PC Strand Basics

PC strand, also known as prestressed concrete strand, is a type of steel reinforcement used in construction. It is made by taking high-tensile steel wire and subjecting it to a process known as prestressing.

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During the prestressing process, the steel wire is stretched to a specific tension and then anchored in place. This creates a compressive force within the concrete that counteracts any tensile forces that may occur during the life of the structure. As a result, PC strand is able to provide a higher level of strength and stability to concrete structures than traditional reinforcing methods.

PC strand is typically made from high-carbon steel and is available in a variety of sizes and grades to suit different construction needs. The wire is made by drawing it through a series of dies to achieve the desired size and shape.

PC Strand Uses

PC strand is used in a variety of construction projects, including bridges, buildings, and other infrastructure projects. It is used to reinforce concrete in pre-tensioned and post-tensioned applications. It is also used in the construction of parking garages, stadiums, and other large structures. It can also be used in the repair and retrofitting of existing structures.  One of the most common uses of PC strand is in pre-tensioned concrete. This method of prestressing involves stretching the PC strand before the concrete is poured, and then anchoring the strand in place. The concrete is then poured around the strand, creating a compressive force that counteracts any tensile forces that may occur during the life of the structure.

In addition to its strength and stability benefits, PC strand also offers other advantages over traditional reinforcing methods. For example, it requires less steel overall, which can reduce the overall weight of the structure and decrease the amount of steel needed to be produced. This can also help to reduce the overall cost of the project.

Another advantage of PC strand is that it can be easily cut and bent to fit into tight spaces, making it an ideal solution for structures with complex or irregular shapes. Additionally, its smooth surface can help to reduce the risk of concrete cracking and improve the durability of the structure.

Madison Steel Is Your Source

PC strand is made in many countries worldwide, with the United States being the largest producer. In the US, Madison Steel is one of the leading distributors of PC strand. They offer a wide range of products for different applications such as bridges, buildings, and other infrastructure projects.

Overall, PC strand is a versatile and reliable reinforcement option for concrete structures. Its ability to provide a high level of strength and stability makes it an ideal choice for a wide range of construction projects. With the help of logistic professionals like Madison Steel, Prestressed strand is widely available and can be easily incorporated into any construction project.  Call 404-343-, us at [ protected] or visit us online at madisonsteel.com/customize-my-solution/ for a quote.

PC strand

PC Strand, or prestressed concrete steel strand, is a twisted steel cable composed of 2, 3, 7 or 19 high strength steel wires and is stress-relieved (stabilized) for prestressed concrete or similar purposes.

 

Classification

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PC strand is classified according to the number of steel wires in a strand: 2 wire strand, 3 wire strand, 7 wire steel strand[1] and 19 wire steel strand. It can be classified according to the surface morphology and can be divided into: smooth steel strand, scoring strand, mold pulling strand (compact), coated epoxy resin steel strand. They can also be classified by diameter, or intensity level, or standard.

 

Specifications

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In the description and list of the table we often see, there are 15-7Φ5, 12-7Φ5, 9-7Φ5 and other specifications of the prestressed steel strand. To 15-7Φ5, for example, 5 said a single diameter 5.0mm of steel, 7Φ5 said seven of the steel wire to form a strand, and 15 that the diameter of each strand of 15mm, the total meaning is "one The beam consists of 7 strands of diameter 15 mm (each having a total diameter of about 15.24 mm, a dimensional deviation +0.40 -0.20; a diameter of about 5.0 mm per filament). The general sectional area is calculated according to 140mm ^ 2. The theoretical breaking value is 140 * = 260.4 kN, which can withstand the tension of 156.24-169.26 kN according to the prestressing standard of 60% -65%.

 

Materials

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Using high-carbon steel wire rod, after surface treatment it is cold drawn into steel wire, and then the strand structure will be a number of steel wires stranded into shares. Next the elimination of stress by way of a stabilization process. In order to extend durability, the wire can have metal or non-metallic coatings, such as galvanized, or epoxy resin coating. In order to increase the bond strength with the concrete, the surface can have nicks and so on. The prestressed strands of the mold are twisted to form a mold compression process, the structure is more compact, and the surface layer is more suitable for anchoring. Production of unbonded prestressed steel strand (unbonded steel strand) using ordinary prestressed steel wire, coated with oil or paraffin after the packaging into high-density polyethylene (HDPE) bags.

