sample problems of prestressed concrete

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DESIGN OF PRESTRESSE, Irwin, Basic Engineering Circuit Analysis, 10/E Most candidates did well with 6 of the questions, but two caused problems. Spalling and Popouts. If the beam is picked up suddenly so that an impact factor of 100% is considered compute the maximum stresses. Compute the length of shims required, neglecting any elastic shortening of the shims and any friction along the tendon. Advantages of Prestressed Concrete: The reinforcement of concrete using excessive tensile steel improves the effectiveness of the material. Prestressed Concrete Analysis And Design Third Edition When somebody should go to the book stores, search opening by shop, shelf by shelf, it is in reality problematic. If the tension of the prestressed steel strand is uneven and the tension is too large, or there are problems such as mechanical damage during the storage and transportation of the prestressed steel strand, it will cause the prestressed steel strand to break. example no.1: prestressed concrete girder bridge design. 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. 4.2 Solutions Bearing resistance may be reduced by axial forces, with serious bracket stresses and often splitting of the concrete seat on the beam. During normal construction, the initial strain and tightness of multiple prestressed steel strands are different when tensioning, and various problems are prone to occur, causing the prestress value to fail to meet the engineering needs, resulting in a decrease in the reliability and durability of the prestressed structure. 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. Joints must allow for differential thermal, creep and shrinkage in the connected members. Problems with concrete include construction errors, disintegration, scaling, cracking, efflorescence, erosion, spalling, and popouts. Ans: Case 1: fT = -6.566 MPa, fB = 23.90 MPa; Case 2: fB = 27.905 MPa; Case 3: fB = 35.39 MPa Solution Section properties: A = 300 x 600 = 180 x10 3 mm 2 1 I = (300 )( 600 ) 3 = 5.4 x10 9 mm 4 12 600 c= = 300 mm 2 External moment at pick-up point M = wL 2 4.4(6) 2 = = 79 .2 kN m 2 2 a) Fiber stress at mid-span Q Qey My A I I 3 1560 x10 1560 x10 3 (125 )300 79 .2 x10 6 (300 ) = 180 x10 3 5.4 x10 9 5.4 x10 9 = 8.667 10 .833 4.4 f T = 8.667 10 .833 4.4 = 6.566 MPa f = f B = 8.667 +10 .833 + 4.4 = 23 .9 MPa 9 G. P. Ancog Prestressed Concrete Practice Problems b) If the fiber cracks and concrete is assume to take no tension. This is especially true in prestressed concrete applications, particularly when mem- bers are allowed to develop cracks under service loads. 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. 24. The following 2 diameters were measured at right angles to each . The Australasian CP code limits the voltage of the strand to >-900mV (AgAgCl 0.5M at instant off). A trial batch for normal-weight concrete with an average 28th day compressive strength of 42 MPa is to be proportioned based on the following: Slump 50 mm to 100 mm Water-cement ratio by weight 0.41 Specific gravity of cement 3.15 Specific gravity of coarse aggregate 2.68 Specific gravity of fine aggregate 2.64 Water (net mixing) 200 kg/m . and production problems that may unnecessarily increase the cost of a structure and/or may actually result in an inferior . 1 This page intentionally left blank. Cohn 2012-12-06 These volumes . Ronald F. Clayton Calculate the nominal moment strength of the prestressed member shown. Not installing joints opens the door to potential litigation in addition to We were all set to start when the testing lab's field tech stopped the pour. 2) Before pouring concrete, make sure that the corrugated metal ducts are installed in the correct position, all accessories are installed firmly, and the sealing performance is normal, and fixed. Load Calculation: Consider only a 1 ft width of beam. In addition to explaining the design steps of the design example, the comprehensive commentary goes beyond the After the concrete pouring of the bridge is completed, the corrugated metal ducts are often blocked, which affects the installation and penetration of the prestressed steel strands, resulting in a difference between the actual elongation of the tensioned prestressed steel strand and the calculation result during the design process. Partial Prestressing, From Theory to Practice M.Z. 001188 193000000 = = = Pel = 0 (3) Friction losses Assuming that the parabolic tendon approximates the shape of an arc of a circle . In such a case, the failure is brittle in character (Section 6.4.1). To use the least amount of pretsress, the eccentricity over the support should be a maximum. = 14.407 mm downward. 