DESIGN OF FRP STRUCTURES IN SEISMIC ZONE · Design of FRP structures in seismic zone Manual by Top...

DESIGN OF FRP STRUCTURES IN SEISMIC ZONE

Giosue' Boscato, Carlo Casalegno, Salvatore Russo

Design of FRP structures in seismic zone

Manual by Top Glass S.p.A. and IUAV University of Venice 1

DESIGN OF FRP STRUCTURES IN SEISMIC ZONE

Giosuè Boscato(**)

Carlo Casalegno(*)

Salvatore Russo(*)

(*) IUAV University of Venice, Department of Design and Planning in Complex Environments,

Dorsoduro 2206, 30123, Venice, Italy, phone +39 041 2571290 fax +39 041 5312988;

[email protected]

(**) IUAV University of Venice, Laboratory of Strength of Materials (LabSCo), Via Torino 153/A -

30173 Mestre, Venice, Italy, phone +39 041 2571481 fax +39 041 5312988; [email protected]

mailto:[email protected]

mailto:[email protected]



Preface

The use of FRP (Fibre Reinforced Polymer) material in the structural engineering field is by now

current practice and supported by theoretical studies as well as many applications and constructions.

FRP material is widely accepted in the strengthening of existing structures (made by reinforced

concrete, steel, wood and masonry) but not yet commonly used for new buildings even if some

recent all-FRP constructions, in particular built with FRP members made by pultrusion process, are

very promising.

The study of the structural behaviour of pultruded FRP members, especially in the case of static

loads, has been widely developed. Instead, for what concerns the dynamic response, very few

experimental and analytical research projects have been proposed. The issue is particularly

interesting because of the mechanical characteristics of pultruded FRP material. The elastic-brittle

constitutive law with anisotropic mechanical behaviour imposes some specific precautions, while

the high durability, the low density of 1700-1900 kg/m3 and the relatively high values of strength

suggest its potential and promising application also in seismic zones.

The dynamic properties of pultruded FRP material are characterized by high periods of vibration,

low frequency and a spontaneous dissipative capacity of the dynamic actions due to its low density.

Currently there are no available guidances for the seismic design for structures with pultruded FRP

members.

The aim of this manual is to address the issues related to the design of pultruded FRP structures

subjected to static and dynamic loading.

After a thorough introduction the manual gives a practical guidance on how to address the structural

design of pultruded FRP structures. The final part – chapter 5 - is dedicated to a new software,

named FRP-Design Software (FRP-DS), with which is possible set up to structural verifications in

supporting the common commercial numerical code.

For the use of this present manual it is considered fundamental that the reader is in possession of the

information already available in the following documents:

CNR-DT205/2007. Guide for the design and constructions of structures made of FRP pultruded

elements, National Research Council of Italy, Advisory Board on Technical Recommendations.

http://www.cnr.it/sitocnr/IlCNR/Attivita/NormazioneeCertificazione/DT205_2007.html.

CEN TC250 WG4L, Ascione, J-F. Caron, P. Godonou, K. van IJselmuijden, J. Knippers, T.

Mottram, M. Oppe, M. Gantriis Sorensen, J. Taby, L. Tromp. Editors: L.Ascione, E. Gutierrez, S.

Dimova, A. Pinto, S. Denton. ‘Prospect for New Guidance in the Design of FRP,’ Support to the

http://www.cnr.it/sitocnr/IlCNR/Attivita/NormazioneeCertificazione/DT205_2007.html



implementation and further development of the Eurocodes, JRC Science and Policy Report

JRC99714, EUR 27666 EN, European Union, Luxembourg, (2016), p 171. ISBN 978-92-79-

54225-1 doi:10.2788/22306

NTC08. Norme Tecniche per le Costruzioni (last update of the Italian Building Code), Decree of

the Ministry of Infrastructures of 14th January 2008. (in Italian).

Eurocode 8 Design of structures for earthquake resistance. Part 1: General rules, seismic actions and

rules for buildings. EN1998-1:2004 (E): Formal Vote Version (Stage 49), 2004.

The development of the manual is the following:

Chapter 1 (pp. 6 - 20), INTRODUCTION, provides a general background on FRP pultruded

profiles, for what concerns the material, the structural behavior, the availability of standards,

guidance documents and manuals; a part is dedicated to notable applications.

In Chapter 2 (pp. 21 - 35), BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS, the synthesis

of the key-aspects related to the seismic design, such as the definition of period of vibration,

damping coefficient, behaviour factor and the dissipation capacity are discussed.

Chapter 3 (pp. 36 - 87), EXAMPLE OF CALCULATION, provides a calculation example of a FRP

spatial truss structure taking into account the different load combinations in static and seismic fields

and the analysis at ultimate and serviceability limit state.

In Chapter 4 (pp. 88 - 94), FINAL EVALUATION FOR DEISGN OF FRP STRUCTURES IN

SEISMIC ZONE, some final considerations for the design of FRP structures in seismic zone are

presented.

Chapter 5 (pp. 95 - 116), FRP DESIGN SOFTWARE (FRP-DS), illustrates the features of the FRP-

Design Software.

Acknowledgements

The authors thank Top Glass SpA (www.topglass.it) for the understanding of the potential capacity

of the pultruded FRP material in civil engineering, architecture and construction fields. This work

was possible thanks to the fundamental support of the Top Glass SpA and OCV Italia Srl - OWENS

CORNING (www.ocvitalia.it) and Polynt (www.polynt.it) as official suppliers of raw materials used

for the manufacturing of profiles used in experimental tests.

The authors thank also Eng. Mauro Calderan, from IUAV University of Venice, Italy, who

collaborated to the build the FRP-DS software.



Index

INTRODUCTION

1.1. Overview

1.2. Materials and manufacturing

1.3. Normative, design guidelines and technical references

1.4. Constructions and applications with pultruded FRP profiles

SYNTHESIS OF BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS

EXAMPLE OF CALCULATION

3.1. Statement of the structural design

3.2. Materials

3.3. Basic assumptions

3.4. Load analysis

3.4.1. Permanent loads

3.4.2. Variable loads

3.4.3. Seismic analysis

3.4.3.1. Modal analysis

3.4.3.2. Spectral analysis

3.4.3.2.1. Elastic response spectrum

3.4.3.2.2. Design spectra for ULS design

3.4.3.2.3. Displacement response spectra

3.4.3.3. Pushover analysis

3.5. ULS analysis

3.5.1. Forces and moments diagrams

3.5.1.1. Axial force

3.5.1.2. Bending moment

3.5.1.3. Shear force

3.5.1.4. Torsional moment

3.5.2. Example of verification of a compressed member

3.6. SLS analysis

3.6.1. Forces and moments diagrams

3.6.1.1. Axial force

3.6.1.2. Bending moment

3.6.1.3. Shear force

3.6.1.4. Torsional moment

3.6.2. Verification of elements

3.6.2.1. Stresses

3.6.2.2. Deformations

3.7. Joint's verification

3.7.1. Net-tension failure of the plate

3.7.2. Shear-out failure of the plate

3.7.3. Bearing failure of the plate

3.7.4. Shear failure of the steel bolt

3.8. References

FINAL EVALUATION FOR DESIGN OF FRP STRUCTURES IN SEISMIC

ZONE

4.1. References

4.2. Symbols

4.3. Verification’s functions

4.4. References

p. 6

p. 20

p. 35

p. 86



1. INTRODUCTION

1.1. Overview

Starting from the 90's there has been a significant increase throughout the world in the use of

pultruded FRP members in primary load-bearing systems for general constructions, as well as for

strengthening and rehabilitation of existing structures. The interest in this material lies in the several

advantages that it offers compared with traditional construction materials, such as the corrosion

resistance, the durability, the high strength to weight ratio, the versatility and the ease of

transportation and erection.

