Unformatted text preview: Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course superimposed dead load, and prestress). These checks are to preclude excessive
creep deflection and to keep stresses low enough to improve long term behavior. Note
that the specified 28day 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 prestressing 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 prestressing steel and
is the
In the above,
specified yield strength of the prestressing steel. The most commonly used prestressing steel in the United States is Grade 270, lowrelaxation, seven wire strand,
defined by ASTM 416. Therefore, for this common prestressing steel,
= 270 ksi
and = 0.90 or 243 ksi. Permissible stresses for other type of prestressing 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 posttensioned systems, and we will only be considering Grade 270
lowrelaxation 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 oneway 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 twoway 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 oneway 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 crosssection.
is graphically defined below for
several typical cross sections.
Act
NA NA
NA Act NA Act Rectangular Beam TEE Beam (Negative Flexure) OneWay Slab For twoway posttensioned 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 prestress losses, does not exceed the following:
2 , so a
Recall that the maximum extreme tension fiber stress in a twoway slab is 6
minimum amount of bottom steel is required for tensile stresses in the range of:
2 6 For twoway posttensioned 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 twoway posttensioned 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 crosssectional 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 – TwoWay 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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