Bé xy dùng Ch­¬ng tr×nh båi d­ìng kü s­ t­ vÊn gi¸m s¸t xy dùng Bµi gi¶ng

The purpose of a friction test is to verify the assumptions for the coefficients of friction and wobble. This test would be appropriate for all but small scale applications where it would suffice to adopt friction and wobble values from other, previous, experience.

A friction test is normally performed on a typical tendon representative of the type or group of tendons being installed - for example, on one tendon in one girder of several in the span or on perhaps two similar cantilever tendons in the top of precast or cast-in-place segments.

For any tendon, there are two unknowns, the coefficients of friction (µ) and wobble (k).However, for any given test set up where the force is measured at each end of the tendon, there can only be one equation and result based upon the standard force loss equation:

P_X = P₀ .e ^{-( µθ + kx )}

Consequently, two unknowns (µ and k) have to be derived from one equation. This is not possible unless one of the unknowns is already known.

For an external tendon in, say a span-by-span bridge, (Figure 3.4) the points of curvature are relatively discrete and the angles consumed are known. In the straight portions there is no wobble. So in such a case, providing that the pre-curved steel pipe ducts in the pier diaphragms and deviator saddles have been correctly installed, then it may be assumed that k = 0. Thus a test on this type of tendon should provide a reasonable result for the effective coefficient of friction, µ, between the tendon and the steel pipes.

For a tendon in the top of a segmental precast or cast-in-place cantilever (Figure 3.6), usually the alignment is relatively, but not completely, straight between two curves at each end anchor. If the duct for this type of tendon has been carefully and well installed so that there is no wobble, then it may be assumed that k = 0 and a test should provide a reasonable result for µ.

On the other hand, if there is uncertainty as to how well a duct has been installed or if it is known to have significant unintentional wobble, it is necessary to make a judgment as to a suitable proportion of loss due to friction and loss due to wobble. It is suggested that the wobble coefficient be taken as the assumed value for "k" - and use the test result to give "µ".

An alternative approach to determine both coefficients µ and k would be to perform the friction test on two similar, say cantilever tendons - a short one and a long one. Assuming the tendons are installed with the same materials and standard of care, this would provide two independent results (i.e. two equations) which could be solved simultaneously for µ and k.

In any event, it is recommended that each friction test be performed on at least two, very similar or identical, tendons - of the same length and curvature layout - for example, in a segmental cantilever, one tendon over the left web and its counterpart over the right web. The average of the pair represents one result (i.e. one equation). In an I-girder with a continuously draped tendon profile, the two tests could be performed on two very similar tendons in the same girder or the same profile of tendon in two parallel girders - where again, the average of the two represents one result (equation).

In general, friction testing is likely to give reasonable results only on relatively long tendons (over about 30M (100 ft)) since it is necessary to measure both forces and elongations under incremental loading to a sufficient level of accuracy. For this reason, an in-place friction test is not appropriate for some applications such as, straight longitudinal or transverse tendons in "flat-oval" ducts or similar in voided precast slabs or transverse deck slab tendons in precast or cast-in-place segments.

It is usual to test a minimum of one tendon in a group of tendons performing the same function - e.g. one tendon in each web of a two-web box. Tendon function may be generally described as:

• 
  Internal cantilever tendon or continuity tendon (e.g. in precast or cip segments)
  
• 
  External draped (deviated) tendon (e.g. in span-by-span construction)
  
• 
  Profiled (draped) internal tendon (e.g. I-girders and cip boxes)
  

The test procedure is to tension the tendon at one anchor assembly and measure the force at the dead end using a load cell or calibrated jack. The tendon should be tensioned to 80% of ultimate in increments of not less than 20%. For each increment, the gauge pressure at the jacking end, the load cell (or jack) force at the dead end and the elongation at the jacking end should be recorded. Also, note the wedge pull-in at both ends. Take into account the loss of force due to friction in the anchorages and wedge plates as the strands deviate slightly through them and any friction in the jack. The manufacturer of the post-tensioning system should be able to provide percentage estimates for these losses. For very long tendons that require multiple jack pulls, it is essential to keep an accurate account of elongation at the jacking end and each corresponding intermediate wedge set (pull-in).