FRP structural profiles are commonly produced through the pultrusion process. General profiles

present the same cross-sectional shapes (I, H, leg-angle, channel, box, etc.) as found in structural

steelwork. They consist of fibre reinforcement with layers of unidirectional roving along Z-direction

covered by continuous mats, in X- and Y-directions, in a resin-based matrix, see Figure 1.1.

Figure 1.1 "I" FRP pultruded open shape

Different fibres, characterized by different mechanical properties, can be adopted. Their percentage

in volume can also be varied, as well as their dimensions, geometry and orientation, defining

different mechanical properties of the final products. Also the resin matrix can have different

characteristics, but the performance of the final product mostly depends on the type and percentage

of reinforcement. Anyway, the matrix plays a significant role in the transverse mechanical behavior,

and in specific performance characteristics as the impact strength and the cyclic behavior. This

production versatility allows the design of the FRP material to be oriented time by time with respect

to specific structural applications.

The mass density of the pultruded FRP material is between 1700-1900 kg/m3, that is about 1/4 of

steel density, while the tensile strength in the longitudinal direction is more than 240 MPa.

Nevertheless, the use of FRP structural profiles in civil engineering presents also some sensitive

aspects, such as the high deformability, the anisotropic and brittle-elastic behavior. The longitudinal

modulus of elasticity lies in the range of 20-30 GPa and both the elastic modulus and the strength

values are significantly lower in the transversal direction, where the influence of the matrix is



dominant due to the pultrusion process. Moreover, the pultruded FRP material presents different

characteristics in tension and compression. In general, the risk of buckling tends to govern the

design.

Due to the brittle-elastic behavior of the material, it is not possible to take advantage of the plastic

deformation and of the related dissipation capacity; this aspect partially influences the seismic

design approach. Nevertheless, some ductile phenomena are observed focusing on structural

systems, particularly on the moment–rotation curves of all-FRP beam-column connections.

Similarly to steel structures, the design of joints represents one of the most important aspects. The

preferred method of connecting the FRP profiles is by means of bolted joints that mimic steel

connections, sometimes used in conjunction with adhesives; the bolts are usually made of steel.

Nevertheless, due to the anisotropy the mechanical behavior of joints is more complex than that

realized with isotropic materials.

1.2. Materials and manufacturing

FRP materials are realized by the combination of fibres and matrix. The fibres generally used for

the realization of structural FRP composite members are carbon, aramid, PVA and glass; the glass

fibre is the most commonly employed, due to the relatively low cost and the good mechanical

properties. In general, pultruded FRP elements are realized with a volume percentage of continuous

filaments of fibres around 40%. The mechanical properties of the fibres are orders of magnitude

greater than those of the polymer resin that they reinforce. The function of the matrix is first of all

to protect the fibres. Moreover, it creates the continuity, through the cohesion, between the

filaments of fibres; it guarantees the transferring of the stresses between the fibres through its shear

stiffness and creates, through also the polymerization process, the desired shape. The matrices most

commonly employed for the realization of the fibre reinforced composites are polyester and

vinylester but they can be also thermoplastic, thermosetting and epoxy type. The mechanical

characteristics of some commonly used fibres and matrices are reported in Tables 1.1 and 1.2. The

tensile behavior of the FRP material is linear elastic up to failure, which is characterized by a brittle

mechanism. The behavior of the FRP material is anisotropic, due to fibres orientation, and - as

already specified - the mechanical performances in the transversal directions is significantly lower

than the one in the longitudinal direction.

The main manufacturing methods used to produce FRP material are the pultrusion process, the hand

lay-up, the filament winding and the molding process. Pultrusion is a continuous process used to

create FRP mono-dimensional elements with constant cross-section. A pultruded member can have



a symmetric or asymmetric open cross-section, a single closed cross-section or a multicellular

cross-section. In the pultrusion process the reinforcing material impregnated with the resin is guided

into a heated die, where it is cured to form the desired part as illustrated in Figure 1.2. The FRP is

cured as the material is pulled through the die by a pulling apparatus. After exiting the die and

extending past the pullers, the part is cut to length. In profiles produced through the pultrusion

process the internal core constituted by continuous longitudinal fibres, called roving, is covered by

an external thin layer of short fibres with random orientation, called mat, whose function is to

increase the transversal stiffness.

Figure 1.2 Pultrusion process (courtesy of TopGlass)

Hand lay-up is a manual method of constructing an FRP composite part by laying up successive

layers of fibres into a mold and impregnating them with a liquid polymer resin, which than cures to

form a solid FRP composite element. Typical products realized through the hand lay-up technique

are boat hulls, tanks and ducts. The filament winding method is used to create tubular and big

hollow products such as stay-in-place column forms, pipes, poles and pressure tanks. The process

consists in wounding continuously a resin-saturated fibre roving around a cylindrical mandrel at a

variety of wind angles. Finally, different variations of open and closed molding can be used to

create panels for FRP bridge deck, sandwich, fender piles, and plates for connections. In this

process, the dry fibres forms are arranged in molds and are saturated with resin and cured.

Indicatively the ranges of physical and mechanical characteristics of pultruded FRP material are

shown in Table 1.3.

Reinforcing fibre Tensile strength (MPa) Elastic modulus (GPa) Ultimate strain (‰)

Carbon 2400-5700 230-400 3-18 Aramid 2400-3150 62-142 15-44 Glass 3300-4500 72-87 48-50 PVA 870-1350 8-28 90-170

Table 1.1. Mechanical properties of fibres

Reinforcing fibre Tensile strength (MPa) Elastic modulus (GPa)

Unsaturated polyester 34-104 2.0-4.4 Epoxy resin 55-130 2.7-4.0

Phenolic resin 50-55 3

Table 1.2. Mechanical properties of resins



Mechanical properties Notations Range values

Tensile strength (L) σZ 200-500 MPa

Tensile strength (T) σX = σY 50-70 MPa

Elastic modulus (L) EZ= EL 20-30 GPa

Elastic modulus (T) EX = EY=ET 8-8.5 GPa

Shear modulus (L) GXY=GL 3.4 GPa

In-plane shear modulus of elasticity (T) GZX=GZY=GT 3 GPa

Poisson’s ratio (L) νZX = νZY= νL 0.23-0.28

Poisson’s ratio (T) νXY= νYX= νT 0.09-0.12

Density γ 1600-2100 kg/m3

Fibres percentage in volume Vf 40%-45%

L=longitudinal, T=transversal

Table 1.3. Range of values of pultruded FRP material

In a conventional manner the FRP pultruded standard profile refers to the coordinate system defined

by the XY plane of cross-section and Z axis orthogonal to it, see again Figure 1.1. Fibres run along

the global Z axis of each element defining the anisotropic behaviour in the Z direction and isotropic

in the X and Y directions. The condition of transversal isotropy is defined by the relationships

EX=EY=ET, νXY= νYX= νT, and GXY=GT. The local co-ordinate system for the wall segments forming

the cross-section and webs and flanges is also defined, with the z-direction in the longitudinal

direction of pultrusion, x in the transverse direction and y for the through-thickness direction.

