Structural assessment of a modern heritage building

Structural assessment of a modern heritage building

Stefano Sorace

^a,⇑

, Gloria Terenzi

^b

aDepartment of Civil Engineering and Architecture, University of Udine, Via delle Scienze 206, 33100 Udine, Italy

bDepartment of Civil and Environmental Engineering, University of Florence, Via S. Marta 3, 50139 Florence, Italy

a r t i c l e i n f o

Article history:

Received 23 January 2012 Revised 16 November 2012 Accepted 3 December 2012 Available online 30 January 2013

Keywords:

Structural assessment Seismic assessment Modern architectural heritage Steel structures

R/C structures Glazed façades Linear analysis Non-linear analysis Seismic retrofit

a b s t r a c t

A structural assessment study on ‘‘Palazzo del Lavoro’’ in Turin, a masterpiece by Pier Luigi Nervi, was carried out within a National Research Project dedicated to the analysis of modern heritage architecture in Italy. Based on the original design documentation collected through records, a complete finite element model of the building was generated. The study included detailed models of the main structural mem- bers, represented by monumental reinforced concrete columns, a mushroom-type steel roof and rein- forced concrete ribbed gallery slabs, and the main non-structural systems, constituted by continuous gallery-to-roof glazed façades. The results of the linear and non-linear analyses developed by these mod- els, aimed at fully understanding the original design concept of the various members, as well as at eval- uating their current static and seismic safety conditions, are reported in this paper. The non-linear computations include a buckling analysis of the slender steel beams constituting the roof, and an ‘‘inte- gral’’ seismic pushover analysis of the monumental columns. The results of the analyses highlight safe conditions and good performance objectives in general, but for some important exceptions. Indeed, the roof beams failed to pass the verifications on global and local panel flexural–torsional buckling, and some cantilever beams of the gallery floors showed poor shear resistance. Retrofit hypotheses are also formu- lated for these elements, so as to help the entire structure to comply with the requirements of the new Italian Technical Standards.

Ó2012 Elsevier Ltd. All rights reserved.

1. Introduction

Growing attention is currently being devoted to the study of modern architectural heritage, and particularly to the edifices built from the aftermath of the Second World War until the late 1960s.

Indeed, that was a very prolific period for architecture and struc- tural engineering, which produced significant theoretical and tech- nical advancements in both fields. As a consequence, a global enhancement of the construction industry was reached, and a great number of exemplary masterpiece structures were designed and erected worldwide. This important stock of buildings is now over 50 years old, and may require important structural maintenance, repair and/or rehabilitation interventions. In view of this, careful evaluation and verification analysis strategies are needed to check the actual safety conditions of these skilled engineering works, and to plan possible retrofit solutions. At the same time, the develop- ment of assessment analyses of these outstanding buildings offers a profitable chance to improve the knowledge on the characteris- tics of their constituting materials, structural details and construc- tion work procedures, as well as on the calculation methods

originally adopted for their design. Moreover, these analyses can provide a better understanding of the original conception of the structures enquired, and evaluations about the attainment of the theoretical and technical objectives targeted in their design, which was carried out without the help of computer software. As a con- sequence, new contributions to the critical interpretation of the activity of the master structural designers of the 20th century can be derived, which are of potential interest also to researchers working in the field of history of modern architecture, as well as to scholars and engineers working in the field of structural assess- ment and rehabilitation.

An Italian masterpiece belonging to this stock named ‘‘Palazzo del Lavoro’’ in Turin, designed by the world-famous structural engineer Pier Luigi Nervi, is examined in this paper. The building, an external and an internal views of which in its current conditions are shown inFig. 1, constituted the most important exhibition hall erected for the celebrations held in Turin for the first centenary of the Unity of Italy, back in 1961. The structure was designed in 1959 and completed by spring 1961, after 16 months only. This repre- sented a really challenging enterprise, which can still arouse admi- ration, especially when the short construction times are compared to the imposing size of the building—160160 mm in plan—

and considering the strict architectural and functional constraints imposed on the design, among which the 40 m-long free spans 0141-0296/$ - see front matterÓ2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.engstruct.2012.12.012

⇑ Corresponding author. Tel.: +39 432 558050; fax: +39 432 558052.

E-mail addresses: stefano.sorace@uniud.it (S. Sorace), terenzi@dicea.unifi.it (G. Terenzi).

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required between each vertical structural element. The solution devised by Nervi consisted in a mesh of 16 reinforced concrete (R/C) monumental columns with variable sections along the height (that is, 20 m from ground to the base of the roof), constituting the most prominent example of Nervi’s principle of ‘‘uniform resis- tance’’[1]applied to vertical members in his works. Each column supports a steel mushroom-type roof panel with 16 radial beams spanning from the center. The panels are mutually separated by a 2 m-wide joint covered by a glass skylight. This solution, illus- trated in the roof plan inFig. 2, confers a suggestive monumental look to the building.

The remaining structural elements also remarkably contribute to the elegant and monumental appearance of the building. The most important elements are the R/C ribbed slabs constituting the two perimeter gallery floors. A plan of the upper floor is shown to the right ofFig. 2. The design solution for the slabs, traced out following the analytical equal-stress lines of their plate model, is also a typical feature of Nervi’s style[2], and was applied to other famous structures of him. An original drawing of the formworks, specially designed to the purpose, and a view of the intrados of the slabs, with the steel roof in the background, are displayed in Fig. 3.

Among the secondary structural elements of the building, the continuous glazed façades, also visible in the images inFig. 1, rep- resent a much advanced technical solution for the time too, as they are an early application of the ‘‘curtain wall’’ concept, with remark- able global dimensions (free height equal to around 16 m, from the first gallery floor to the top, and total surface greater than 12,000 m²).

This paper offers a synthesis of the structural and seismic assessment analyses carried out on the building, which make a part of the studies developed within a National Research Project fi- nanced by the Italian Ministry of Education, University and Re- search dedicated to innovative structural designs and the correlations between the leading engineering and architectural activities in Italy, during the 1950s and 1960s. The computational models generated for the analyses, as well as the verifications car-

ried out for all members, were entirely based on the original design documentation collected through extensive record research, be- cause field testing activities have never been developed on the building structure. However, the original documents, also includ- ing the certificates of the structural materials tested during the various stages of the construction works, are exhaustive enough to fix with certitude all input data for the numerical assessment enquiry.