 

Features

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The main characteristic of the prestressed steel strand is high strength and relaxation performance is good, the other when the more straight. Common tensile strength levels of MPa, as well as , , , , MPa and the like intensity levels. The yield strength of this steel is also higher.

 

Application

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In most of the post-tensioned and pre-tensioned prestressed project, smooth steel strand is the most widely used prestressed steel. Stranded strand is mainly used to enhance the project, but also for nuclear power and the like works. Galvanized steel strand commonly used in the bridge of the tie rod, cable and external prestressing works. Epoxy coated steel stranded wire is similar to galvanized prestressed steel wire.

 

Standards

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Countries have standards for prestressed strand, such as: China Standard GB / T , American Standard ASTM A416, British standard BS and the Japanese standard JIS G, the Australian standard AS / NZS , Brazilian standard NBR-[2]

 

References

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PGSuper: Permanent Strands

This tab allows you to specify the possible locations of permanent prestressing strands.

General Information

The strand grid defines the possible locations of permanent strands in a girder and the order in which the strand positions are filled. Another way to think of this is a template for strand placement. Actual strands are placed in a project by specifying the number of strands, or by individually selecting locations, to be filled in the template in the Strands Tab of the Girder Editing dialog.

There are two basic types of permanent strands.

Straight Permanent Strands can be placed anywhere within a girder section and are straight along the entire length of the girder.

Adjustable Strands are permanent strands that have the unique capability to be vertically adjusted within the web region of a girder. Adjustable strands can only be placed in the girder's web(s). There are two types of Adjustable Strands: Harped Strands and Adjustable Straight strands.

Harped strands are draped at the girders harping points. Harping (draping) is created by the difference in vertical adjustment between the strand group at the girder ends and harping points.

Adjustable Straight Strands are straight along the entire length of the girder. The entire group can be vertically adjusted. Adjustable Straight Strands located above the girder's upper kern location can be used by the automated design algorithm to alleviate girder end stresses.

Permanent strands are placed and tensioned at casting time and remain in the girder for its lifetime. Adjustable strands are bonded along the entire length of the girder. Individual straight strands can be debonded only if the "allow debonding" option is selected for the strands in question.

Adjustable Strand Settings

Item Description Adjustable Strand Type The type of adjustable strands can be designated as Straight, Harped, or "Harped or Straight". If "Harped or Straight" is selected, the type of strand can be set by the end user when editing the girder. Coerce Odd Number of Adjustable Strands When selected, PGSuper will force (coerce) the highest (last in the fill order) pair of adjustable strands to alternate between a single strand at X=0.0, and two strands at the prescribed +/- X values. This allows a strand grid that contains only pairs of coordinates to place strands one at a time. This feature is uncommonly needed for most users, and is used on some WSDOT I-Beams or Ribbed Girders with an odd number of webs. Use Different Harped Locations at Girder Ends This option allows you to define different locations of a harped strand at the ends of the girder and at the harping points. This option is most often used to describe the "fanned" harped bundles at harping points used on WSDOT I girders.

NOTE: All end strands in the web strand grid must have positive X values (i.e., filled in pairs) when the "Coerce Odd Number of Harped Strands" option is selected.

NOTE: The "Use Different Harped Strand Locations at Girder Ends" option is not needed if the relative distance between harped strands is the same along the entire length of the girder (i.e., strands are always parallel). In this case, harping is achieved by adjusting the vertical offset of strand patterns at the girder ends and harping points.

Strand Grid (Potential Strand Locations)

The strand grid lists the possible strand locations and fill order of permanent straight and adjustable strands in the girder.

Item Description Fill # Fill sequence number Xb,Yb Strand position at the harping point measured from the bottom center of the cross section Type Strand Type Xt,Yb Strand position at the ends of the girder measured from the top center of the cross section [Insert] Insert a strand position at the current location in the grid [Append] Append a strand position at the end of the fill sequence [Edit] Edit the strand position description. See Strand Location. [Delete] Delete the selected strand positions [Move Up] Moves a selected strand position up in the fill sequence [Move Down] Moves a selected strand position down in the fill sequence [Reverse Adjustable Strand Sequence] Reverses the fill sequence of the adjustable strands [Generate Strand Positions] Activates a tool to generate a uniform layout of strand positions

NOTE: Double click on a strand position to quickly edit its properties

NOTE: The strand grid shows the strand positions on both sides of the vertical axis of the cross section

NOTE: Strands listed as "Straight" are straight strands and cannot be debonded

NOTE: Strands listed as "Straight-DB" are straight strands that can be debonded

Grid Status

The Grid Status region provides summary information about the strand grid.

