UNIT 6 SIMPLE DESIGN AND

APPLICATIONS
Structure
6.1 Introduction
Objectives
6.2 Design Loads and Strengths in Limit State Method
6.3 Strength and Serviceability Limit States
6.4 Design of Rectangular Prestressed Sections
6.5 Prestressed Concrete Pipes
6.6 Prestressed Concrete Poles
6.7 Summary
6.8 Answers to SAQs

A safe, serviceable and economical design of concrete structures requires a

comprehensive knowledge of the loads expected to be applied on the structure in
its service life, properties of materials and behaviour of the structure when it is
subjected to such loads. In the design of structures it is to be ensured that the
structure satisfies the requirements of serviceability (to function well) under
working loads as well as those of safety against total collapse due to various
causes.
Most of the times, the design process is an interactive and trial procedure in
which the cycle of analysis - design - analysis is followed. For the structure
which is to be designed, we have to estimate the loads, consider trial sections for
the structure and analyse it for the internal forces and moments etc., induced due
to external loads. Then the structure is designed and re-analysed for the induced
internal stresses. If these induced stresses exceed material strengths then the
design is to be modified. The primary object of structural design is to provide a
structure with safety and economy during its entire service life.
Objectives
We have gone through certain aspects of the prestressed concrete construction. In
these units of study, it has been the endeavour to make the student understand the
basic concept and the working of the system of prestressing in this type of
construction. It is important to know various aspects related to design, for any
structural member.
After studying this unit, you should be able to
understand various approaches to design,
appreciate how the design of prestressed concrete members is
considered in the limit state method,
learn how to design a prestressed concrete section for flexure, and
know about various applications of prestressing in different types of
structural members.
Prestressed Concrete
6.2 DESIGN LOADS AND STKENGrTFfSIN LIMIT
STATE METHOI)
111the past, working stress method was followed for the dcsign ol'str~~cturcs. In
this method, pioneered by Morsch, a German professor. uorliing loads or service
loads are considered and permissible stresses in steel and concrete arc considcrcd
to be fixed fractions ofthe specified strengths of thc rcspectivc materials. A
constant modular ratio is assumed for all the loading conditions and clastic
behaviour of concrete and steel is assumcd. ?he factor of satkty applied to thc
constituent materials (in terms of permissible stresses) docs not present a rcalist~c
picture of the degree of safety against the collapse as we may not bc able to
foresee as to what happens when working loads are exceed and the material gocs
in the inelastic range of behaviour.

'The main feature of the ultimate load method, which was followed aiicrwards. is
the application of varying load factors for different types of loads to an-ivc at the
required ultimate load for which the structure is to bc designed. As only the
collapse load is considered, the behaviour of the structure at working or scrvicc
loads is not known. A structure designed solely on the basis ol'~~lti111atc loads
shall be safe against collapse but may not be serviceable, For cxamplc. duc to
excessive deformations or cracking at working loads.

Drawbacks, inherent in both the above two methods, have pavcd the way for the
development of Limit state method of design which involves the critcria of safety
and serviceability both.

Fundamentally, lirnit state method of design of structures is a method ol'

designing structures based on a statistical concept of safety and the associated
statistical probability of failure. It also ensures an acceptable probability that the
structure will not become untit for its intended use during its lilk timc. [:or it.
various limit states which are conditions (or various forms of failure), when the
structure either collapses or is not in a condition (or stale) of being used for its
intended purpose, are considered. Two limit states of failure limit statcs ol'
collapse and limit states of serviceability consist of several typcs 01' failurc
patterns. l'he limit states of serviceability may include cxccssivc dcflcction or
displacement (which may adversely affect the finishes o r cause discoml'ort to thc
inhabitants of the structure) and/or excessive local damage resulting in cracking
or spalling or concrete (which may impair the elTiciency or appcarancc ofthe
structure). ?'he limit state of collapse may bc attained d i ~ cto cxccssivc loading
fatigue. vibrations due to wind or earthquakes. impact due to explosions or
disintegration due to frost or fire.

In the limit state method, the design loads for various li~nitstates arc obtained as
products of the characteristic loads and partial salety factors. I hcsc arc cuprcssed
as below :

F,,
=- Y, F,

where, F(,- Appropriate design load.

y, - Partial safety factor for loads, and
F, Characteristic load.
- mean load t k . Standard deviation
In the calculation of the characteristic load, the value of 'k' is normally chosen to be Simple Design and
1.64.This ensures the probability that the characteristic load is exceeded by only 5 Applications
percent during the lifetime of the structure. The characteristic load is independent of
the limit state being considered. In India, nominal imposed loads specified in IS : 875-
1987 [Indian Standard Code of Practice for Design Loads (other than earthquakes)
for buildings and structures (second revision), Bureau of Indian Standards,New
Delhi, 19891are taken as characteristic loads.
IS : 1343-1980specifies the Partial safety for various load combinations as under.