In detail, for the characterization of pultruded FRP material it must be distinguished between two

different products in function of the layering ways. A greater amount of mat increases the

transversal stiffness classifying the FRP with grade 23 (EN 13706), see Table 1.4; while a minor

percentage of mat (i.e. TopGlass standard profiles) favors the increment of longitudinal stiffness

(Table 1.5).

Properties Notation Value

Longitudinal tensile modulus of elasticity Ez = EL 28.5 (GPa)

Transverse tensile modulus of elasticity Ey = Ex = ET 8.5 (GPa)

Transverse shear modulus of elasticity Gyx= GL 3.5 (GPa)

In-plane shear modulus of elasticity Gxz = Gyz = GT 2.5 (MPa)

Longitudinal Poisson’s ratio νzx = νzy= νL 0.25

Transversal Poisson’s ratio νxy= νyx= νT 0.12

Bulk weight density γ 1850 (kg/m3)

Longitudinal tensile strength σzt = σLt 350 (MPa)

Transverse tensile strength σxt = σyt = σTt 70 (MPa)

Longitudinal compressive strength σzc = σLc 413 (MPa)

Transverse compressive strength σxc = σyc= σTc 80 (MPa)

Shear strength τxy= τxz = τyz 40 (MPa)


Table 1.4. Mechanical properties of pultruded FRP profiles (Grade E23)



Properties Test method Notation Value

Flexural Modulus (L) EN 13706 - 2 (full scale) EL 28 (GPa)

Shear Modulus (L) EN 13706 - 2 (full scale) GL 3 (GPa)

Tensile strength (L) ASTM D638 σtL 400 (MPa)

Tensile strength (T) ASTM D638 σtT 30 (MPa)

Compressive strength (T) ASTM D695 σcL 300 (MPa)

Compressive strength (L) ASTM D695 σcT 70 (MPa)

Flexural strength (L) ASTM D790 σfL 420 (MPa)

Flexural strength (T) ASTM D790 σfT 70 (MPa)

In plane shear strength ASTM D2344 τ 28 (MPa)

Bearing strength (L) ASTM D953 170 (MPa)

Bearing strength (T) ASTM D953 70 (MPa)

Tensile modulus (L) ASTM D638 EtL 29 (GPa)

Tensile modulus (T) ASTM D638 EtT 8 (GPa)

Compressive modulus (L) ASTM D695 EcL 20 (GPa)

Compressive modulus (T) ASTM D695 EcT 7 (GPa)

Poisson's ratio (L) ASTM D638 0.28

Poisson's ratio (T) ASTM D638 0.12

Bulk weight density ASTM D792 γ 1820 (Kg/m3)

Glass content by weight ASTM D2584 60%

Glass content by volume ASTM D2584 42.5%

Thermal conductivity EN 12667/EN 12664 0.3 (W/mK)

Surface resistivity EN 61340 1012

(Ω)


Table 1.5. Mechanical properties of pultruded FRP standard profiles (TopGlass)

1.3. Normative, design guidelines and technical references

The static behavior of the FRP material and of FRP structural systems is nowadays studied quiet in-

depth, as demonstrated by the availability of several manuals, handbooks and scientific

publications. Nevertheless, to date a normative reference for the structural design with FRP

materials is not yet available, unless the recent CEN TC250 WG4 which gives finally a depth and

support in this so strategic design field. For what concerns the seismic response of pultruded FRP

elements/structures the researches are still growing. In the following the main normative references,

concerning the material properties, and the main available guidelines and literature references for

the design of FRP structures are listed.

Normative references:

EN 13706-1:2002 Reinforced plastic composites – Specification for pultruded profiles – Part 1:

Designation


Methods of test and general requirements


Specification requirements

EN 13121-1:2003 GRP tanks and vessels for use above ground – Part 1: Raw materials –

Specification conditions and acceptance conditions



EN 13121-2:2003 GRP tanks and vessels for use above ground – Part 2: Composite materials –

Chemical resistance

EN 13121-3:2008 GRP tanks and vessels for use above ground – Part 3: Design and

workmanship

EN 13121-4:2005 GRP tanks and vessels for use above ground – Part 4: Delivery, installation

and maintenance

EN-ISO 14125:1998 Fibre-reinforced plastic composites. Determination of flexural properties

EN-ISO 14126:1999 Fibre-reinforced plastic composites. Determination of compressive

properties in the in-plane direction

EN-ISO 14129:1997 Fibre-reinforced plastic composites. Determination of the in-plane shear

stress/shear strain response, including the in-plane shear modulus and strength, by the ±45°

tension test method

EN-ISO 14130:1997 Fibre-reinforced plastic composites. Determination of apparent interlaminar

shear strength by short-beam method

EN 16245:2013 Fibre-reinforced plastic composites – Part 1-5: Declaration of raw material

characteristics

ASTM D 790:2010 Standard test method for flexural properties of unreinforced and reinforced

plastics and electrical insulating materials

ASTM D 2344:2006 Standard test method for short beam strength of polymer matrix composite

materials and laminates

ASTM D 3039:2008 Standard test method for tensile properties of polymer matrix composite

materials

ASTM D 3410:2008 Standard test method for compressive properties of polymer matrix

composite materials with unsupported gage section by shear loading

ASTM D 3518:2007 Standard test method for in-plane shear response of polymer matrix

composite materials by tensile test of a ±45° laminate

ASTM D 4255:2007 Standard test method for in-plane shear properties of polymer matrix

composite materials by the rail shear method

Guidelines:

CEN TC250 WG4L, Ascione, J-F. Caron, P. Godonou, K. van IJselmuijden, J. Knippers, T.

Mottram, M. Oppe, M. Gantriis Sorensen, J. Taby, L. Tromp. Editors: L.Ascione, E. Gutierrez,

S. Dimova, A. Pinto, S. Denton. ‘Prospect for New Guidance in the Design of FRP,’ Support to

the implementation and further development of the Eurocodes, JRC Science and Policy Report

JRC99714, EUR 27666 EN, European Union, Luxembourg, (2016), p 171. ISBN 978-92-79-

54225-1 doi:10.2788/22306

CUR 96 Fibre reinforced polymers in civil load bearing structures (Dutch recommendation,

1996)



EUROCOMP Structural design of polymer composites (Design code and background document,

1996)

BD90/05 Design of FRP bridges and highway structures (The Highways Agency, Scottish

Executive, Welsh Assembly Government, The Department for Regional Development Northern

Ireland, 2005)

CNR-DT 205/2007 Guide for the design and construction of structures made of pultruded FRP

elements (Italian National Research Council, 2008)

ACMA Pre-standard for load and resistance factor design of pultruded fiber polymer structures

(American Composites Manufacturer Association, 2010)

DIN 13121 Structural polymer components for building and construction (2010)

ASCE, 1984, Structural Plastics Design Manual, 1984, ASCE Manual No. 63, ASCE, VA.

