Prestressed Concrete Notes

By Deepanshu Rastogi|Updated : September 1st, 2021

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Prestressed Concrete 

Introduction

  • Prestress is defined as a method of applying pre-compression to control the stresses resulting due to external loads below the neutral axis of the beam tension developed due to an external load which is more than the permissible limits of the plain concrete.
  • Prestressed concrete is basically concrete in which internal stresses of a suitable magnitude and distribution are introduced so that the stresses resulting from the external loads are counteracted to a desired degree.

Terminology

1. Tendon: A stretched element used in a concrete member of structure to impart prestress to the concrete.
2. Anchorage: A device generally used to enable the tendon to impart and maintain prestress in concrete.
3. Pre tensioning: A method of prestressing concrete in which the tendons are tensioned before the concrete is placed. In this method, the concrete is introduced by the bond between
steel & concrete.
4. Post-tensioning: A method of prestressing concrete by tensioning the tendons against hardened concrete. In this method, the prestress is imparted to concrete by bearing  

Materials for prestressing concrete members

1. Cement: The cement used should be any of the following


(a) Ordinary Portland cement conforming to IS269
(b) Portland slag cement conforming to IS455. But the slag content should not be more than 50%.
(c) Rapid hardening Portland cement conforming to IS8041.
(d) High strength ordinary Portland cement conforming to IS8112.

2. Concrete: Prestress concrete requires concrete, which has a high compressive strength reasonably early age with comparatively higher tensile strength than ordinary concrete. The concrete for the members shall be air-entrained concrete composed of Portland cement, fine and coarse aggregates, admixtures and water. The air-entraining feature may be obtained by the use of either air-entraining Portland cement or an approved air-entraining admixture. The entrained air content shall be not less than 4 per cent or more than 6 per cent.

  • Minimum cement content of 300 to 360 kg/m3 is prescribed for the durability requirement.
  • The water content should be as low as possible.

3. Steel:- High tensile steel, tendons, strands or cables

High strength steel should contain:

  • 0.7 to 0.8% carbons,
  • 0.6% manganese,
  • 0.1% silica

Why high grade of concrete & steel?

  • Higher the grade of concrete higher the bond strength which is vital in pre-tensioned concrete
  • Also, higher bearing strength which is essential in post-tensioned concrete as well as in pre-tensioned concrete
  • Creep & shrinkage losses are minimum with high-grade concrete.
  • Generally, minimum M30 grade concrete is used for post-tensioned & M40 grade concrete is used for pre-tensioned members
  • The losses in pre-stress members due to various reasons are generally in the range of 250 N/mm2 to 400 N/mm2
  • If mild steel or deformed steel is used the residual stresses after losses is either zero or negligible

Advantage of Prestressed Concrete

  • The use of high strength concrete and steel in prestressed members results in lighter and slender members than is possible with RC members.
  • In fully prestressed members the member is free from tensile stresses under working loads, thus the whole of the section is effective.
  • In prestressed members, dead loads may be counter-balanced by eccentric prestressing.
  • Prestressed concrete member posses better resistance to shear forces due to effectof compressive stresses presence or eccentric cable profile.
  • Use of high strength concrete and freedom from cracks, contribute to improving durability under aggressive environmental conditions.
  • Long span structures are possible so that saving in weight is significant & thus it will be economic.
  • Factory products are possible.
  • Prestressed members are tested before use.
  • Prestressed concrete structure deflects appreciably before ultimate failure, thus giving ample warning before the collapse.
  • Fatigue strength is better due to small variations in prestressing steel, recommended to dynamically loaded structures.

Disadvantages of Prestressed Concrete

  • The availability of experienced builders is scanty.
  • Initial equipment cost is very high.
  • Availability of experienced engineers is scanty.
  • Prestressed sections are brittle
  • Prestressed concrete sections are less fire resistant.

Classifications and Types

Prestressed concrete structures can be classified in a number of ways depending upon the feature of designs and constructions. 

  1. Pre-tensioning: In which the tendons are tensioned before the concrete is placed, tendons are temporarily anchored and tensioned and the prestress is transferred to the concrete after it is hardened.
  2. Post-tensioning: In which the tendon is tensioned after the concrete has hardened. Tendons are placed in sheathing at suitable places in the member before casting and later after hardening of concrete.