The following aspects of the study are presented and discussed in the next sections: a modal analysis of the entire building; basic resistance and global/local buckling verifications of the steel roof beams, with comparisons of the results derived from the normative expressions of the critical stress of panels and the global lateral–

torsional buckling resistance of beams with the corresponding fi- nite element buckling computations; linear and non-linear seismic analyses of the R/C columns, the latter being carried out by an unconventional ‘‘integral’’ pushover approach, with the numerical model constituted by a full mesh of solid octahedral smeared cracking ‘‘concrete’’ elements with embedded steel reinforce- ments; the analysis and verification of the ribbed R/C gallery floors, including an evaluation of the correlation of their equal-stress line original conception to relevant finite element solutions; and the seismic analysis and evaluation of the glazed façades, developed by referring to non-structural performance limitations specially formulated to the purpose.

2. Modal analysis of the building

A modal analysis of the entire building was developed as a first step of the assessment enquiry, in order to evaluate its general dy- namic characteristics[3]. The analysis was carried out by a finite element model generated by the SAP2000NLcalculus program[4], where all the structural elements—mesh of light alloy profiles sup- porting the glazed façades and ‘‘pennon’’ beams constituting the vertical load bearing and bold bracing system of the façades in- cluded—were reproduced. Views of the model without the façade elements and the perimeter beams of the mushroom roof panels, and its complete layout, are shown inFig. 4. Each monumental col- umn is reproduced by 7 frame elements with different cross sec- tions, as discussed in Section4.1, and each radial beam of the roof panels by a single frame element with variable section. Ten frame elements are used to model each of the 20 steel frames con- stituting the circular drums situated on top of the columns, as de- scribed in detail in Section3. The mesh of perimeter steel edge beams connecting the free extremities of the radial beams of the mushroom panels is made of 420 frame elements. In total, the assembly of the 16 R/C columns and relevant mushroom panels includes 3364 frame elements. The slabs of the two gallery floors are reproduced by a mesh of inner square and outer rectangular shell elements, with 1 m1 m and 1 m2 m sides, respectively, for a total of 12,240 elements for the two floors. The longitudinal, Fig. 1.External and internal views of the building in its current conditions.

Fig. 2.Plans of the roof and the upper gallery.

transversal, internal perimeter and cantilever beams of the floors are modelled by a set of 5720 frame elements. Each one of the 256 R/C bearing columns supporting the floors is constituted by a single frame element. The glass panes of each façade are modelled by a mesh of 650 shell elements with average sides of 2.5 m; 720 vertical and 504 horizontal frame elements are incorporated to reproduce the supporting light alloy profiles, and 320 frame elements for the 32 pennons.

The results of the modal analysis show that the first two modes are mixed rotational around the vertical axisz/translational along the two main directions in plan,xandy. Both modes, whose shapes are plotted inFig. 5, feature a vibration period of 1.36 s; effective masses associated to the relevant translational component are equal to around 20.8% of the total seismic mass of the building;

and effective masses associated to the rotational component are equal to around 7%. The first two modal shapes are dominated by the deformation of the 16 couples of R/C columns and supported roof panels, which respond independently one from another, as a consequence of the existing separation joints at roof level. The first two building periods of 1.36 s correspond to a ‘‘mean’’ of the different first vibration periods of the internal, side and corner columns–roof panels couples taken separately, the differences being determined by the interaction with the bracing system of the façades. The three periods are equal to: 1.44 s—central couples, 1.35 s—side couples (interfaced on one side with the façades), and 1.27 s—corner couples (interfaced on two sides).

Concerning the superior modes of the building, ‘‘crowds’’ of 4 through 6 modes are repeatedly observed in correspondence with specific vibration periods, with negligible associated masses, as these ‘‘secondary’’ modes are essentially related to local response effects. Several dozen modes are required to gradually find signif- icant mass contributions and, in total, 83 modes are needed to acti- vate a summed mass greater than 85% (the minimum share required by the Italian Technical Standards[5]for the development of a modal superposition seismic analysis) along the two directions in plan, and around the vertical axis.

Portions of the global model of the building, and more refined models of the main structural members taken separately, were used subsequently to carry out the linear seismic assessment en- quiry reported in Sections4.1, 5 and 6.

3. Analysis of steel roof beams

The 20 cantilever steel radial beams forming the corolla of each one of the 16 mushroom panels of the roof have fixed-end bolted connections to a circular drum, constituted by 20 rectangular steel frames, 2800 mm high and 1900 mm wide. As shown in the origi- nal structural design drawing inFig. 6, each frame is supported by a triangular steel plate—with a 1500 mm-long vertical side and a 1900 mm-long horizontal side—placed over a 200 mm-deep groove on the upper section of the R/C column. The I-section Fig. 3.Original drawing of a formwork and intrados view of a R/C ribbed slab of the gallery floors.

Fig. 4.Internal and complete views of the global finite element model of the building.

x y

z

x y

z

Fig. 5.First and second modal shapes of the global finite element model of the building.

S. Sorace, G. Terenzi / Engineering Structures 49 (2013) 743–755

welded beams, which are joined on their free end to a continuous C-shaped steel edge beam outlining the square perimeter of the mushroom panel (Fig. 7), are 2800 mm to 700 mm high, and their top and bottom flanges are 690 mm to 200 mm wide. The beams have three different spans, ranging from 15,750 mm (type 1 beams, orthogonal to the C edge profile) to 20,250 mm (type 3 beams, close to the diagonal of the square). The constituting steel is equiv- alent to the current S235JR type, as it is typical of medium-to-high rise Italian steel structures built in the late 1950s through the late 1960s [6], with nominal yielding and ultimate stress values fy= 235 MPa andfu= 355 MPa, respectively. The web of beams is very thin (5 mm—type 1 through 7 mm—type 3), which results in great slenderness of cross sections, especially in the areas close to the fixed end. The web is subdivided in 13 (type 1 beam) through 17 (type 3) panels by a set of vertical stiffening plates welded to the web and to the top and bottom flanges. The different web thickness and stiffener spacing values determine a very simi- lar resistance of the three types of beams to bending and shear stresses, as well as to local and global buckling, as planned in the original design of the metallic roof (carried out by engineer Gino Covre, who worked with Pier Luigi Nervi for this part of the build- ing structure). In view of this, the finite element and verification analyses are synthesized below for type 1 beams, whose dimen- sions are reported inFig. 7, as they are also exhaustively represen- tative of the remaining two beam types.

It is noted that the analyses reported below are referred to the effects of gravitational loads, constituted by the dead and live (snow-related) loads of the roof, plus the self-weight of the beams.

Indeed, the stress states deriving from the normative probabilistic combinations of these loads at the ultimate limit states (with mul- tipliers of dead and live loads equal to 1.3 and 1.5, respectively) are greater than the ones obtained from the combination with the

effects of seismic action, vertical component included (with the multipliers of gravitational loads normatively fixed at 1 for this type of combination).

