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Unformatted text preview: at the edge of the floor plate, only half of the
larger bay is used. Therefore,
0.00075 0.00075 1920 1.44 . . The width over which this area of bonded reinforcing is distributed is 1.5h on both sides
of the column face, or 16 + (2x1.5x8) = 40 inches. The minimum length extended
beyond the column face is one-sixth the clear span, or (20-1.33)/6 = 3.11 feet. So, we
will use 5#5 top bars, 7'-7" long, equally spaced in a 40-inch wide strip centered on the
column, both ways. 5#5 x 7'‐7 both ways 5#5 x 7'‐7 both ways 14#5 x 6'‐3 both ways 20'‐0" span Minimum Bonded Reinforcing – Two-Way Slab Example www.SunCam.com Copyright 2010 John P. Miller Page 38 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Ultimate Flexural Strength
Let us now begin our investigation into the ultimate flexural strength of a pre-stressed
member. The design moment strength may be computed using the same methodology
used for non pre-stressed members. That is, a force couple is generated between a
simplified rectangular compression block and the equal and opposite tensile force
generated in the reinforcing steel, which is in our case pre-stressing steel.
For purposes of this course, we will narrow our focus to post-tensioned members with
unbonded tendons, and we will use the approximate values for the nominal stress in the
pre-stressing steel, fps, instead of using strain compatibility. For more accurate
determinations of the nominal stress in the pre-stressing steel, and for flexural members
with a high percentage of bonded reinforcement, and for flexural members with prestressing steel located in the compression zone, strain compatibility should be used.
Referring to the figure below: b C a dp T The rectangular compression block has an area equal to a times b. Equating the
compression resultant, C, to the tensile resultant, T, the nominal moment capacity can
be written as: Where is 2 2
2 the area of pre-stressed reinforcement, is the stress in the pre-stressed reinforcement at nominal moment strength, and is the strength reduction factor (0.90
for flexure). ACI 318 defines the approximate value for can be calculated as follows,
depending on the span-to-depth ratio:
www.SunCam.com Copyright 2010 John P. Miller Page 39 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course For ≤ 35: For 10,000 100 60,000 > 35: 10,000 300 30,000 Where is the effective stress in the pre-stressing steel after all losses. The depth of
the compression block is defined as: 0.85
The simply supported post-tensioned beam from page 12 and shown below.
= 7000 psi = 270 ksi = 684 kips
16" x 36" beam with 7" x 100" flange
26 ½" diameter tendons; = 26 x 0.153 = 3.98 sq. in.; 14" = 3.98/(16x32) = 0.00777 Neutral Axis Drape = 18" Span Length L = 60' – 0" www.SunCam.com Copyright 2010 John P. Miller Page 40 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Find:
The nominal moment capacity, , neglecting any bonded reinforcing. Solution:
The span-depth ratio is 60/3 = 20 which is less than 35. Therefore, 10,000 100 684 1000
3.98 . .
190.9 7000 100 0.00777 Use 191 ksi 270 60,000 10,000 231.9 Next, determine depth of compression block, a: 0.85 3.98 . . 191 0.85 7 100 1.28 7 Now we can compute the nominal flexural capacity at mid-span of this beam section: 0.90 3.98 2 . 1788 1.28 . 1
2 32 . . 191 Let's now consider including the contribution of the bonded reinforcing steel to the
nominal moment capacity. Assuming the bonded reinforcement is at the same depth as
the pre-stressing steel in the beam (a slightly conservative assumption since the center
of gravity of the mild reinforcing is often closer to the face of the beam, i.e. deeper, than
the center of gravity of a bundle of tendons), the tensile component of the moment
couple becomes the sum of both pre-stressing steel and the bonded reinforcement and
can be written as follows: www.SunCam.com Copyright 2010 John P. Miller 2
Page 41 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course The depth of the compression block then becomes: 0.85
The simply supported post-tensioned beam from the previous example. In addition to
the post-tensioning tendons, the beam has 3#10 bars in the bottom with a yield strength
of 60 ksi.
The nominal moment capacity, , including the bonded reinforcing. Solution:
From the previous example, the effective stress in the pre-stressing steel at nominal
moment strength is unaffected by the bonded reinforcing and so it is the same:
191 Determine depth of compression block, a: 0.85
3.98 . . 191 0.85 7 3 1.27 .
100 . 60 1.66 . 7 And the nominal flexural capacity of this beam section is: 0.90 3.98 191 www.SunCam.com 2 3 1.27 60 32 1.66 1
2 12 2311 Copyright 2010 John P. Miller Page 42 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part O...
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This document was uploaded on 01/28/2014.
- Spring '14