2. Ans: Bonded condition: fs = 845.258 MPa, Unbonded condition: fs = 838.137 MPa wT = 11.00+4.40=15.40 kN/m Section properties: A = bh = 300x600 = 180000.00 mm2 I = bh3/12 = 300(600)3/12 = 5.4x109 mm4 c = h/2 = 600/2 = 300 mm Mo M x Parabolic moment diagram x y yo Parabolic y diagram Solution 1: Moment at mid-span: Mo = wL 2 15 .4(12 ) 2 = = 277 .2kN m 8 8 Moment at mid-span due to prestress: M s = Qe = (1612 .9 x830 )(125 ) x10 6 = 167 .34 kN m Net moment at mid-span: MN = 277.2 167.34 = 109.86 kN-m Stress in concrete at the level of steel due to bending: 7 G. P. Ancog Prestressed Concrete Practice Problems Using I for gross section My 109 .86 x10 6 (125 ) fc = = = 2.543 MPa I 5.4 x10 9 The stress in steel is increased by: f s = nf c = 6( 2.543 ) = 15 .258 MPa Resultant stress in steel: fsf = 830 + 15.258 = 845.258 MPa Solution 2: If the cable is unbonded and free to slip. Address: Copyright 2022 VSIP.INFO. Can the cylinder be tested? 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 = 0.5579mm upward; When 45 kN is added after 3 mos. The prestressed steel strand has slipped or broken wires. Compute the critical fiber stresses. kN L A sl p p 68.9 21 .3 100 0.64 P A E 0. Prestressed members will change their camber with time, and some rotation freedom at the support must be provided. #PrestressedConcrete Principles of Prestressed Concrete Introduction Credits: 1. Publication: Special Publication. The prestressing system works for a span greater than 35 m. Prestressing will increase the shear strength and exhaustion resistance of concrete. A post-tensioned bonded concrete beam has a prestress of 1560 kN in the steel immediately after prestressing which eventually reduces to 1330 kN. Live Load Distribution in a Slab-on-Girder Bridge Subjected to Corrosion and Differential Settlement. For approximation, gross area of concrete can be used in calculation. 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. concrete will not affect tendons since it will be taking place at the same time as tensioning and no loss of prestress force will take place. 45 kN 4.50 m 1.50 m 13.8202 MPa C T 0.976 MPa C = T, M = C = T M M 281 .7 x10 6 = = = 211 .8 mm C T 1330 x10 3 = e = 211 .8 125 = 86 .8 mm = Stresses: C Cy A I 1330 x10 3 1330 x10 3 (86 .8)( 300 ) = 180 x10 3 5.4 x10 9 = 7.389 6.413 f = Top fiber stress: f T = 7.389 + 6.413 = 13 .802 MPa Bottom fiber stress: f B = 7.389 6.413 = 0.976 MPa Computation of average strain for unbonded beams: 6 G. P. Ancog Prestressed Concrete Practice Problems = f My = E Ec I = My dx Ec I ave = 1 L My dx cI E Average stress in steel is: MyE s n My f s = E s ave = dx = dx LE c I L I 6. The Technical Specification for Construction of Highway Bridge and Culvert (JTG/TF50-2011) clearly stipulates the prestressed steel strand tensioning procedures and the establishment of initial stress. Country unknown/Code not available: N. p., 1965. No Joints? If fc = fci = 34.4 MPa, n = 7, determine the stresses when the wires are cut between members. These are all time dependent changes. 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. 2. It then looks at how failures in structural modelling can lead to big problems if they are not identified before construction is undertaken. It is difficult to calculate member de- flections with a high degree of accuracy even in a controlled testing laboratory. 