3.1. Bending and shear resistance and lateral–torsional buckling verifications

The verification of resistance to the in-plane bending moment at the ultimate limit states—referred to the effective properties of Class 4 cross sections, to which the considered members belong according to Eurocode 3 – Part 1-1 rules[7]—fails to be met. In- deed, the ratio of the design value of bending moment to the cor- responding design resistance is significantly greater than 1 (and it reaches 1.57 for the fixed-end section) along over 3/4 of beam span. On the other hand, the shear resistance test is met for all sec- tions. The verification at the serviceability limit states concerning vertical deflection, developed according to the current Italian Tech- nical Standards[5](as Eurocode 3 devolves this specification to the National Annexes), is widely met too.

The verification of beam resistance to lateral–torsional buckling was carried out by considering the only effect of the major axis bending, since the compression axial force induced by the slope of the center-line of the beams is very low (with a maximum of 22 kN at the fixed-end section). The relevant verification formula is:

M_Ed Mb;Rd

<1 ð1Þ

whereMEd,Mb,Rdare the design value of the moment and the design buckling resistance moment, respectively, withMb,Rdexpressed as:

M_b;Rd¼

v

_LTW_y fy

c

_M1 ^ð2Þ

beingWy=Weff,yfor Class 4 sections (Weff,yis computed by deter- mining the effective section as a function of the reduction factor

q

for the compressed portion of the web and the compressed flange),fy= 235 MPa, as noted above, and

c

M1= 1.05;vLTis given by the following relation:

v

_LT¼ 1 U_LTþ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

U²_LTk²_LT

q ð3Þ

whereULT¼0:5 1 þ

a

LTðkLT0:2Þ þk²_LT

,

a

LTis an imperfection fac- tor, equal to 0.76 for welded I-sections with height-to-base ratio greater than 2,kLT¼ ffiffiffiffiffiffiffiffi

Wyfy Mcr

q

, and Mcris the elastic critical moment for lateral–torsional buckling evaluated according to the following expression in Annex F of Eurocode 3 – Part 1-1[7]:

Circular steel drum Inner hole of R/C column Triangular steel plates Groove on R/C column

Fig. 6.Original design drawing of the vertical section of the connection system of the steel roof beams to the upper zone of the R/C columns.

1610 2300 275 255

+20,0

2500

2200 250 1390 500

2820 2821

1887

15750

518 887 938 1046 1149 1158 1289 1325 1492 1556 1629 1641 1015

5 6

4 9 10 11 12 13

2 3

1 7 8

Fig. 7.View of a type 1 steel roof beam (dimensions in millimeters).

Mcr¼C1

p

EIz

ðkLÞ²

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k

kw

2

Iw

IzþðkLÞ²GIT

p

²EIz

þ ðC2zgC3zjÞ² s

ðC2zgC3zjÞ 2

4

3 5

ð4Þ where C1,C2, C3= coefficients that depend on loading conditions and end constraints;L= length of the beam between lateral con- straints;Iw= warping constant;kw,k= effective length coefficients;

zg=za–zs, withza= coordinate of the point of application of load, andzs= coordinate of the center of torsion;zj= [0.8(2bt1)hs]/2, with:bt=Itc/(Itc+Ift),Itc= moment of inertia of the flange in com- pression with respect to the minor axis of the section,Ift= moment of inertia of the flange in tension with respect to the minor axis of the section, andhs= distance between the centers of torsion of the flanges.

By applying the relations above, the ratio of MEd (equal to 2414 kN m) to Mb,Rd (1415 kN m) results to be equal to 1.706, and thus the verification inequality(1)is definitely not met. The unsafety factor is obtained by inverting the ratio between the two moments (Mb,Rd/MEd= 1/1.706), i.e. 0.586.

3.2. Web panel buckling verifications

The web panels are much more sensitive to buckling than the flange plates are, as a consequence of the high slenderness of the web determined by the geometrical characteristics of the beams.

The verification analysis is carried out in this case by referring to the criterion proposed in a previous edition of the Italian Standards for steel structures[8], where the effects of normal and shear stres- ses are jointly considered, assuming an ideal critical stress

r

cr,idto be compared to the design ideal stress computed according to Von Mises rule. The expression of

r

cr,idis derived from Massonnet nor- mal critical stress–shear critical stress domain[9]as follows:

r

_cr;id¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r

²₁þ3

s

²

q

1þw 4 _r^r_cr¹þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3w 4 _r^r_cr¹

2

þ_s^s_cr2

r ð5Þ

where

r

1= 130.9 MPa and

s

= 20.1 MPa are the design normal and shear stress values;

r

cr=kr

r

cr,0,

s

cr=ks

r

cr,0, beingkr,ksthe nor- mal and shear stress buckling factors, and

r

cr,0the elastic critical plate buckling stress of the equivalent orthotropic plate, expressed as

r

cr;0¼_12ð1^p2E_{mÞ h}^t 2

, witht= plate thickness andh= plate width (or mean width in case of variable section); andwis a coefficient defin- ing the linear variation of normal stress over the section, which can be set as equal to1 in this case, by neglecting the very little con- tribution of the axial force to

r

1, quantified by a normal stress of 1.6 MPa. Panel 4 (Fig. 7) results to be the most critical one of the 13 web panels of type 1 beams. Considering its geometrical charac- teristics (base =b= 1050 mm, h= 2445 mm, t= 5 mm), kr= 27.6, ks= 33 and

r

cr,0= 0.78 MPa values come out, from which

r

cr= 21.6 MPa and

s

cr= 25.9 MPa are derived. By applying formula (5),

r

cr,idresults to be equal to 22.2 MPa.

The values of the normal and shear stress buckling factors are computed in[8]as a function of the aspect ratio

a

=b/h(whose average value is equal to 0.427 for panel 4) according to the expressions

kr¼15:87þ1:87

a

^{2 þ8:6}

a

²

a

62

3 ð6Þ

ks¼4þ5:34

a

²

a

<1 ð7Þ

which provide good analytical approximations of Timoshenko–Gere [10]original instability curves for linearly varying (withw61) nor- mal stress, and uniform shear stress distributions, respectively. The difference between the

r

cr,idand

r

crvalues above (22.2 MPa against

21.6 MPa) is so little because of the great prevalence of

r

1over

s

, which generates poor influence of shear stress in the critical stress interaction domain.

A second observation concerns

r

cr, which is greater than the va- lue of 19.1 MPa derived by the Eurocode 3 – Part 1-5[11]formula kp¼

ffiffiffiffiffiffiffi fy

r

_cr

s

¼ b=t 28:4

e

^{ffiffiffiffiffiffi}kr

p ð8Þ

wherebis the web width,

e

¼ ffiffiffiffiffiffi

235 fy

q , andkr= 23.9 forw=1. The difference between the two

r

crestimates obtained from[8,11]is caused by the twokrvalues adopted (27.6[8]—formula 6—against 23.9[11]). Indeed, unlike Standards[8], Eurocode 3 – Part 1-5[11]

prudentially assumes the minimal theoretical value of 23.9—corre- sponding to

a

= 2/3 in formula(6)—for any aspect ratio of panels, whenw=1.

