Prestressed Steel Beam

Report Titled

Prestressed Steel Beam

Submittedin partial fulfillment of

the requirements of the degree of

M Tech (Civil Engineering with Specialization in Structural Engineering)

ByVaibhav M Gaykar

122040009

2013

Prof. P. W. Kubde(Guide / Supervisor)

Structural Engineering DepartmentVeermata Jijabai Technological Institute

Mumbai 400 019

2013

VEERMATA JIJABAI TECHNOLOGICAL INSTITUTE

CERTIFICATE

This is to certify that the seminar on ‘Prestressed Steel Beam’ is in partial fulfillment of the

requirements of the Semester II syllabus of the M-Tech. (Civil Engineering with specialization in

Structural Engineering) Course conducted in VEERMATA JIJABAI TECHNOLOGICAL

INSTITUTE as prescribed by the UNIVERSITY OF MUMBAI for the academic year 2012-2013.

Submitted by,

VAIBHAV MADHUKAR GAYKAR

(Roll No. 122040009)

________________ ________________ _______________

Project Guide External Examiner External Examiner

Prof. P.W. Kubde Dr. M.A. Chakrabarti Dr. K.K. Sangle

_________________

Head of Department

Dr. A.N. Bambole

ACKNOWLEDGEMENT

I acknowledge my sincere thanks to my guide Prof. P.W. Kubde., professor in civil engineering for

his invaluable guidance, kind assistance and excellent counseling. His active participation in the

endeavor not only resulted in a resulted in a successful partial completion of the project but also

rendered the whole experience pleasant. I am grateful for the confidence that he has placed in me

during the project; taking keen interest at every stage of my work. He also directed me skillfully

transforming me into a cohesive unit and getting the work done through channelized the work.

Also I acknowledge with thanks, the assistance provided by the department staff, central library staff

and computer faculty staff. I would like to thank my colleagues and friends who directly or indirectly

helped me for the same.

Vaibhav Madhukar Gaykar

(Roll No. 122040009)

TABLE OF CONTENTS

Chapters

List of Figures i

Abstract ii

Chapter 1: Introduction 1

1.1 General 1

1.2 Basic Principles of prestressing 1

1.3 Advantages of Prestressed Beams 1

1.4 Disadvantages of prestressed Beams 2

Chapter 2: Literature Review 3

2.1 Method of Prestressing 3

2.1.1 Inroduction 3

2.1.2 Technology 4

2.2 Analysis of prestressed steel structure 7

2.2.1 General 8

2.2.2 Static analysis of section 8

2.2.3 Bending 8

2.2.4 Shear 10

2.2.5 Deflection 11

Chapter 3: Behavior of prestressed steel beams 13

3.1 Introduction 13

3.2 Description of analyzed steel beam 13

3.3 Finite Element Analyses of the analyzed prestressed beam 16

3.3.1 Failure during Tensioning 16

3.3.2 Beam with two deviators 18

3.3.3 Beam with five deviators 19

3.3.4 Beam with eleven deviators 20

3.3.5 Remarks concerning the results of NLFE analyses 20

3.3.6 Increase in Beam Capacity Provided by prestressing 22

Chapter 4: Experimentation 24

4.1 Introduction 24

4.2 Description 24

4.3 Results 26

Chapter 5: Conclusion 28

References 29

LIST OF FIGURES

Figures Title Page No.

2.1 Prestressed Steel Beam 3

2.2 Section A-A 3

2.3 Details of deflector stud 4

2.4 System of anchoring 5

2.5 Ferrule for anchoring strands 5

2.6 Box girder 6

2.7 Di-symmetrical Double T- Girder 6

2.8 Prestressed steel Girder - principle of function 7

2.9 Prestressed concrete Girder - principle of function 8

2.10 at transfer condition 9

2.11 at service condition 9

2.12 Shear 10

2.13 Deflected shape of prestressed I- beam 12

3.1 Beam with two, five and eleven deviators 13

3.2 Cross section at midspan 14

3.3 Horizontal displacement versus prestressing force curves 17

3.4 Deformed shape at failure during tensioning a) T2 b) T11 beam 18

3.5 Beam with two deviators 19

3.6 Beam with five deviators 19

3.7 Beam with eleven deviators 20

3.8 Failure load versus prestressing force 21

3.9 Applied load versus mid-span horizontal displacement 22

3.10 Increase in beam capacity versus prestressing force 23

4.1 Girder 24

4.2 Sliding bearing 25

4.3 Anchoring the ends 25

4.4 Distribution of load 26

4.5 Initial-Measurement of deflection at transfer phase 27

4.6 Final-Measurement of deflection at service phase 27

i

Abstract

The use of Prestressed concrete in structural field has been done for a long time, along with it

the use of Prestressed steel also started taking place. But due to the lack of knowledge and

calculation methods the use of Prestressed steel is very limited.