Limit State of

Note 1
DL is the dead load, LL is the live load andWL is the wind load.
Note 2
This value of 0.9 is to be considered when stability against overturning or
stress reversal is critical.
Note 3
While considering earthquake effects, substitute EL for WL.
Note 4
For the limit state of serviceability, the values of $ given in this table are
applicable for short-term effects. While assessing the long-term effects due
to creep, the dead load and the part of the live load, likely to be permanent,
may only be considered.
The design strengths of materials are calculated by dividing the
characteristic strengths by the partial safety factors for materials. The
design strength of a material is expressed as below.

where, f , = Characteristic strength of material. It corresponds to the 28 day

cube compressive strength of concrete or the tensile strength of
tendons below which the failures are not more than 5 percent,
and

y, = Partial safety factor for the material. It has a value which

depends upon the importance of the limit state being
considered. The values of for reinforcement and concrete, as
specified in IS : 1343-1980 are 1.15 and 1S O , respectively.
Prestressed Concrete
6.3 STRENGTH AND SERVICEABILITY LIMIT
STATES
Limit State of Collapse
For estimating the ultimate strength of prestressed concrete members in
flexure, 'Strain Compatibility method' may be used. For calculating the
ultimate strength, code provisions are based on simplified and idealized
stress blocks of concrete in compression. The Indian code method is
limited to the determination of ultimate strength of under-reinforced
sections in flexure based on the effective reinforcement ratio.
Following assumptions are taken in the design for the limit state of collapse
in bending or flexure.
Plane sections normal to the axis remain plane after bending.
The maximum strain in concrete at the outermost compression
fibre is taken as 0.0035 in bending.
The relationship between the compressive stress distribution in
concrete and the strain in concrete may be assumed to be
rectangle, trapezoid, parabola or any other shape which results
in prediction of strength in good agreement with the results of
tests. For design purposes, the compressive strength of
concrete in the structure is assumed to be 0.67 times the
characteristic strength. The partial safety factor for material
strength, equal to 1.5, is applied in addition to this.
The tensile strength of concrete is ignored.
The stresses in bonded prestressing tendons are derived from
the representative stress-strain curve for the type of steel used,
given by the manufacturer. For design purposes, the partial
safety factor for material strength, equal to 1.15 for steel, is
applied. Typical stress-strain curves for concrete and steel may
be obtained from IS : 456-1978.
If tendons are unbonded in post-tensioned members, the stress
in the tendons can be obtained from a rigorous analysis or from
tests.
Limit States of Serviceability
The following limit states of serviceability are considered by the code.
Limit State of Serviceability :Deflection
In the consideration of this limit state, the deflection of a structural
member is considered. The code recommends that the deflection of a
structure or part of it should not adversely affect the appearance the
efficiency of the structure or finishes or partitions. Some limits on the
maximum value of deflection have been recommended by the code.
Following are the guidelines as per the code in this regard :
For Type 1 and 2 Members
If short-term deflections are considered, the instantaneous
deflection due to design loads may be calculated using
elastic analysis based on the uncracked section and the
Young's modulus of elasticity of concrete.
 For long-term deflections, the total long-term deflection due Simple Design and
to the prestressing force, dead load and any sustained Applications
imposed load may be calculated using elastic analysis, taking
into account the effects of cracking and of creep and
shrinkage. Due allowance is given to loss of prestress after
the period considered.
For Q p e 3 Members
Where the permanent load is less than or equal to 25% of the
design imposed load, deflections may be calculated using
any elastic method. When permanent load is more than 25%
vertical deflection limits for beams and slabs may generally
be assumed to be satisfied provided that span to effective
depth ratios are not greater than the values specified.
Basic values of span to effective depth ratios for spans upto
10m may be taken as 7, 20 and 26 for cantilever, simply
supported and continuous members respectively. For spans
above 10 m, these values may be multiplied by lO/(span in
m) except for cantilever in which case deflection calculations
should be made.
Limit State of Serviceability :Cracking
Cracking of concrete should not affect the appearance or durability of the
structure. The criteria of limit state of cracking for the three types of
prestressed concrete members are as follows :
For type 1 prestressed concrete members : no tensile stresses
are allowed
For type 2 prestressed concrete members : tensile stresses are
allowed but no visible cracking should be there.
For type 3 prestressed concrete members : cracking in these
members is allowed but it should not affect the appearance or
durability of the structure. The acceptable limit of cracking
in this case depends on the type of structure and
environment. Any maximum limit to cracking is not
specified in this case. But as a rough guide, it has been
recommended that the surface width of cracks should not, in
general, exceed 0.1 rnrn for members exposed to aggressive
environment and it should not exceed 0.2 mm for all other
members.
Another limit state of serviceability for maximum compression also has
been specified by the code. The maximum values of compressive stresses
at the transfer stage as well as under the design loads should be within
limits, specified by the code. The code also guides that structures
designed for unusual or special functions should comply with any other
relevant additional limit states considered appropriate to that structure.

