technical report and design calculation · technical report and design calculation ... the purpose...

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[email protected]

TECHNICAL REPORT AND DESIGN CALCULATION

OBJECT:

PRESTRESSED PRECAST CONCRETE BEAMS

"LISTOTECH" FOR DECKING FLOOR

COMMISSIONER:

TYPE:

[email protected]

(L=4,0 m. - span=500 mm.)

DESIGN ENGINEER:

ANNEX:

DATE:

Ing. Alberto CALZAVARA

___________________________________________________________________

APPENDIX A - APPENDIX B

__________________________________________________________________

Thursday, October 14th, 2010

Ascoingegneria S.r.l.

v.le Navigazione Interna n. 51/B - Padova PD (Italy)

Tel. 049772632 – Fax. 0498072121

[email protected]

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Summary

Summary ...................................................................................................................................................... 2

Abstract ........................................................................................................................................................ 4

Chapter 1 - General Provisions .......................................................................................................................... 6

1.1 Scope ................................................................................................................................................. 6

1.2 Purpose .............................................................................................................................................. 6

1.3 General description ........................................................................................................................... 6

1.4 Use ..................................................................................................................................................... 7

1.5 Applicability ....................................................................................................................................... 7

1.6 Placing ................................................................................................................................................ 9

Chapter 2 - Main data ...................................................................................................................................... 10

2.1 General ............................................................................................................................................ 10

2.2 Software .......................................................................................................................................... 10

2.3 Codes ............................................................................................................................................... 10

2.4 Characteristic Loads ......................................................................................................................... 10

2.5 Construction stages - TDA ............................................................................................................... 10

2.5.1 Definition ................................................................................................................................. 10

2.5.2 Losses ....................................................................................................................................... 12

2.5.3 Construction Stage ST1 ............................................................................................................ 12




2.6 Loads ................................................................................................................................................ 14

2.7 Combinations ................................................................................................................................... 15

2.8 Section and tendon ......................................................................................................................... 15

2.9 Materials .......................................................................................................................................... 16

2.9.1 Concrete .................................................................................................................................. 16

2.9.2 High tensile tendon ................................................................................................................. 18

2.10 Beam strand pattern ....................................................................................................................... 18

2.10.1 Initial stress and force ............................................................................................................. 18

2.10.2 Transmission lenght ................................................................................................................. 18

2.11 Concrete Exposure ........................................................................................................................... 18

Chapter 3 - Results and Checks ....................................................................................................................... 19

3.1 APPENDIX B...................................................................................................................................... 19

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3.2 Specific considerations .................................................................................................................... 19

3.3 Beam particularity ........................................................................................................................... 19

3.4 Shear ................................................................................................................................................ 19

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Abstract

In this document we design and check a typical Listotech continuous beam, total length 4,0

m. The element is placed on support every 0,5 m., thus it's a continuous beam by 8 equal span.

The scope is to define, for a pre-determinate schema, the maximum characteristic live loads

(point forces or line forces) allowable by the User.

Since the listotech elements are not each other connected, the structural approach must take

in account only a single isolated element subject to point forces (N) or line forces (N/m)), put on the

individual beam with no chance of load's partition along adjacent beams. In fact, should be incorrect

a design in order to allow the Listotech system such as capable of a definite capacity and response

with reference to a surface distributed load (N/m2), put on a generic "square meter" of indefinite

deck slab.

Two simplified different schemas of loads are taken in account:

schema 1: live distributed line force qk = 3500 N/m

schema 2: live concentrated point force Pk = 1000 (N) at the middle of every

span.

Obviously

We show, in this document, that the values qk = 3500 N/m (for line force) or Pk = 1000 (N) (for

point force), are the maximum against the allowed limit of serviceability.

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The most limitative, for checking, is the serviceability limit state (and not ultimate capacity

and response), and specifically the restriction of maximum allowable principal stress 1 (at time

infinite (t=18000 days), after all losses), which value must be less or equal than the maximum

allowed tension design concrete value fctd, where fctd = 2,75 Mpa, as that the concrete used is

Concrete Class C 90/105(*)

.

Note (*):

Concrete C 90/105 →fctk0,05 = 4,13 Mpa; c =1,5 →fctd = fctk0,05/c= 4,13/ 1,5=

2,75 Mpa

The section where 1 is higher, is:

for schema 1: x= 500 mm. (or symmetrically x=3500 mm.) (bending moment M-)

for schema 2: x= 250 mm. (or symmetrically x=3750 mm.) (bending moment M+)

In practice, we suggest the User to consider only the possibility of concentrated point forces

(schema 2), determined for example by same table legs.