3.3. Finite element buckling analysis

The finite element model of type 1 beams generated for the buckling analysis is constituted by a mesh of quadrilateral isopara- metric shell elements with an average side of 150 mm. This dimen- sion determines a number of constituting elements of each beam panel varying from around 80 to around 120, which is generally deemed appropriate for an accurate simulation of local buckling ef- fects in laterally loaded stiffened or non-stiffened plates [12,13].

Fixed end restraints are imposed to the internal end section of beams, connected to the steel drum, whereas only the lateral dis- placements are blocked on the tip end section, so as to accurately reproduce the restraint offered by the perimeter C-shaped edge beam of each mushroom roof panel. These boundary conditions are obtained by introducing displacement restraints for all three axes of the local coordinate system in the nodes of the shell ele- ments situated on the internal end section of beams, and displace- ment restraints acting only along the horizontal axis in the nodes of the elements placed on the opposite end. The buckling analysis is developed in SAP2000NL [4] by a classical eigenvalue formulation:

½KE þk½KG

ð Þf

v

_{g ¼ f0g ð9Þ}

where [KE] and [KG] are the elastic and geometric stiffness matrixes of the structural element or system,kis the generic eigenvalue, and {

v

} is the corresponding eigenvector. The solution of Eq.(9)provides the instability factorskiand the instability modal vectors {

v

_{i}. The}

least of the ki multipliers computed by the program represents the first (or critical) eigenvaluek1. Ifk1is greater than 1, no buckling occurs under the imposed loads.

The first mode buckling configuration of type 1 beams resulting from the analysis, displayed inFig. 8, highlights that the maximum lateral deformation is achieved in panel 4, consistently with the analytical assessment predictions commented in Section3.2. The relevantk1factor is equal to 0.259. By multiplying this value by the maximum von Mises ideal stress obtained in the central zone of the panel for the first buckling mode deformed configuration, equal to 90 MPa, the following finite element critical ideal stress estimate

r

cr,id,FEis deducted:

r

cr,id,FE= 23.3 MPa. This value is close to the

r

cr,idnormative estimate of 22.2 MPa given by formula(5), with a percent difference not exceeding 5%. Similar correlations are obtained for the subsequent local buckling modes too (the sec- ond mode achieves the maximum lateral displacements in panel 5, the third mode in panel 3, etc.), as the differences between

r

cr,id

and

r

cr,id,FE never exceed 5%. The seventh and eighth buckling modes are the first two involving a global (lateral–torsional) insta- bility deformed shape. The maximum lateral displacements and stresses are reached in the eighth mode, visualized inFig. 9with an amplification factor of 5000. The horizontal projection is also S. Sorace, G. Terenzi / Engineering Structures 49 (2013) 743–755

plotted in this drawing, showing that the deformed shape corre- sponds, as for the seventh mode, to the first theoretical global buckling mode of the beams. Thek8eigenvalue is equal to 0.524, which must be compared to the unsafety factorMb,Rd/MEd= 0.586 resulting from the lateral/torsional buckling verification discussed in Section3.1. The difference between the two values is around 12%, and the numerical result in this case is more conservative than the normative factor estimate.

As is known, the data obtained from a computational analysis are always a function of the geometrical dimensions of the mesh.

In view of this, mesh-sensitivity was investigated by varying the sides of the shell elements by factors 2, 1.5, 0.75 and 0.5 with re- spect to the reference average dimension of 150 mm. As a general result of this enquiry, no appreciable influence on eigenvalues and eigenvectors was observed when passing to the most refined meshes. A trend towards a progressive rise in eigenvalues emerges when increasing the sides (e.g.,

r

cr,id,FEin panel 4 becomes equal to 24.1 MPa and 25.3 MPa for mesh factors 1.5 and 2, respectively), even if the shapes and the hierarchy of buckling modes are kept unchanged. Based on these observations, the average sides of the shell elements assumed for this analysis appear to be the greatest values compatible with the accuracy of the solution, and thus they

can represent a credible balance point between the need to reach accurate results and to restrict the computational effort.

3.4. Proposal of a retrofit intervention

Based on the results of the assessment analyses, a simple retro- fit solution was proposed, which consists in strengthening the beams by a line of horizontal steel plates placed at mid-height of the cross sections, plus a diagonal plate positioned in the lower half of the panels that proved to be the most sensitive to buckling (the first 7 out of 13, in the model represented inFig. 8), all welded to both sides of the web, as shown by the modified finite element model inFig. 10. The first buckling factor in strengthened configu- ration grows from 0.259 to 1.33, guaranteeing a satisfactory safety margin with a low-impact intervention. The same retrofit solution is extended to type 2 and type 3 beams too, involving the first 8 out of 15, and the first 9 out of 17 panels, respectively, and producing similar increases in the corresponding first buckling factors.

4. Analysis of R/C columns

The shape of the cantilever monumental columns constantly varies from the base (cross-type section with 6 m-long and 1 m- wide sides) to the top (circular-type Section, 2.5 m wide), as illus- trated by the photographic image of the building interiors inFig. 1, and by the sequence of geometrical cross sections along the height reproduced inFig. 11. This variable shape was designed in order to obtain nearly ‘‘uniform resistance’’ members with respect to the combined effects of bending moments and axial force, as observed in the Introduction. The top section, reduced to a diameter of 2 m, is prolonged for further 1.6 m to form the groove where the trian- gular steel plates supporting the circular drum of the mushroom roof are located (Fig. 6). The original drawings of the structural sec- tions at the fixed-end base, at an intermediate height and on top, displayed inFig. 12, show an eccentric inner hole (also visible in the vertical section inFig. 6), where a spiral steel staircase to access the roof, and a conductor pipe, are housed.

The foundations of the columns consist in cross-type plinths with 10.4 m-long and 2.4 m-wide sides, supported by groups of 16 pedestal (Franki)-type reinforced concrete piles with a diameter of 500 mm (Fig. 13). The verifications carried out both on the piles and the plinths, based on the complete geotechnical data of the soil, which are not reported here for brevity’s sake, are largely met for all static and seismic load design combinations.

Fig. 8.Deformed shape of type 1 beams obtained for the first buckling mode.

DEFORMED BEAM AXIS UNDEFORMED BEAM AXIS

Fig. 9.5000-Times magnified deformed shape of type 1 beams obtained for the eighth buckling mode.

