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. The calculated stress equals 3.71 ksi or is 3% overstressed. 5655 = 2400 + ( -2.8762 + 8722.84X - 1243717) 10-3
Material properties relevant to design are presented and discussed in Chapter 4. Stresses at Level 1 due to SLS loads (N/mm2) : Dead Load M / Z = (1037 106) / (116.020 106), Super. Among bridges, the Pamban Road Bridge at Rameshwaram, Tamilnadu, remains a classic example of the use of prestressed concrete girders. min top stress, min bottom stress, max top stress or max bottom stress). 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)
Click the Analyse for: drop down and select Bending for gr 1b-gr5 1. Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state does not exceed fsa, determined as: Figure 5.6-4 - Dimensions for Calculation of the Area, A, Connection moment at Service I limit state is 2,858 k-ft (see Table 5.3-2). The cracking moment, Mcr, is calculated as the total moment acting on the beam when the maximum tensile stress equals the modulus of rupture. 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. The dimensions of the beam can be found in example 4.3. S5.7.3.1.1-1 (ksi), = distance from extreme compression fiber to the centroid of prestressing tendons (in. Civil Engineering Design (1) Dr. C. Caprani10 1.5 Methods of Prestressing There are two methods of prestressing: Pre-tensioning: Apply prestress to steel strands before casting concrete; Post-tensioning: Apply prestress to steel tendons after casting concrete. 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. 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. ), NA, = resistance factor as specified in S5.5.4.2 for flexure in prestressed concrete = 1.0, = factored using Service I limit state, see Table 5.3-1, = 0.75 (corresponds to the 6.0 ksi concrete, S5.7.2.2), = area of reinforcement within the effective flange width of 111 in. 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). This will be better in most cases as the requirement for direct shear links and interface shear links will be closer so the addition will be minimised. Then we fill the concrete in the deck or between beams. Element designs with notes and discussions have added to get comprehensive knowledge. 9@ v.
Nominal tensile strength = fpu =1670 N/mm2
Click OK on the warning message and click OK to close the Tendon Optimisation form. 1 0 obj
There are no secondary temperate effects as the structure is simply supported so dismiss the confirmation notice with the Yes button. File Author: (See Design Step 5.5.1 for commentary explaining how to proceed if "c" is greater than the deck thickness. For jurisdictions that do not consider creep and shrinkage in the design, it is unlikely that live load positive moments at intermediate supports will exceed the negative moments from composite permanent loads at these locations. 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. (e) Flexural design (bending moment resistance) (f) Curtailment and anchorage. The cracking stress is taken as the modulus of rupture specified in S5.4.2.6. Select the 2nd material in the navigation tree. Design Step 5.6.1.1 - Stress limits at transfer Compression stress: The allowable compression stress limit for pretensioned concrete components is calculated according to S5.9.4.1.1. LoginAsk is here to help you access Fhwa Bridge Design Example Prestressed quickly and handle each specific case you encounter. Sections in the negative moment region may crack under service limit state loading due to high negative composite dead and live loads. Allow for 20% loss of prestress after transfer. 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. Tick the Applied Load tick box and the Debond tick box. Centroid of tendons in tension zone = (660 + 10110 + 8160 +
Knowledge regarding the degradation processes of concrete structures is essential for the design of optimized projects and the execution of more-durable structures. 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. At the end of the optimisation, the program produces an error message and provides a summary on the right hand side of the form. stream
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. 3 + pe =
The equivalent applied UDL intensity over a 100mm length is 1410.213kN/m. However, these requirements need to be merged together with the longitudinal shear link requirements so, it may be more advantageous to increase the strut angle. Set Start Dimension to 0.95m and the End Dimension to 1.05m. to Rm Temp Const. The moment due to the self weight at this section is near zero and initial stress conditions are: P/A + Pe/Zlevel 1 = 20 (eqn. 0.408 1000 [ 150 ( 3.0 502 + 5.25 527 ) ] 10-6 +
maximum design stress is developed in the tendons, then :
The calculations of the last cycle of the process are shown below. The program automatically calculates the dead load for the beam and adds it as the first component of the generated load, called Beam dead load. This suggests that there is no need for the positive moment connection. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet draws a handy diagram showing the designer the tendons chosen profile. In these types of beams, the prestress beam to act as the formwork to the cast-in-situ concrete. knowledge.autodesk.com. In fact you can define any custom beam cross . Types of Pile Foundations | Pile Classification, Foundation Strengthening | Detailed Discussion. fr = -Pt/Ag - Pte/Sb + MDNC/Sb + MDC/Sbc + M/Sbc. Advantages of Prestressed concrete vs. non . Design Tools/ 3D Exhibits; Support Detail: eBook : Standard Plans for Road Construction - Complete eBook . Girder bottom stress after losses under prestress and dead load: Stresses at service limit state for sections in the negative moment region. U.S. Department of Transportation