In such way the only two things to do is simply verify that:

1) There is not any value of concentrated live load Pk more than 1000 N

2) There is not more than one Pk along each every span (0,5 m.).

The Pk live loads can be in the number of height (one every height span), positioned at the middle

of each span, as schema 2 drawing, but, more realistically, can be in any number and any position,

randomly, dealing only same span.

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Chapter 1 - General Provisions

1.1 Scope This technical report shall apply to the use of "Listotech" products as floor decking in multi-span continuous

beam. This document is completed by joints:

APPENDIX A

APPENDIX C

1.2 Purpose The purpose of this technical report shall be the design and calculation of Listotech prestressed precast

beam in accordance with the exceptions EC2 codes, with the exceptions treated at Chapter 2, to valuate

ultimate and serviceability state limits for designed spans and loads.

1.3 General description LISTOTECH is a high-strength concrete precast prestressed beam, by a thin section.

The beam section is (mm) (Figure 1.3 (a):

Figure 1.3 (a)

LISTOTECH can be used in various fields of application, either vertically, as cladding, or horizontally, as

decking floor.

Further, LISTOTECH, when used as floor, can lean, either:

On continuous bed surface (sand)

Over multiple supports-points, as a continuous beam, having a not negligible internal forces

bending moments and shear, so the beam must testify an appropriate structural behavior.

Therefore in this case binds over same commensurate design and calculation, in this document

treated.

The maximum length makeable of each LISTOTECH element is 4,0 m.

http://it.dicios.com/enit/fields-of-application

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1.4 Use

Recovering argument of previous § 1.3, the LISTOTECH decking floor, over several points-supports, can be used in several general practices (generally outdoor but even indoor), such as, for example, in order of use like:

floor around swimming pool

deck floor of restaurant balcony

deck floor of ballroom

catwalk

footbridge

gangplank

and so on For all these cases the design must ensure the safety and serviceability requirements, according structurals codes, for limiting stress and strains, deflection, crack width, similary to any other kind of decking structural continous precast prestressed beam. Indeed, as yet above poited, not all EC2 requimements can be respected, caused by thin section thikness, low concrete cover, no presence of specific minimum shear reinforcement (even if the design is in the case of no shear reinforcement required), and no transversal connections for redristribution among accosted elements. For that, in a parallel way, shall be done a series of testing with official laboratory to confirm and ratify the theoretic calculation, and shall be to dispacht all procedures to obtain the authorizations the element from public Structural Departement, according practices indicates by Codes. Therefore, this design calculation with a parallel dossier of conformity, shall be intended for the use of LISTOTECH elements as structurals elements, in a system of undefined approached beams to create, all toghether, a decking surface floor. loaded by the maximun possible values of characteristic live loads:

qk line forces distributed (1). or

Pk point forces concentrated (1).

1.5 Applicability For the purpose, this document shall apply to beams according to the following statically schema and load

condition (Figure 1.5 (a))

Type L (mm) span

n. s (mm)

LISTOTECH 50/400 4000 8 500

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Figure 1.5 (a)

In the Figure 1.5 (b) a more detailed draw of LISTOTECH 50-400, which is the case treated in this document,

representative a LISTOTECH beam above 9 support (8 span 500 mm. each). Thus the total lenght of beam is

4000 mm., maximum allowable through production and uptake & transport stage.

This document shall not apply to the following:

Transversal continous support in aluminium (or metal cold formed)

Vertical supports

Figure 1.5 (b)

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1.6 Placing The entire deck is shaped by placing LISTOTECH beam elements went alongside by span of 100 mm. (Figure

1.6 (a):

Figure 1.6 (a)

No transversal connections are contemplated, therefore every element is disconnected with each other .

As in Abstract said, since the listotech elements are not each other connected, the structural approach

must take in account only a single isolated element subject to point forces (N) or line forces (N/m)), put on

the individual beam with no chance of load's partition along adjacent beams. In fact, should be incorrect a

design in order to allow the Listotech system such as capable of a definite capacity and response with

reference to a surface distributed load (N/m2), put on a generic "square meter" of indefinite deck slab.