Prestressed steel beams are lighter than the traditional ones of the same length and the

vertical load capacity, this option could make them economically advantageous and a viable

solution in many practical solutions. In this project, the method of prestressing steel beam is

described along with the analysis methodology for the bending, shear and deflection. Also,

the behavior of the Prestressed steel beam is shown with the help of non-linear finite element

results with different deviator configurations. In the end some experimental work is also

presented which shows the advantages that the widespread use of Prestressed Steel can bring

to the sphere of the construction sector.

ii


CHAPTER 1

INTRODUCTION

1.1.General

The necessity for economy in steel in view of large quantities needed for construction and

rehabilitation of various steel structures prompted the requirement of saving steel. This is

possible by using more reinforced concrete and prestressed concrete than steel. But for long

spans where prestressed concrete is not viable, prestressed steel is the ideal solution. The

concept of prestressing steel is not a new frontier in the field of Civil Engineering. But it is

being widely considered only in the recent past, despite a long and successful history of

prestressing concrete members.

1.2.Basic principles of prestressing

The term ‘prestressed steel’ means application of a pre-determined concentric or eccentric

force to a steel member so that the state of stress in the member resulting from this force and

from any other anticipated external loading will be restricted to certain specified limit. This is

done by inducing opposite stresses in a structure before it is put to its actual use by

application of external forces. These forces are controlled in magnitude and direction to

counter act the developed stresses in beam due to working loads. It is very difficult to

establish a bond between the prestressing tendon and a steel beam. Hence external

prestressing technique is adopted for prestressing of steel beams.

1.3.Advantages of prestressed Steel Beams

Lighter and slender members are possible by use of prestressed steel when compared with un-

prestressed steel beams. The whole cross-section is effective in prestressed steel beams.

Prestressing of steel beams enhances its elastic range of the material and makes it more

ductile when compared with un-prestressed steel beams. Prestressing of steel beams improves

fatigue life of a structure and hence the technique is recommended for dynamically loaded

structures. The external prestressing technique can be applied to improve the load carrying

capacity of existing un-prestressed steel beams which is not always possible in Reinforced

Cement Concrete beams. We can temporarily improve the load carrying capacity of a beam

steadily by stage-by-stage prestressing to acquire the required load carrying capacity.

Standard components required for prestressed steel beams can be manufactured in factories

1


and hence a lot of time is saved. Prestressing remarkably reduces ultimate deflection and

hence high span depth ratios can be achieved. Prestressing steel girders increase the level of

the stress at which the beam starts to buckle. The total loss of tensile prestressed force in

cables is small in case of prestressed steel structures when compared with prestressed

concrete structures. Tendons of External prestressed beams can easily be designed to be

replaceable and re-stressable without major cost implications. Generally the webs can be

made thinner resulting in a comparatively lighter structure thereby facilitating execution.

1.4.Disadvantage of prestressed Steel Beams

Longer spans are not preferred to avoid possible bulking. Externally prestressed members can

easily be damaged with minor equipment. For certain cross-sections and construction

procedures, the handling of the tensioning devices is difficult. The availability of builders and

engineers experienced with the technique of external prestressing of steel is scanty. Initial

equipment cost is very high. Prestressing tendons are brittle as high strength steel is used. The

tendons are more exposed to environmental influences, fire, aggressive chemicals etc. The

deviators and anchor plates which are delicate components, have to be placed very

accurately. As the tendons are not bonded to the member (or bonded only at particular points)

the ultimate strength is developed in the ultimate design resulting in a higher prestressing

steel consumption. Usually cross-section cannot be fully utilized. Therefore a greater depth or

additional prestressing is required.

2


CHAPTER 2

LITERATURE REVIEW

2.1 Method of Prestressing

2.1.1 Introduction

The technique for realizing prestressed steel is achieved through external cables.

