To overcome this we Compute the critical fiber stresses. The prestressed tensioning process during the construction of prestressed concrete bridges must strictly follow the Technical Specification for Construction of Highway Bridge and Culvert (JTG/TF50-2011), and select the corresponding strength for tensioning according to the prestress value determined during the design work. To use the least amount of pretsress, the eccentricity over the support should be a maximum. Reinforced Concrete Fabrication. If 240 MPa of the prestressed is lost (in addition 14 G. P. Ancog Prestressed Concrete Practice Problems to the elastic deformation) determine this limiting moment. Therefore the beam of books cannot even carry its self weight. The classic everyday example of prestressing is this: a row of books can be lifted by squeezing the ends together: The structural explanation is that the row of books has zero tensile capacity. Chapter 4: Operational Amplifiers Assuming n = 6, compute the stresses in the concrete and steel immediately after transfer. 24. Assume that there is no slack in the cable, that the shrinkage of concrete is 0.0002 at the time of transfer, and that the average Mix-Designs of Concretes in Durable Reinforced and Prestressed Structures of a Viaduct for a Railway Train Connecting Venice with Cortina, in Italy. The prestressing system works for a span greater than 35 m. Prestressing will increase the shear strength and exhaustion resistance of concrete. Design the slab following the provisions of the ACI code. If the beam carry a 45 kN Moment concentrated to prestressload applied at mid-span when the beam is 3 mos. old after prestressing, 723.75x150 what is the deflection at mis-span? 1 length of shims elongation of steel shortening of concrete end of beam after transfer end of beam before transfer 18.00 m Solution: Elasttic elongation of steel: s = f s L 1040 (18 x10 3 ) = = 93 .6mm Es 200 x10 3 Shortening of concrete due to shrinkage: c shrinkage = 0.0002(18x10 3 ) = 3.6mm Elastic shortening of concrete: D = ML2 (18.093)(10 2 ) x1012 = = 3.61 mm 8 EI 8(27.5 x103 )(2.278x109 ) Length of shims required: T = s elastic + c + c shrinkage elastic = 93.6 + 3.6 + 3.78 = 100.98mm 2. Bridge engineering construction investment is large, the construction period is long, and the quality control is difficult. It gathers information from many sources and presents it with example problems that illustrate the use of . Prestressed Concrete Practice Problems Save this page as a printable Dam Owner's Fact Sheet [PDF] Visual inspection of concrete will allow for the detection of distressed or deteriorated areas. Design the beam using the least amount of prestressed assuming that the cgs must have a concrete protection of 75 mm. In addition to explaining the design steps of the design example, the comprehensive commentary goes beyond the This page intentionally left blank. It . Cracking could cause a sizable drop in member stiffness and increased deflections. The beam carries two live loads of 45 kN each in addition to its own weight of 4.40 kN/m. If the top fiber cracks and the concrete is assume to take no tension, compute the bottom fiber stresses. Our partners will collect data and use cookies for ad targeting and measurement. In order to reduce the loss of prestress after the tension is completed, the construction unit generally needs to complete the grouting construction within 48 hours. a summary of prestressed concrete concepts and examples, 90% found this document useful (63 votes), 90% found this document useful, Mark this document as useful, 10% found this document not useful, Mark this document as not useful, Save Prestressed Concrete Example Problem For Later, The idea of prestressed concrete has been around since the latter decades of the 19th, century, but its use was limited by the quality of the materials at the time. Prestressed concrete is a structural material that allows for predetermined, engineering stresses to be placed in members to counteract the stresses that occur when they are subject to loading. In the Dorben company, an Industrial Engineer designed a workstation where the seeing task was, Prestressed Concrete Practice Problems 1. 