Two alternative simplified different schemas of loads are taken in account:

schema 1: live distributed line force qk = 3500 N/m

schema 2: live concentrated point force Pk = 1000 (N) at the middle of every span.

http://it.dicios.com/enit/transversal

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Chapter 2 - Main data

2.1 General The design is controlled by a specific software but also by direct valuation regarding shear capacity and generally regarding checks of portion nearest of first (and, symmetrically, last) node. For entire design this document is finished also by data included in APPENDIX A.

2.2 Software Software used for structural Analysis & Design: Scia Engineer 2010. Producer: Nemetschek Scia Group nv - Industrieweg 1007 - B-3540 Herk de Stad - Belgium. Release: 2010. License: n. 553497 licensee to Ing. Alberto Calzavara, v.le della Navigazione Interna 51/B – 35129 Padova (Italy).

2.3 Codes

The design shall be in accordance with:

EN 1990: Basic of structural design

EN 1991: Action of structures

EN 1992: Design of concrete structures

2.4 Characteristic Loads

The beam shall be verified as subject to following loads: Permanent G1 : self Weight Variables:

In Schema 1: Live line loads qk: 3500 kN/m in each span. or, alternatively

In Schema 2: Live point loads Pk: 1000 kN/m in each span.

2.5 Construction stages - TDA

2.5.1 Definition

Design evaluations shall be done out the following construction stages, each through TDA calculation (Time

Dependant Analysis):

ST1: prestressing and "cutting" strands in stressing beds - Time 1 (t=0)

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ST2: removal of element from stressing bed by raising and transport at storage (temporary

supports); raising and transport from storage into final definitive supports positioning to

form decking floor (1)- Time 2 (1 day (steam curing))

ST3: placing with lives loads supposed in Schema 1, in final position - Time 3 (t=28 days)

ST4: lives loads in final position supposed in Schema 2 - Time 4 (t=18000 days - t=∞ - end of

construction life)

Via TDA analysis the full process of aging is taken in account, including relaxion of the steel reinforcement,

creep and shrinkage of concrete.

Note (1): To simplify the different cases of ST2 are merged in only one case: raising and transport on

temporary support (crane hook) at t=1 th day.

Figure 2.5.1 (a) describes the four construction stages.

Figure 2.5.1 (a)

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2.5.2 Losses

During all construction life the beam is subject to varying degrees of losses (1) (2):

I. Loss due to anchorage's relocation

I. Loss due to elastic deformation of beam

II. Conjoint losses due to steel relaxion

III. Conjoint losses due to: steel relaxion -shrinkage of concrete - creep of concrete

Note (1)

In fact under prestressing sustained permanent load, the beam tends to develop some

amount of plasticity and will not return completely to its original shape. There has

been an irreversible deformation or permanent set. Shrinkage of concrete, "creep" of

concrete and relaxion of steel reinforcement are sources of prestress loss and are

provided for in the design of prestressed concrete by TDA analysis. The magnitude of

shrinkage depends on the environmental conditions and type of concrete. With pre-

tensioning, shrinkage starts as soon as the concrete is poured.

Note (2):

In this document (and generally), the sum of all losses (I+II+III+IV) are called and known by the only

denomination as "creep".

"Creep" are variable along beam's section, where the highest losses are at the begin and at the end of

beams.

2.5.3 Construction Stage ST1

General

This first phase consists of pre-tensioning by application, before casting, of a tensile force to high tensile

steel tendons around which the concrete is to be cast. When the placed concrete has developed a sufficient

compressive strength, a compressive force P0 is imparted to it by releasing the tendons, so that the

concrete member is in a permanent state of prestress.

Time - Losses Heat treatment is used to accelerate the strength-gaining rate of concrete to allow cutting strands the day

after concrete casting. Time t=1 day (t=0).

Total "Creep" at the moment of tendon's releasing, are: I+II+ a small amount of III.

Loads and Static schema The beam is placed on stressing bed. Tendon has none eccentricity, therefore no bending moment is

created.

The beam is subjected to:

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P0 - prestressing

G1 - self weight


General

This phase consists of transport condition from stressing bed to storage and from storage to final placing.

Time - losses Hereto we unify all that condition in only one at 27 days (from storage to placing) whenas we have the

greater losses. (t=27).

Total "Creep" at 27 days are I+II+III+IV .

Loads and Static schema The beam is raised by two hook crane at 900 mm. from begin and end nodes.

The beam is subjected to:

G1 - self weight

Qdin - increase of 30%*G1, to take in account dynamic condition.