This procedure requires a preliminary phase of preparation which includes the following

operations:

a. Preparation of the girder through the insertion of contrast elements to the cable which

define the passage along the girder (deflectors);

b. Formation of the cable;

c. Placing the cables in position and their subsequent anchoring;

d. Applying tension to the reinforcements with jacks and tightening them;

e. Eventual re-tightening;

All this must be done with maximum care and requires a specialized workforce.

Figure 2.1-Prestressed steel beam

Figure 2.2-Section A-A

3


2.1.2 Technology

The first operation to carry out is to single out the line of the resulting cable and then to

position the contrasts, made up of symmetrical studs which define the line of the cables

themselves whose barycentric line is known as the “resulting cable”. Technically, the

contrasts are realized through symmetrical studs with regard to the web of the girder. The

studs are capped at one end to keep the cable in position and are welded to the web. Their

number depends on the length of the girder and the stresses in play (figure 2.3).

Figure 2.3-Details of deflector stud

Once this operation is completed, the next stage is the formation of the cables. During this

operation the strands are laid symmetrically in relation to the web and are freely left to run

around the deflectors which have been greased or lubricated to avoid friction. The strand,

which is made of high tensile steel is more susceptible by nature to corrosion than normal

steel and is therefore protected against this risk. The protection is done through zinc-plating

(galvanized strand) or through sheathing (sheathed strand) which consists in placing the

strand (often zinc-plated) in a high density polyethylene sheath in which it can slide freely

due to the presence of grease or wax which also act as protection against corrosion. With this

technique it is also possible to replace strands which turn out to be unsuitable. Protection

against corrosion can also be obtained by using a sheath of HDPE into which the strands are

inserted. The sheath will subsequently be injected with cement paste as occurs with

reinforced concrete. The next phase is anchoring which is the most delicate phase of the

entire operation. A very simple system of anchoring is shown in figure 2.4. It is made up of :

− A rigid plate

4


− Blockings

− Steel stiffeners.

Figure 2.4- System of anchoring

In particular, anchoring the strands foresees the use of conical-trunk ferrules inside of which

are toothed wedges of the same shape that hold the steel before tensioning (fig.2.5). Indeed,

tightening is assured precisely because of the contact between the strand and the wedge since

the strand, tending to pull in on itself, drags the wedge with it and thus self-blocks.

Figure 2.5-Ferrule for anchoring strands

After the preparation phase, the next step is to determine the action acting upon the girder, as

well as those associated with those induced by pretensioning. It must be added that the

sections most adapted to prestressing are those boxed beams (fig. 2.6) and those with a plate

5


girder (a di-symmetrical double T) (fig.2.7) since these are the ones that most suit this

technique, allowing for maximum exploitation of the material.

Figure 2.6- Box Girder

Figure 2.7- Di-symmetrical Double T-girder

6


2.2 Analysis of Prestressed Steel Structure

2.2.1 General

A prestressed system consists quite simply in “subjecting a structure to loads that produce

opposing stresses to those when it is in service”. Prestressing can be usefully applied to any

material and, in particular to steel (figure 2.8), thus improving considerably its resistance

characteristics.

In the case of P.C., the effect of prestressing enables beams to pass from being partial

reagents to become total reagents (only compression), (figure 2.9). The increase in the

characteristics of resistance is solely due to a greater use of the section. In the case of steel

this is taken for granted. The methods used for analyzing the sections are:

Figure 2.8: Prestressed steel Girder - principle of function

The static method is in which each section considers the effect of prestressing as an eccentric

pressure (traditional method).

The equivalent loads method, in which the effect of prestressing is analyzed through the

introduction of a system of equivalent forces of external provenance which exert pressure

upon the girder and are called “equivalent loads”.

7


Figure 2.9: Prestressed concrete beam - principle of function

2.2.2 Static analysis of section

With reference to a simply supported prestressed steel beam, it will be necessary to assess

whether in the section most under stress, the tensions owing to the loads and the prestressing

are lower than those allowed for by the limit state under consideration. An admissible value

for tension loss for P.S., on account of friction and steel relaxation is 5%. The value we take

into consideration is 10% (generally for P.C., tension losses due to friction, creep shrinkage

etc. are presumed to be 25% - 30%). Two load conditions will be taken into account, more

precisely, an initial or “at transfer” condition and a final or “at service” condition. In the first

case the prestressing force P will be increased through the application of a co-efficient β=

1.10 to take account of the total (or final) tension loss.