If wedges are not installed, and if the available jacking equipment can facilitate it, forces and elongations measured while gradually releasing the jacking load should reveal a lag or hysteresis resulting from the reverse effect of friction (Fig. 3.6). The force and elongation may not immediately return to zero due to residual friction effects.

When performing friction tests, it is recommended that forces and elongations be reconciled within a tolerance of 5% for all tendons. The 5% to 7% tolerance in AASHTO LRFD Construction Specifications is for production tendon elongations - no guidance is given for friction tests.

If the total measured elongation is different to the anticipated (calculated) elongation by more than 5% then the reasons for it should be investigated. It may be necessary to make more detailed calculations or to run a similar test on another tendon. It is suggested that assumed values for friction (µ) and wobble (k) not be varied by more than 10% when attempting to reconcile measured and anticipated results.

A significant shortfall in elongation is indicative of poor duct alignments or obstructions. The likely causes should be examined and appropriate corrective measures taken.

Figure 3.6 - On-site Friction Test

The modulus of elasticity, E, is provided per coil of strand, or bundle of bars for each of the manufacturers lots. This is derived from proof tests performed by the manufacturer as part of his quality control of the strand, or bar, production.

The modulus of elasticity for an individual strand is generally about 193 to 200GPa (28,000 to 29,000 ksi.) There is a school of thought that the effective modulus of elasticity of a bundle of strands made up into a multi-strand tendon may be slightly less than that of an individual strand because of the bundle effect or the "un-wrapping", if any, as strands are stressed. This is not necessarily so. In some bench-tests performed on an approximate gauge length of 9M (30 feet) with no contact between tendon and duct, the modulus of the group of strands proved to be the same as that of an individual strand once appropriate allowance was made for losses in the jack and anchors. Therefore it is recommended that calculations of elongations be based upon appropriate assumed or actual production values for strand only. It is also recommended that when calculating elongations, proper allowances be made for all force loss effects.

Figure 3.7 - On-site Bench Test for Modulus of Elasticity

• 
  For small projects with less than approximately 45T (100,000 lbs) of PT: no bench tests, providing that strands are from the same supplier with certified copies of proof of modulus from production sampling and testing.
  
• 
  For larger projects: one per 45T (100,000 lbs) of PT: one test if from the same supplier or one test per each supplier.
  

Early post-tensioning anchors for strand tendons consisted of a simple rectangular or square steel bearing plate supporting a wedge plate (Figure 3.8). The flare of the strands is accommodated within a cone or trumpet attached to the back of the bearing plate. The cone is made of galvanized sheet metal or plastic. Nowadays, these simple types of bearing plates have mostly been superseded by multi-plane anchors or special composite anchor systems.

Figure 3.8 - Basic Anchor Bearing Plate

3.3.2 Multi-Plane Anchor

Multi-plane anchors (Figure 3.9) induce local bearing stress greater than the limit allowed for standard (basic bearing plate) plate. Therefore, multi-plane anchors need special reinforcement for confinement of the local anchor zone.This is normally supplied by the manufacturer of the anchor - usually in the form of a spiral (not shown).

Figure 3.9 - Multi-plane Anchor

Some manufacturers have introduced special composite anchors. These require special local zone confinement reinforcing similar to multi-plane anchors.

3.3.4 Anchor Plates for Bar Tendons

Anchor plates for bar tendons are usually square or rectangular (Figure 3.10). A separate bearing plate is used for each bar. Other types of confined,circular, anchors are also available.

Figure 3.10 - Anchor Plate for PT-Bar

Regardless of the type of anchor, it is essential to provide reinforcement in the local anchor zone - this is the region directly behind the anchor bearing plate(s). For longitudinal strand tendons, mostly, this usually comprises a spiral (Figure 3.11). Grids or rectangular links may be used instead of or to supplement spiral reinforcing. Local zone reinforcement should be placed as close as possible (i.e. 12mm (1/2 inch) maximum) to the main anchor plate in all applications.

