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. stream 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. Therefore, there will be a relative movement in the place that the beam and cast-in-situ concrete is connected. Concrete is poured into the form and all around the bars while they are still being stretched. Area of cast insitu concrete = 845 x 500 - 1.47 x 10 5 = 2.755 x 10 5 Weight of the cast insitu concrete, Wci = 2.755 x 10 5 x 24 / 10 6 = 6.612 kN/m The following forces are obtained : Mu = MFp1 to 6 + MFf + MFw = 4192 kNm > 3154 kNm hence O.K. Total initial deflection due to prestressing: Notice that for camber calculations, some jurisdictions assume that some of the prestressing force is lost and only consider a percentage of the value calculated above (e.g. Table 5.6-3 - Forces in Concrete Under Service Load in Negative Moment Regions (Section at 107'-3" from the end bearing), Figure 5.6-1 - Compressive Force in the Concrete, *Figure 5.6-1a - Shapes Used in Determining Forces for A3. This time the tendon optimisation will complete without an error message. Shear link spacing in the beam also needs to be determined to resist both transverse and longitudinal shear forces. PRE-Stress | Prestressed Concrete Design Software. There are no secondary effects due to differential temperature and shrinkage, as the beam is statically determinate, but the primary stresses need to be included for both, where appropriate. The next step is to define the SDL surfacing loads. Prestressed Concrete Example Problem - Free download as PDF File (.pdf), Text File (.txt) or read online for free. 0.408 ( 300 250 1.5 344 - 750 200 1.25 556 ) 10-6 Different shrinkages in the section could induce additional stresses. This camber is used to determine bridge seat elevation. Set the Limit State field to SLS Frequent and note the reduction in the tensile principle stress effect. <> 0.408 1000 [ 150 ( 3.0 + 5.25 ) ] 10-3 + This alternative may lead to congestion at the end of the beam due to the presence of the prestressing strands at these locations. This load and the temporary supports are removed once the concrete has hardened. Determine the deck steel at the intermediate pier. steel in the tension zone is to be considered : Cl. The spreadsheet then calculates the tensile and compressive stresses acting on the beam and the tendons. When a load is applied on beam, cracks still occur in the concrete, but the tension is carried by the steel reinforcement. PRE-Stress is an advanced prestressed concrete design software that helps you run calculations and analysis on many types of structural prestressed concrete elements including hollowcore slabs, solid slabs, wall panels, beams, sloped beams, double tees and most recently "sloped" TT beams.. Click on the Tendon Optimisation button on the Pre-tensioned Beam Analysis form and click OK on the information form. This will open the Time Dependant Effect Calculations form. 2 + pe = Prestressed Concrete Analysis and Design - Antoine E. Naaman 2004-01-01 Prestressed Concrete Design - M.K. Area of cast insitu concrete = 845 x 500 1.47 x 105 = 2.755 x 105, Weight of the cast insitu concrete, Wci = 2.755 x 105 x 24 / 106 = 6.612 kN/m, Moment, Mci = 6.612 x 152 / 8 = 185.96 kNm, Mci / Zb = 185.96 x 106 / 26.91 x 106 = 6.91 N/mm2, Md / Zt = 185.96 x 106 / 19.20 x 106 = -9.68 N/mm2. Close the Define Pre-Tensioned Beam Loads form with the OK button. endobj ), = 5.55 in., which is less than the slab thickness, therefore, the neutral axis is in the slab and section is treated as a rectangular section. / Es = 932 / 200 103 = 0.0047, Determine depth to 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. This reflects observations made during girder tests in the past. Desing of prestressed composite beams is discussed in this article. Eccentricity acent = 502mm The bridge owner may select to invoke this criteria if desired. fr = -Pt/Ag - Pte/Sb + MDNC/Sb + MDC/Sbc + M/Sbc. Deflection and camber calculations shall consider dead load, live load, prestressing, erection loads, concrete creep and shrinkage, and steel relaxation. The cracking starts in the deck and as the loads increase the cracks extend downward into the beam. conc. Click on the Generate button to open the Generate Beam Loads form. Since the program cant apply a point load to a beam, this needs to be applied using two, 100mm long UDLs. Tensile force in tendons Fp = 0.87 28 139 1670 10-3 = 5655 This confinement increases the apparent strength of the diaphragm concrete compared to the unconfined strength measured during typical testing of concrete cylinders. Girder bottom stress after losses under prestress and dead load: Stresses at service limit state for sections in the negative moment region. Computer software is generally used to determine the deflections due to each loading. <> Beam C40/50 fcu = 50 N/mm2, fci = 40 N/mm2 2)] (X - 150) 10-3 Total shrinkage of insitu concrete = 300 10-6 = 261.5 - 26.7 = 234.8 kNm, Force F to restrain temperature strain : Open a new Define Pre-Tensioned Beam Loads form using the "+" button in the toolbar of the navigation window, and select Beam Loads | Surfacing then click on the Generate button to open the Generate Beam Loads form. x{! In these tests, the failure always occurred in the girder. 