General

This phase is the final definitive placing phase at 28 days when lives loads can be applied.

Time - losses Total "Creep" at 28 days are I+II+III+IV.

Loads and Static schema Definitive schema:

The beam is subject to:

G1 - self weight

qs1; qs2.....qs8 , live variable loads, on heaviest combinations (1).

Note (1) The choice is to apply only variable loads without any permanent led load.

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General

This phase is the final definitive placing phase at t=∞ (t=18000 days (50 years)) by all possible

combinations of lives loads applied.

Time - losses Total "Creep" at 18000 days are I+II+III+IV.

Loads and Static schema Definitive schema (the same of ST3):

The beam is subject to:

G1 - self weight

Ps1; Ps2.....Ps8 , live variable loads, on heaviest combinations (1).

Note (1) The choice is to apply only variable loads without any permanent led load.

2.6 Loads

The value of characteristic variable load is:

3500 N/m in each span, for ST3 construction stage

1000 N in each span, for ST4 construction stage

The beam wide is 100 mm. and the elements are accosted with each other, without any connection.

The choose of coefficients of combinations shall be for the most conservative case of use, the Category E (Table 2.6 (a),

Category Intended use

A Residential homes, Hotels (excluded crowded areas)

B1 Private offices

B2 Public offices

C1 Hospitals, Restaurants, Banks, Scools

C2 Balcony, Galleries, Cinema Theatres, Congress rooms, Churchs, Stands (fix places)

C3 Museum, Show rooms, Stations, Dance-Halls, Gym, Stands (mobile places), Public Events areas, Concert Hall, Sport Hall

D1 Retail shop. Stores,

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D2 Shopping Center, Bookshop, Markets,

E1 Library, Archives, Storages, Industrial Laboratories

E2 According specific use

F Parking Pcar<30 kN

Table 2.6 (a)

with the following coefficients:

0j 1j 2j

1,0 0,9 0,8

2.7 Combinations

For checking ULS the combinations are:

ULS (STR/GEO Set B): G1∙G1+p∙P+Q1∙Qk1+∑i=2,n(Qi∙0i∙Qki)

For checking SLS adopted for serviceability the combinations are:

SLS Ch. : G1+P+Qk1+∑i=2,n(Qi∙0i∙Qki)

SLS Fr. : G1+P+11∙Qk1+∑i=2,n(Qi∙2i∙Qki)

where P=prestressing force

In APPENDIX A all coefficients and cases are indicated. To maximize the internal forces are considered all

combinations (span loaded, span unloaded).

2.8 Section and tendon The real cross section of the beam is (Figure 2.8 (a) ):

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Figure 2.8 (a)

The calculated cross section of the beam is (Figure 2.8 (b)):

Figure 2.8 (b) Self weight G1= 72,83 N/m Properties of concrete section (only concrete, area deducted bore holes, and concrete+tendons) are indicated in APPENDIX A.

2.9 Materials

2.9.1 Concrete

The precast LISTOTECH beam is built by C90/105 high-strength concrete.

Main characteristic at 28 days

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Main characteristic during maturity period:

1 day: fck(1)=40 [MPa] by steam curing

7 days: fck(7)=67,5 [MPa]

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28 days: fck(28)=90,0 [MPa]

2.9.2 High tensile tendon

The precast LISTOTECH beam is prestressed by a tendon up n. 2 strands 2x2,25 in the sectional strand

pattern pointed at Figure 2.1(b). The strands bore holes are Y symmetrical towards the CG section,

therefore the eccentricity of tendon is ep=0.

Main data:

Ap (1 strand) = 7,9525 mm2

Ap=2*7,9525 = 15,905 mm2

fpk=1790 Mpa

fp0,1k=1530 Mpa

Initial stress P0= 900 Mpa

2.10 Beam strand pattern

2.10.1 Initial stress and force From section x=140 mm. to section x=3640 mm. ( wherein the transmission of tendon stress has been totally realised (see § 2.2)) , stress and forces values are:

Initial assumed stress σp0= 900 Mpa

Initial assumed force P0= 900 N/mm2* 15,905 mm2 = 14314,5 N

Initial assumed stress after first loss σpm0= 874,4 Mpa

Initial assumed force after first loss Pm0= 874,4 N/mm2* 15,905 mm2 = 13907,3

2.10.2 Transmission lenght

The value of transmission strands length into concrete, calculated in accordance to codes, is:

ltl=200 mm.