2.2.3 Bending

It may be said that prestressing was invented for bending girders and it is for this state of

stressing that we gain the most benefits. In reference to figure 2.10, it may be verified, at

transfer:

8


Figure 2.10-condition at transfer

σ i0=

−γ p βP

A−

γ p βPe

Zb

+M min

Zb

≤ f d

σ s0=

+γ p βP

A+

γ p βPe

Z t

−M min

Z t

≤ f d

where: A and Z are respectively the area and the section modulus of the steel girder, γp is the

partial coefficient of safety applied to the prestressing, Mmin is the minimum moment

calculated, taking into account the partial coefficients of safety applied to the loads, e is the

distance of the resulting cable from the centroid G.

Figure 2.11-at service condition

σ i1=

−γ p P

A+

γ p Pe

Zb

−M max

Zb

≤ f d

9


σ s1=

−γ p P

A−

γ p Pe

Z t

+M max

Z t

≤ f d

where - Mmax is the maximum moment taking into consideration the partial safety coefficients

applied to the loads.

2.2.4 Shear

For a prestressed steel beam and generic section S,

figure 2.12, we have:

Figure 2.12-Shear

V r=V−P sin∝

or,

V r0=V 0−γ p βP sin∝

V r1=V 1−γ p P sin∝

τ max=V r

t h

Where, t and h are respectively the thickness and the height of the web and thus:

τ max ≤f d

√3 for pure shearing

σ id=√σ2+3 τ2 ≤ f d for pure bending and shearing

10


2.2.5 Deflection

2.2.5.1 Importance of control of Deflection

Deflection forms an important criterion for safety of any structure. Suitable control on

deflection is very essential for the following reasons.

a. Excessive sagging of any structural members is unsightly and may sometimes render the

floor unsuitable for use by causing damage to finishes, partitions and associated structures.

b. Large deflections under dynamic effects and under the influence of variable loads may

cause discomfort to users.

2.2.5.2 Effect of Tendon Profile on Deflection

In the most of the cases of prestressed beams and tendons are located with eccentricities

towards the soffit of beams to counteract the sagging bending moments due to transverse

loads. Consequently the prestressed beams deflect upwards (camber) on the application of

prestress. Since the bending moment is the product of the prestressing force and eccentricity,

the tendon profile itself will represent the shape of the bending moment diagram.

2.2.5.3. Expressions for Estimation of Deflection

The method of computing deflections of simply supported eccentrically prestressed beam

with straight cable in two different approaches will be discussed in the following sections

a. Combined Effect of Prestress and External Load on Deflection

Consider a simply supported beam of span ‘l’, Flexural rigidity EI subjected to a total

uniformly distributed load of w/unit length and prestressed by a force ‘P’ at an eccentricity

‘e’. Let the deflection of the beam at a distance ‘x’ from left support be ‘y’. (Figure 2.13)

Then bending moment at any section at a distance of ‘x’ from left support is given by

M x=(w l x2 )−( w x2

2 )−P (e− y )

Hence from theory of pure bending,

E I xd2 ydx2 =

−( w l x )2

+(w x2

2 )+P (e− y )

11


Figure 2.13-Deflected shape of prestressed I- beam

Solving we get,

y=(w E I x

P2 −e)X {cos (√ PE I x

X (x− l2 ))

cos (√ PE I x

Xl2 )

−1}+(w x2 P )X ( x−l )

This is the generalised expression for finding the deflection of a simply supported eccentrically

prestressed beam considering the combined effect of prestress and total load.

Maximum deflection by symmetry occurs at x=l/2

Hence,

ymax=( w E I x

P2 −e)X {sec( PE I x

Xl2 )−1}−( wl2

2 P )

12


CHAPTER 3

BEHAVIOUR OF PRESTRESSED STEEL BEAMS

3.1 Introduction

Prestressing techniques for steel beams were developed many years ago, both for the

construction of new structures and for the rehabilitation of existing structures. Although

tensioning principles were initially formulated and developed for reinforced concrete

structures, the prestressing technology began to be applied also to steel beams by Dischinger

and Magnel and by other engineers. The prestressed steel technique has been adopted mainly

for bridges and rarely for roof structures.

This chapter analyses the behaviour of I-shaped prestressed steel beams having a medium

span _i.e., a span in the range (35-45m) for use as roof elements for buildings. In particular,

the effects on the beams’ response, of the number of deviators (which impose the shape of the

tendons by fixing the distance between tendons and beam) and of the prestressing force

value, are thoroughly investigated.

