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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
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
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
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 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.
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
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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