Fig. 10.Deformed shape of type 1 beams obtained for the first buckling mode in retrofitted conditions.

4.1. Linear analysis

The geometry and the cross sections of the linear finite element model of columns, generated by SAP2000NL[4]too, are illustrated inFig. 14. As mentioned in Section2, the model is subdivided in se- ven portions, which correspond to the seven cast zones constitut- ing the columns. Each portion consists of a frame element with constant section, equal to the average section of the cast zone. This type of discretization was necessary because the section-builder option offered by the program, which was used to reproduce the rather complex geometry of the columns (internal hole included),

does not allow generating continuously varying sections along the axis of a frame member. The reinforcing bars were not included in the model.

The pseudo-acceleration design response spectrum adopted for the seismic analyses carried out at the basic design earthquake le- vel (BDE, with a 10% probability of being exceeded over the refer- ence time periodVR= 200 years fixed for the building, obtained by multiplying the assumed nominal structural life of 100 years by a coefficient of use equal to 2, as imposed by Standards[5]for stra- tegic buildings) is plotted inFig. 15. The spectrum is referred to the city of Turin and C-type soil conditions (deep deposits of dense or medium-dense sand, gravel or stiff clay from several ten to several hundred metres thick, according to the identical soil classifications of Standards[5]and Eurocode 8[14]), as resulting from the geo- technical testing campaigns enclosed to the original design docu- mentation. A behavior factorqequal to 1.5 was selected for the BDE to scale the ordinates of the corresponding elastic response spectrum, in consideration of the low-ductility inverted pendulum structural configuration of columns. The vertical loads considered in the analysis are the ones transferred by the steel roof, plus the self-weight of the columns.

The concrete used for the columns, as well as for the gallery slabs, was ‘‘680’’-type, featuring a high characteristic value of com- pressive strengthfckfor in situ cast R/C structures at the time, equal to 42 MPa. Indeed, in the 1960s throughout the 1970s, similarfck

values were more typical of concretes used in prefab R/C buildings [15,16]. The reinforcing steel was ‘‘R50/60’’-type, with nominal yield stressfyof 370 MPa and limit stressfuequal to 545 MPa.

The results of the linear assessment analysis are demonstra- tively displayed, for the three cross sections shown in Fig. 12, in the diagrams plotted inFig. 16, reproducing the axial force–bend- ing moment interaction domains of the sections and the represen- Fig. 11.Sequence of the geometrical cross sections of the R/C columns.

Fig. 12.Original drawings of the structural sections at the base, an intermediate height and the top of the R/C columns.

Fig. 13.Original drawings of the foundations of the R/C columns.

S. Sorace, G. Terenzi / Engineering Structures 49 (2013) 743–755

tative points of the maximum combined effects derived from the finite element computations. Similar results are obtained for the remaining sections, omitted herein for brevity’s sake. The graphs inFig. 16highlight that the verification points largely remain with- in relevant safety domains, and their distance from the edges of the domains is comparable in the three cases. As this holds true for all the remaining sections, the results of the linear analysis seem to

confirm that the columns have an approximately uniform resis- tance along the height, also according to the most recent normative verification criteria.

4.2. Non-linear analysis

Based on the outcome of the first-level linear assessment anal- ysis, a second-level step was started, which consisted in a non- classical pushover analysis, carried out by an integrally non-linear model generated by the ANSYS calculus program[17]. The model is constituted by a full mesh of 8400 solid octahedral smeared crack- ing ‘‘concrete’’ elements with embedded steel reinforcements that can be freely oriented with respect to the global coordinate system.

No reductions to simplified models were considered in this en- quiry, as the uniform resistance columns should ideally reach the first significant cracked configurations, and then the plasticization of vertical reinforcements, simultaneously in several sections along the height. This ‘‘full-cracking’’ application offers a more direct and realistic simulation of the evolution of the non-linear response of columns as compared to models including lumped plastic hinges or fiber-composed plastic zones, but it requires a greater computa- tional effort and proper checks on the stability and accuracy of the solution.

The Willam–Warnke triaxial failure domain[18]is adopted to model the ultimate compressive, tensile and mixed compressive–

tensile triaxial ultimate response of the concrete material. The classical Drucker–Prager yield criterion [19] is assumed by the Fig. 14.Geometry of the linear finite element model of the R/C columns.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Period [s]

Pseudo-Acceleration [g]

Design Spectrum BDE Level q = 1.5

Fig. 15.BDE-scaled pseudo-acceleration design response spectrum.

Fig. 16.Axial force-bending moment domains of sections inFig. 12and verification points derived from the analysis.

program for plastic deformations. A bilinear strain-hardening elas- to-plastic behavior is assigned to reinforcing steel. The main mechanical parameters of the concrete model are as follows:

sto= shear transfer coefficient for an open crack,stc= shear transfer coefficient for a closed crack,ftd= uniaxial cracking design stress, fcd= uniaxial crushing design stress,fcb= biaxial crushing design stress,Ec= Young modulus, and

m

c= Poisson ratio. The parameters of reinforcing steel are: fy= yielding stress, sh= kinematic strain hardening ratio,Es= Young modulus, and

m

s= Poisson ratio. The parameters defining the surface of the Drucker–Prager domain are:c= cohesion,/= friction angle, and w= dilatancy angle. The following basic values were adopted in the analysis: sto= 0.3, stc= 0.85, ft= 1.7 MPa, fcd= 23.8 MPa, fcb= 1.2fc, Ec= 35,600 MPa,

m

_{c= 0.2, fy}= 321.6 MPa, sh= 0.015, Es= 206,000 MPa, and

m

s= 0.3, according to the characteristics of the materials; and c= 2.12 MPa,/= 30°andw= 0°(associated flow rule), from litera- ture suggestions concerning the plasticity domain for concrete- type elements[18,20,21].

The gravitational loads are the same as introduced in the linear analysis but, unlike the linear model, the geometry reproduces the real one with continuity. The horizontal load for the develop- ment of the pushover process was applied to the top of the col- umn. Geometrical non-linear effects were taken into account, in view of the expected high maximum displacements. As for all types of incremental analysis, the critical parameter for the con- vergence and the accuracy of the numerical solution was repre- sented by the number of sub-steps to be developed in the ramped loading process within any single load step, with the lat- ter fixed at 10 mm. A displacement-based criterion for conver- gence control was adopted, with a tolerance of 5%. The following numbers of sub-steps were finally selected, after several tentative choices: 50 (corresponding to 0.2 mm) for steps 1 through 13, characterized by moderate cracking effects in the concrete elements; 200 (0.05 mm) for steps 14–27—extensive cracking in the tension zones; 300 (0.033 mm) for steps 28–70—

softening response phase. These data confirm general suggestions [20] about the preferable values (ranging from 0.1 mm to 0.01 mm) of the displacement increments in full-cracking/crush- ing problems when the non-linear behavior of a significant por- tion of the model is activated. Further increases in the number of sub-steps in the more accentuated non-linear response phases did not show any practical impact on the accuracy of the solution.