Figure 3.1-Beam with two, five and eleven deviators

3.2. Description of the analysed prestressed steel Beam

Prestressed steel I-beams are analysed; the dimensions of the beams and the tendon shapes

are illustrated in Fig. 2.14, depending on the number of deviators. A span equal to 40 m has

13


been selected as the average value (35–45 m) of the range assumed for medium-span beams.

In order to allow comparison of results obtained with nonlinear finite element (NLFE)

analyses, all beams have the same span (40 m), the same I-shaped cross section, two tendons,

and 15 ribs. The ribs are located at beam ends and along the longitudinal axis (x direction).

The cross section is asymmetric with respect to the z axis (Fig. 3.2). Because the number of

stiffening ribs slightly affects the stiffness of the beam, all the beams have the same number

of ribs. Grade S275 steel, having a yielding strength of 275 MPa and an ultimate strength of

430 MPa, is adopted for beams and stiffening ribs. Tendons are composed of low-relaxation,

highstrength prestressing strands with a 0.6-inch diameter. Strands are made of steel with a

tensile strength fpk of 1,860 MPa. The geometrical features of the analysed beams are

summarized in Table 1. It should be noted that in Table 1 beams with tendons comprised of

four strands are indicated with an asterisk (for example T5*) while beams with tendons

comprised of 12 strands are indicated without the asterisk (for example T5).

Beams are named according to their number of deviators and according to the applied

prestressing force; for example, “T2-1000” is a beam with two deviators and a total axial

force of Np=1,000 kN.

Figure 3.2-Cross section at midspan

14


Table 1-Geometrical features

No lateral restraints are imposed during in situ pretensioning, Step b, except for the case of

“delayed tensioning” (see below). In Steps c–f, bracing at the top and at the bottom flanges

are usually connected to the beam, providing lateral stability. In Table 2, the italicized data

indicate load steps without bracing, whereas the rests indicate load steps with bracing. As

previously stated, NLFE analyses are carried out by assuming bracing both at the top and

bottom flanges except for some analyses which were performed with top flange bracing only.

These analyses are identified with the letters “-BTS.” For example, “T2-1000-BTS” is a

beam with two deviators, prestressed with axial force Np=1,000 kN and with top flange

bracing only. Furthermore, the beams identified with the letters “-NI” were analysed without

taking into account geometrical imperfections and with bracing at the top and bottom flanges,

except beams identified with letter “-NI-BTS” which have the bracing only at the top flange.

Table 2-Load multipliers, referring to the steps and the Load combinations considered in the analyses

In the analyses with delayed tensioning, bracing at the top and bottom flanges are present in

Step b also when the prestressing force is introduced (see Table 2). Stress losses in tendons

15


are not considered because friction losses are negligible for unbounded tendons and

relaxation losses are negligible.

3.3. Finite-Element Analyses of the Analysed Prestressed Steel Beams

Buckling and nonlinear finite element analyses _with both mechanical and geometrical

nonlinearities_ were carried out with the ABAQUS code. Four-node shell elements _S4_

were employed for beam and stiffening ribs, three-dimensional pipe elements (B31) for

deviators having a radius of 70 mm and a thickness of 12 mm, and tube-tube contact elements

(ITT31) for modelling the finite-sliding interaction where tendons are inside the deviators.

Fixed boundary conditions were imposed to simulate supports and lateral restraint resulting

from the bracing.

A plasticity model with isotropic hardening behaviour was used to define the mechanical

properties of the steel for the beam.

NLFE analyses were carried out in load control by adopting Newton’s method as

convergence criteria. This means that the beam capacity was identified in correspondence of

the peak value of the applied load corresponding to the last converging solution. It is well

known that by standard load-control iterative procedures, it is not possible to describe

softening branch or to detect bifurcation phenomena, etc. in the structural response. However,

in the section titled “Remarks concerning the results of NLFE analyses,” it is shown that

convergence fails after the yielding of the steel, in correspondence with high levels of

deformation. Even if higher values of displacement could be achieved with more refined

solution techniques, no significant increase in applied loads can be obtained; in addition,

higher values of deformation are not germane to this study because they cannot be accepted

in practice.

3.3.1 Failure during Tensioning

The beam behaviour during tensioning was analysed in order to evaluate the maximum

prestressing force that can be applied. The maximum prestressing force during tensioning

was evaluated by applying the self-weight load and by increasing the prestressing until failure

occurred. Fig. 3.3 depicts the top flange horizontal displacement (z direction) at the mid-span

versus the prestressing force value for beams T2, T5, and T11; the initial horizontal

displacement is not zero because of the imposed geometrical imperfection and self-weight.