2.11 Concrete Exposure

For check of wc concrete cracking in tension member under SLS frequent combination exposure Class

considered is XD2.

http://it.dicios.com/enit/eccentricity

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Chapter 3 - Results and Checks

3.1 APPENDIX B In APPENDIX B all Results and Checks, made by Scia Engineer 2010.

3.2 Specific considerations The LISTOTECH beam has same particularities that doesn't permit a complete respect of all requirements.

For that matter, as said, in a parallel way, shall be necessary to dispacht all procedures to obtain the

authorizations the element from public Structural Departement, according practices indicates by Codes.

3.3 Beam particularity LISTOTECH beam has following characteristics:

Thin thickness

High strength concrete

No minimum shear reinforcement

Low concrete cover value at bottom an top (9 mm.)

No connections among each member with the adjacent

3.4 Shear The formulae given by EC2 for design of reinforcement concrete members without shear reinforcement are

empirical and have been chosen to fit with extensive test data. The main characteristic governing the shear

strength of members without shear reinforcement are concrete strength, amount of longitudinal

reinforcement in tension, and absolute values of section depth. The longitudinal reinforcement contents

contributes to the shear resistance in two ways:

Directly by dowel action;

Indirectly by controlling crack widths. These in turn influence the amount of shear that can be

transferred across the cracks by aggregate interlook.

The member depths have also been shown to have a significant influence on shear strength and EC2 takes

account of this by defining a depth factor, k, given by

k=1+√ ≤ 2,0

where d is the effective depth to longitudinal tension reinforcement (mm).

In our case d=20 mm → k=1+√ =4,16 > 2,0

EC2 gives the following expression for calculating the shear strength of sections without shear reinforc

ement:

VRd,c = (CRd,c . k

. (100 . l . fck)

1/3+kl . cp) bw d ;

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wh6(1-ere:

l =Asl/ bw d

Asl is the area of longitudinal which extends of a minimum of a design anchorage

length and an effective depth beyond the section

bw is the smaller width of the cross section in the tensile zone (the minimum is

quite conservative)

But EC2 further limits the applied shear force (without reduction factor) to a maximum of 0,5 bw d

fcd , where fck/250)

As no shear reinforcement is required on the basis of the design calculation should nevertheless be

provided in accordance with the detailing requirement of EN 1002-2. It would be impractical to put links in

flat slab of decks allows minimum reinforcement to be omitted from members where transverse

redistribution of loads is possible such as slabs. For typical deck built by a series of beam, it's recommended

here that minimum links are always provided in accordance with EN 1992-2 they will, in any case, usually be

needed for the transverse Vierendel behavior of such a deck.

Shear tension failures occur in regions of beams that are un-cracked in flexure where the maximum flexural

tensile stress is smaller than ctfctk0,05/c.

The shear failure criterion for a section with no shear reinforcement assumed in EC2 is that the principal

stress anywhere in the section exceeds the tensile strength of the concrete, fctd.

Equating principal tensile stress to the tensile strength of the concrete gives the following

equation:

- fctd =cp +bend)/2 - (cp +bend)2/2 +2)1/2

where:

cp : prestressing stress after losses and including appropriate partial safety

factor

bend : stress due of bending

VRd,c A.S/Jbw (S: first moment - J: second moment)

Substitution forin the above leads the following expression for shear resistance:

VRd,c = Jbw /S . (fctd2

+cp +bend)2 . fctd)1/2

Assuming the principal tensile stress occurs the centroid of the section and introducing a factor1 gives:

VRd,c = Jbw /S . (fctd2

+1 cp fctd)1/2 (formulas a)

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For x=0 cp =0; A=2914 mm2; J=214700 mm3; S=96*15*7,5=10800 mm3

fctd =2,30 Mpa

VRd,c = (214700.96 /10800) . 2,3 = 4389 N

By formulas:

VRd,1 =k. rd . (1,2+40.

1) .Ac

where:

rd = 0,25. fctk 0,05/c ; rd = 0,25.3,5/1,5 = 0,583 Mpa

k=1

1=Ap/Ac ; 1=15,89/2914 = 0,00545

VRd,1 =1. 0,583 . (1,2+40. 0,0545) .2914 N (formulas b)

Then:

by formulas a we get VRd=4389 N

by formulas b we get VRd=2914 N

by software formulas we get VRd=5019 N

In any case (ULS-ST3), VEd = 1626 N < VRd1=2914 N

Ing. Alberto Calzavara

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