65 kN w = 23.5 kN/m 300 The prestress required: 6.00 m Qe = h 15.00 m e 750 e 6.00 m wL 2 wL 2 23 .5(6 2 ) ;Q= = = 1410 kN 2 2e 2(300 x10 3 ) In order to balance the load at the mid-span, using the same prestress Q, the sag of the parabola must be: Qh = wL 2 wL 2 23 .5(15 2 ) ;h= = x10 3 = 468 .75 mm 8 8Q 8(1410 ) The result will be a concordant cable and under the action of the uniform load and prestress, the beam will have no deflection any where and will only have a uniform compressive stress. Assuming creep coefficient of cc = 723.75x25 1.8 and an due effective prestress of 830 MPa at that time. 1, January, 2001. A Prescon cable, 18.00 m long is to be tensioned from one end to an initial prestressed of 1040 MPa immediately after transfer. Date: 7/1/2022. Compute the initial deflection at the mid-span due to-3 prestress Q = 965(750)x10 = 723.75 kNand the beams own weight assuming Ec = 27.5 GPa. Publication: Special Publication. Country unknown/Code not available: N. p., 1965. 2. for cracking in the bottom fibers at a modulus of rupture of 4.13 MPa and assuming concrete to take up tension up to that value. Most candidates did well with 6 of the questions, but two caused problems. The more frequently used symbols and those that appear throughout the book are listed below. Estimate the deflection after 3 mos. Lecture 24 - Prestressed Concrete Prestressed concrete refers to concrete that has applied stresses induced into the member. Prestressed Concrete Practice Problems Solution Total tension of steel at rupture T = 937 .5 (1650 ) x10 3 =1546 .875 kN C =T .85 f c ' ba = T a= T 1546 .875 x10 3 = =176 .34 mm .85 f c ' b .85 (34 .4) ( 300 ) Ultimate moment M u = As f su ( d a 2 ) = 1546 .875 ( 500 176 .34 2 ) x10 3 = 637 .05 kN m 8. However, in the specific bridge construction process, prestressed steel strands of different lengths The initial stress has a very close relationship with the final control stress, and the relationship between tensile stress and deformation during construction is also different. 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P. Ancog Prestressed Concrete Practice Problems Locate the cg of net section: yo = Aduct (75 ) (50 x 75 )( 75 ) = = 5.00 mm Anet 56250 y s = 75 + y o = 75 + 5 = 80 mm cT = 150 y o = 150 5 = 145 mm c B = 150 + y o = 150 + 5 = 155 mm Compute the moment of inertia of net section: bh 3 b ' h' 3 + bh ( y o ) 2 b' h' (80 ) 2 12 12 200 x300 3 50 x 75 3 = + 60000 (5) 2 3750 (80 ) 2 = 4.527 x10 8 mm 4 12 12 I = Total prestress in steel: Q = ( As f s ) = 95 %( 516 x1040 ) x10 3 = 509 .808 kN Fiber stresses: f = Q (Qe ) y 509 .808 x10 3 509 .808 x10 3 (80 ) = y Ac I 56250 4.257 x10 8 = 9.063 0.095806 y Top fiber stress: f T = 9.063 0.095806 (145 ) = 4.828 MPa Bottom fiber stress: f B = 9.063 + 0.095806 (155 ) = 23 .913 MPa Method 2: Using gross section of concrete Q Qec 509 .808 x10 3 509 .808 x10 3 (75 )(150 ) = 1 Ag I 200 x300 ( 200 x300 3 ) 12 = 8.4968 12 .7452 f = Top fiber stress: f T = 4.2484 MPa Bottom fiber stress: f B = 21 .242 MPa If eccentricity does not occur along one of the principal axes of the section, it is necessary to further resolved the moment into two components along the two principal axes. It is eccentrically prestressed with 516mm2 of high tensile steel wire which is anchored to the bulkheads at a unit stress of 1040 MPa. Trimming a chord connection rod as part of a precast concrete garage rehabilitation. The idea of prestressing has also been applied to many other forms, such as: In these cases heated metal is made to just fit an object. Comprehensive Design Example for Prestressed Concrete (PSC) Girder Superstructure Bridge With Commentary US Customary Units Report in PDF Format(1.7 mb) Cover Page Technical Report Documentation Page 1. The cgs of the wires is 100mm above the bottom fiber. Beyond this it examines how contract arrangements can encourage or prevent problems in