Indeed, by amplifying the number of sub-steps by a factor up to 10, that is, by assuming up to 2000 sub-steps for steps 14–27, and up to 3000 sub-steps for steps 28–70, differences no greater than 0.1% on base shear were found.

For the assumed set of mechanical parameters, the pushover analysis was concluded at the end of step 70, corresponding to a top displacementdtopof 700 mm and a drift ratio (ratio of top displacement to column height)drequal to 3.5%. This was fixed as the numerically determined structural collapse condition. The only two parameters not related to the specific characteristics of the constituting materials—sto and stc—were varied in their technical ranges of interest (sto from 0.2 to 0.4,stcfrom 0.65 to 0.9) to check their influence on response, which resulted to be negligible.

The capacity curve obtained from the analysis by plotting the reaction force in the fixed-end base (base shear) as a function of top displacement is displayed in Fig. 17. A median vertical section reproducing the cracked configuration of the model at the end of the last step of the pushover analysis, and a view orthogonal to the loading direction showing the distribu- tion of the axial stress in reinforcing bars, are shown in Fig. 18. The following observations can be drawn from Figs. 17 and 18.

– A remarkably smooth shape of the capacity curve emerges, as a consequence of the high number of sub-steps adopted in the analysis.

– The curve is rather linear up to around 1500 kN (withdtop= 20 mm anddr= 0.1%), that is up to around 60% the maximum base shear, equal to 2390 kN; then, cracking begins to develop signif- icantly in the elements situated on the tension side, and the curve visibly gets non-linear.

– This second response phase goes on up to a force of 2200 kN, with corresponding top displacement of 110 mm (dr= 0.55%), when the first plasticization of reinforcing bars occurs.

– The plasticization then increases, determining nearly a plateau zone extended from around 250 mm to around 450 mm; the maximum shear force is reached fordtop= 300 mm (dr= 1.5%).

– A softening branch follows, featuring a strength degradation of around 0.2 kN/mm up to the last two steps, where degradation reaches accentuated values of 0.5 kN/mm (step 69) and 2 kN/mm (step 70), while it does not mean a sudden drop in strength in proximity to the numerical solution divergence point.

– Cracking extends rather uniformly over the tension side, whereas crushing is never attained. The maximum compression values in the external fiber of base section are no greater than 0.25fc. This indicates that concrete is far from ultimate strength conditions on the compression side of the columns at the last step of the analysis.

– Plasticization of reinforcing bars in tension is disseminated over about 1/3 of the height. The extent of the macroscopic plastic hinge zone of columns determined via numerical analysis shows that the hypothesis of uniform resistance is not verified in the non-linear field, although cracking is spread rather uni- formly along the height. The greatest rotations are obtained during the entire loading process in the cross section situated at a distance of 3.3 m from the base, which practically coincides with the mid-height section of the plastic hinge zone.

These observations underline that numerical collapse is not determined by a failure of the constituting materials, but by an excessive deformation of the octahedral elements in various por- tions of the mesh. Deformation is not sensitive to the number of sub-steps, which was increased further to a value of 10,000 in the 70th step, without any practical consequences. Moreover, the response curve highlights satisfactory behavioral capacities of col- umns, with an elastic response for rather high base shear values, and good ductility resources. A formal interpretation of the results of the pushover enquiry is presented in the next section.

0 100 200 300 400 500 600 700 800 0

500 1000 1500 2000 2500 3000

Top Displacement [mm]

Base Shear [kN]

Fig. 17.Response curve obtained from the pushover analysis.

S. Sorace, G. Terenzi / Engineering Structures 49 (2013) 743–755

4.3. Formal seismic assessment based on the pushover analysis response

The pushover response was evaluated for the four reference seismic levels established by Standards[5], that is, in addition to the basic design earthquake—BDE, the frequent design earthquake (FDE, with a 81% probability of being exceeded over the reference time periodVR), the serviceability design earthquake (SDE, with a 50%/VR probability), and the maximum considered earthquake (MCE, with a 5%/VRprobability). Relevant top displacement de- mands dtop,FDE, dtop,SDE, dtop,BDE, and dtop,MCE were calculated by referring to the site-dependent displacement response spectra pre- scribed for the city of Turin[5], scaled at the amplitude of the four earthquake levels. The maximum response displacements came out for the internal columns, as they are characterized by the high- est vibration period as compared to the remaining columns, as noted in Section2. However, due to the little differences existing with the periods of the side and corner columns, little differences with the relevant displacement demands resulted too. The values calculated for the four seismic levels proved to be:dtop,FDE= 19.8 mm (drFDE= 0.1%), dtop,SDE= 25.9 mm (drSDE= 0.13%), dtop,BDE= 52.9 mm (drBDE= 0.26%), anddtop,MCE= 59.7 mm (drMCE= 0.3%).

The response was assessed by referring to the four classical structural performance levels considered by Standards [5], i.e., similarly to most performance-based international Seismic Stan- dards, Operational (OP), Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP). The top displacement limitations for the four levels were fixed as follows. At the OP structural limit state, the response must be elastic, although not strictly linear.

Looking at the response curve inFig. 17, the OP-related limit can be assumed as a rounded average of the values corresponding to the end of the linear and non-linear elastic stages, dtop= 20 mm (dr= 0.1%) and dtop= 110 mm (dr= 0.55%), that is, dtop,lim,OP= 60 mm (drlim,OP= 0.3%). The 0.3% drift value also coincides with the non-structural performance limit normally adopted by interna- tional Seismic Standards and Recommendations for the assessment and rehabilitation of existing buildings—among which ASCE/SEI 41-06[22]—for the OP level in the presence of damageable non- structural elements directly interacting with the main structural members (in this case represented by the glazed façades interact- ing with the side and corner columns, as discussed in Section6). At the IO structural limit state, little and easily reparable damage is accepted, with very limited reductions in terms of resistance and horizontal stiffness. This condition practically corresponds to the early plastic response stage following the first plasticization of

the bars in the critical zone of columns (which begins at a displace- ment of 110 mm, as noted above, but develops appreciably beyond 120 mm). Therefore, the top displacement limit for the IO level dtop,lim,IOcan be fixed at 120 mm (drlim,IO= 0.6%).

