Post-Tensioned Concrete Fundamentals

Also note that the above stress checks only address

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Unformatted text preview: Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course superimposed dead load, and pre-stress). These checks are to preclude excessive creep deflection and to keep stresses low enough to improve long term behavior. Note that the specified 28-day concrete compressive strength is used for these stress checks. The maximum permissible concrete stresses at the service load state are as follows: 0.45 Extreme fiber stress in compression: 0.60 Extreme fiber stress in tension: If the above stresses are exceeded, then additional bonded reinforcement shall be provided in the tensile zone to resist the total tensile force. Also note that the above stress checks only address serviceability. Permissible stresses do not ensure adequate structural strength. The tensile stress in pre-stressing steel shall not exceed the following: Due to Jacking Force: 0.94 But not greater than 0.80 manufacturer. or the maximum recommended by the anchor Tendons Immediately After Transfer: 0.70 is the specified tensile strength of the pre-stressing steel and is the In the above, specified yield strength of the pre-stressing steel. The most commonly used prestressing steel in the United States is Grade 270, low-relaxation, seven wire strand, defined by ASTM 416. Therefore, for this common pre-stressing steel, = 270 ksi and = 0.90 or 243 ksi. Permissible stresses for other type of pre-stressing steel, including deformed bars, vary slightly and can be found in the ACI 318 commentary. Since the scope of this article is limited to unbonded post-tensioned systems, and we will only be considering Grade 270 low-relaxation steel, the permissible stresses for other steels are not given here. Minimum Bonded Reinforcing All flexural members with unbonded tendons require some amount of bonded reinforcing. For beams and one-way slabs, this bonded reinforcing is required www.SunCam.com Copyright 2010 John P. Miller Page 32 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course regardless of the services load stresses. For two-way slabs, the requirement for this bonded reinforcing depends on the services load stresses. This bonded reinforcing is intended to limit crack width and spacing in case the concrete tensile stress exceeds the concrete's tensile capacity at service loads. ACI requires that this bonded reinforcement be uniformly distributed and located as close as possible to the tension face. For beams and one-way slabs, the minimum area of bonded reinforcing is: 0.004 is defined as the area of that part of the cross section between the flexural tension face and the center of gravity of the cross-section. is graphically defined below for several typical cross sections. Act NA NA NA Act NA Act Rectangular Beam TEE Beam (Negative Flexure) One-Way Slab For two-way post-tensioned slabs with unbonded tendons, bonded reinforcing is not required in positive moment areas (in the bottom of the slab) if the extreme fiber tension at service loads, after all pre-stress losses, does not exceed the following: 2 , so a Recall that the maximum extreme tension fiber stress in a two-way slab is 6 minimum amount of bottom steel is required for tensile stresses in the range of: 2 6 For two-way post-tensioned slabs with unbonded tendons, the minimum area of bonded reinforcement in positive moment regions is: 0.5 www.SunCam.com Copyright 2010 John P. Miller Page 33 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Where is the tension force in the concrete due to unfactored (service) dead plus live load and is illustrated below. CG Nc When 2 0.5 6 ft For two-way post-tensioned slabs with unbonded tendons, the minimum area of bonded reinforcement required in negative moment regions at column supports is 0.00075 Where is defined as the area of the larger gross cross-sectional area of the slabbeam strips in two orthogonal equivalent frames intersecting at the column. The dimensions and geometry are as defined in ACI 318 Chapter 13 – Two-Way Slab Systems and will not be reiterated here. The bonded reinforcing required in negative moment regions at columns shall be distributed between lines that are 1.5h outside both sides of the face of the column support, shall be a minimum of four bars, and shall be spaced no more than 12" on center. ACI 318 also requires a minimum length of bonded reinforcing in positive and negative moment regions. It should be evident that the minimum lengths and areas of bonded reinforcement required by the ACI 318 may be exceeded by structural demand, as we will see later on. The minimum length of bonded reinforcing is shown below. As ⁄6 ⁄6 As As As As 0.33 Clear Span ⁄6 ⁄6 0.33 Clear Span Minimum Lengths of Bonded Reinforcing www.SunCam.com Copyright 2010 John P. Miller Page 34 of 49 Fundamentals of Post‐Tensioned Concrete Design for Bu...
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