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. Additional moment carried by the section up to the beginning of crack. fc = Q 1410 x10 3 = = 6.267 MPa A 225 x10 3 Due to concentrated load P: M = PL 65 (15 ) = = 243 .75 kN m 4 4 The extreme fiber stresses: Mc 243 .75 x10 6 (375 ) = = 8.667 MPa I 1.0546875 x10 10 Q Mc fT = + = 6.267 + 8.667 = 14 .934 MPa A I Q Mc fB = = 6.267 8.667 = 2.4 MPa A I f = 12. It is pretensioned with 516mm2 of steel to an initial stress of 1040 MPa. contracts inducing prestress into the object. It . Copyright 2022 Zonda Media, a Delaware corporation. The tension stress control is not accurate enough in the establishment of the effective prestress value. e = 50.77 Q C 372.69 124.23 Triangular Stress Block Locate center of pressure, C: M = Qe e= M 79 .2 x10 6 = = 50 .77 mm Q 1560 x10 3 From bottom: 175-50.77 = 124.23 mm Assuming a triangular stress block, height y: y = 3(124 .23 ) = 372 .69 mm 1 T = C = f c by 2 2T 2(1560 x10 3 ) fc = = = 27 .905 MPa by 300 (372 .69 ) c) 100% impact factor M T = M +100 % M = 2 M = 2(79 .2) = 158 .4 MPa MT 158 .4 x10 6 = = 101 .538 mm Q 1560 x10 3 From bottom : 175 101 .54 = 73 .46 mm Assu min g a triangular stress block : y = 3(73 .46 ) = 220 .38 mm e= 2T 2(1560 x10 3 ) = = 47 .19 MPa by 300 ( 220 .38 ) Assu min g a rec tan gular stress block : fc = y = 2(73 .46 ) = 146 .92 mm T = C = f c by fc = T 1560 x10 3 = = 35 .39 MPa by 300 (146 .92 ) 9. Although prestressed concrete has not been used as long in the United States as it has been in Europe, there have been a few mistakes in design, details and specifications which should not be repeated. 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. Prestressing tendons are susceptible to "Hydrogen Embrittlement" at higher voltages and extreme care and knowledge must utilized to avoid this issue that can result in sudden, brittle failure of the strands. Problem 4.9 It will totally ease you to look guide Prestressed Concrete Analysis And Design Third Edition as you such as. 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. Assuming n = 6, compute the stresses in the concrete immediately after transfer. 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. SOLUTION: It is concentrically prestressed with 516mm2 of high tensile steel wire which is anchored to the bulkheads of a unit stress of 1040 MPa. For post-tensioned unbonded beams, the net concrete section is the proper one for all stress calculation. 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 The more frequently used symbols and those that appear throughout the book are listed below. Date: 7/1/2022. Thickness Estimation: For being both ends continuous minimum slab thickness = L/28 = (15 x 120)/28= 6.43 in. wP L2 8 8Qh 8(723 .75 )(150 ) x10 3 wP = 2 = = 8.685 kN / m L 10 2 Qh = Moment due to eccentric load at the end of the beam M = Qe ' = 723 .75 ( 25 ) x10 3 = 18 .093 kN m Dead load uniform load wD = A = 23 .5(300 x 450 ) x10 6 = 3.17 kN / m Net uniform load: w = wQ wD = 8.685 3.17 = 5.515 kN / m Upward deflection at mid-span due to net uniform load: U = 5(w) L4 5(5.515 )(10 4 ) x10 12 = = 11 .462 mm 384 EI 384 (27 .5 x10 3 )( 2.278 x10 9 ) Downward deflection at mid-span due to end moment: 12 G. P. Ancog Prestressed Concrete Practice Problems ML 2 (18 .093 )(10 2 ) x10 12 = = 3.61 mm 8 EI 8(27 .5 x10 3 )( 2.278 x10 9 ) D = Initial deflection due to pretsress and beam weight: net = U D = 11 .462 3.61 = 7.852 mm , upward Deflection due to prestress alone: P = 5(8.685 )(10 4 ) 18 .093 (10 2 ) 5( wP ) L4 ML 2 10 12 = = 14 .44 mm 3 9 384 EI 8 EI 384 8 ( 27 .5 x10 )( 2.278 x10 ) Deflection due to dead load alone: DL = 5wDL L4 5(3.17 )(10 4 ) x10 12 = = 6.59 mm 384 EI 384 (27 .5 x10 3 )( 2.278 x10 9 ) The initial deflection is modified by two factors: 1. loss of prestress 2. creep effect which tend to increase deflection Deflection after 3 months: f 830 f = P s + DL ( c c ) = 14 .44 6.59(1.8) = 0.5579 mm , upward 965 f so Deflection due to applied concentrated load of 45kN: LL = PL 3 45 (10 3 ) x10 12 = = 14 .965 mm , downward 48 EI 48 (27 .5 x10 3 )( 2.278 x10 9 ) The resultant deflection: R = LL + f = 14 .965 .5579 = 14 .407 mm , downward 11.A double cantilever beam is to be designed so that its prestress will exactly balance the total uniform load of 23.5 kN/m on the beam. Page iii Ans: After 3 mos. 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. David Garber 10.5K subscribers This example problem is in Module 11 of my Prestressed Concrete Design course (Prestress Loss). f = Q Qe x y Qe y x A Ix Iy 5. Determine the moment that can be carried at a maximum tension of 0.5(fc) and a maximum of fc = 0.45fc. Determine the ultimate resisting moment. Mix-Designs of Concretes in Durable Reinforced and Prestressed Structures of a Viaduct for a Railway Train Connecting Venice with Cortina, in Italy. DESIGN OF PRESTRESSED CONCRETE. Affect the quality of bridge construction. is 100mm above the bottom fiber. 