Question

ELABORATE:

1. Why is there a difference between the relaxation loss of SRT compared to that of LRT?

2. Why are anchorage slip and friction losses not considered for pre-tensioned Pc sections?

Answer 1

DIFFERENCE BETWEEN SRT AND LRT IN RELAXATION LOSS (PRESTRESSED CONCRETE DESIGN)

Seldom are such acronyms used in my experience,but SRT would be STRESS-RELIEVED and LRT would bee LOW-RELAXATION.Not sure what 'T' is - maybe tendon.

LR stand is stress-relieved,but SR stand is not low-relaxation.Just about all strand manufactured today is low-relaxation,which is a process,after stranding,where the strand passes through a induction furnace under tension-so heat+tension-resulting in low-relaxation properties compared to stress-relieved.

In PRE-tensioning there is no "anchorage" within the element,as such (c.f POST-tensioning)-it relies upon bond of strand to concrete to transfer the prestressing forces.There is,however,strand slippage that occurs when the strands are cut from the precast bd and transferred to the strand,and hence the concrete element.When the strand is cut,there is also the Hoyer effect (reverse dialation of strand due to poisson's ratio and helical wire 'compaction') that provides some 'wedge-like' behavior to the strand as it tries to slip.

Most PRE-tensioning strands are straight from end-to-end,so no friction,as compared to POST-tensioning,where there is intensional tendon curvature(drape) and unitensional tndon curvature(wobble).For those precast elements that have draped/harped tendons-like a bridge girder or maybe a deep DT-there are friction losses at the mechanical dviators in the precast bed,and such losses are accounted for in the prestress calculations by the precaster.

INTRODUCTION IN PRESTRESSED:-In prestressed concrete applications,the most important variable is the prestresing force.In the early days,it was observed that the prestressing force does not stay constant,but reduces with time.Even during prestressing of the tendons and the transfer of prestress to the concrete member,there is a drop of the prestressing force from the recorded vlue in the jack gauge.The various reductions of the prstressing force are termed as the losses in prestress.

1. FRICTION-The friction generated at the interface of concrete and steel during th stretching of a curved tendon in a post-tensioned member,leads to a drop in the prestress along the member from the strtching end.The loss due to friction does not occur in pre-tensioned members because tthere is no concrete during the stretching of the tendons.

The friction is generated due to the curvature of the tendon and the vertical component of the prestressing force.In addition to friction,the stretching has to overcome the wobble of the tendon.The wobble refers to the change in position of the tendon along the duct.The losses due to friction and wobble are groupd together under friction.

The formulation of the loss due to friction is similar to the probleem of belt friction.

The derivation of the expression of P is based on a circular profil.Although a cable profile is parabolic based on the bnding moment diagram,the error induced is insignificant.

The friction is proportional to the following variables.

1. Coefficient of friction (u) between concrete and steel.

2. The resultant of the vertical reation from the concrete on the tendon (N).

From the equilibrium of forces in the force triangle,N is giveen as follows.

N=2Psinda/2

2Pda/2=Pda

The friction over the length dx is equal to uN=uPda.

Thus the friction (dP) depends on the following variables.

1. Coefficient of friction(u).

2.Curvature of the tndon(da).

3. The amount of prestressing force(P).

The wobble in the tendon is effected by the following variabls.

1. Rigidity of sheathing.

2. Diameter of sheating.

3. Spacing of sheath supports.

4. Type of tendon.

5. Typ of construction.

The friction due to wobble is assumed to be proportional to the following.

1. Length of the tendon.

2. Prestressing force.

For a tendon of length dx,the friction due to wobble is expressed as kPdx,where k is the wobble coefficient or coefficient for wave effect.

VALUES OF COEFFICIENT FRICTION

Type of interface u

For steel moving on smooth concrete 0.55

For steel moving on steel fixed to duct 0.30

For steel moving on lead 0.25

The value of k varies from 0.0015 to 0.0050 per meter length of the tendon depending on the type of tendon.The following problem illustrates the calculation on the type of tendon.

2. ANCHORAGE SLIP:-In a post-tensioned member,when the prestress is transferred to the concrete,the wedges slip through a little distance before they get properly seatd in the conical space.The anchorage block also moves befor it settles on the concrete.There is loss of prestrss due to the consequent reduction in the lngth of the tendon.

The total anchorage slip depends on the type of anchorage system.In absence of manufacture's data,the following typical values for some systems can be used.

Anchorage System Anchorage Slip

Freyssinet system 12-5mm fi strands 4mm

Magnel system 8mm

Dywidag system 1mm

Due to the setting of the anchorage block,s the tendon shortens,there is a reverse friction.This length is denoted as l(set).

In most post-tensioning systems when the tendon force is transferred from the jack to the anchoring ends,the friction wedges slip over a small distance.

Anchorage block also moves before it settles on concrete.

Loss of prstress is due to the consequent reduction in the length of th tendon.

Certain quantity of prestress is released due to this slip of wire through the anchorages.

Amount of slip depends on type of wedge and stress in the wire..

Loss of prestres due to slip can be calculated:

(P/A)=EsDEL/L

Where,DEL=Slip of anchorage

L=Length of cable

A=Cross-sectional area of the cable

E=Modulus of Elasticity of steel

P=Prestressing Force in the cable.