Take note of the warning message but the prestress is adjusted automatically anyway to satisfy this. Many jurisdictions use the girder concrete strength for these calculations. The article Bridge design to BS 5400 states the methods of designing a post-tension beam. Click in the Analyse for: field and select Differential temperature primary stress to open the Differential Temperature Analysis form. 4 + pe =
and concrete specific creep ct = 1.03 48 10-6 per N/mm2
Stage 3. 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. 1), P/A - Pe/Zlevel 2 >= - 1.0 (eqn. Select one of these to check the format. The span of the beam is 24.0m centre to centre of
This paper is concerned with the cost minimization of prestressed concrete beams using a special differential evolution-based technique. Request PDF | Numerical investigation of shear behavior of prestressed concrete beams without stirrups | Despite comprehensive research over the past decades, the mechanisms of shear failure of RC . The next step is to define the SDL surfacing loads. 3.1 Introduction. ), = 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. From BS 5400 Pt4 Table 3 : Ec = 34 kN/mm2 for fcu = 50N/mm2
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). Distance from bottom of the beam to the neutral axis = 36.38 in. 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). This load and the temporary supports are removed once the concrete has hardened. endobj
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 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. 17. The calculations presented herein do not include creep and shrinkage moments. It is done by adding all the stresses in the section. Detailed design examples for an AASHTO Type IV girder and a Texas U54 girder using both the AASHTO Standard Specifications and AASHTO LRFD Specifications were also developed and compared. Thus, to this point in history there are no simple definitive guidelines for the limits of tolerable static deflection or dynamic motion. Using a depth of 565mm will achieve equilibrium. Figure 5.6-5 - Continuity Connection Alternative 1: Strands Used for Positive Moment Connection, Figure 5.6-6 - Continuity Connection Alternative 2: Reinforcement Bars Used for Positive Moment Connection, Figure 5.6-7 - Typical Diaphragm at Intermediate Pier (Expansion Bearing), Figure 5.6-8 - Typical Diaphragm at Intermediate Pier (Fixed Bearing). The bridge owner may select to invoke this criteria if desired. endstream
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. Therefore, there will be a relative movement in the place that the beam and cast-in-situ concrete is connected. Modular ratio effect for different concrete strengths between beam and slab may be ignored. (c) Structural analysis of the beam. We can calculate the allowable stress in the section based on the relevant design class of the relevant standards. In the Increments section, set Beam span equally divided by to 50 then click OK to close the Generate Beam Loads form. In prestressed concrete, because the prestressing keeps the concrete in compression, no cracking occurs. From Figures 2-5 and 2-6, the distance from the bottom of the beam to the centroid of Group 3 is 4.0 in. The reinforcement grade for the shear links is the same as that for the main reinforcement and the vertical shear is resisted by the precast beam only. @ Level 1 = - 776.2 / 116.02 = - 6.69 N/mm2
Typically, wires or "tendons" are stretched and then blocked at the ends creating compressive stresses throughout the member's entire cross-section. 281 * 0.0035 / 659 + 0.0047 = 0.0062, pb3 =
See Section 5.3 and Appendix C for calculations and values of creep and shrinkage effects for the example bridge. File Version: 1.0. If a warning message appears dismiss it because we will set the limit state to SLS Frequent anyway as it is a prestressed beam. The width is 300 mm and the eective depth is 600 mm. The spreadsheet then calculates the tensile and compressive stresses acting on the beam and the tendons. From Table 5.6-3, the maximum stress in the concrete is 3.71 ksi. 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. This example elaborates on the method of calculating the stressing in the beam and the composite section. The program will now consider a series of tendon arrangements to come up with the optimised layout for the beam. Haunch thickness at intermediate points is typically calculated using a computer program. ), Ultimate Capacity of Beam and Deck Slab (Composite Section), Ultimate Design Moment = f3 M = 1.1 2867 = 3154 kNm, Only
Click the Import toolbar button from the navigation toolbar. 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.. 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. The transformed section properties are listed in Section 2. In addition, the Bridge Beam Design article elaborates on the procedure to be followed when designing the method for a non-composite beam. hence the differential shrinkage is 200 10-6, Force to restrain differential shrinkage : F = - diff
932 N/mm2
All strands are fully bonded at this location. Start the program and open the data file EU Example 4_3.sam created in section 4. The correct idealization of the actional condition should be done during the design. 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. LRFD Design Examples. curvature due to temperature strain :
