Post-Tensioned Concrete Fundamentals

6 but 700 need not be less than 2 and shall not be

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Unformatted text preview: ne A SunCam online continuing education course Ultimate One-Way Shear Strength The treatment of one-way, or so called "beam shear," will not be rigorous in this course. ACI 318 offers a simplified approach to computing the shear capacity of a pre-stressed member and this is what will be used here. In general, just as in a non pre-stressed member, the following basic equation must be satisfied: Where is the strength reduction factor (typically 0.75 for shear), is the nominal shear capacity, and is the ultimate, or factored, applied shear demand. The nominal shear capacity is the sum of the nominal shear strength provided by the concrete, , and the nominal shear strength provided by the steel, , and is written as follows: For pre-stressed members, the nominal shear strength provided by the concrete is: 0.6 But 700 need not be less than 2 and shall not be greater than 5 and / shall not be greater than 1.0. is a modification factor for lightweight concrete. A minimum amount of shear reinforcement is required anytime the ultimate applied shear demand, , is greater than 0.5 . The minimum amount of shear reinforcing is the largest of: 0.75 50 80 Note that the only place the pre-stressing force comes into play is the third equation above. Otherwise, the minimum amount of shear reinforcement for pre-stressed www.SunCam.com Copyright 2010 John P. Miller Page 43 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course members is identical to that for non pre-stressed members. The design of concrete members for torsional forces is outside the scope of Part One of this course but will be covered in Part Two. Likewise, the investigation of the shear strength of two-way slabs is not covered here in Part One but will be covered in Part Two. Where shear reinforcement is required by structural demand, that is when , and it is perpendicular to the axis of the member, the nominal shear strength provided by the steel is: Therefore, the nominal shear capacity of a pre-stressed concrete member may be written as: gives: Solving for the required area of shear reinforcing The maximum spacing of shear reinforcement in pre-stressed members shall not be greater than 0.75h nor 24 inches. Example Given: The simply supported post-tensioned beam shown below and: o o o = 5000 psi = 60 ksi = 270 ksi www.SunCam.com Copyright 2010 John P. Miller Page 44 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course o o o o 16" x 36" beam 16-½" diameter tendons; = 16 x 0.153 = 2.45 sq. in. Beam dead load = 3.0 klf, unfactored; beam live load = 1.5 klf, unfactored 24" x 24" columns 14" Neutral Axis d = 28" Center‐to‐Center of Columns L = 60' – 0" Find: Design the shear reinforcing at a distance "d" from the face of the support. Solution: The factored uniformly distributed load is: 1.2 3.0 1.6 6.0 30 1.5 6.0 / 180 This yields a shear diagram as follows: Vu@d = 160 kips 180 K 40" www.SunCam.com 30'‐0" Copyright 2010 John P. Miller Page 45 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course At a distance d = 28 inches from the face of support, or 40 inches from the centerline of the support, the factored shear and moment are: 180 @ @ 12 6.0 / 180 3.33 160 567 2 700 160 12 160 2.33 567 0.6 28 0.66 1.0 0.75 0.6√5000 700 0.66 16 28 /1000 169 Remember that: 5 2 0.75 2 1.0√5000 16 28 47.5 0.75 169 5 1.0√5000 16 28 118.8 118.8 . This is the maximum nominal shear strength Therefore we must use that can be provided by the concrete alone. Let's now compute the amount of shear reinforcing required by structural demand at a distance "d" from the face of the support: 160 118.8 0.75 60 28 12 0.39 #@ As a check, let's find the minimum amount of shear reinforcing required and will be the largest of the following three results: www.SunCam.com Copyright 2010 John P. Miller Page 46 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course 0.75 0.75√5000 80 50 50 2.45 80 16 12 60,000 16 12 60,000 0.17 0.16 270 12 28 16 60 28 / 0.08 / None of these are greater than the reinforcing required by structural demand and so the minimum shear reinforcing does not control. Therefore, #5 @ 18 " o.c. double leg stirrups would work, giving us 0.41 in2 per foot. Most designers would space the stirrups in convenient groups of incrementally larger spacing away from the support until they are no longer required by structural demand or minimum reinforcing requirements. However, it is common practice to use stirrups throughout the entire span to have something to which to tie the tendon bundle support bars. www.SunCam.com Copyright 2010 John P. Miller Page 47 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Conclusion Part One of this two-part course covers many of the fundamentals of post-tensioned concrete for building structures using unbonded tendons. With a good understanding of the material in Part One of this course, you should know something about the historical background of post-tensioned concrete and the difference between post-tensioned members and pre-tensioned members. You should also understand the load balancing concept, hyperstatic moments, pre-stress losses, and the basic requirements of ACI 318 (Building Code Requirements for Structural Concrete). We also covered nominal flexure and shear capacities of post-tensioned members, including a few examples. Specifically, you should now be able to: Compute effective pre-stress force Fe for a given drape and balanced load Understand allowable stresses according to ACI 318-08 Understand pre-stress losses Compute the balanced and hyperstatic moments for a continuous structure Determine the minimum amount of flexural and shear reinforcing required Calculate the nominal moment capacity Mn and nominal shear capacity Vn of a cross section To be comfortable performing a preliminary design by hand or to be able to quickly check a computer generated design or an existing design by hand, Part Two of this course must also be completed. In Part Two, we will use the material learned in Part One to design several different structural systems commonly used in buildings and parking structures, including a one-way slab, a two-way slab, and a continuous beam. Also in Part Two, several more advanced topics are covered, such as punching shear for two-way slabs, anchorage zone design, deflections, redistribution of moments, and torsion in beams. Several important practical issues, such as constructability and pour strips, are also addressed. www.SunCam.com Copyright 2010 John P. Miller Page 48 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course References Building Code Requirements for Structural Concrete, ACI 318-08, American Concrete Institute, 2008. Notes on ACI 318-08, Portland Cement Association, 2008. Design of Prestressed Concrete Structures, T.Y. Lin and Ned H. Burns, Third Edition, John Wiley & Sons, 1981 Design Fundamentals of Post-Tensioned Concrete Floors, Bijan O. Aalami & Allan Bommer, Post-Tensioning Institute, 1999 Design of Post-Tensioned Slabs Using Unbonded Tendons, Post-Tensioning Institute, Third Edition, 2004 Post-Tensioning Manual, Post-Tensioning Institute, Fourth Edition, 1985 Precast and Prestressed Concrete, PCI Design Handbook, Precast Concrete Institute, Third Edition, 1985 www.SunCam.com Copyright 2010 John P. Miller Page 49 of 49...
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This document was uploaded on 01/28/2014.

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