Tensioning Devices

  • Mechanical devices: The mechanical devices generally used include weights with or without lever transmission, geared transmission in conjunction with pulley blocks, screw jacks with or without gear devices and wire-winding machines.
  • Hydraulic devices: These are simplest means for producing large prestressing force, extensively used as tensioning devices
  • Electrical devices: The wires are electrically heated and anchored before placing concrete in the mould. This method is often referred to as thermo-prestressing and used for tensioning of steel wires and deformed bars.
  • Chemical devices: Expanding cement are used and the degree of expansion is controlled by varying the curing condition. Since the expansive action of cement, while the setting is restrained, it induces tensile forces in tendons and compressive stresses in concrete.

Prestressing System

  1. Pretensioning system: In the pre-tensioning systems, the tendons are first tensioned between rigid anchor-blocks cast on the ground or in a column or unit –mould types pre-tensioning bed, prior to the casting of concrete in the mould. The tendons comprising individual wires or strands are stretched with constant eccentricity or a variable eccentricity with tendon anchorage at one end and jacks at the other. 

2. Post-tensioned system: In post-tensioning, the concrete unit is first cast by incorporating ducts or grooves to house the tendons. When the concrete attains sufficient strength, the high-tensile wires are tensioned by means of jack bearing on the end of the face of the member and anchored by wedge or nuts.

Most of the commercially patented prestressing systems are based on the following principle of anchoring the tendons:

  • Wedge action producing a frictional grip on the wire.
  • Direct bearing from the rivet or bolt heads formed at the end of the wire.
  • Looping the wire around the concrete.

Methods:


1. Freyssinet system
2. Gifford-Udall system
3. Magnel blaton system
4. Lee-McCall system

Differences of Prestressed Concrete Over Reinforced Concrete:

  • In prestressed concrete member steel plays an active role. The stress in steel prevails whether the external load is there or not. But in R.C.C., steel plays a passive role. The stress in steel in R.C.C members depends upon the external loads. i.e., no external load, no stress in steel.
  • In prestress concrete the stresses in steel is almost constant where as in R.C.C the stress in steel is variable with the lever arm.
  • Prestress concrete has more shear resistance, where as the shear resistance of R.C.C is less.
  • In prestress concrete members, deflections are less because the eccentric pre stressing force will induce couple which will cause upward deflections, where as in R.C.C., deflections are more.
  • In prestress concrete fatigue resistance is more compared to R.C.C. because in R.C.C. stress in steel is external load dependent where as in P.S.C member it is load independent.
  • Prestress concrete is more durable as high grade of concrete is used which is denser in nature. R.C.C. is less durable.
  • In prestress, concrete dimensions are less because external stresses are counterbalanced by the internal stress induced by prestressing. Therefore reactions on column & footing are less
    as a whole the quantity of concrete is reduced by 30% and steel reduced by about 60 t  70%. R.C.C. is uneconomical for long span because in R.C.C. dimension of sections are large requiring more concrete & steel.

Comparative Study: Pretension Vs Post-tensioned Member

Pretension member Post-tensioned member
In pre-tensioned prestress concrete, steel is tensioned prior to that of concrete. It is released once the concrete is placed and hardened. The stresses are transferred all along the wire by means of the bond.Concreting is done first then wires are tensioned and anchored at ends. The stress transfer is by end bearing not by the bond.
Suitable for short span and precast products like sleepers, electric poles on mass production.Suitable for long span bridges
In pre-tensioning, the cables are basically straight and horizontal. Placing them in curved or inclined position is difficult. However, the wire’s can be kept with eccentrically. Since cables can not be aligned similarly to B.M.D. structural advantages are less compared to that of post-tensioned.The post-tensioning cables can be aligned in any manner to suit the B.M.D due to external load system. Therefore it is more economical, particularly for long span bridges. The curved or inclined cables can have a vertical component at ends. These components will reduce the design shear force. Hence post-tensioned beams are superior to pre-tensioned beams both from flexural and shear resistances point
Prestress losses are more compared to that of post-tensioned concrete.Losses are less compare to pre-tensioned concrete

 

Analysis of Prestress Member

Basic Assumptions

1. Concrete is a homogeneous elastic material.
2. Within the range of working stress, both concrete & steel behave elastically, notwithstanding the small amount of creep, which occurs in both the materials under the sustained loading.
3. A plane section before bending is assumed to remain plane even after bending, which implies a linear strain distribution across the depth of the member.