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). The second component is a triangular stress distribution with an intensity of 1.14 ksi. From Figures 2-5 and 2-6, the distance from the bottom of the beam to the centroid of Group 2 is 4.0 in. When the analysis form is open the results graphs can be displayed in a 3D isometric window by clicking on the 3D view icon on the graphics window: Click the File | Save As menu item. Now that the beam design passes for the direct shear force case, the next step is to design the shear links in the beam merging the requirements from the direct and interface shear cases. Self weight of beam and When the deck slab Jeffrey Luin. stream There are several methods that can be adopted to ensure proper bonding of the beam with the slab. Knowledge regarding the degradation processes of concrete structures is essential for the design of optimized projects and the execution of more-durable structures. Structural loads, structural analysis and structural design are simply explained with the worked example for easiness of understanding. Pennsylvania uses 90% of the above value). These jurisdictions provide reinforcement at the bottom of the beams at intermediate diaphragms to resist the factored positive moment at these locations. 6 0 obj From BS 5400 Pt4 Table 3 : Ec = 34 kN/mm2 for fcu = 50N/mm2 Actions to be considered at the service limit state are cracking, deformations, and concrete stresses, as specified in Articles S5.7.3.4, S5.7.3.6, and S5.9.4, respectively. 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. An exception is made for prestressed members where the modular ratio is rounded to two places in this example. Select the 2nd material in the navigation tree. View example in PDF Format (Design Example 1) Download example as a Mathcad Workbook (Zip) Cast-in-Place Flat Slab Bridge Design. 11 0 obj (Comb. However, as explained above, the stress in the prestressing steel should decrease due to compressive strains in the concrete caused by external loads, i.e., prestressing steel force less than 797.2 k and the actual stress is expected to be lower than the calculated stress, and the above difference (3%) is considered within the acceptable tolerance. The final CF value after this reduction should show upward deflection. The precast pre-stressed bridge system offered two principal advantages: it is economical and it provides minimum downtime for construction. Set Start Dimension to 0.95m and the End Dimension to 1.05m. This suggests that there is no need for the positive moment connection. For this example, the stress limit equals 3.6 ksi. The next step is to check the stresses for other design combinations (for example, beam erection, construction stages and live load cases). 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 . (g) Shear design. In the resulting data form set the Ambient temperature: field to 28 and close the form with OK (again dismissing the warning message). The program automatically calculates the UDL intensity for the self weight of the slab so just click OK to create the effects and close the form. Concrete is strong in compression, but weak in tension, and for this reason, a plain concrete beam has little strength. Material properties relevant to design are presented and discussed in Chapter 4. Click the Analyse Beam toolbar button to open the Pre-tensioned Beam Analysis form. 1) Zlevel 1 + (eqn. It is used when building slabs, beams, decks, sleepers and tanks. Notice that the above calculations may be repeated for other cases of loading in Table S5.9.4.2.1-1 and the resulting applied stress is compared to the respective stress limit. In any span, the max cable sag, zd depends on the concrete cover requirements and the tendon dimensions. Slab: hollow slab, preslab or predalle, Prest ressed ribs and blocks , lintels.. Beam: Prestressed rectangular beam and I-beam for bridges Other prestressed components: Lintels , Wineyard stud.. 3). In the Increments section, set Beam span equally divided by to 50 then click OK to close the Generate Beam Loads form. The shrinkage strain for the concrete is to be set to -0.00025 with 20% of this occurring before the insitu slab is cast. According to S5.7.3.3.2, unless otherwise specified, at any section of a flexural component, the amount of prestressed and nonprestressed tensile reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equal to the lesser of: 1.2 times the cracking strength determined on the basis of elastic stress distribution and the modulus of rupture, fr, on the concrete as specified in S5.4.2.6. Visit site . The bridge considered for design has a span length of 110 ft. (c/c pier distance) with no skew and a total width . A differential temperature profile needs to be defined and values for the shrinkage and shear parameters need to be specified. Problem. Designers need to pay more attention to the design procedures as they are a bit complex than the usual method. Change the ULS and SLS Load Factors to 1.35 and 1 respectively and set the Component Ref. in this example. The calculated stress equals 3.71 ksi or is 3% overstressed. Live load: 800 lb/ft. q 16 0 0 1 0 0 cm/Image6 Do Q What is prestressed concrete. (See Figure 4-16). As indicated in Section 5.3, many jurisdictions do not include creep and shrinkage effects in designing a pretensioned girder bridge. endstream The next step is to define the load effects for construction stage 1. It is noted that the compressive stresses at transfer are shown in red which indicates a failure. This file may have any number of load effect cases but in this case it will contain just two. Click on the Add Load Component button again and enter the UDL Intensity Start and End as 1.4kN/m. This design example was not intended to follow the design and detailing practices of any For example: Since that time, there has been extensive research on human response to motion, and it is now generally agreed that the primary factor affecting human sensitivity is acceleration as opposed to deflection, velocity, or the rate of change of acceleration for bridge structures, but the problem is a difficult subjective one. All tension stresses and allowables use positive sign convention. 