid of nonprestressed tensile reinforcement (in. But there is an increase in the cost due to the formwork provided. 503 + 2.6 543 ) ] 10-6 The specification is silent about the strength of the concrete in the connection zone. But high tension steel has an ultimate strength of 2100 N/mm 2 and if initially, to say 1000 N/mm 2 there will still be large stress in the reinforcement after making a . This introduction of internal stresses is called "prestressing" and is usually accomplished through the use of tendons that are tensioned or pulled tight prior to being anchored to the concrete. endobj Click OK to close the error message then click the OK button to close the optimisation form. The haunch depth is ignored in the following calculations. Change the navigation window to Design Beam and click on the Analyse Beam toolbar button to re-analyse the beam. a summary of prestressed concrete concepts and examples . Detailed calculations are presented below. All loads are factored according to Table 3.4.1-1 in the AASHTO LRFD Specifications for Service I and Service III limit states as applicable. In this example, the gross section properties are used for this calculation. Set the UDL Intensity Start and End as 1410.213kN/m. Positive bending about a horizontal axis causes tension in the bottom . Visit site . Beam C40/50 fcu = 50 N/mm2, fci = 40 N/mm2 Concrete is cast into the beam mould and allowed to cure to the required initial strength. View example in PDF Format (Design Example 1) Download example as a Mathcad Workbook (Zip) Cast-in-Place Flat Slab Bridge Design.
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