The LS and CP structural limit states are assessed in terms of plastic response levels. Detailed criteria for the evaluation of R/C columns are offered in[22], where a series of acceptable limits for the plastic rotation angles are formulated as a function of the geometrical and reinforcement characteristics of the members, as well as of the axial force computed from the analysis. Although these limits are suggested for columns belonging to frame struc- tures, in the absence of specific indications for the special case of free-standing cantilever columns, they can be reasonably extended also to this type of elements. Based on the characteristics and the axial force values calculated for the columns of Palazzo del Lavoro, the suggested limits of plastic rotations result to be equal to 0.012 radians—LS, and 0.016 radians—CP, respectively. By assigning the two values to the median section of the plastic hinge zone situated at the height of 3.3 m, where the maximum response rotations are recorded in the pushover analysis (Section4.2), the following top displacements are derived: 472 mm and 606 mm. These values are then assumed as the displacement limitations for the LS and CP performance levels,dtop,lim,LSanddtop,lim,CP, with corresponding drift limits drlim,LS= 2.36% and drlim,CP= 3.03%, respectively. It is noted that these drift limits fall within the reference ranges ([2–

3%]—LS, [3–4%]—CP) typically proposed for R/C structures, when no direct correlation with member rotations or other local re- sponse parameters is formulated.

By comparing the top displacement demands relevant to the four reference seismic levels with the limitations established for the four basic response limit states, a remarkably high seismic per- formance of the columns emerges. This is a consequence both of their overstrength factors, already highlighted by the linear dy- namic analysis, and of the low seismicity of the site of the building.

Concerning the latter, the numerical enquiry was completed by examining what the performance of columns would be should the building be located in a high seismicity zone in Italy, rather than in Turin, i.e. a low-to-moderate seismicity area. In this hypo- thetical situation, the spectral ordinates would be up to three times greater than in the Turin spectra, averagely for the four seismic lev- els. By assuming this mutual rounded amplification factor in the computation of displacement demands, they would increase to dtop,FDE,inc= 59.4 mm (drFDE,inc= 0.3%),dtop,SDE,inc= 77.7 mm (drSDE,inc= 0.39%), dtop,BDE,inc= 158.7 mm (drBDE,inc= 0.79%), and dtop,MCE,inc= 179.1 mm (drMCE,inc= 0.9%). For these magnified values, the Fig. 18.Cracked configuration of the model and stress distribution in reinforcing bars at the end of the last step of the pushover analysis.

assessment analysis gives the following results: dtop,FDE,inc= - dtop,lim,OP, dtop,SDE,inc<dtop,lim,IO, drBDE,inc<dtop,lim,LS, and dtop,MCE,inc<dtop,lim,LS, where the conditions expressed by the sec- ond, third and fourth inequalities are met with wide margins. This corresponds again to a very satisfactory performance, giving rise to three ‘‘diagonal’’ (FDE–OP, SDE–IO, BDE–LS), and an ‘‘over-diago- nal’’ (MCE–LS) correlations between performance levels and earth- quake levels. This underlines again that the columns were conceived with considerable structural redundancy—also observed in similar columns included in other outstanding R/C buildings de- signed by Nervi in the same period—with the aim of emphasizing their monumental look and warranting prudentially wide safety margins with respect to the higher performance demands that could have been imposed in future generations of Technical Stan- dards, rather than ‘‘optimizing’’ their original dimensions.

5. Analysis of R/C gallery floors

A set of symmetrical technical joints separates the R/C gallery floors in four identical angular zones and eight identical central zones. As mentioned in Section4.1, concrete and steel are of the same types as used for the R/C monumental columns. The most stressed members belong to the four angular portions, the original design drawing and finite element model of which are displayed in Fig. 19. The model, generated again with SAP2000NL[4], is more de- tailed as compared to the one incorporated in the global model of the building by which the modal analysis was carried out, illus- trated in Section2. Indeed, in this case the geometry of the shell elements simulating the flat slabs exactly follows the shape of the formworks. Furthermore, the ribs are expressly modelled by a set of additional frame elements. Based on these refinements, the model shown inFig. 19totals 11,264 shell and 3266 frame ele- ments (the model of the same corner zone included in the global model of the building discussed in Section2is composed of 846 shell and 384 frame elements).

The diagrams of the bending moment on the beams resulting from the analysis are also drawn inFig. 19, showing high peak neg- ative and positive values on the robust perimeter beams of the internal square slab fields. The equal tension stress lines on a slab field are plotted inFig. 20in superimposition to the plan of the ribs, traced out in the background, showing a remarkable correlation between the computational solution and the original design of R/

C members. The verifications carried out on the various elements always gave positive results for bending moments, while a lack of shear resistance was found in some terminal sections of the lon- gitudinal and internal perimeter beams, as well as in the cantilever beams. A carbon fiber reinforced plastics (CFRP) U-jacket was pro- posed as strengthening solution for these members, as illustrated inFig. 21for the cantilever beams. One 0.165 mm-thick sheet rein- forcement was sufficient for all members, except for the longitudi-

nal beams, where a double sheet was required. Here too, the interventions are characterized by a low architectural impact, and they are respectful of the monumental value of the building.

6. Analysis of glazed façades

The first gallery floor subdivides the façades in two independent zones in vertical direction, with interstory heights of 4 m (ground zone) and 16 m (top zone), respectively. The top zone can be con- sidered as a continuous façade supported by a number of vertical steel pennon beams with rounded triangular section, which act both as vertical load bearing and bold bracing elements. Each pen- non beam, hinged at the bottom to a triangular cantilever slab belonging to the first gallery floor and on top to the perimeter beam that connects the external mushroom panels, is bonded to the horizontal light alloy profiles of the façades (which constitute

Fig. 19.Original design drawing and finite element model of an angular portion of the gallery floors, and bending moment diagrams on the beams resulting from the analysis.

Fig. 20.Original design drawing of a slab field, and tensile stress lines with background draw of the ribs.

Fig. 21.CFRP-based U-jacket strengthening of the cantilever beams.

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a mesh with sides of about 2.5 m, as observed in Section2) by short and rigid steel beams.

These curtain wall-type façades are among the most sensitive non-structural elements to in-plane and out-of-plane interstory drifts. In order to avoid local damage to the glass panes and the supporting profiles, the maximum values of both types of drifts should be constrained within 5‰ of the interstory heights [23,24]. Therefore, this can be assumed as the limit threshold for the non-structural OP performance level,drNS,lim,OP. Beyond this le- vel of deformation, a first series of hairline cracks appears on the glass panes, reparable without interrupting the use of the building until the drift approximates 1%. This value can be adopted as the limit for the non-structural IO performance level,drNS,lim,IO. Irrepa- rable cracks are observed on the surface of the panes for drifts equal to about 1.5%, and cracks extended to the entire surface at about 2%, with the latter value marking the acceptable boundary for the LS non-structural performance level,drNS,lim,LS. The glass panes become fallout-prone for drifts around 3%, which can be fixed as the upper limit for the CP non-structural performance le- vel,dNS,lim,CP.