Books:

P. K. Mallick, Fiber-reinforced composites, Marcel Dekker Ltd., New York, 1993

D. Gay et al., Composite materials: design and applications, CRC Press, Boca Raton, 2002

L. C. Bank, Composites for construction – Structural design with FRP materials, John Wiley &

Sons Inc., New Jersey, 2006

B. D. Agarwal et al., Analysis and performance of fiber composites, John Wiley & Sons Inc.,

New Jersey, 2006

Russo, S. Strutture in composito. Sperimentazione, teoria e applicazioni, Hoepli, Milano, 2007.

Boscato G. (2011). Dynamic behaviour of GFRP pultruded elements. Published by University of

Nova Gorica Press, P.O. Box 301, Vipavska 13, SI-5001 Nova Gorica, Slovenia.

Pecce, M. and Cosenza, E., ‘FRP structural profiles and shapes, in Wiley. Encyclopedia of

Composites, 2012 - Wiley Online Library.

Dedicated conference series:

CICE (Composites in Civil Engineering)

ACIC (Advanced Polymer Composites for Structural Applications in Construction)

ICCS (International Conference on Composite Structures)

Main dedicated journals:

Advances in Structural Engineering

Applied Composite Materials

Composite Structures

Composites Part B: Engineering

Composites Science and Technology

International Journal of Adhesion and Adhesives

Journal of Composites for Construction, ASCE

Journal of Reinforced Plastics and Composites

http://cedb.asce.org/cgi/WWWdisplay.cgi?42891

http://www.multi-science.co.uk/advstruc.htm

http://www.springer.com/materials/characterization+%26+evaluation/journal/10443

http://www.elsevier.com/wps/find/journaldescription.cws_home/405928/description#description




http://scitation.aip.org/cco/

http://jrp.sagepub.com/



1.4. Constructions and applications with pultruded FRP profiles

The pultrusion process for producing FRP profiles was developed first in 1950s. Although the first

profiles were realized primarily for industrial applications, the potentials related to their adoption as

substitutes for conventional beams and columns in civil engineering applications were always

envisioned. By the late 1960s and early 1970s, in fact, a number of pultrusion companies were

producing I-shaped and tubular profiles.

The first large FRP structures were single-story frames realized for the electromagnetic and

computer industry. The electromagnetic transparency was the key advantage offered by the FRP

pultruded profiles in this field. In 1985 the Composite Technology Inc. designed and realized an

innovative EMI (electromagnetic interference) composite building for Apple Computer. Similar

structures where realized for IBM and others in the 1980s. Another significant use of FRP profiles

is found in the construction of cooling towers. In the bridge engineering field, pultruded FRP

profiles have been widely used since the mid-1970s. Hundreds of FRP footbridges have been

designed and realized all around the world. In 1992 a FRP footbridge 131 m long has been realized

in Aberfeldy, Scotland. A 127 m long FRP footbridge has been realized in 2012 in Floriadebrug,

Netherlands. The first pedestrian bridge (25 m of span length) in Italy has been realized in 2011 in

Prato. Another FRP pedestrian bridge 148 m long is actually under construction in Salerno. FRP

profiles have not been yet widely employed in multi-story residential and commercial buildings.

Neverthless, a significant prototype of a multi-story frame, called Eyecatcher, has been realized by

Fiberline in Basilea, Switzerland, in 1999. To date, the largest FRP strut and tie spatial structure

ever realized is probably represented by the 1,050 m2 by 30 m high FRP temporary shelter located

inside the church of Santa Maria Paganica in L’Aquila, Italy, in order to protect the monument after

the 2009 earthquake. Among other structural types, in 2014 a FRP grid-shell, made with pultruded

tubes, has been realized in Creteil, France. Also a demonstrative composite house has been built in

2012 in Borne, UK. More generally, a depth and updated overview of the all more significant

pultruded FRP structures realized is reported in CEN TC250 WG4L.



Besides, it is important to outline that the characteristics of pultruded FRP profiles, such as the

reduced density, the durability and the ease of erection make them particularly suitable for the use

in the field of the reinforcing of RC (reinforced concrete) structures or traditional masonry

structures, with particular regards for historical constructions. The structural reinforcement of these

buildings through the use of pultruded FRP profiles represents an efficient solution that allows

realizing non-invasive, reversible and durable interventions for the improving of the structural

performance with a very limited added structural mass.

Examples are the reinforcement of the timber deck of the Collicola Palace in Spoleto, Italy, through

H-shaped pultruded FRP profiles; the reinforcement of roof of the San Domenico Church in Siena,

Italy; the reinforcement of the Paludo bridge in Venice, Italy, which was necessary due to the

serious deterioration of the iron structure induced by the aggressive environment conditions.

Another example of interaction between FRP structural systems and historical construction is the

realization of an auxiliary floor in the Cogollo house in Vicenza (Figure 1.3), Italy, realized in order

to optimize the available space.



Following are illustrated some all-FRP constructions which are new and built in existing sites.

FRP spatial frame, Cogollo house in Vicenza (Italy)

The beams of the spatial frame, illustrated in Figure 1.3, are wide flanges "H" shapes

(200x200x20x10 mm), while the built-up columns are assembled from four off-the-shelf pultruded

leg-angle-shaped sections having same cross-section dimensions (100x100 mm) and wall thickness

of 8 mm. The connection elements (angle) between FRP members, the bolts, and the braces are

made of stainless steel; the circular deck (diameter of 5 m) is made of 5 cm thick multilayer wooden

panels.

Figure 1.3 FRP spatial frame, Cogollo house in Vicenza, Italy, 1999 (measures in meters)



FRP auxiliary floor in Verona (Italy)

The auxiliary floor, shown in Figure 1.4, made of pultruded FRP profile, has been built in Verona

(Italy) and is constituted by:

- a double frame that with four and two vertical “I” (200x100x10 mm) FRP profiles supports,

through the steel cables, the auxiliary deck;

- the deck that is realized by coupled “I” FRP profiles that together with individual “I” profiles form

a structural grid; for all joints steel bolts and flanges have been used and the deck is realized by self

bearing panels with a capacity equal to 250 kg/ m2;

- the backstays that are steel cables of 6 mm of diameter.

Figure 1.4 Auxiliary floor, Verona, Italy, 2006 (measures in metres)



Structural rehabilitation of an historic pedestrian bridge

The pedestrian “Paludo” bridge is a typical venetian bridge built at the end of XIX century, with

arch static scheme – 12.7 meters for the length and 3.25 meters for the width - built entirely with

iron and wood materials.

