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:
But 700 need not be less than 2
and shall not be greater than 5
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.
The simply supported post-tensioned beam shown below and:
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 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.
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:
[email protected] = 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
0.6 28 0.66 1.0 0.75 0.6√5000 700 0.66 16 28 /1000 169 Remember that:
0.75 2 1.0√5000 16 28
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
80 16 12
60,000 16 12
0.16 270 12 28
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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