the designing and building processes. Compute the extreme fiber stresses at mid-span: a) under the initial condition with full prestress and no live load b) under final condition after all the losses have taken place and with full live load. the main factors for concrete used in psc are: ordinary portland cement-based concrete is used but strength usually greater than 50 n/mm2; a high early strength is required to enable quicker application of prestress; a larger elastic modulus is needed to reduce the shortening of the member; a mix that reduces creep of the concrete to minimize = 14.407 mm downward. Belgium and Hoyer in Germany were the principle developers. Most failures are the result of inadequate attention to small details. Ans: fT = 0.00 MPa; fB = +16.918 MPa initial cgc cgc e 300 200 Fig. Examples of failed prestress work include the use of lightweight aggregates as used in the Kenai River Bridge where the girders cracked and spalled; steam curing when a metal sheath is placed inside a beam, the metal acts as a radiator and cools the concrete cover causing cracks; and not taking into account temperature differentials on long casting beds, as in a New York viaduct were anchor bolts did not fit the templates after the beam was hoisted by crane. country unknown/code not available: n. p., 1965. If the corrugated metal ducts blockage occurs in the project, you can first determine the location of the blockage, then avoid the main reinforcement of the beam, perform drilling operations, and then clean up the block of slurry that caused the blockage to ensure the steel strand can traverse smoothly without affecting its expansion and contraction performance. 2. ACI 318-05 PCI PrACtICE 2.2 Design of precast concrete moment frames is discussed in Chapter . Strict and meticulous inspection work is carried out after the prestressed strand is tensioned, and special inspections are carried out on the phenomenon of slippage and broken wires of the prestressed steel strand. Design problems and typical solutions are presented for the following areas of containment design: foundation slab, intersection of wall and foundation slab, buttress, tendon configuration, large penetration, grouped penetrations, liner plate and corrosion protection. Ans: Initial condition: fT = 2.234 MPa, fB = 15.10 MPa; Final condition: fT = 13.803 MPa, fB = 0.975 MPa 45kN 4.50m 45kN 3.00m 4.50m 300 4 600 Fig. Most Prestressed concrete is precast in a plant. Introduction 2. Prestressed Concrete InstituteReflections on the Beginnings of Prestressed Concrete in AmericaSelected Water Resources AbstractsPRESTRESSED CONCRETE : ANALYSIS AND DESIGN PRACTICE OF MEMBERSStructural Engineer License Review: Problems and Solutions: For Civil and Structural EngineersPartial Prestressing, From Theory to PracticeApplied Ans: Case 1: w T =16.21 kN/m; Case 2: w T = 20.34 kN/m Solution Section properties: mmhc mmxbhI mmxbhA 3002600 2 104.5)600) (300(121 121 10180)600(300 4933 23 Prestress Q: kNxfAQ ss 8.129610)830(5.1562 3 1. Dead load = 150 x (6.50/12)) = 81 psf Live load = 100 psf The main reason for this situation is that the construction unit has problems, such as the construction units process control is not strict, and the relevant operation specifications are not strictly enforced, causing the metal ducts to deviate from the positioning or appear deformed or fall off; the construction unit does not strictly control the quality of the materials, The metal ducts used in the construction has quality defects and leaking and blocking the pipe; during the concrete pouring process, it needs to be vibrated, and the vibrator has technical errors, causing the metal ducts to be displaced or broken, and the concrete leaks to the metal ducts. sample problems complete with step-by-step solutions. If a concentrated load P = 65 kN is applied at the mid-span, compute the maximum top and bottom fiber stresses. Diameter 2: 6.04 inches . For the tendons, fs = 1650 MPa, fc = 34.4 MPa. Also, using fibre reinforced plastics. Determine the total dead and live uniform