The flexural stiffness has been increased substituting the existing longitudinal wood beams with

double "I" shape pultruded FRP profiles (120x60x8 mm) assembled by bolted FRP plates (Figure

1.5). The details of Figure 1.5 show the workers operating facility to execute the cut (a), the holes

(b) and the final assemblage (c), the mechanical connection with the bridge abutments through the

galvanic steel gussets (d), the two “I” FRP profiles and the beam-beam joint realized through the

FRP pultruded plates and stainless bolts (e) and the final positioning in the thickness of the deck (f).

Figure 1.5 Rehabilitation of historic pedestrian bridge, Paludo bridge, Venice, Italy (2007).



FRP pedestrian bridge in Prato (Italy)

The pedestrian bridge is fully made with pultruded FRP profiles, except steel bolts. The total length

of the footbridge is equal to 25 meters, with reinforced concrete piers and FRP ramps, see detail of

Figure 1.6; at the edges the access ramps have been designed with a staircase made in FRP and an

elevator. With a load bearing capacity of 5 kN/m² the bridge weighs only 8 tons. With the spatial

truss configuration the top chord is able to resist compression, while the lower chord has to resist

only to tension. The two frame trusses are strongly braced by a lateral system in the plane of its

chord in order to diminish the buckling effective length.

Figure 1.6 Plan, views and details of the spatial strut and tie all-FRP pedestrian bridge, Prato,

Italy (2013)



Spatial all-FRP truss structure

The temporary covering-structure of S.M. Paganica church, in L'Aquila, has been made of

pultruded FRP members (Figure 1.7) produced with grade 23 (EN 13706), see Table 1.4. The

structure is still inside the historic church and mentioned in CEN TC250 WG4L (2016). The truss

members are built-up “C” shape members connected with stainless steel bolts.

As shown in Figures 1.7 and 1.8, Structure 1 covers 607 m2 for the nave, having a maximum height

of 22.5 m; Structure 2 covers 266 m2 for the apse, having a maximum height of 29.4 m; Structure 3

(130 m2) protects cells along one longer side; Structure 4 (76 m

2) is protecting the entrance-façade.

Figure 1.7 Plan and view of the spatial truss all-FRP structure, L’Aquila, Italy, 2010 (measure

in meters)



Figure 1.8 All-FRP sub-structures; L’Aquila (2010)

The frame joints use conventional steel bolts and gusset plates of FRP material made by the bag

molding process, see Figure 1.9. Detail (a) shows the built-up member’s cross-section comprising

four channel (C) profiles having same cross-section dimensions 152x46x9.5mm; while detail (b)

shows the connection between the built-up member’s cross-section of four channel (C) profiles

having same cross-section dimensions 300x100x15mm and bracings.

Figure 1.9 Details of joints of structure 1 (a) and structure 2 (b); L’Aquila (2010)



2. SYNTHESIS OF BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS

To facilitate the reading of this manual, in the following a short introduction in the form of sheets to

some aspects and based concepts of seismic design is presented.

1. Single Degree of Freedom (SDoF)

2. Multiple Degrees of Freedom (MDoF)

3. Natural period of vibration

4. Damping coefficient

5. Response spectra

6. Spectral analysis

7. Pushover analysis

8. Dissipative capacity

It is noted that the insights discussed in these short presentations are specific of the analyzes and

studies carried out in this manual. For more clarification, the specific texts present in the literature

and cited in every sheet are the following:

Chopra AK. Dynamics of structures, 3rd Ed., Pearson Prentice Hall, 2007.

Eurocode 8 Design of structures for earthquake resistance. Part 1: General rules, seismic actions

and rules for buildings. EN1998-1:2004 (E),: Formal Vote Version (Stage 49), 2004.

NTC08. Norme Tecniche per le Costruzioni (last update of the Italian Building Code), Decree of the

Ministry of Infrastructures of 14th January 2008. (in Italian).



1- Single Degree of Freedom (SDoF)

SDoF (Single Degree of Freedom) system is characterized

by mass m and a spring with stiffness k (N/m).

The stiffness k is the external force that keeps the system

in equilibrium when a unit displacements u=1 is applied.

Dynamic equilibrium

0)()()( tumtkutp

)(tum frictions inertia force (product of mass time its

acceleration )(tk elastic stiffness force

)(tu acceleration imposed on mass

)(tp external force

Free vibration

Undamped system

The structure depends by its static equilibrium. The

system vibrates without any applied forces through the

following equation of motion:

0 kuum

Viscously damped system

The linear viscous damper (c) gives a friction in the

structure. The linear viscous damper develops a force

proportional to the velocity (fD)

)(tucfD

The equation of motion is: 0 kuucum

Assuming:

damping coefficient m

c

n

2

damped pulsation 21 nD

Equation of motion of damped system is:

02 2 uuu nn

Coulomb-damped system

The Coulomb-damped free vibration is controlled by

sliding of two dry surfaces through friction.

The friction force is F=Nμ where:

μ=equal coefficients of static and kinetic friction

N=normal force between the sliding surfaces

F=independent to velocity of the motion with direction

opposed to the motion.

The equations of motion from left to right or viceversa

are;

Fkuum

k

FtBtAtu nn )sin()cos()( 2,12,1

The constant A1, B1, A2, B2 depend on the initial

conditions.

SDoF subjected to seismic action

The equation of dynamic equilibrium is:

msv FFF

Where

vF viscoelastic force proportional to relative velocity

sF elastic force proportional to relative displacement

mF inertial force proportional to the absolute

acceleration ug

then:

))()(()()( tutumtkutuc g

and finally

))()()(2)( 2 tutututu g



2a - Multiple Degrees of Freedom (MDoF)

MDoF (Multi Degrees of Freedom) is characterized by

following equation )(tpukucum

with

[m] mass matrix; [c] damping matrix; [k] stiffness matrix

Mass and stiffness matrices depend on the structure's

discretisation and on the choice of the degrees of freedom

that are involved. The damping cannot be calculated by

discretisation.

For the analysis of multiple-degrees-of-freedom (MDoF)

elastic systems, the development of the code-based

equivalent lateral force (ELF) procedure (scheme a) and

modal superposition analysis must be carried out.

In the analysis of MDoF the basic assumptions are: the

vertical and rotational masses are not required; horizontal

mass be lumped into the floors; floors are axially rigid; for

each joint (12, scheme b) three d.o.f. (degree of freedom)

must be computed (see joint 12, scheme b); motion is

predominantly lateral (see joint 4, scheme b).

The 36 static degrees of freedom may be reduced to only 3

lateral degrees of freedom for the dynamic analysis. The

three dynamic d.o.f. are u1, u2 and u3 (see scheme c).

The relative displacements not include the ground

displacements.

The flexibility matrix is simply a column-wise collection of

displaced shapes. The lateral deflection under any loading

may be represented as a linear combination of the columns

in the flexibility matrix (see schemes d, e and f).

K may be determined by imposing a unit

displacement at each DOF while restraining

the remaining DOF. The forces required to

hold the structure in the deformed position

are the columns of the stiffness matrix.