Figure 3.11 - General and Local Anchor Zone in End of I-Girder

Local anchor zones for transverse deck slab tendons anchored in the relatively shallow depth at the edge of segments are most effectively reinforced by multiple-U shaped bars placed in alternating up and down arrangement, beginning very close to the anchor plate (Figure 3.12).

This arrangement has been found to be very effective for intercepting potential cracks that might originate at the top or bottom corner of the anchor bearing plate and travel diagonally through the adjacent surface - apart from the classical splitting stress along the line of the tendon itself.

Figure 3.12 - Local zone reinforcing for edge anchor in thin slab

Correct duct alignment and profile is of paramount importance to the proper functioning of a post-tensioning tendon, whether that tendon is internal or external to the concrete. Duct alignment and profile should be clearly and sufficiently defined on the plans and approved shop drawings by dimensions to tangent points, radii, angles and offsets to fixed surfaces or established reference lines and by entry and exit locations and angles at anchorage or intermediate bulkheads. Alignment, spacing, clearance and details should be in accordance with AASHTO LRFD Specifications 5.10.3.3 thru 5.10.4.3.2.

General recommendations for fabrication are that ducts should be:

• 
  Installed to correct profile (line and level) within specified tolerances
  
• 
  Tied and properly supported at frequent intervals
  
• 
  Connected with positively sealed couplings between pieces of duct and between ducts and anchors
  
• 
  Aligned with sealed couplers at temporary bulkheads
  
• 
  Positively sealed at connections made on-site and in cast-in-place splice joints
  
• 
  The elevations and alignments of ducts should be carefully checked
  

Recommendations for ducts in concrete in I-girders (Figure 3.13):

• 
  Maximum allowable size of aggregate should be specified
  
• 
  The distance between the outside of the duct and the side of the web should be adequate to accommodate the vertical reinforcing and specified cover and provide the minimum concrete section to satisfy design requirements.
  

Figure 3.13 - Duct spacing and clearance in post-tensioned precast girders

In addition to the above general recommendations ducts should be:

• 
  Installed to connect correct duct location in bulkhead with correct duct location in match-cast segment
  
• 
  Correctly aligned with respect to the orientation of the segment in the casting cell and the direction of erection
  
• 
  Elevations and alignments of longitudinal and transverse ducts should be carefully checked (Fig. 3.14)
  

Figure 3.14 - Check longitudinal and transverse duct alignments

In addition to the above general recommendations, during erection:

• 
  Ducts should have positively sealed connections between external duct and steel pipes and between individual lengths of duct*
  
• 
  When installing HDPE pipes to connect with deviator and diaphragm pipes,installation should be checked to make sure the correct tendons are connected
  
• 
  Joints between match-cast segments should be properly prepared and sealed with epoxy as necessary according to the specific project contract requirements
  

3.4.1.4 Alignment at Anchors

For both internal and external tendons, anchors should be:

• 
  The correct type and size for the type and size of tendon used.
  
• 
  When required, supplied with permanent, heavy duty, plastic caps with a seal against the anchor plate.
  
• 
  Properly aligned and well supported by formwork.
  
• 
  When required, set in a recess (anchor pocket or block-out) of correct size, shape and set to orientation.
  
• 
  Provided with correct local and general zone reinforcement at correct location and spacing.
  

Figure 3.15 - Anchor recess and checking of duct alignment

Figure 3.16 - Unacceptable Duct Connections and Mistakes

Nowadays, commercial systems generally offer a positive, sealed and aligned connection.

3.4.1.5 Cover

Cover is an integral part of corrosion protection. Cover should be checked to rebar and longitudinal and transverse post-tensioning ducts.