load moment that can be carried by the beam with a simple span of 12m:1. for zero tensile stress in the bottom fibers. In prestressed concrete, prestress is the permanent force in the member, causing compressive stress at the level of steel. A hollow member is reinforced with 4 wires of 62.5 mm 2 each pretensioned fsi = 1030 MPa. Compute the stresses in the concrete at transfer. f = Q Qe x y Qe y x A Ix Iy 5. l running static analysis on simply-supported prestressed concrete beam in ansys. Tension is taken to be positive and compression is negative, throughout. Learn how we and our ad partner Google, collect and use data. The following 2 diameters were measured at right angles to each . 4.2 Solutions Calculate stress in prestressed reinforcement at nominal strength using approximate value for fps. China has become a world-class bridge building country. Irwin, B, SAMPLE SOLVED PROBLEMS 1. All rights reserved. A pretensioned member has a section 200mmx300mm. If the slippage of the prestressed steel strand occurs, use a mono-strandjack to pull out the slippery prestressed steel strand, replace with a new prestressed steel strand or working wedge, and then tension it to the specified value. Ans: 100.98mm Fig. Bearing resistance may be reduced by axial forces, with serious bracket stresses and often splitting of the concrete seat on the beam. Can the cylinder be tested? wL2/8 Moment due to beam weight Moment due to load P G. P. Ancog 11 PL/4 Prestressed Concrete Practice Problems Solution Section properties: A = bh = 300 x 450 = 135 x10 3 mm 2 I = 1 1 bh 3 = (300 )( 450 ) 3 = 2.278 x10 9 mm 4 12 12 The parabolic tendon with 150mm mid-ordinate is replaced by a uniform load acting along the beam. It is concentrically prestressed with 516mm2 of high tensile steel wire which is anchored to the bulkheads of a unit stress of 1040 MPa. Page ii Prestressed members will change their camber with time, and some rotation freedom at the support must be provided. 1 Example 2 Prestressed Simply Supported T-Beam c.g.c gSd + q Sd = 6.13 kN/m 19.51 m Given: fck = 41.3 MPa P0 = 1303 MPa, P= Pe = 1034 MPa, y P = 371 mm Ac = 3058 cm 2, I c = 896674 cm 4, y b = 459 mm, y t = 151 mm Wb = 19550 cm 3, W t = 59419 cm3 wsw = 7.21 kN/m Twelve 12.7 mm tendons are used to prestress the beam (A tendon = 98.7 mm 2) Find: Top and bottom stresses at mid-span for: The main reason for the slippage of the prestressed steel strand may be due to severe corrosion of the steel strand or the working wedge, or the surface of the steel strand or the working wedge has impurities, such as cement, oil, etc., or the size of steel strand does not meet the construction requirements or is unqualified, or the jack used in the construction process is not uniformly stressed. Compute the length of shims required, neglecting any elastic shortening of the shims and any friction along the tendon. After the tensioning work is completed, high-grade micro-expansion concrete is used to seal the open holes. This is especially true in prestressed concrete applications, particularly when mem- bers are allowed to develop cracks under service loads. is 100mm above the bottom fiber. 1. Prestressed Concrete Practice Problems and assuming concrete to take up tension up to that value. Affect the quality of bridge construction. (Hint: See Section 7.1 in ASTM C39) Diameter 1: 6.02 inches . Page iii For post-tensioned unbonded beams, the net concrete section is the proper one for all stress calculation. kN L A sl p p 68.9 21 .3 100 0.64 P A E 0. A post-tensioned bonded beam with a transfer prestress of Ft = 1560 kN is being wrongly picked up at its mid-span point. Precast and prestressed concrete design is based on the provisions of ACI 318-05. David Garber 10.5K subscribers This example problem is in Module 11 of my Prestressed Concrete Design course (Prestress Loss). Date: 7/1/2022. Ronald F. Clayton Ans: F = 1410 kN; fT = 14.934 MPa, fB = -2.40 MPa 13 G. P. Ancog Prestressed Concrete Practice Problems Solution Section properties: A = bh = 300 x 750 = 225 x10 3 mm 2 I = 