The mass matrix is obtained by imposing a

unit acceleration at each DOF while

restraining the other DOF. The columns of

the mass matrix are the (inertial) forces

required to impose the unit acceleration.

There are no inertial forces at the restrained

DOF because they do not move. Load F(t)

and displacement U(t) vary with time.



2b - Multiple Degrees of Freedom (MDoF)

For three-story frame MDOF the coupled equations of

motion for undamped forced vibration is:

)()()( tftKUtUM and then:

)(

)(

)(

)(

)(

)(

0

0

)(

)(

)(

00

00

00

3

2

1

3

2

1

323

2211

11

3

2

1

3

2

1

tf

tf

tf

tu

tu

tu

kkk

kkkk

kk

tu

tu

tu

m

m

m

The equations are solved transforming the coordinates from

normal coordinates (displacements at each of the three

original DOF) to modal coordinates (amplitudes of the

natural mode shapes).

Through the orthogonality property of the natural mode

shapes the equations of motion can be solved by

simplifying in SDOF equations.

For system in undamped free vibration field the modal shapes and frequencies are expressed by: 0)()( tKUtUM

Where ttU sin)( and ttU sin)( 2

Then 02 MK has three solutions



2c - Multiple Degree of Freedom (MDoF)

Idealized mode shapes for a 3-story building

The modal shapes depend by boundary conditions;

noteworthy is the relationship between modal

shapes and nodes. The displaced shapes are obtained

by the following linear combination: YU

3

2

1

3,32,31,3

3,22,21,2

3,12,11,1

y

y

y

U

3

3,3

3,2

3,1

2

2,3

2,2

2,1

1

1,3

1,2

1,1

yyyU

Where ji, modal shape; while 1y modal

coordinate, amplitude of modal shape

The orthogonality condition 321 allows the

full uncoupling of the equations of motion: MDoF equation )(tFKUUCUM

With YU

Then )(tFYKYCYM

And )(tFYKYCYM TTTT

Obtaining the following uncoupled equations of motions

)(

)(

)(

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

tf

tf

tf

y

y

y

k

k

k

y

y

y

c

c

c

y

y

y

m

m

m

Generalized mass

*

3

*

2

*

1

m

m

m

MT

Generalized stiffness

*

3

*

2

*

1

k

k

k

KT

Generalized damping

*

3

*

2

*

1

c

c

c

CT

Generalized force

)(

)(

)(

*

3

*

2

*

1

tf

tf

tf

FT

Expliciting, with y=amplitude and *=generalized quantities

we have:

mode 1 )(*

11

*

11

*

11

*

1 tfykycym

mode 2 )(*

22

*

22

*

22

*

2 tfykycym

mode 3 )(*

33

*

33

*

33

*

3 tfykycym

Dividing by mass m* and defining

ii

ii

m

c

*

*

2

mode 1*

1

*

11

2

11111

)(2

m

tfyyy

mode 2*

2

*

22

2

22222

)(2

m

tfyyy

mode 3*

3

*

33

2

33333

)(2

m

tfyyy

MDoF system subjected to earthquake force

The inertial force = sum of two vectors through the

influence coefficient vector R; R=1 for each mass that

produces an inertial force triggered by horizontal

acceleration.

For each floor the inertial force iF is equal to mass times

M the total acceleration (ground acceleration (gu scalar)

and relative acceleration (iru ,

vector)).

)()(

)()(

)()(

)(

3,

2,

1,

tutu

tutu

tutu

MtF

rg

rg

rg

i



2d - Multiple Degree of Freedom (MDoF)

Definition of modal participation factor

For earthquakes

)()(*

2 tuMRtf g

T

i

Than the typical modal equation is

)()(

2**

*2 tu

m

MR

m

tfyyy g

i

T

i

i

iiiiiii

With

i

T

i

T

i

i

T

ii

M

MR

m

MRp

*

Modal partecipation factor p with 3 first mode shape normalized, x=1

Effective modal mass for each mode i is

iii mpm 2

Where: -the sum of effective modal mass

is equal to the structural mass; -the value

of effective mass not depend by mode

shape scaling; - are needed a number of

modes to reach the activation of modal

mass at least of the 90% of the total

structural mass (as defined by standard

codes).

The effective modal mass not depend on

modal scaling as, instead, the modal

participation factor.

The modal shape is normalized, x=1



3 - Natural period of vibration

The natural period of a structure T is the time needed by the structure to perform a whole oscillation, triggered by an

initial perturbation. The natural period of vibration depends by mass (m) and stiffness (k) of structure.

0

0

2

2

0

0

2

1

2

1

u

u

kk

kk

u

u

m

m

A pendulum (SDoF) with a short period of vibration (i.e. stiffer or less mass) tends to move with the support (i.e. soil)

and then not records any earthquake, a pendulum with a greater period of vibration tends to remain stationary while the

support varies.

The natural period of vibration depends by mass (m) and

stiffness (k) of structure.

The natural period of vibration T affects the response of

structure to seismic action both for the acceleration and

displacement. Buildings with different T subjected to same

seismic action record different acceleration values.

Resonance phenomenon:

the soil is also characterized by a natural period of vibration. When the natural period of vibration of the ground is very

close to that of the building, the stress of building increases.

m

k (rad/sec)

Natural circular frequency

2

1

Tf (Hz)

Natural frequency

For every structure the natural modes of vibration correspond to the number of degree of freedom and represent the free

periodic oscillations of undamped elastic system.

When the system oscillates according to one of the natural modes, all the masses oscillate with the same pulse

(corresponding to the mode) and the same phase, by keeping unchanged the relationships between the amplitudes.

For each oscillation the masses reach the point of maximum displacement in the same instant.

Adapted from Chopra (2007)



Damping coefficient

The equivalent viscous damping coefficient ζ is the most used approach to analyze the dissipative capacity of structures

in dynamic field. ζ depends by effects induced by hysteretic behavior, internal friction of the material, geometrical

characteristics and typology of ground taking into account the structural response in the variation of time.

Free vibration with 10% damping coefficient ζ

Free vibration with 3% damping coefficient ζ

Logarithmic decrement method

The logarithmic decrement is an experimental approach

that takes into account a linear viscoelastic damping ζ.

To evaluate the reduction in the amplitude values that the

sinusoidal oscillatory behaviour exhibits in the time

domain, the method used is that of the logarithmic

decrement obtained from the ratio between two consecutive

maximum amplitudes in the time range of a damped period

of one or more cycles, as in:

nx

x

cn

0ln1

where δ=logarithmic decrement; cn=cycles number;

x0=initial amplitude; xn=final amplitude.