The evaluation of the performance of the glazed façades was carried out by modal superposition analyses, scaling the input re- sponse spectra to the four normative earthquake levels discussed in Section4.3. The analyses were developed by the complete finite element model of the building described in Section2, combining the contributions of the 83 modes needed to activate a summed mass greater than 85% along thexandyaxes in plan, as well as around the vertical axis z, as discussed in Section2.

The maximum drifts were obtained in the upper area of the faç- ades, caused by horizontal displacements of the first and second gallery floors always notably greater than those of the roof panels.

Furthermore, the out-of-plane components were always around two times greater than the in-plane ones. As way of example of the results obtained from the analysis at the FDE earthquake level, the maximum deformed configuration of the model alongxdirec- tion in plan, and a zoomed view of a terminal zone, are displayed in Fig. 22. These images highlight the differential displacements be- tween floors and roof, which induce the most accentuated out- of-plane deformations. The deformed configurations derived from the remaining levels of the seismic action are totally similar from a qualitative viewpoint.

The maximum out-of-plane drift values computed for the four earthquake levels are: drfaç,FDE= 1.28%, drfaç,SDE= 1.55%, drfaç,BDE= 2.19%, anddrfaç,MCE= 2.39%. By comparing these demands with the limitations established for the four basic non-structural limit states, the following inequalities are found: drfaç,FDE<

drNS,lim,LS, drfaç,SDE<drNS,lim,LS, drfaç,BDE<dNS,lim,CP, drfaç,MCE<

dNS,lim,CP. The resulting performance is relatively poor, with local (FDE) and extended (SDE) irreparable cracks on the glass panes only satisfying the requirements for the Life Safety non-structural performance level, as concerns the two lower earthquake levels, and very severe damage, with drifts just below the limit relevant

to the Collapse Prevention state, for the upper earthquake levels.

Therefore, the façades represent the most vulnerable elements of the building, as a consequence of the marked differences existing between the displacements of the gallery floors and the roof.

7. Conclusions

The assessment study carried out on ‘‘Palazzo del Lavoro’’ al- lowed improving the knowledge on its constituting materials and construction details, as well as getting a better understanding of the design concept of its structural members, and checking the de- gree of correlation of the computed stress states to the original cal- culations and the geometrical shapes conceived by Pier Luigi Nervi and co-workers. At the same time, the actual safety conditions of the building and the seismic performance of the main members were evaluated according to the criteria of current Technical Stan- dards, and retrofit hypotheses were proposed for the steel roof beams and some beams of the R/C gallery floors, which failed to pass some of the verifications. Specific remarks deriving from the results of the study are reported below.

– Neither type of buckling verifications carried out on the beams of the mushroom steel roof—global lateral–torsional and local web panel—was met. The values of the critical stress and the unsafety factors obtained from the normative formulas were close to the values deducted from the finite element analysis.

This is an interesting result of this section of the study since the output of buckling calculations developed by commercial calculus programs is generally limited to the list of buckling eigenvalues and eigenvectors, with no direct indications about the critical stress values to be considered in structural verifica- tions, which leaves a considerable margin of uncertainty for professional users. For web panel verifications, the best correla- tion to the values derived from the finite element analysis is particularly obtained by the formula included in a previous edi- tion of the Italian Standards on steel structures, where the effects of normal and shear stresses are jointly considered in the calculation of the ideal critical stress, unlike in the latest Standards edition.

– The unsafe conditions of the steel beams coming out from the buckling analysis could be easily overcome by the low-impact and respectful retrofit intervention proposed, which allows reaching over 500% increase of the first buckling factor, as com- pared to the initially computed value, for all beams.

– The pushover analysis carried out on the monumental R/C col- umns by an integrally cracking/crushing computational model showed remarkable response capacities of these members, with top displacement demands constrained below the limitations established for the Operational performance level up to the highest normative seismic input amplitude. The first reason of this very good performance lies in the wide safety margins Fig. 22.Global and detailed views of the deformed configuration of the façades obtained in the analysis at the FDE level.

assumed in the original calculation of columns, also confirmed by the results of the linear modal superimposition dynamic analysis, which highlights that the original design attempted to emphasize the monumental look of columns also by increas- ing their cross-sections (although by not impairing elegance, thanks to a refined and daring development of geometry along the height), rather than by optimizing their dimensions. The second reason of the high performance of columns is repre- sented by the low seismicity of the site of the building. To test the influence of this parameter—also considering that the design had necessarily included, at the time, only a gross esti- mation of seismic forces—the assessment analysis was repeated by hypothesizing to ideally locate the building in a high seis- micity zone in Italy. This originated a satisfactory output too, consisting in three ‘‘diagonal’’ (FDE–OP, SDE–IO, BD–LS) and an ‘‘over-diagonal’’ (MCE–LS) correlations between perfor- mance levels and earthquake levels.

– At the final stage of the pushover process, the extent of yielding in the reinforcing bars on the tension side of columns is limited to about 1/3 of the height. This underlines that Nervi’s design hypothesis of uniform resistance, approximately confirmed by the linear analysis, is not verified in the non-linear field.

– The equal tension stress lines-governed design concept of the flat slabs of the R/C gallery floors was precisely confirmed, instead, by the computational solution. The CFRP U-jacket strengthening solution proposed for the nominally unsafe rib members is non-invasive and respectful of the monumental value of the building, as in the case of the interventions outlined for the steel roof beams.

– The seismic assessment analysis of the glazed façades, devel- oped by referring to non-structural performance limitations specially formulated in the study, revealed that they represent the most vulnerable building technology included in the edifice.

Since effective retrofit interventions on relevant load bearing and bracing systems are difficult to be carried out at reasonable costs and limited cosmetic impact, and considering that the cur- tain wall façades have also rather limited thermal and acoustic insulation capacities as compared to the current standards, a complete technological–structural redesign of the façades appears to be necessary in any possible future architectural refurbishment projects of the building.

In addition to the detailed information gathered on ‘‘Palazzo del Lavoro’’, the study offered new contributions to a critical interpre- tation of Nervi’s design activity, as well as to an analysis of the modern heritage R/C structures belonging to the same period.

Acknowledgements

The study reported in this paper was financed by the Italian Ministry of Education, University and Research within the PRIN

2008 Project (Research Programme ‘‘Conceiving structures: engi- neering and architecture in Italy in the 1950s and 1960s. A mul- ti-disciplinary research’’). The authors gratefully acknowledge this financial support.

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