6.4 DESIGN OF RECTANGULAR PRESTRESSED

SECTIONS
In the case of prestressed concrete members, it is important to decide how much
prestressing force is to be provided in a structural member. If we wish to
Prestressed Concrete introduce more force in the member, we shall have to provide a larger arca oi'
steel tendons. This shall lead to a cost increase. We also can recall tli'it the
moment due to the prestressing force is equal to tlie product of'thc prestressing
force and the eccentricity of tendon at a section. So we increase thc ccccntricity
of tendons upto the ~naximunipossible limit rather than to incl-ca\i' the
prestressing lbrce only. Dependent on the maximum value ol'thc eutcn~alload
bending moment and the depth of the member. a suitable nia\irnum vali~cof
eccentricity may be calculated. This eccentricity may vary along the length of the
member (i.e., the profile ofthe tendons) depending on the distribution ol'loads on
tlie prestressed concrete member.
f'rcstressed concrete sections under tlie action of bending s l i o ~ ~ 4211141)
ld ~ l l cI~mits
specified for permissible stresses at the stage of transfer of prc\tre\s and tlic stage
of working or service loads. Expressions for the ~ n i n i ~ n uscct~on
~ii moduli
required. the amount of prestressing force and the eccentric~tjoi'tcndonh are
required for a section. These expressions niay be applied l i ~ various
r scc~ions
along the length ofthe concrete member and the amount ofeccenLric~tyol'
tendons can be varied along the length. These expressions arc dc~clopcd
considering the two critical combinations of prestress and moments at the two
extreme fibers at a section. The general critical combinations considered arc as
follous :
I'he maximum prestressing force at transfer, together with tlie
minimum moments sustained by the section and
l h e minimum prestressing force after all losses in combi~ialionwith
the maximum design moment for the serviceability limit state
I'he usual steps for the design of a section for a given combination ol' dead and
live loads are as follows :
(a) Calculate the minimum section modulus required Iy the I h I I o ~ i n g
expression.

-
where. '44, Bending moment due to live loads at tlie section.
M - Bending moment due to self load at the section.
q = Loss ratio, lying generally in the range of 0.75-0.80 li)r
pre-tensioned members and between 0.80-0.85 Ihr
post- tensioned members.
fb =T f,lA,,,
-

where, fi, = permissible stress at top fiber in compression, and

f;l, = Permissible stress at bottorii fiber in tension.
(b) Calculate the minimum value of prestressing force by the fbllowing
expression.

where, A - Area of cross sectio~lof'tlie memher.

j;, = Bottom fiber stress at the section due LO loads. and
.f, = Top fiber stress at the section due to loads
 (c) Calculate the eccentricity required at the section. Simple Design and
Applications

Generally the section selected is somewhat bigger than the

dimensions which are calculated in terms of the section modulus,
calculated in the first step of the above procedure. Consequently, the
prestress can lie between an upper and lower limit. Taking some
middle value of the prestressing force, eccentricity of the tendons can
be calculated.
-
Example 6.1

A post-tensioned prestressed beam has the following details.

Width of the section = 250 rnrn
Imposed load = 12 kN/m
Span of beam = 12 m
Loss of prestress = 15%
The stress in concrete must not exceed 17 N/mm2 in compression and
1.4 N/mm2 in tension at any time.
Calculate :
(a) The minimum possible depth of the beam.
(b) Minimum prestressing force and the corresponding eccentricity
Solution
Using the above equations, given in the procedure we get the value of the
depth of the section as 580 mm. The minimum prestressing force is
1170 kN and the corresponding eccentricity.is 167.5 mm.