The damping coefficient (ζ) is determined through: 5.0

2

241

Equation can be simplified for small values of ζ i.e., when

(1- ζ2)

0.5 is close to 1, becoming

2

Band-width method

The Half Power Bandwidth (HPB) method in the frequency

range is employed to analyze experimentally the capacity

of the specimens to dissipate the accumulated energy from

the dynamic excitation. The bandwidth (BW) is the

frequency within a range of 3 dB, corresponding to the

measured dominant (first natural) frequency, f1, from the

action of the piling machine. This quantifies, indirectly, the

velocity from the accelerometer response from initial

frequency fi to final frequency fi+1; where fi and fi+1 are the

two frequency limits for calculating BW. Damping

coefficient ζ is given in terms of f1 and BW = (fi+1 - fi,) by

2222221 1122111221 NNfBW

where N = U/U* and U = U* - 3 dB, and U* is the peak

amplitude at f1. The relationship in Equation between ζ and

BW/f1 holds only for ζ 0.353, and by letting N=21/2

the

expression for the damping coefficient is simplified to

12 f

BW

The representation of the seismic action components is the elastic response spectrum for a conventional damping

coefficient ζ of 5%. It provides the maximum acceleration response of the generic dynamic system with natural period

of T≤4s and is expressed as the product between the spectral shape and the maximum acceleration of the ground.

On the right the deformation response factor and phase angle for a damped system.

For NTC08 and Eurocode8 the equivalent viscous damping

coefficient ζ is taken into account through the damping

correction factor η=√(10/(5+ζ))≥0.55;

This equation vales for ULS (Ultimate Limit State); then

assuming ζ=5% (reinforced concrete RC structure) we have

η=1 (unchanged spectrum); with ζ=2-3% (steel structure)

η=1.2-1.12 (amplified spectrum); while with ζ=0% η=1.41

(amplified spectrum).

In brief passing from RC to steel structure increase the

horizontal components of the design response spectrum which

tend to maximize for ζ=0, that is for a elastic structure and,

therefore, extremely rigid with respect to a dissipative structure.



5a - Response spectra

SDoF Systems

SDoF system is subjected to ground motion ug(t); u(t)is

the calculated displacement response.

EQUIVALENT STATIC FORCE

fs(t)is the static force which must be applied to create the

displacement u(t)

RESPONSE SPECTRA

A response spectrum is a plot of a

maximum response, in

displacement or velocity or

acceleration form, of a SDoF

system with respect to a given

ground acceleration against

systems parameters (Tn (natural

period of vibration) and ζ

(damping coefficient)).

A response spectrum is calculated

numerically (through Duhamel

integral or time integration

methods) for (Tn and ζ). Adapted from Chopra (2007)

DETERMINATION OF RESPONSE SPECTRA

Starting from the seismic action for specific soil

characterized by )(tug :

-I apply )(tug to SDoF system with Tn and fixed

damping coefficient ζ;

-I solve the problem calculating u(t) and plotting the

graph ω2u(t)in time domain;

-I calculate the maximum value of

spectral displacements SDe={u(t)}max

spectral pseudo-velocity SVe=ω{u(t)}max

spectral pseudo-acceleration SVe=ω2{u(t)}

max

Following the relationship:

AeDe StuS2

max 1

For a given seismic action the D-V-A

(Displacement, pseudo-Velocity, pseudo-

Acceleration) elastic response spectra summarizes

the behavior in term of maximum D-V-A of all

elastic SDoF system with 0<Tn< and fixed

damping coefficient.

In detail pseudo-velocity is related to energy while

pseudo-acceleration is proportional to static load.

Combined D-V-A response spectrum for El-Centro ground motion

with ζ=0, 2, 5, 10 and 20%, (Chopra 2007).



5b - Response spectra

The elastic response spectrum is obtained by many seismic events, and it isn't refered to the real earthquake.

The spectrum which characterizes the site is obtained as the envelope of the most response spectra.

The development of response spectra for a specific site requires a study of geological and seismological characteristics

of the site. It is known that the characteristics of seismic action are affected by the source that triggers the earthquake,

from the wave's directions up to the site and by local conditions.

For the equivalent static force Fsmax

The seismic analysis becomes the equivalent static

analysis.

Response spectrum (ζ =0, 2, 5 and 10%) and peak values

of ground acceleration (A), ground velocity (V) and

ground displacements (D) for i.e. El Centro ground

motion, (Chopra 2007).

For a SDOF:

The elastic design spectrum is defined through the

accelerograms recorded during past earthquakes with

similar seismic characteristics.

Construction of elastic design spectrum (Chopra 2007)

Response to El Centro earthquake (i.e.) of different

buildings changing T0 and ζ fixed:

-with higher T0 (→∞) the maximum pseudo-acceleration

→0;

-with lower T0 (→0) the maximum pseudo-acceleration

→maximum ground acceleration.

Response to El Centro earthquake (i.e.) of different

buildings changing T0 and ζ:

-the maximum displacements tend to grow with increasing

the natural period (T0)

-the maximum displacements decrease with increasing

damping coefficient (ζ)



6a- Spectral analysis

The seismic loading for structural design is described by response spectra (Eurocode 8, 2004; NTC08, 2008). Design

that is in accordance with the requirements of Eurocode 8 has only ULS spectra. Working to the Italian Building Code

(NTC08 2008] requires there to be both SLS and ULS spectra.

Structures in seismic regions shall be designed and constructed taking into account the reference seismic action

associate with a reference probability of exceedance or a reference return period.

For NTC08 the seismic action depends by VR=CUxVN (where VN=service life while CU=structural class).

The period return TR= VR/(ln(1-PVr) where PVr=probability of exceedance that changes in function of the different

damage levels (SLO=operational; SLD=immediate occupancy; SLV=life safety; SLC=collapse prevention).

For EC08 the recommended values for the no-collapse requirement are PNCR=10% (probability of excedeence) and

TNCR=475 years (return period) while for the damage limitation requirement are PDLR=10% (probability of excedeence)

and TDLR=95 years (return period).

Eurocode 8, 2004 and NTC08, 2008 shall be take into account for basic informations about ground conditions, seismic

actions and general parameters.

Elastic Response Spectra

The reference action model to describe the seismic motion at floor (ground) level is the elastic response spectra for

horizontal and vertical components. In this sheet the notation, the design process and equations are, where applicable,

in accordance with the requirements of Part 1 of Eurocode 8 (2004). Euroocde 8 sesimic loading is more severe than

the Italian seismic loading the approach is for a conservative and pragmatic design.

The two elastic response spectra for horizontal and vertical components were established from the normalised spectrum

in Eurocode 8 with reference to an assumed viscous damping coefficient (ζ) of 0.05, which is independent of the

seismicity level. EN 1998-1-1:2004 states that these elastic response spectra may be applied to structures having a

vibration period < 4 s. This criterion is acceptable for FRP structure.

Equations in the right are used to present the four stages of

the elastic response spectrum for the horizontal

component.

The parameters in Eqs. (a) to (d) are: Se(T) for the elastic

horizontal ground acceleration response spectrum (also

called "elastic response spectrum”) with units of

acceleration (g); T for the vibration period of a linear

oscillator, namely Single Degree of Freedom (SDoF),

defined by its natural period and by its damping factor; S

for the soil factor; η for a damping correction factor, which

is calculated from 550100510 ./ ; TB, TC and

TD are for time periods, depending on type of ground, to

define the different stages in the spectrum; Fo (NTC08

2008) is for the horizontal amplification factor. Note that

Fo is the notation taken from publication NTC08, an

alternative notation in Eurocode 8 is Fh, where the

subscript ‘h’ is for horizontal component.