Item Description # Debondable Strands Number of strand positions that have been designated as debondable # Straight Strands Number of strand positions used for straight strands # Harped Strands Number of strands positions used for harped strands [View at Ends] Press this button to see the strand positions at the end of the girder [View at Mid-Girder] Press this button to see the strand positions at the center of the girder

Vertical Adjustment of Adjustable Strands

The parameters defined in this group control the vertical range over which adjustable strands can be moved from their default position as defined in the strand grid as well as the adjustment increment used for design. Harped strands can be offset differently at the girder ends than at harping points, thus forming the harped drape. Adjustable Straight Strands use a single offset because the strands are straight and parallel to the top of the girder.

Item Description Allow Check the box to allow vertical adjustment Design Increment In general, adjustable web strands can be adjusted continuously up and down within their adjustment limits through user-input adjustment values in the girder editing dialog. The design increment defines the step size to be used by the automated design algorithm when adjusting strand offsets. The increment must be less than or equal to the maximum adjustment value. If this value is zero, the design algorithm will make continuous adjustments within the offset limits. Lower Strand Limit
Upper Strand Limit These values define the range of possible uppermost and lowermost adjustable strand Y locations. Adjustable strands may not lie above or below these limits. Limits can be measured downward from the top of the girder or upward from the bottom.

Bridges & Structures

Comprehensive Design Example for Prestressed Concrete (PSC) Girder Superstructure Bridge

Design Step 5 Design of Superstructure

 

Design Step 5.5 Stress in Prestressing Strands

 

Design Step 5.5.1 - Stress in prestressing strands at nominal flexural resistance

The stress in prestressing steel at nominal flexural resistance may be determined using stress compatibility analysis. In lieu of such analysis a simplified method is presented in S5.7.3.1.1. This method is applicable to rectangular or flanged sections subjected to flexure about one axis where the Whitney stress block stress distribution specified in S5.7.2.2 is used and for which fpe, the effective prestressing steel stress after losses, is not less than 0.5fpu. The average stress in prestressing steel, fps, may be taken as:

fps    = fpu[1 - k(c/dp)] (S5.7.3.1.1-1) where:   k = 2(1.04 - fpy /fpu) (S5.7.3.1.1-2)

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The value of "k" may be calculated using the above equation based on the type and properties of prestressing steel used or it may be obtained from Table SC5.7.3.1.1-1.

The distance from the neutral axis to the compression face of the member may be determined as follows:

for T-section behavior (Eq. S5.7.3.1.1-3):

 

for rectangular section behavior (Eq. S5.7.3.1.1-4):

 

T-sections where the neutral axis lies in the flange, i.e., "c" is less than the slab thickness, are considered rectangular sections.

From Table SC5.7.3.1.1-1:

k = 0.28 for low relaxation strands

Assuming rectangular section behavior with no compression steel or mild tension reinforcement:

c = Apsfpu /[0.85f&#;cβ1b + KAps(fpu /dp)]

For the midspan section

Total section depth, h    = girder depth + structural slab thickness
= 72 + 7.5
= 79.5 in. dp    = h - (distance from bottom of beam to location of P/S steel force)
= 79.5 - 5.0
= 74.5 in. β1 = 0.85 for 4 ksi slab concrete (S5.7.2.2) b = effective flange width (calculated in Section 2 of this example)
= 111 in. c = 6.73(270)/[0.85(4)(0.85)(111) + 0.28(6.73)(270/74.5)]
= 5.55 in. < structural slab thickness = 7.5 in.
The assumption of the section behaving as a rectangular section is correct.

