sample problems of prestressed concrete

The parabolic cable has an area of 1612.9mm2, n = 6. For post-tensioned members, the prestressing force in a tendon is applied through the anchorages as a concentrated force. 001188 193000000 = = = Pel = 0 (3) Friction losses Assuming that the parabolic tendon approximates the shape of an arc of a circle . Jeffrey Luin. The c.g.s. (18-3) reduces to: It took until, the 1920s and 30s for its materials development to progress to a level where. Estimate the deflection after 3 mos. 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. 127, No. In such a case, the failure is brittle in character (Section 6.4.1). 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 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. The following 2 diameters were measured at right angles to each . Date: 7/1/2022. For post-tensioned and bonded beams, for any load applied after the bonding has taken place, transformed section should be used. = 0.5579mm upward; When 45 kN is added after 3 mos. 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. For post-tensioned unbonded beams, the net concrete section is the proper one for all stress calculation. 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 compression in concrete is 5.50 MPa along the length of tendon. 5 G. P. Ancog 175 Mid span section Prestressed Concrete Practice Problems Solution To be theoretically exact, net concrete section should be used up to the time of grouting, after which the transformed section should be considered. prestressed-concrete-problems-and-solutions 5/6 Downloaded from cobi.cob.utsa.edu on October 31, 2022 by guest Concrete is an integral part of twenty-first century structural engineering, and . StructuresNuclear Science AbstractsPrestressed ConcreteProblems & Solutions Prestressed Concrete, 2eFinite Element Analysis of Prestressed Concrete Structures Using Post-Tensioning SteelPrestressed ConcreteJournal - Prestressed Concrete InstituteSix-minute Solutions for Structural I PE Exam Problems Precast concrete garages are usually . In most cases, these provisions are fol- . This page intentionally left blank. Positive bending about a horizontal axis causes tension in the bottom . Extreme Fiber Calculation 5. It . 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. These are all time dependent changes. Joints must allow for differential thermal, creep and shrinkage in the connected members. Section Properties: Ag = bh = 300 x 600 = 180000 mm 2 Ig = 1 1 bh 3 = (300 x 600 3 ) = 5.4 x10 9 mm 4 12 12 Initial condition M = f = wL 2 4.4 x12 2 = = 79 .2 kN m 8 8 Qo Q ey My 1560 x10 3 1560 x10 3 (125 )( 300 ) 79 .2 x10 6 (300 ) o = Ag Ig Ig 180000 5.4 x10 9 5.4 x10 9 = 8.667 10 .833 4.40 Top fiber stress: f T = 8.667 10 .833 + 4.4 = 2.234 MPa Bottom fiber stress: f B = 8.667 + 10 .833 4.4 = 15 .10 MPa Final condition Live load moment at mid-span: M L = Pa = 45 ( 4.5) = 202 .5 kN m Dead load moment at mid-span: MD = wL 2 4.4(12 2 ) = = 79 .2 kN m 8 8 Total moment: MT = 79.20 + 202.5 = 281.7 kN-m Stresses: f = Q Qey M T y Ag Ig Ig 1330 x10 3 1330 x10 3 (125 )( 300 ) 281 .7 x10 6 (300 ) 180 x10 3 5.4 x10 9 5.4 x10 9 = 7.389 9.236 15 .65 f = 5 G. P. Ancog Prestressed Concrete Practice Problems Top fiber stress: f T = 7.389 9.236 + 15 .65 = 13 .803 MPa Bottom fiber stress: f B = 7.298 + 9.236 15 .65 = 0.975 MPa Note: For pre-tensioned beam, steel is always bonded to the concrete before any external moment is applied. Ans: fT = 0.00 MPa; fB = +16.918 MPa initial cgc cgc e 300 200 Fig. 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: This example goes through how to calculate prestress loss of a. Compute the critical fiber stresses. In prestressed concrete, prestress is the permanent force in the member, causing compressive stress at the level of steel. Problem 4.9 Premature failure of prestressing steel in prestressed concrete structures is usually induced by corrosion. The prestressing system works for a span greater than 35 m. Prestressing will increase the shear strength and exhaustion resistance of concrete. Live Load Distribution in a Slab-on-Girder Bridge Subjected to Corrosion and Differential Settlement. Insufficient initial stress in the tensioning stage causes the effective prestress to fail to meet the bridge design requirements. A new requirement was seen to be entering specifications whereby the quantity of bleeding of water and air from the grout should be determined in accordance with fib Bulletin 20 Guide to good practice: Grouting of tendons in prestressed concrete (2002). Concrete Construction: Resources for contractors and specifiers including construction methods, materials and practices. convergence. 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. In the process of bridge construction, detailed and sufficient analysis of the properties of the project, material properties, and equipment performance is carried out, the project is specifically qualitative, and the appropriate method is selected to solve the effective prestress problem, instead of uniformly selecting the tension method to deal with prestressed concrete. After the tensioning work is completed, high-grade micro-expansion concrete is used to seal the open holes. 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. This is why we offer the books compilations in this website. contracts inducing prestress into the object. Affect the quality of bridge construction. 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. SOLUTION: 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. The intentions were very sound, but the reality was ; except for concrete cast against and permanently exposed to earth, where minimum cover shall be 3 inches. 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. If the beam is picked up suddenly so that an impact factor of 100% is considered compute the maximum stresses. 