3.4.2 Duct Supports

In order to secure post-tensioning ducts to a profile, prevent floatation, or displacement or disconnection, supports should be provided at frequent intervals (Figure 3.17).

• 
  Duct supports may be tie-wire, rebar, D4 wire tied to web reinforcing, or an approved commercial device. Use of tie-wire alone is satisfactory providing that it is not tightened so much as to distort the rebar cage or crimp the duct
  
• 
  Support bars may be straight, L, U or Z-shape reinforcing bar as necessary
  
• 
  Supports should be at intervals of no more than 0.6 to 1.0M (2 to 3 feet),or per recommendations of duct supplier.
  
• 
  Minimum cover and clearances should be maintained.
  

Figure 3.17 - Duct supports in post-tensioned precast I-griders

Figure 3.18 - A possible result of poorly supported and connected ducts

In the past, various methods were used to connect separate pieces of duct depending upon the type of duct (e.g. spiral wound, semi-rigid or flexible, corrugated or smooth, steel or plastic ducts) and to connect ducts to anchors. Often, connections were made using an oversized piece of the same duct wrapped around and secured with tie-wire or duct tape. Connections were also made solely with duct tape. Such connections are not sealed. They allow the migration of moisture or chlorides; possibly eventually leading to corrosion. Duct tape should not be used to join or repair ducts or make connections

Traditionally, galvanized steel ducts have provided some degree of sacrificial passive protection. In recent years, there has been a shift to more robust systems comprising impermeable plastic ducts, usually of high density polyethylene (HDPE) or high density polypropylene (HDPP) with purpose-made (sealed) connections; usually an outer plastic duct connector clips tightly around the duct.

Consequently, it is recommended that positively sealed connections be made between ducts and anchors and between separate pieces of duct. It is important to make sure that supports do not fail and connections do not separate during casting (Figure 3.18).

3.4.4 Grout Inlets and Outlets

It is recommended that locations for grout inlets and outlets be shown on the Shop Drawings or in a Grouting Plan for approval. Examples of recommended locations for grout inlets and outlets are given in Chapter 4.

3.4.5 Size of Pipes for Grout Inlets, Outlets and Drains

Pipes for grout inlets and outlet vents should be of sufficient diameter to allow the escape of air, water, bleed-water and the free flow of grout.

Grout pipes should be connected to ducts and anchor components in a manner that creates a seal and does not allow leaks or ingress of water, chlorides or other corrosive agents.

To facilitate inspection and complete filling of a tendon with grout, grout vents at high points (crests) may exit the top (riding) surface providing that the grout outlet vent can be properly capped and sealed. Alternatively, the outlet should exit another suitable surface. It is recommended that caps and seals be provided at all inlet and outlet vents to prevent ingress of water or corrosive agents into the tendon.

3.4.6 Positive Shut-Offs

Positive shut-off valves or other approved means of closing grout inlets and outlets should be provided at all vents. At high points or other locations, where it is suspected that air or water voids could accumulate and require filling by secondary vacuum assisted grouting, suitable connections and valves should be provided (Figure 3.19).

Figure 3.19 - Connections for secondary, vacuum grouting, operations

Wet concrete when discharged into forms and consolidated by vibration can exert significant pressure and local forces on reinforcing cages and post-tensioning ducts. It is essential that reinforcing cages be securely tied and held firmly in place by cover, spacer blocks or chairs. Likewise post-tensioning ducts must be well supported and attached to the reinforcing cage at frequent intervals.

Ducts, being hollow, tend to float. A duct that is not well secured can easily be displaced resulting in excess wobble (Figure 3.20). This affects the intended location of the post-tensioning tendon and causes a loss of force through excess friction. The result is a reduction in post-tensioning force and eccentricity. In some cases, excessive wobble, or improperly aligned duct (for example, Figure 2.21), can make it difficult or impossible to install a tendon.

Figure 3.20 - Unintentional excess wobble

Figure 3.21 - Excess wobble due to rebar and duct conflict

Figure 3.22 - Duct size in post-tensioned girders