Notice that if "c" from the calculations above was greater than the structural slab thickness (the integral wearing surface is ignored), the calculations for "c" would have to be repeated assuming a T-section behavior following the steps below:

Assume the neutral axis lies within the precast girder flange thickness and calculate "c". For this calculation, the girder flange width and area should be converted to their equivalent in slab concrete by multiplying the girder flange width by the modular ratio between the precast girder concrete and the slab concrete. The web width in the equation for "c" will be substituted for using the effective converted girder flange width. If the calculated value of "c" exceeds the sum of the deck thickness and the precast girder flange thickness, proceed to the next step. Otherwise, use the calculated value of "c".

Assume the neutral axis is below the flange of the precast girder and calculate "c". The term "0.85 f&#;cβ1(b - bw)" in the calculations should be broken into two terms, one refers to the contribution of the deck to the composite section flange and the second refers to the contribution of the precast girder flange to the composite girder flange.

fps    = fpu[1 - k(c/dp)]      (S5.7.3.1.1-1)
= 270[1 - 0.28(5.55/74.5)]
= 264.4 ksi

Design Step 5.5.2

Transfer and development length    = 60(Strand diameter)     (S5.11.4.1)
60(0.5 in.)
= 30 in.

Development Length = ld &#; κ[fps - (2/3)fpe]db      (S5.11.4.2-1)

From earlier calculations:

fps    = 264.4 ksi (Design Step 5.4.8) fpe = 162.83 ksi (Design Step 5.5.1)

From S5.11.4.2, κ = 1.6 for fully bonded strands

From S5.11.4.3, κ = 2.0 for partially debonded strands

For fully bonded strands (32 strands):

ld &#; 1.6[264.4 - (2/3)162.83](0.5) = 124.7 in. (10.39 ft. or 10'-4 11/16")

For partially debonded strands (two groups of 6-strands each):

ld &#; 2.0[264.4 - (2/3)162.83](0.5) = 155.8 in. (12.98 ft. or 12'-11 ¾")

 

Design Step 5.5.3 - Variation in stress in prestressing steel along the length of the girders

According to S5.11.4.1, the prestressing force, fpe, may be assumed to vary linearly from 0.0 at the point where bonding commences to a maximum at the transfer length. Between the transfer length and the development length, the strand force may be assumed to increase in a parabolic manner, reaching the tensile strength of the strand at the development length.

To simplify the calculations, many jurisdictions assume that the stress increases linearly between the transfer and the development lengths. This assumption is used in this example.

As shown in Figures 2-5 and 2-6, each beam contains three groups of strands:

Group 1: 32 strands fully bonded, i.e., bonded length starts 9 in. outside the centerline of bearings of the noncomposite beam
Group 2: 6 strands. Bonded length starts 10 ft. from the centerline of bearings of the noncomposite beam, i.e., 10'-9" from the end of the beam
Group 3: 6 strands. Bonded length starts 22 ft. from the centerline of bearings of the noncomposite beam, i.e., 22'-9" from the end of the beam

For each group, the stress in the prestressing strands is assumed to increase linearly from 0.0 at the point where bonding commences to fpe, over the transfer length, i.e., over 30 inches. The stress is also assumed to increase linearly from fpe at the end of the transfer length to fps at the end of the development length. Table 5.5-1 shows the strand forces at the service limit state (maximum strand stress = fpe) and at the strength limit state (maximum strand stress = fps) at different sections along the length of the beams. To facilitate the calculations, the forces are calculated for each of the three groups of strands separately and sections at the points where bonding commences, end of transfer length and end of development length for each group are included in the tabulated values. Figure 5.5-1 is a graphical representation of Table 5.5-1.