At T = 0 s, the spectral acceleration given by Se(T) equals

the design ground acceleration on type A ground multiplied

by the soil factor S.

Elastic response spectrum for the horizontal component

Se(T) used in Eurocode 8 (2004) and NTC08 (2008).



6b- Spectral analysis

The elastic response spectrum for the vertical ground

acceleration (Sve(T)) is defined by the four expressions in

the right Table. In Equs. (a) to (d) the new parameters

respect to horizontal component are: avg for the design

ground acceleration in the vertical direction that is given by

0.9 ag and Fv for the vertical amplification factor that is

given by 1.35Fh(avg/g)0.5

.

Elastic response spectrum for the vertical component Sve(T)

used in Eurocode 8 (2004) and NTC08 (2008).

The horizontal component of acceleration is always higher than in the vertical direction. It can be seen that the elastic

response spectra from Eurocode 8 are significantly higher, and have different time differentials, than those obtained on

using NCT08.

Design spectra for ULS design

For the purpose of seismic design the dissipation capacity of any structure can be taken into consideration by

introducing a reduction factor to the elastic spectral accelerations. This is accomplished in Eurocode 8 (2004) and in

Italian Building Code (NCT08, 2008) by introducing q.

To ensure the structural design for the structure could be conservative, and when the material plasticity is minimal, the

factor q was set to be 1.0. In other words there was no reduction in the spectrum’s accelerations for the structural

analysis to establish the seismic performance.

Displacement response spectra

To gain an insight into how much horizontal displacement the structure is to experience due to ground movement the

displacement response spectrum, SDe(T), is obtained from the acceleration response spectrum (Se(T)), by using the

relationship:2

eDe2

)()(

TTSTS



7 - Pushover analysis

In performance-based engineering it is necessary to obtain realistic estimates of inelastic deformations in structures so

that these deformations may be checked against deformation limits as established in the appropriate performance

criteria. Two basic methods are available for determining these inelastic deformations: Nonlinear static “pushover”

analysis and Nonlinear Dynamic Response History analysis.

In the non linear static analysis method a structure is subjected to gravity loading and a displacement-controlled

lateral load pattern which continuously increases through elastic and inelastic behavior until an ultimate condition is

reached. Lateral load may represent the range of base shear induced by earthquake loading.

Different types of non linear behaviour exist: mechanical (connected to the non linearity of the material), geometrical

(connected to the fact that the application point of the loads changes increasing the actions) and of beam-column

joints (connected to the interaction of structural elements).

The pushover analysis is based on: 1-Definition of capacity curve of MDoF system; 2-Definition of equivalent SDoF

system; 3-Calculation of capacity displacement (umax); 4-Calculation of displacement demand (dmax); 5-Comparison

between umax and dmax; 6-Validation when umax >dmax (see figure below).

The capacity curve= relationship between the horizontal displacement and horizontal force.

The demand curve is basically an elastic response spectrum that has been modified for expected performance and

equivalent viscous damping. The demand curve is used in concert with the capacity curve to predict the target

displacement.

The expected displacement is determined locating on the capacity curve the displacement compatible with the seismic

action of the site. The identification of this displacement is pursued by operating in Acceleration Displacement

Response Spectrum (ADRS), and then describing the capacity curve and the response spectrum in terms of spectral

acceleration and spectral displacement. In the space ADRS the response spectrum and capacity curve should

respectively take the name of the Demand spectrum and Capacity spectrum capacity. The different forms of horizontal actions are:

a)Uniform load proportional to the mass distribution

b)Triangular load proportional to the mass distribution

c)Horizontal load proportional to the lateral force distribution of the mode with the highest mass participation

‘‘Modal’’.

The P-Δ effect must be taken into account. The P-Δ effect is a destabilizing moment equal to the force of gravity

multiplied by the horizontal displacement a structure undergoes when loaded laterally.



8a – Dissipative capacity

For the seismic design the dissipation capacity of any structure can be taken into consideration by introducing a

reduction factor to the elastic spectral accelerations. This is accomplished in standard codes by the behaviour factor q.

The design seismic action Sd(T) is given by the elastic response spectra with the elastic accelerations (forces) adjusted

downward by dividing by q. The determination of the q depends on the: materials; structural form; hyperstaticity degree

of structure; structural response (e.g. its ductility); soil-structure interaction. To ensure the structural design for the

structure could be conservative the factor q =1.0. In other words there was no reduction in the spectrum’s accelerations

in the elastic response spectrum for the structural analysis to establish the seismic performance.

The q factor is determined through kinematic or energetic equivalence conditions.

Kinematic equivalence for structure with higher period of

vibration

qu

u

F

Fq

yy

e max

Energetic equivalence for structure with short period of

vibration

221 max yy

e

y

e

u

u

u

u

F

F

12212 qq

Hence, considering the previous criteria

sifTq

sTsifq

sifTq

1.01

5.01.012

5.0

Generalizing the SDoF, the q of MDoF could be evaluated through the relationship between the different peek ground

acceleration (PGA) of collapse and yielding state:

y

u

PGA

PGAq

or through the pushover analysis considering the static forces equivalent to seismic actions:

y

uq

Elastic response spectra in SLS for horizontal and vertical

components based on Eurocode 8 (2004) and NTC08 (2008).

Design response spectrum for ULS structural analysis

based on using Eurocode 8 (2004) and NTC08 (2008).



8b - Dissipative capacity

The displacement response spectrum, SDe(T), is obtained

from the acceleration response spectrum (Se(T)).

This is valid for a vibration period T< 4.5s (4.5 s is time

parameter TE for a type A ground). The acceleration

response spectra and the displacement response spectra

have three time zones that are proportional to the imposed

ground acceleration. Between times TB and TC there is a

zone of constant spectral acceleration. This is followed to

time TD by the zone of constant spectral velocity and for

higher times to TE there is the zone of constant

displacement response too. Horizontal displacement response spectra based on

Eurocode 8 and NTC08 for SLS and ULS design.

The dashed lines show the displacements calculated with NTC08 and EC8 considering q=1. In the same the elastic

displacement response spectra is calculated considering q=1.5. Figure shows that the structure responds to design

seismic action resisting to a maximum displacement of 116mm for EC8 and 124mm for NTC8. The effect of the

behaviour factor is shown through the reduction of the displacements induced by design seismic action.

For the seismic spectral analysis the response-spectrum analysis (RSA) has been carried out. It is a linear-dynamic

statistical analysis method which measures the contribution from each natural mode of vibration to indicate the likely

maximum seismic response of an essentially elastic structure. Response-spectrum analysis provides insight into

dynamic behavior by measuring pseudo-spectral acceleration, velocity, or displacement as a function of structural

period for a given time history and level of damping. It is practical to envelope response spectra such that a smooth

curve represents the peak response for each realization of structural period. Response-spectrum analysis is useful for

design decision-making because it relates structural type-selection to dynamic performance. Structures of shorter period

experience greater acceleration, whereas those of longer period experience greater displacement.

DESIGN OF FRP STRUCTURES IN SEISMIC ZONE · Design of FRP structures in seismic zone Manual by Top...

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