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 . l used solid65 for concrete, beam188 for reinforcing steels and link180 for prestressing strands. If the prestressed steel strand is broken, use the jack to remove all the prestressed steel strands, replace them with new prestressed steel strands, and re-tension the strands. If fc = fci = 34.4 MPa, n = 7, determine the stresses when the wires are cut between members. Country unknown/Code not available: N. p., 1965. The beam carries two live loads of 45 kN each in addition to its own weight of 4.40 kN/m. For approximation, gross area of concrete can be used in calculation. a) volume of concrete = 1 m 3 b) volume of cement = (mass of cement / specific gravity of cement) x (1/100) = (383.2/3.15) x (1/1000) = 0.122 m 3 c) volume of water = (mass of water / specific gravity of water) x (1/1000) = (191.6/1) x (1/1000) = 0.1916 m 3 d) volume of total aggregates = a - (b + c ) = 1 - (0.122 + 0.1916) = 0.6864 m 3 e) mass 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. of 17 Prestressed Concrete Practice Problems 1. 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. Page ii 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. 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. Bridge engineering construction investment is large, the construction period is long, and the quality control is difficult. Prestressed Concrete Practice Problems For bundled bars, minimum concrete cover shall be equal to the equivalent diameter of the bundle, but need not be greater than ____ in. It is difficult to calculate member de- flections with a high degree of accuracy even in a controlled testing laboratory. 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. Moment for zero tensile stress at the bottom: Q Qey My + =0 A I I 1296 .8 x10 3 1296 .8 x10 3 (125 )( 300 ) Mx 10 6 (300 ) 0= + 180 x10 3 5.4 x10 9 5.4 x10 9 M = 291 .78 kN m 8M 8( 291 .78 ) w= 2 = = 16 .21 kN / m L 12 2 fB = Top fiber stress: Q Qey My + A I I 3 1296 .8 x10 1296 .8 x10 3 (125 )( 300 ) 281 .78 x10 6 (300 ) = + 180 x10 3 5.4 x10 9 5.4 x10 9 = 13 .853 MPa fT = 2. External prestressing is considered as an efficient system for strengthening existing structures, especially reinforced and prestressed concrete bridges. However, the problems that arise during the construction of prestressed concrete need to be solved by scientific and effective measures to ensure the smooth development of the construction of prestressed concrete bridges. Hence there is creep strain in the member. 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. A Prescon cable, 18.00 m long is to be tensioned from one end to an initial prestressed of 1040 MPa immediately after transfer. Partial Prestressing, From Theory to Practice M.Z. country unknown/code not available: n. p., 1965. Can the cylinder be tested? Each case is analyzed to identify its cause and how it might have been prevented. 4 yo 50x75 cgs 75 Beam Section cgs 75 Solution Method 1: Using net section of concrete Ac = Ag Aduct = 200 x300 50 x75 = 56250 mm 2 3 G. 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. A Prescon cable, 18.00 m long is to be tensioned from one end to an initial prestressed of 1040 MPa immediately after transfer. 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. When calculating the first stage elongation, it is common practice to break the force coefficient diagram into two parts, identified as areas A and B in the above diagram. Chapter 4: Operational Amplifiers A Prescon cable, 18.00 m long is to be tensioned from one end to an initial prestressed of 1040 MPa immediately after transfer. It is eccentrically prestressed with 516mm2 of high tensile steel wire which is anchored to the bulkheads at a unit stress of 1040 MPa. 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. Prestressed concrete construction requires complicated crafts and technologies to ensure the smooth implementation of the project. This had been emphasised in lectures. 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. Bearing resistance may be reduced by axial forces, with serious bracket stresses and often splitting of the concrete seat on the beam. Dead load = 150 x (6.50/12)) = 81 psf Live load = 100 psf = 14.407 mm downward. 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. Values of A, y and I should be computed on the basis of transformed section. Most recognised that the presence of untensioned reinforcement causes a loss of prestress in the concrete but the question asked for the effect of the loss of force in the tendon where the loss of force is reduced. This is especially true in prestressed concrete applications, particularly when mem- bers are allowed to develop cracks under service loads. In the process of bridge construction, designers, site managers, and construction personnel need to consider many issues. 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. 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. Assume a gross cover of 75mm, emax = 750/2-75 = 300 mm. 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 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. ABSTRACT: The Softened Truss Model Theory applied to a prestressed concrete multiple cell box is developed in this study. A pretensioned member has a section 200mmx300mm. Mix-Designs of Concretes in Durable Reinforced and Prestressed Structures of a Viaduct for a Railway Train Connecting Venice with Cortina, in Italy. n My dx L I x 2 M = M o 1 L 2 fs = x y = y o 1 L 2 n fs = LI 2 2 x 2 L 2 M o y o 1 L 2 dx L 2 L/2 nM o y o 2 x3 x5 = + x LI 3 ( L 2 ) 2 5( L 2 ) 2 L 2 = 8 nM o y o 8 (15 .258 ) = 8.137 MPa = 15 I 15 Resultant stress in steel: fsf = 830 + 8.137 = 838.137 MPa Ultimate strength analysis: .85fc a/2 a = 1c C c = 0.0034 c d z T s C = .85 f c ' ba = T = As f s ' a= As f s ' C = .85 f c ' b .85 f c ' b z = d a 2 M = As f s ' ( d a 2 ) 7. 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. B. It is pretensioned with 516mm2 of steel to an initial stress of 1040 MPa. If the beam carry a 45 kN Moment concentrated to prestressload applied at mid-span when the beam is 3 mos.

Calamity Melee Weapons, Cd Ciudad De Lucena Vs Ad Cartaya, Harlow Greyhound Tips, Celebrationmk10 Console, Complete Polish Shine On The Go Kit, Barber License Renewal Florida, Rhodes College Class Roster, Sociology Essay Introduction, Httprequestexception Status Code, Usa Women's Volleyball Live, Norton Antivirus Premium Apk, Sugar Magnolia Takery,