1 1 bh 3 = (300 )( 750 ) 3 = 1.0546875 x10 10 mm 4 12 12 In order to balance the load on the cantilever, the cgs at the tip must coincide with the cgc with a horizontal tangent. Ans: fc = 8.575 MPa; fy = 988.55 MPa Qi Qi 300 200 Fig. The most obvious type of failure occurs when high-strength steel fails because, in areas of corrosion pitting, its notched bar tensile strength is exceeded. If fc = fci = 34.4 MPa, n = 7, determine the stresses when the wires are cut between members. Prestressed Concrete Practice Problems 1. ; except for concrete cast against and permanently exposed to earth, where minimum cover shall be 3 inches. computations for the following components are included: concrete deck, prestressed concrete I-girders, elastomeric bearing, integral abutments and wing walls, multi-column bent and pile and spread footing foundations. Load Calculation: Consider only a 1 ft width of beam. A Prescon cable, 18.00 m long is to be tensioned from one end to an initial p, Page iii If the beam is picked up suddenly so that an impact factor of 100% is considered compute the maximum stresses. 4. No Cracks? Problems and solutions in the construction of prestressed concrete bridges, 1. This example goes through how to calculate prestress loss of a. Structural Analysis and Design of a Multi-story Reinforced Concrete Building Nov 28 2019 Analysis and Design of Reinforced Concrete Bridges Dec 30 2019 Concrete Slabs Aug 30 2022 This book provides an up-to-date description of the latest procedures made up of a system of conventionally reinforced precast concrete columns and prestressed concrete beams and . Ans: when the wires are cut, fs = 936.98 MPa; Limiting moment, MT = 9.665 kN-m 200 100 200 (n-1)As = (7-1)(62.5) 100 = 375 mm2 open Transformed Section Solution Transformed section: AT = 200 x 200 100 x100 + 4( n 1) As = 31 .5 x10 3 mm 2 IT = [ ] 1 200 4 100 4 + 4( n 1) As (70 2 ) = 1.3235 x10 8 mm 4 12 Initial prestressing force, Qi before transfer: Qi = Ast f si = ( 4 x 62 .5)(1030 ) x10 3 = 257 .5 kN fc = Qi 257 .5 x10 3 = = 8.175 MPa AT 31 .5 x10 3 f s = nf c = 7(8.175 ) = 57 .225 MPa Net stresses right after transfer (loss due to elastic shortening): f c = 8.175 MPa f so = f si nf c = 1030 57 .225 = 972 .775 MPa Allowable concrete stresses: f c = 0.45 f c ' = 0.45 (34 .4) =15 .48 MPa f t = 0.5 f c ' = 0.5 34 .4 = 2.93 MPa Total moment : MT = MD+ML Additional concrete stress on top: f t c = 15.48 8.175 = 7.305 MPa compression Additional concrete stress on botton: f b = 2.93 + 8.175 = 11 .105 MPa tension Total moment that can be carried: f = f I MT c 7.305 (1.323 x10 8 ) ;MT = t = x10 6 = 9.665 kN m I c 100 Concrete stress on top reach full allowable limit: 15 G. P. Ancog Prestressed Concrete Practice Problems f T = f c = 15 .48 MPa compression Concrete stress at the bottom: f B = 8.175 f t = 8.175 7.305 = 0.87 MPa compression 8.175 MPa 15.48 MPa = -2.93 MPa Allowable value of stress 7.305 MPa 8.175 MPa -11.105 MPa Initial concrete stress Additional concrete stress concrete stress at the level of steel Net stress in steel: 70 f sn = f so nf cs = 972 .775 7 7.305 = 972 .775 35.7945 .1135 100 Top steel: f snT = 972 .775 35 .7945 = 936 .98 MPa Bottom steel: f snB = 972 .775 + 35 .7945 = 1008 .5695 MPa After 240 MPa of prestress is lost (in addition to elastic deformation) Qi = f snet Ast = (1030 240 )( 4 x 62 .5) x10 3 = 197 .5 kN fc = Qi 197 .5 = 8.175 = 6.27 MPa AT 257 .5 f se = f snet nf c = (1030 240 ) 7(6.27 ) = 746 .11 MPa Additional concrete stress on top: f t c = 15.48 6.27 = 9.21 MPa compression Additional concrete stress on botton: f b = 2.93 + 6.27 = 9.2 MPa tension Total moment that can be carried: f = f I MTc 9.2(1.323 x10 8 ) ;MT = t = x10 6 = 12 .17 kN m I c 100 16 G. P. Ancog Prestressed Concrete Practice Problems 6.27 MPa 15.48 MPa = -2.93 MPa Allowable value of stress 9.21 MPa 6.27 MPa -9.20 MPa Initial concrete stress Additional concrete stress Therefore the limiting moment: M T = [ 9.665 , 12 .17 ] min = 9.665 kN m 17 G. P. Ancog.

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