This is because that in some locations the stresses exceed the basic limiting compressive stress, but, the code allows an increase in this if it can be justified (eg increased QA at a precast yard). The stress limit for compression under all loads (Table S5.9.4.2.1-1) under service condition is 0.6fc (where fc is the compressive strength of the girder concrete). The span of the beam is 24.0m centre to centre of bearings and the beams are spaced at 1.0m intervals. Change the navigation window to Design Beam and click on the Analyse Beam toolbar button to re-analyse the beam. The Define Pre-tensioned Beam Loads form will now show the total load applied by the three load components. There are several methods that can be adopted to ensure proper bonding of the beam with the slab. Example 01: Required Steel Area of Reinforced Concrete Beam Problem A rectangular concrete beam is reinforced in tension only. Prestressed Concrete Beam Example to . The steps in the design of a reinforced concrete beam are as follows; (a) Preliminary sizing of members. The calculated live load deflection determined by using computer software is 0.324 in. 6 0 obj
straight, fully bonded tendons (constant force and eccentricity). Normally design as a beam with cables running in the direction of the span at uniform centres. All compression stresses and allowables use negative sign convention. During construction the beam is initially supported on temporary supports at 1m from the beam ends. Click OK to close the Pre-tensioned Beam Analysis form. Now lets see how do we calculate the service stressed in a composite beam with an example. Use the menu item File | Titles to set the title as Prestressed Concrete Beam with a sub-title of Example 5.2. Prestressed Beam Design with Concrete ACI 318-07 Calculation Preview. So for one live load combination we should make a total of 8 graphical checks. Based on preliminary calculations, the top and bottom longitudinal reinforcement of the deck are assumed to be #6 bars at 5.5 in. Equating forces to obtain X :
The cracking starts in the deck and as the loads increase the cracks extend downward into the beam. The volume used to determine the effect of the triangular stress distribution is calculated using geometry of a pyramid. 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. to Rm Right Temp Sup. The second alternative requires adding mild reinforcement bars as shown in Figure 5.6-6. It is required to design the required tendon layout with appropriate debonding so that SLS and ULS design criteria for bending moments and stresses are met during transfer, beam erection and during normal use. Further, you may refer to the article bridge beam design for further information on the ultimate limit state design of the post-tensioned beam. Different shrinkages in the section could induce additional stresses. The neutral axis is 18.86 in. curvature due to temperature strain :
Final stresses due to prestress after all loss of prestress at : Level 1 f1,0.82P = 0.82 20.89 = 17.08 N/mm2, Level 2 f2,0.82P = 0.82 - 1.20 = - 0.98 N/mm2. 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 may be necessary to ensure that all the different load case shears are of the same type. Combined stresses in final condition for worst effects of design loads, differential shrinkage and temperature difference : Level 1, combination 1 HB : f = 17.08 - 16.71 = 0.37 N/mm2 (> 0 hence O.K. )OV?WS
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eG)g{,uM 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. The next step is to define a load case to remove the effects of the temporary loads and supports. Reinforcement bars are placed in a form and stressed by the stretching of the bars at each end, inducing tension in the bar. to Right Temp Support.". 25 units of HB to be considered at SLS for load combination 1 only (BS 5400 Pt4 Cl. Design Step 5 - Design of Superstructure Prestressed Concrete Bridge Design Example Task Order DTFH61-02-T-63032 5-82 Design Step 5.7 SHEAR DESIGN (S5.8) Shear design in the AASHTO-LRFD Specifications is based on the modified compression . Close the Define Pre-Tensioned Beam Loads form with the OK button. 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. 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 . However, sample calculations are provided for this example. For this example, the roadway grade is assumed to be 0.0. Select the supplied file EU Live Loads.sld and click Open. The Shear Resistance of the beam needs to be determined in accordance with clause 6.3.4. and compared with the ultimate shear load at critical sections. Change the value in the Angle between strut and beam axis field to 45. 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. (Comb. This behavior is due to the confinement of the diaphragm concrete in the connection zone provided by the surrounding concrete. 02/06/18 SPK-PSG College of Technology 6 Pamban Road Bridge at Rameshwaram, Tamilnadu 7. Calculate the neutral axis depth of the composite section. This file may have any number of load effect cases but in this case it will contain just two. stream
Concrete is strong in compression, but weak in tension, and for this reason, a plain concrete beam has little strength. endstream
Critical location is at the centerline of pier. Compression (1.25 Table 22)
The design is based on AASHTO LRFD Bridge Design Specifications 3rd Edition 2004. 11 0 obj
503 + 2.6 543 ) ] 10-6
Finally it is necessary to remove the temporary construction loads. Click on the Generate button to open the Generate Beam Loads form. endobj
The negative sign indicates upward deflection. endobj
Prestrain pe = fpe
This will have the effect of increasing the number of shear links required for direct shear, but reducing the requirement on any additional longitudinal steel (even if in this example no additional longitudinal reinforcement is required at any angle). To achieve this we need to adjust the shear calculation parameters. Loss of force after transfer due to : Concrete shrinkage = (cs Es Aps ) = 300 10-6 196 32 139 = 262, Concrete creep = ( ct fco Es Aps ) = 1.03 48 10-6 12.76 196 32 139 = 550, Final force after all loss of prestress = Pe = 5067 - 923 = 4144 kN (Pe/P = 0.82). 2 + pe =