  • Prestress Concrete is one in which there have been introduced internal stresses of such magnitude and distribution that stresses resulting from given external loading is counter balanced to a desired degree.

Analysis of prestress and Bending stress

Following are the three concepts of analysis

  1. Stress concept analysis
  2. Strength concept analysis
  3. Load balancing method

Stress concept Method-

Following are the two cases for analysis

Case-(i) Beam provided with a concentric tendon:

image001

Let, P prestressing force applied by the tendon. Due to this prestressing force, the direct compressive force induced is given by, image002.

If due to dead load & external loads, the bending moment at the section is M, then the extreme stresses at the section due to bending moment alone is image003

Hence final stress at the extreme top edge image004 and stress at the extreme bottom edge image005

Case–(ii): Beams with eccentrics tendon:

image006image007

(i) Direct stresses due to prestressing force image008

(ii) Extreme stresses due to an eccentricity of the prestressing force image009

(iii) Extreme stresses due to bending moment image010

Final stresses

Stress at top fibre image011

Stress at bottom fibre image012

By providing an eccentricity to the tendon, a hogging moment (P.e.) is developed which will produce stresses, which will counteract the stresses due to external bending moment.

Strength Concept method-

Consider a beam of length l provided with a tendon at an eccentricity e. Suppose the beam is lying on the ground i.e. the beam is not subjected to any external load. Hence there is no external bending moment on the beam.

image013

image014

The following equal forces are existing

(i) The P-force which is the tension in the tendon.

(ii) The C-force which is the compressive force acting on the concrete.

Stresses in concrete are produced entirely due to C-force.

In the absence of any external bending moment the C-force and P-force act at the same level. Line of action of P-force is called the P-line. The P-line is nothing but the tendon line itself. The line of action of the C-force is called the C-line or Pressure line. Hence in the absence of any external bending moment the P-line and the C-line coincide.

Suppose the beam is subjected to a bending moment M, then the C-line will be shifted from the P-line by a distance 'a' called lever arm.

image015

Extreme stresses in concrete are given by

image016

Load Balancing Concept-

Prestressed Beam with Bent Tendon

image017

By providing bent fendons, the tendons will exert an upward pressure on the concrete beam and will therefore counter act a part of the external downward loading.

Considering the concrete as a free body. We find an upward force 2P sin θ.

The net downward load at the centre will be (W-2P sinθ)

The axial longitudinal force provided by the tendon = Pcosθ = P {since θ is small}

Direct stress on the section image018

Net BM, image019

Where, w = dead load per unit length of the beam. Extreme fibre stress image020

It may be realized that the profile of the tendon should follow the shape of the bending moment diagram for the given external loads in order it may offer considerable and effective upward forces. For e.g., if the loading on the beam is a uniformly distributed load, the tendon may be provided along a parabolic profile.

Tendon with Parabolic Profile

image021

Let l be the span of the beam and h be the dip of the cable.

The cable will exert an upward udl = wC/m on the beam, but the cable will be subjected to downward udl of wC per unit run.

Let V and H are vertical and horizontal components of P.

image022

The cable is an absolutely flexible member, therefore BM at every section of cable is zero. Hence BM at the centre of the cable is

image023

Since dip of the cable is very small, we can make approximation

cosα = 1 and Pcosα = P

Now consider the beam, it is subjected to

(i) External load w per unit length

(ii) Upward udl transmitted by the cable = wC per unit length.

Net UDL = w – wC

Net BM at the centre image024

Extreme stresses image025

Losses of Prestress

The steel wires of a prestressed concrete member do not retain all the preliminary prestress. A certain amount of loss of prestress always takes place.

Losses may be classified as follows:

image026

image027

image028

image029

 

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Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
cracked GATE DTU AIR 1130-GATE
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