Deformed shapes at failure are shown in Fig. 17 for beams T2 and T11. Geometrical

imperfection generates for T2 beam (with the greatest spacing between deviators (13.333 m))

16


the largest horizontal displacements at mid-span; these horizontal displacements reach, in

correspondence with the maximum prestressing force (1,559 kN), a value of 375 mm. For the

T11 beam, the maximum value of the prestressing force (3,291 kN) is much higher than the

value for the T2 beam and the horizontal displacements at mid-span reach, in correspondence

with the maximum prestressing force, a value of 136 mm.

Figure 3.3-Horizontal displacement versus prestressing force curves

The maximum value of the prestressing force for the T5 beam (3,121 kN) is between the

values of beams T2 and T11. Even if, during tensioning, the behaviour of the T5 beam is

similar to the behaviour of the T11 beam, it can be pointed out that the maximum values of

prestressing forces for beams T5 and T11 are similar, but the corresponding horizontal

displacements are quite different. Indeed, the displacement of the T11 beam is about 60% of

the displacement of the T5 beam (219 mm).

17


Figure 3.41-Deformed shape at failure during tensioning a) T2 b) T11 beam

3.3.2 Beam with Two Deviators

Fig. 18 shows, for T2 beams, midspan deflection versus applied load curves obtained, taking

into account _in NLFE analyses_ the effects of geometrical imperfection. Fig18_a_ refers to

beams with bracing only at the top flange, whereas Fig3.5_b_ refers to beams with bracing at

the top and bottom flanges. Fig. 3.5a_ shows that, for beams with bracing only at the top

flange, a very low value of prestressing force of 500 kN _T2_-500-BTS beam_ is about the

greatest value that can be applied. Indeed, using a prestressing force value of 500 kN, the

vertical load capacity of the beam increases with respect to the nonprestressed beam _T2_-0-

BTS_, but a prestressing force value equal to 1,000 kN _T2_-1000-BTS_ causes a decrease in

beam strength with respect to the nonprestressed beam _T2_-0-BTS_. In fact, owing to

geometrical imperfections, the deformation of the T2_-1000-BTS beam is so amplified by the

prestressing force _during step loads a and b_ that, when vertical loads are applied _from step

load c to f_, failure is quickly reached because of large horizontal displacements.

For the same reason, the stiffness of T2_-1000-BTS in the elastic range is lower than T2_-0-

BTS. Fig. 3.5_b_ shows that for beams with bracing at the top and bottom flanges, a

prestressing force up to 1,000 kN _T2_-1000_ can be applied, increasing the vertical load

capacity of the beam with respect to the nonprestressed beam _T2_-0_. Indeed, the bracing at

the bottom flanges _applied after load Step b_ fixes out-of-plane displacements and avoids

lateral instability; as a result, in Fig. 3.5_b_, the slopes of all the curves in the elastic range

are the same.

18


Figure 3.5-Beam with two deviators a) Bracing only at top span b) Bracing at top and bottom flanges

3.3.3. Beam with Five Deviators

In Fig. 3.6, midspan deflection versus applied load curves obtained with NLFE analyses,

taking into account the effects of geometrical imperfections, shows that for beams with

bracing only at the top flange, the optimal value of prestressing force of 2,000 kN _T5-2000-

BTS_ corresponds to the highest vertical load capacity of the beam. While, for beams with

bracing at the top and bottom flanges, Fig. 3.6_b_ shows that the optimal prestressing force

value is 3,000 kN. In the section titled “Remarks concerning the results of NLFE analyses,” it

is shown that even if the vertical load capacities of beams T5-3000 and T5-2000 are similar,

the horizontal displacements of the T5-3000 beam are much higher than those of the T5-2000

beam, as seen in Fig. 3.6_b_.

Figure 3.6- Beam with five deviators a) bracing only at top flange b) bracing at top and bottom flanges

19


3.3.4. Beam with Eleven Deviators

Fig. 3.7_a_ refers to T11 beams with bracing at the top flange only, whereas Fig. 8_b_ refers

to T11 beams with bracing at the top and bottom flanges. The prestressing force value of

3,000 kN corresponds to the highest vertical load capacity of the beam, both for beams with

only top flange bracing, Fig. 3.7_a_, and for beams with bracing at the top and bottom

flanges, Fig. 3.7_b_. Fig. 3.7_a_ illustrates midspan deflection versus applied load curves

obtained without taking into account the effects of geometrical imperfection _“-NI”_.