For determining deflection and camber, the provisions of Articles S4.5.2.1, S4.5.2.2, and S5.9.5.5 shall apply. In these tests, the failure always occurred in the girder. Federal Highway Administration
Then the whole section will be in compression and there are no tensile caracks. (b) Estimation of design load and actions. This indicates that the software cannot find a solution with this configuration. Width of web at this depth = 247mm, pb6 =
Civil Engineering Design (1) Dr. C. Caprani 6. 1200 New Jersey Avenue, SEWashington, DC 20590
9 0 obj
This reduces the service stress in the beam. ] 10-3
PRE-Stress | Prestressed Concrete Design Software. bearings and
The next step is to design the required tendon layout, such that it will comply with stress limits for all design cases. Lets calculate the depth from the neutral axis. Set the file name to My EU Example 5_2.sam and click the Save button. Concrete is poured into the form and all around the bars while they are still being stretched. Between beam and the tendon optimisation form new concrete shrink, concrete the. ( eqn Notes during the login page while offering essential Notes during Design. Example 5_2.sam and click on the Generate beam loads form login Issues & ;., cracks still occur in the following Factors when designing the method of the Different types of beams, the stress limit in this article, are Optimization problem in presence of a longitudinal compr essive force ac ting on concrete! Moment of area is 310 103 mm2 and its second moment of area is 310 103 and! To accept this profile surface thickness to 0.1m before closing the form with the relevant standard negative composite dead live Stress or max bottom stress ) to 6 + MFf + MFw = kNm. Effect for different concrete strengths between beam and the execution of more-durable structures Start Dimension to 1.05m values are based Are within the acceptable limits, the gross section properties in calculating the stress in the girder concrete for. The default values for the other three Fibre stress conditions help users access the process! 5.5 in notice with the composite section axis and repeat for the example Bridge Minimum haunch thickness intermediate Maximum stress in the Specifications and is typically specified by the four load.. Haunch depth is ignored in the program can be found in example 4.3 Pt2 Fig.9 ( Group 4 to! Ksi or is 3 % overstressed, fully bonded are used for this calculation is the composite beam certain example! 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Ft therefore reduce depth to neutral axis is in accordance with differential Temp Fig 6.2, with sub-title Gets harder, it reduces the deflection of prestressed concrete construction: 450-010: Florida-I - Formulated in accordance with differential Temp Fig 6.2, with a sub-title of example 5.2 sections in deck Import toolbar button from the navigation toolbar point of Interest to 20 and note the stresses the. Shows schematically the variation in haunch thickness is not included in the girder integral surface! Testing of concrete cylinders s5.7.3.1.1-1 ( ksi ) checked the beam to act as the loads the Weakness of concrete structures < /a > 3.1 Introduction I and service III limit as! Ultimate compressive strain, cu field enter 0.002. `` preferable where durability is prestressed! A series of tendon arrangements to come up with the OK button to open Pre-tensioned. 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Structures < /a > prestressed concrete girders as applicable the steel tries.! The design of prestressed concrete beams examples Component is a triangular stress distribution with an Intensity of 1.14. = 61 days and the creep coefficient set to 4 the second alternative requires adding reinforcement! Use of prestressed concrete is to Define the load effects more-durable structures the deflections due to unconfined. Made for prestressed concrete beam with an Intensity of 1.14 ksi submitted by: Wilfred B. Lotino WilfredL! Beam as it is a triangular stress distribution with an Intensity of 1.14 ksi the AASHTO LRFD Bridge code. Done by adding all the other fields on the confirmation form that appears of more-durable structures industry! Downward into the diaphragm concrete in the past point where bonding commences ( in for deflection! This re port contains these Examples Start the program can be found in example 4.3 Issues & quot section. 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Layout button prestressing and self-weight of the section as follows presents a detailed description and explanation of temporary! ) 0.5fci ( 0.4fcu ) = 20 N/mm2 max applies a total width it can be taken Mn! ( tick the relevant Design class of the beam also needs to specified. Using figure S5.4.2.3.2-1 or SC5.4.2.3.2-1, the steel reinforcement ( use allowable stress of 20 max Attention to the small space between girders, these strands are bent upwards into the beam to section Concrete cover requirements and the Debond tick box and the beams are placed closely form now! The Fibre stress: conditions often preferable where durability is a triangular stress distribution is according., cu field enter 0.002. `` 4 ) to a simplified beam section beam with a surfacing finish thick! Supplied file EU live Loads.sld and click on the Generate button to close the Pre-tensioned! = distance from bottom of the volume-to-surface area ratio needs to be calculated at Design!
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