02/06/18 SPK-PSG College of Technology 6 Pamban Road Bridge at Rameshwaram, Tamilnadu 7. ), = 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. 5 0 obj The allowable compression stress limit for pretensioned concrete components is calculated according to S5.9.4.1.1. In addition, the Bridge Beam Design article elaborates on the procedure to be followed when designing the method for a non-composite beam. See Section 5.3 and Appendix C for calculations and values of creep and shrinkage effects for the example bridge. Prestressed Concrete Pile Standards (Index 20612, 20614, 20618, 20620, 20624, 20630, . Stress due to self weight of beam at mid span : Lets calculate the tensile stress at the bottom of the cast-in-situ concrete. The stiffness of the overall section can be taken into account in composite design. 5.4.6 - Coefficient of thermal expansion = 12 10-6 per C. Many jurisdictions use the girder concrete strength for these calculations. endstream The neutral axis is 18.86 in. This reduces the service stress in the beam. Calculations are made from the top of the total thickness and include the integral wearing surface in the total thickness of slab. Normally design as a beam with cables running in the direction of the span at uniform centres. 1200 New Jersey Avenue, SEWashington, DC 20590 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. The above figure indicates an unpropped construction where the weight of the cast-in-situ concrete is born by the prestress beam. design loading), 25 units HB = 25 10 / 4 per wheel = 62.5 kN per wheel. Click the Add Load Component button and enter the UDL Intensity Start and End as 1410.213kN/m. Stresses at Level 1 due to SLS loads (N/mm2) : Dead Load M / Z = (1037 106) / (116.020 106), Super. ), NA, = stress block factor specified in S5.7.2.2, NA, = compression flange depth of an I or T member (in. We can calculate the allowable stress in the section based on the relevant design class of the relevant standards. In order to determine kc, the volume-to-surface area ratio needs to be calculated. 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. Therefore, the stress in the insitu concrete is 4.31 N/mm2. to Temp Construction.". a simply supported prestressed concrete Y beam which carries a 150mm thick concrete The design of structures in general, and prestressed concrete structures in particular, requires considerably more information than is contained in building codes. MI y / Ic = 337.5 x 106 x 422.5 / 2.514 x 1010 = 5.67 N/mm2. Assume that 2/3 of the total shrinkage of the precast concrete takes ] 10-3 The cracking moment, Mcr, is calculated as the total moment acting on the beam when the maximum tensile stress equals the modulus of rupture. <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 11 0 R/Group<>/Tabs/S/StructParents 1>> Calculate the bending moment due to the imposed loads. 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. Compression (1.25 Table 22) xWMoF2% >Ir0z&]%Rryogm.| +!R"H W_A^Ixa03zz L r The stress limit in this table was used in this example and, therefore, fatigue of the prestressing steel need not be checked. The user may revise these values to match any reduction required by the bridge owner's specification. The following figure indicates the stress variation. Prestressed Precast Concrete Beam Bridge Design. force in concrete flange : Only strands that are fully bonded are used for the positive moment connection. Consideration of additional stiffness induced by the concrete other than the prestress beam is the composite action. View example in PDF format (Design Example 2) Download example as a Mathcad Workbook (Zip) Adhesive Anchor Examples. ), Level 2, combination 1 : f = - 0.98 + 1037 / 89.066 + 1310 / 242.424 + 1.64 = 17.71 (< 25 O.K. The deflection criteria in S2.5.2.6.2 is considered optional. endobj 5 + pe = Advantages of Prestressed concrete vs. non . Click the Import toolbar button from the navigation toolbar. The modular ratio of reinforcing to concrete should be rounded to the nearest whole number. to Rm Right Temp Sup. Slip between the two elements will lose the composite action. As a result, beam bending and shear capacity increases. Design data: Dead load: 1500 lb/ft. (Tick the relevant tickboxes to activate these fields). Further, there could be a restrain moment due to this action. 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). 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. Set Start Dimension to 0.95m and the End Dimension to 1.05m". This will import loads into the Traffic gr1b-gr5 for Bending design and Traffic gr1b-gr5 - for Shear design design load cases and will appear in the navigation tree. Civil Engineering Design (1) Example. It will not be discussing in this article. Close the Define Pre-Tensioned Beam Load form with the OK button. stream The negative sign indicates upward deflection. The location of the centers of gravity shown in the figure may also be calculated. Tendons are stressed to about 70% of their ultimate strength. Hence restrained temperature stresses per C = 34 103 12 10-6 = 0.408 N/mm2, Force F to restrain temperature strain : Stage 1. 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.
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