Therefore, web strengthening is required to increase the vertical load capacity of the beam, as

shown in Fig. 3.7_b_.

Figure 3.7 Beam with eleven deviators a) Bracing only at top span b) Bracing at top and bottom flanges

3.3.5. Remarks concerning the Results of NLFE Analyses

Some remarks are in order pertaining to the NLFE analyses reported in this paper on

prestressed steel beams.

3.3.5.1.Maximum Prestressing Force

In the first loading phase, which is tensioning, the maximum prestressing force values

increase as the number of deviators increases and so, the spacing between the deviators

decreases _e.g.,

in Fig. 3, the maximum prestressing forces are 1,559 and 3,291 kN for beams T2 and T11,

respectively_.

3.3.5.2. Optimal Prestressing Force

In the second loading phase, that is, loading after tensioning _when vertical loads are

applied_, the optimal value of prestressing force _providing the maximum load capacity of

the beam_ can be identified. Fig. 21 refers to beams with bracing at the top and bottom

20


flanges and shows the failure load versus the prestressing force curves. It can be mentioned

that the optimal value of prestressing forces _which are 1,000, 3,000, and 3,000 kN for beams

T2, T5, and T11, respectively_ increase as the number of deviators increases. For the T5

beam, however, a value for the prestressing force of 2,000 kN must be considered as the

“preferred value” because for a prestressing force value of 3,000 kN _which is the optimal

value as defined in the introduction_, the horizontal displacements, illustrated in Fig. 3.9_b_,

cannot be accepted in practice.

Figure 3.8 Failure load versus prestressing force for beams with the bracing at the top and bottom flanges

3.3.5.3. Bracing Effects on Lateral Stability

The advantages provided by a double bracing _at the top and bottom flanges_ can be pointed

out in Figs3.9_a and b_ in which applied load versus mid-span horizontal displacement

curves are shown for T5 beams. Horizontal displacements at the top flange and bottom flange

are shown in Fig. 3.9_a_ for beams with only top flange bracing and in Fig. 22_b_ for beams

with bracing both at the top and bottom flanges. Focusing on beam T5-2000-BTS, as an

example, Fig. 3.9_a_ shows that at the end of tensioning, the top flange reaches a positive

horizontal displacement of +114 mm; after tensioning, bracing is placed at the top of the T5-

2000-BTS beam, so this horizontal displacement value remains fixed. The bottom flange

reaches a positive value at the end of tensioning of +27 mm, after tensioning no bracing is

placed at the bottom flange for beam T5-2000-BTS, so the horizontal displacement reaches a

negative value at failure of _252 mm. This means that large rotations of the section about the

x axis also occur. For a prestressing force value of 3,000 kN _T5-3000-BTS_, Fig.3.9_a_

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shows that the horizontal displacement at failure of the bottom flanges reaches a negative

value of _495 mm, which is unacceptable in practice. For beams with both top and bottom

flange bracings, midspan horizontal displacements remain fixed in both flanges when vertical

loads are applied, as shown in Fig. 3.9_b_. For this reason, these beams are able to carry

higher values of load than beams with only top flange bracing.

Figure 3.9- Applied laod versus midspan horizontal displacement for beams with five deviators a) bracing

at top flange b) bracing at top and bottom flange

3.3.6. Increase in Beam Capacity Provided by Prestressing

3.3.6.1. Effects

With the aim of quantifying the benefits of tensioning, the increase in beam capacity, _

LOAD, of the prestressed beams with respect to non-prestressed beams is shown in Fig. 3.10,

which considers beams with bracing at the top and bottom flanges. Note that the non-

prestressed beams have two tendons _the same as those of prestressed beams_, which work

under loads, even though they are non-prestressed.

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Figure 3.10-Increase in beam capacity versus prestressing force

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CHAPTER 4

Experimentation

4.1. Introduction

Having described the techniques for employing prestressed steel it would be useful to present

the results of an experiment which started in April ’99 under the guidance of the engineer, Mr

Nunziata. The test consisted in observing and studying the behaviour of a 21.40-meter pre

stressed steel girder. It goes without saying that the girder had first been studied theoretically

to determine its dimensions, loads and other characteristics, after which it was realized. The

girder is shown in figure 4.1.