Table 5.5-1 - Prestressing Strand Forces

Dist. from Grdr End
(ft) Dist. from CL of Brg
(ft) Initial Prestressing Force at Transfer Group 1
(k) Group 2
(k) Group 3
(k) Total
(k) 0* -0.75* 0.0     0.0 0.75 0.00 277.3     277.3 2.50 1.75 924.4     924.4 7.75 7.00 924.4     924.4 10.39 9.64 924.4     924.4 10.75** 10.00** 924.4 0.0   924.4 11.75 11.00 924.4 69.3   993.7 13.25 12.50 924.4 173.3   1,097.7 17.25 16.50 924.4 173.3   1,097.7 22.75*** 22.00*** 924.4 173.3 0.0 1,097.7 23.73 22.98 924.4 173.3 67.9 1,165.6 25.25 24.50 924.4 173.3 173.3 1,271.0 28.25 27.50 924.4 173.3 173.3 1,271.0 33.75 33.00 924.4 173.3 173.3 1,271.0 35.73 34.98 924.4 173.3 173.3 1,271.0 39.25 38.50 924.4 173.3 173.3 1,271.0 44.75 44.00 924.4 173.3 173.3 1,271.0 50.25 49.50 924.4 173.3 173.3 1,271.0 55.25 54.50 924.4 173.3 173.3 1,271.0 55.75 55.00 924.4 173.3 173.3 1,271.0 61.25 60.50 924.4 173.3 173.3 1,271.0 66.75 66.00 924.4 173.3 173.3 1,271.0 72.25 71.50 924.4 173.3 173.3 1,271.0 74.77 74.02 924.4 173.3 173.3 1,271.0 77.75 77.00 924.4 173.3 173.3 1,271.0 83.25 82.50 924.4 173.3 173.3 1,271.0 85.25 84.50 924.4 173.3 173.3 1,271.0 86.77 86.02 924.4 173.3 67.9 1,165.6 87.75+++ 87.00+++ 924.4 173.3 0.0 1,097.7 88.75 88.00 924.4 173.3   1,097.7 94.25 93.50 924.4 173.3   1,097.7 97.25 96.50 924.4 173.3   1,097.7 99.75++ 99.00++ 924.4 0.0   924.4 100.11 99.36 924.4     924.4 103.25 102.50 924.4     924.4 108.00 107.25 924.4     924.4 109.75 109.00 277.3     277.3 110.5+ 109.75+ 0.0     0.0

*, **, *** - Point where bonding commences for strand Groups 1, 2, and 3, respectively

+, ++, +++ - Point where bonding ends for strand Groups 1, 2, and 3, respectively

Table 5.5-1 (cont.) - Presstressing Strand Forces

Dist. from Grdr End
(ft) Dist. from CL of Brg
(ft) Prestressing Force After Losses Force at the Nominal Flexural Resistance Group 1
(k) Group 2
(k) Group 3
(k) Total
(k) Group 1
(k) Group 2
(k) Group 3
(k) Total
(k) 0* -0.75* 0.0     0.0 0.0     0.0 0.75 0.00 239.0     239.0 239.0     239.0 2.50 1.75 797.2     797.2 797.2     797.2 7.75 7.00 797.2     797.2 1,128.1     1,128.1 10.39 9.64 797.2     797.2 1,294.5     1,294.5 10.75** 10.00** 797.2 0.0   797.2 1,294.5 0.0   1,294.5 11.75 11.00 797.2 59.8   857.0 1,294.5 59.8   1,354.3 13.25 12.50 797.2 149.5   946.7 1,294.5 149.5   1,444.0 17.25 16.50 797.2 149.5   946.7 1,294.5 185.1   1,479.6 22.75*** 22.00*** 797.2 149.5 0.0 946.7 1,294.5 234.0 0.0 1,528.5 23.73 22.98 797.2 149.5 58.6 1,005.3 1,294.5 242.7 58.6 1,595.8 25.25 24.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 149.5 1,686.7 28.25 27.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 176.2 1,713.4 33.75 33.00 797.2 149.5 149.5 1,096.2 1,294.5 242.7 225.1 1,762.3 35.73 34.98 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 39.25 38.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 44.75 44.00 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 50.25 49.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 55.25 54.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 55.75 55.00 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 61.25 60.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 66.75 66.00 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 72.25 71.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 74.77 74.02 797.2 149.5 149.5 1,096.2 1,294.5 242.7 242.7 1,779.9 77.75 77.00 797.2 149.5 149.5 1,096.2 1,294.5 242.7 216.2 1,753.4 83.25 82.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 167.3 1,704.5 85.25 84.50 797.2 149.5 149.5 1,096.2 1,294.5 242.7 149.5 1,686.7 86.77 86.02 797.2 149.5 58.6 1,005.3 1,294.5 242.7 58.6 1,595.8 87.75+++ 87.00+++ 797.2 149.5 0.0 946.7 1,294.5 234.0 0.0 1,528.5 88.75 88.00 797.2 149.5   946.7 1,294.5 225.1   1,519.6 94.25 93.50 797.2 149.5   946.7 1,294.5 176.2   1,470.7 97.25 96.50 797.2 149.5   946.7 1,294.5 149.5   1,444.0 99.75++ 99.00++ 797.2 0.0   797.2 1,294.5 0.0   1,294.5 100.11 99.36 797.2     797.2 1,294.5     1,294.5 103.25 102.50 797.2     797.2 1,096.6     1,096.6 108.00 107.25 797.2     797.2 797.2     797.2 109.75 109.00 239.0     239.0 239.0     239.0 110.5+ 109.75+ 0.0     0.0 0.0     0.0