6.5 PRESTRESSED CONCRETE PIPES

Liquid retaining structures, such as circular pipes, tanks and pressure vessels are
suited for circular prestressing. The circumferential hoop compression produced
in concrete by prestressing counterbalances the hoop tension developed due to
the internal fluid pressure. A reinforced concrete pressure pipe requires a large
amount of reinforcement to ensure low-tensile stresses resulting in a crack-free
member. Circular prestressing produces the required condition of a crack-free
member and the material is used more efficiently. Shrinkage cracks also are
eliminated in such a situation.
In circular prestressing, tendon wires are wrapped under tension over the
concrete pipes which are pre-cast. The tension in the tendon wires is produced by
pulling it through a die. Prestressed concrete pipes are ideally suited for a
pressure range of 0.5 to 2 N/mm2.For this pressure range, cast iron pipes and
steel pipes are not economical. Reinforced concrete pipes also are not practicable
for use as these have limited tensile strength. The technique of prestressing of
pipes was first introduced in 1930 and numerous pipelines have been installed
since then.
Prestressed Concrete According to the Indian standard code IS : 784, the design of prestressed concrete
pipes should cover the following five stages :
(a) Circumferential prestressing, winding with or without longitudinal
prestressing,
(b) Handling stresses with or without longitudinal prestressing,
(c) Condition in which a pipe is supported by saddles at extreme points
with full water load but zero hydrostatic pressure,
(d) Full working load conforming to the limit state of serviceability, and
(e) The first crack stage corresponding to the limit state of local damage.

PRESTRESSED CONCRETE POLES

In the past decades, prestressed concrete poles have become popular and have
replaced the traditional poles made of timber, steel or reinforced concrete. The
earliest prestressed concrete poles were designed in 1933 by Freyssinet.
Prestressed concrete poles are commonly mass produced and are used in most
countries for power transmission, antenna masts etc. The main advantages of
prestressed concrete poles are the following :
(a) Resistance to freeze-thaw effects in cold climate,
(b) Resistance to corrosion in moist conditions and to erosion in desert
areas,
(c) Easy handling and transportation due to less self weight,
(d) Fire resistance,
(e) Easy installation,
(f) Clean and neat appearance, and
(g) Increased crack resistance and improved rigidity.
These advantages have promoted the use of prestressed concrete poles all over
the world. In India, prestressed concrete poles are generally manufactured by the
long line method.
The maximum amount of resistance in a pole is generally required at the base
and, so, the maximum cross sectional area is required at the base section. Poles
are generally tapered with a hollow core to reduce the weight. For small lengths
of upto 12 m length, square or rectangular cross sections are generally provided.
These shapes are easy to construct and transport. I-section shapes are also
provided to the poles. However, these may be prone to more corrosion as a larger
area of the surface may be exposed to environment. Tubular sections are
preferred for large lengths of poles.
Prestressed concrete poles are generally designed as members with uniform
prestress since they are subjected to bending moments of equal magnitude in
opposite directions. The poles are generally designed for the following critical
load combinations :
(a) Bending due to wind load on the cable and on the exposed faces,
(b) Combined bending and torsion due to eccentric snapping of wires,
(c) Maximum torsion due to skew snapping of wires,
(d) Bending due to failure of all the wires on one side of pole, and
(e) Handling and erection stresses in the poles.
U n i f o d y prestressed members designed for equal flexure in opposite directions, Simple Design and
without permitting tensile stresses under working loads, require a larger Applications
cross-section and prestressing force. Poles, therefore, may be made in three
different types of prestressed members of type 1, 2 and 3.

(a) What are different approaches or methods of design of prestressed

concrete members?
(b) What are important considerations in the design of prestressed
concrete pipes and poles?'
(c) What do you understand by limit states?
(d) What are different limit states of serviceability?

6.7 SUMMARY
In this unit, we have been exposed to various applications and uses of prestressed
concrete. Various limit states, which are considered in the design of other types
of conventional structural systems also, are presented. In this connection, it shall
be a good exercise to refer Indian standard codes which present standard design
guidelines.
Design of rectangular prestressed concrete sections has been presented in a short
manner to impress upon the student how structural safety may be combined with
economy in the case of prestressed concrete construction also. The applicability
of prestressed concrete in the construction of pipes and poles also has been
presented and some of the requirements have been discussed. It may be of help to
the student to understand that prestressed concrete is a versatile material and
dependent on special requirements its use may be a worthwhile choice among the
engineers.

6.8 ANSWERS TO SAOs

Please refer the preceding text for all the Answers to SAQs.
Prestressed Concrete
FURTHER READINGS
N. Krishna Raju, Prestressed Concrete, (3d Edition), Tata McGraw-Hill
Publishing Company Limited, New Delhi.
James R. Libby, Modem Prestressed Concrete, (31dEdition), CBS Publishers and
Distributors, New Delhi.
Lin T. Y. and H. Bums Ned, Design of Prestressed Concrete Structures,
(3rdEdition), John Wiley and Sons, New York.