Figure 4.1-Girder

4.2 Description

The girder has the following characteristics:

It has a height of 80 cm., and is prestressed with ten strands, foreseeing a total capacity of

21.6 kN/m, (equal to 10,2 kN/m for dead loads and 11,4 kN/m for imposed loads) excluding

its own weight which is equal to 1.72 kN/m. The beam was positioned in an outdoor

courtyard and rested on two supports, one of which was a sliding bearing and the other a

hinge (fig.4.2).

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Figure 4.2-Sliding bearing

The strand deflectors were positioned, which in turn, were anchored at the ends of the girder

with blockings (fig.4.3). Finally, we proceeded to the distribution of the load with blocks of

cement of 25 kN (fig.4.4) and to the tightening of each strand with a force of an intensity

equal to 151 kN.

Figure 4.3-Anchoring the ends

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Figure 4.4-Distribution of load

After this, we passed to the measurement of the deflection in the middle span with a fiftieths

calibre for the three fundamental phases (fig.4.5 & 4.6).

4.3 Results

The following results were obtained:

a. In the at transfer phase, the deflection is equal to 54.54 mm.

b. In the loading phase, taking into account the climatic conditions, the following values were

recorded:

− -68.32 mm. immediately after loading phase;

− -76.04 mm. after three days;

− -76.00 mm. after one week;

− -77.80 mm. after twelve days;

− -78.70 mm. after thirteen days;

− -79.84 mm. after about a month;

− -79.64 mm. after over two months.

c. In the unloading phase, we recorded an elastic return and the final deflection was 37.84

mm.

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Figure 4.5 Initial-Measurement of deflection at transfer phase

Figure 4.6-Final-Measurement of deflection at service phase

Through this experiment, even though it was carried out under difficult conditions, the results

obtained were significant and underline two particular facts:

a. The superiority in terms of resistance and deformation of structures in prestressed steel

compared to analogous structural typologies;

b. The economy and simplicity of execution of the proposed technology which can be

realized with simple elements and is accessible to all.

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CHAPTER 5

CONCLUSIONS

The number of deviators and the prestressing force are investigated as critical

parameters in the design of Prestressed steel beams of medium span. Indeed, a general

outcome of this study is that, mainly due to mitigation of buckling and consequently.

thanks to the higher value of prestressing force that can be applied, the vertical load

capacity increases with the number of deviators.

For practical solutions, it is not recommended to impose the shape of tendons by only

two deviators. Indeed, for beams with two deviators, the lowest values of prestressing

force can be applied and lowest values of vertical load capacity can be achieved.

Furthermore, the deformed shape of a beam with two deviators is characterized at

midspan by a decrease in the distance between the tendons and the beam axis as the

load increases; this phenomenon causes a loss in tendon eccentricity and consequently

a loss in vertical load capacity of the beam.

For an assigned number of deviators, and for the same prestressing force value, a

beam having bracing both at the top and bottom flanges performs better than a beam

having only bracing at the top flange.

The presented information in a very concise manner, it has illustrated some structures

in prestressed steel and a technology which is very simple. This is in the hope that

such a technique will become more widely used since prestressed steel is a material

which can bring both economic benefit and technical benefit to the sphere of the

construction industry.

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REFERENCES

1. A. Masullo, V. Nunziata, “Prestressed steel structures: historical and technological

analysis”, Structure in acciaio precompresso, Nunziata, Vincenzo 1999.

2. B. Belletti and A. Gasperi, “Behavior of Prestressed Steel Beams”, J. Struct. Eng.,

ASCE September 2010 vol.136:1131-1139.

3. M. Raju Ponnada and R. Vipparthy, “Improved Method of Estimating Deflection in

Prestressed Steel I-Beams”, Asian Journal Of Civil Engineering (BHRC) vol. 14, no.

5 (2013), Pages 765-772.

4. M.S.Troitsky (1990), “Prestressed Steel Bridges Theory and Design”, Van Nostrand

Reinhold Company.

5. Nunziata, V. _2004_, Strutture in acciaio precompresso, D. Flaccovio, ed., D.

Flaccovio Publishers, Palermo, Italy (in Italian).

6. V. Nunziata, “Prestressed Steel Structures Design: A New Frontier for Structural

Engineering”, Structure in acciaio precompresso, Nunziata, Vincenzo 1999.

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Prestressed Steel Beam