*, **, *** - Point where bonding commences for strand Groups 1, 2, and 3, respectively

+, ++, +++ - Point where bonding ends for strand Groups 1, 2, and 3, respectively

 

Figure 5.5-1 - Prestressing Strand Forces Shown Graphically

 

Transfer length = 30 in.
Development length, fully bonded = 124.7 in.
Development length, debonded = 155.8 in.

Figure 5.5-1 (cont.) - Prestressing Strand Forces Shown Graphically

Design Step 5.5.4 - Sample strand stress calculations

 

Prestress force at centerline of end bearing after losses under Service or Strength

Only Group 1 strands are bonded at this section. Ignore Group 2 and 3 strands.

Distance from the point bonding commences for Group 1 strands = 0.75 ft < transfer length

Percent of prestressing force developed in Group 1 strands    = 0.75/transfer length
= (0.75/2.5)(100)
= 30%

Stress in strands = 0.3(162.83) = 48.8 ksi

Force in strands at the section = 32(0.153)(48.8) = 239 kips

Prestress force at a section 11 ft. from the centerline of end bearing after losses under Service conditions

Only strands in Group 1 and 2 are bonded at this section. Ignore Group 3 strands.

The bonded length of Group 1 strands before this section is greater than the transfer length. Therefore, the full prestressing force exists in Group 1 strands.

Force in Group 1 strands = 32(0.153)(162.83) = 797.2 kips

Distance from the point bonding commences for Group 2 strands = 1.0 ft. < transfer length

Percent of prestressing force developed in Group 2 strands =    1.0/transfer length
= (1.0/2.5)(100) = 40%

Stress in Group 2 strands = 0.4(162.83) = 65.1 ksi

Force in Group 2 strands at the section = 6(0.153)(65.1) = 59.8 kips

Total prestressing force at this section = force in Group 1 + force in Group 2 = 797.2 + 59.8 = 857 kips

Strands maximum resistance at nominal flexural capacity at a section 7.0 ft. from the centerline of end bearing

Only Group 1 strands are bonded at this section. Ignore Group 2 and 3 strands.

Distance from the point bonding commences for Group 1 strands, i.e., distance from end of beam = 7.75 ft. (7'- 9")

This distance is greater than the transfer length (2.5 ft.) but less than the development length of the fully bonded strands (10.39 ft.). Therefore, the stress in the strand is assumed to reach fpe, 162.83 ksi, at the transfer length then increases linearly from fpe to fps, 264.4 ksi, between the transfer length and the development length.

Stress in Group 1 strands    = 162.83 + (264.4 - 162.83)[(7.75 - 2.5)/(10.39 - 2.5)]
= 230.41 ksi

Force in Group 1 strands = 32(0.153)(230.41)
= 1,128.1 kips

Strands maximum resistance at nominal flexural capacity at a section 22 ft. from centerline of end bearing

Only strands in Group 1 and 2 are bonded at this section. Ignore Group 3 strands.

The bonded length of Group 1 strands before this section is greater than the development length for Group 1 (fully bonded) strands. Therefore, the full force exists in Group 1 strands.

Force in Group 1 strands = 32(0.153)(264.4) = 1,294.5 kips

The bonded length of Group 2 at this section = 22 - 10 = 12 ft.

Stress in Group 2 strands    = 162.83 + (264.4 - 162.83)[(12 - 2.5)/(12.98 - 2.5)]
= 254.9 ksi

Force in Group 2 strands = 6(0.153)(254.9) = 234.0 kips

Total prestressing force at this section    = force in Group 1 + force in Group 2
= 1,294.5 + 234.0
= 1,528.5 kips

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