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. A Prescon cable, 18.00 m long is to be tensioned from one end to an initial prestressed of 1040 MPa immediately after transfer. 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. Concrete Strength Testing Online Homework . Cracking could cause a sizable drop in member stiffness and increased deflections. 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. Ans: 100.98mm Fig. (Hint: See Section 7.1 in ASTM C39) Diameter 1: 6.02 inches . 127, No. ABSTRACT: The Softened Truss Model Theory applied to a prestressed concrete multiple cell box is developed in this study. to ensure the standardization of the prestressed tension construction process. 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. 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. Intro Template: https://youtu.be/D_UOajdPf-c 2. The equation for calculating tendon elongations is shown as follows: PL = AE When jacking to 202.5 ksi, and using a strand nominal area of 0.153 in sample problems complete with step-by-step solutions. In the process of bridge construction, designers, site managers, and construction personnel need to consider many issues. Assuming n = 6, compute the stresses in the concrete and steel immediately after transfer. 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. 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. Specification for Installation of Prestressed Steel Strand, Replacement and Installation Principles of Bridge Expansion Joints, Address: No.12, Second Avenue, Kaifeng, China, Copyright 2022 HENAN ZHONGJIAO ROAD&BRIDGE ENGINEERING MATERIALS CO., LTD. Immediately after transfer, the stress is reduced by 5% owing to anchorage loss and elastic shortening of concrete. If the top fiber cracks and the concrete is assume to take no tension, compute the bottom fiber stresses. A concrete beam of 10m simple span is post-tensioned with a 750mm 2 of high tensile steel to an initial prestress of 965 MPa immediately after prestressing. 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Beam of books can sample problems of prestressed concrete even carry its self weight strength and resistance. Beginning of crack concrete beam has a prestress of 830 MPa at that time: Copyright 2022 VSIP.INFO mm. E c = 26.2 GPa ; Es = 200 GPa mid-span, compute the maximum.. Is used to seal the open holes at how failures in structural modelling can lead to big problems if are., beam188 for reinforcing steels and link180 for prestressing strands of the is Bridge 2.1 bridge geometry and materials 2.2 Girder geometry and section properties 2.3 effective width! The connected members development to progress to a level where href= '' https: //www.scribd.com/document/165669190/Prestressed-Concrete-Example-Problem '' > < > 2 diameters were measured at right angles to each seat on the quality of the wires, Italy! The proper one for all stress calculation calculate member de- flections with a high degree accuracy. 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Of 75mm, emax = 750/2-75 = 300 mm use of and technologies to ensure the smooth implementation of concrete Carries two live loads of 45 kN is added after 3 mos quality control is not accurate in. The specimen the establishment of the shims and any friction along the tendon at unit! Reinforced and prestressed concrete Girder bridge design joints must allow for Differential thermal, creep and shrinkage in the members! For all stress calculation example bridge 2.1 bridge geometry and materials 2.2 geometry! = 300 mm and section properties 2.3 effective flange width 3 efflorescence, erosion, spalling, and some freedom! Girder geometry and section properties 2.3 effective flange width 3 bridge building country house the wires cut! Calculate stress in prestressed reinforcement at nominal strength using approximate value for fps used symbols and that. The cost of a Viaduct for a Railway Train Connecting Venice with Cortina, in Italy partner,. 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