Input Data in FEM Design: A Simple Example of the Structural Seismic Assessment of RC Stairs

ALESSANDRO CALVI1, GIORGIA SAVIO2

alessandro.calvi84@gmail.com1, saviogiorgia91@gmail.com2

INTRODUCTION

This report of structural calculation, according to point § 10.1 of DM 17/01/18, includes a description of the general criteria for analysis and verification too. Following addition to the information provided in § 10.2 of DM same regarding analysis and verification conducted with the help of calculation codes.

Location of the structure
Region PIEMONTE
Longitude 7.964
Latitude 45.042


Parameters of the structure
Use class


Life Vn [years] Use parameter Vr period [years]


II 50.0 1.0 50.0



In the following origin and characteristics of the software codes; title, producer and distributor, version, extremes of licensing agreements:

Origin and Characteristics of the Codes of Calculation
Title: PRO_SAP PROfessional Structural Analysis Program
Version: e-TIME (build 2021-05-192)
Producer-Distributor 2S.I. Software e Servizi per l’Ingegneria s.r.l., Ferrara


A careful preliminary examination of documentation accompanying the software made it possible to assess the reliability and fitness for particular case. The documentation provided by the manufacturer and distributor of software, contains a comprehensive description of the theoretical basis and algorithms used, identification of fields of use, and test cases entirely resolved and commented, accompanied by the input file necessary to reproduce the elaboration:

Reliability of codes used
2S.I. has tested the reliability and robustness of the software code through a significant number of cases in which the results of numerical test were compared with theoretical solutions.

Documents containing some of the most significant cases handled are at the following address: http://www.2si.it/Software/Affidabilità.html


In the following is indicated kind of structural analysis (static, dynamic, linear or nonlinear) and the method adopted to solve the structural problem and the methods followed for the design and verification of sections. It reports load combinations and in the case of non-linear calculations, the load paths followed; load configurations used for the design of structure in question were comprehensive for design-verification.

Kind of structural analysis
Linear analysis YES
Seismic static linear  NO
Seismic dynamic linear  YES
Seismic static nonlinear (prop. masses) NO
Seismic static nonlinear (prop. mode) NO
Seismic static nonlinear (triangular)  NO
Project-verifying the data 
Reinforced concrete  D.M. 17-01-2018
Steel  D.M. 17-01-2018
Wood D.M. 17-01-2018
Masonry D.M. 17-01-2018
Seismic action
Standard applied for seismic action D.M. 17-01-2018
Combinations of load cases 
Allowable tension NO
SLU YES
SLV (SLU with earthquake) YES
SLC NO
SLD YES
SLO NO
SLU ground  A1 NO
SLU ground A2 NO
SLU ground G NO
Combination caracteristic (rare)  YES
Combination frequent  YES
Combination almost permanently (SLE) YES
SLA (accidental fire)  YES


The structural elements are controlled for safety according to the construction theory methods.

To estimate the tensile-deformation state induced by the static loads, the structural analysis is carried out according to the displacement method .

To estimate the tensile-deformation state induced by the dynamic loads (among which the seismic load), the structural analysis is carried out according to the method of the modal analysis and response spectra in terms of acceleration.

The structural analysis is carried out according to finite element method. This method schematize the structure by using elements connected in a fixed number of points, i.e. nodes.

The nodes are defined according to three Cartesian coordinates within global reference system.

The unknowns of the problem (within the methods of displacements) are the components of the nodes referred to a global reference system (displacements with respect to X, Y, Z, rotations around X, Y, Z).

The problem is solved by means of a system of linear algebraic equations, whose know terms represent the loads applied to the structure and appropriately concentrated on nodes:

K * u = F where K = stiffness matrix

u = nodal displacement vector

F = nodal force

The element actions and/or tensions, which are generally referred to the local reference system, are deduced from the displacements obtained by means of the problem solution.

The utilized reference system is composed of a clockwise system of Cartesian coordinates XYZ. Axis Z is assumed as vertical and directed upwards.

The elements utilized for the simulation of the structure static scheme are listed below:

TRUSS type element (truss)

BEAM type element (beam)

MEMBRANE type element (membrane)

PLATE type element (plate - shell)

BOUNDARY type element (boundary)

STIFFNESS type element (stiffness matrix)

BRICK type element (solid element)

SOLAIO type element (macro element made up of several membranes)

Structural model achieved with:
nodes


19
elements D2 (trusses, beams, columns) 10
elements D3 (walls, mats, shells) 6
elements solaio 0
elements brick 0
Model structural size [cm]:
X min = 0.00
X max = 239.00
Y min = 0.00
Y max = 200.00
Z min = 0.00
Z max = 286.00
Vertical structures:
Trusses NO
Pillars YES
Walls YES
Shear walls (membrane behavior) NO
Properties not vertical:
Trusses NO
Beams NO
Shells YES
Membranes NO
Orizzontamenti:
Solaio with rigid floor NO
Solaio without rigid floor NO
Type of boundary conditions:
Nodes bound rigidly NO
Nodes bound elastically NO
Nodes with seismic isolators NO
Foundations point (plinths / plinths on pole) NO
Foundations type beam YES
Foundations type mat NO
Foundations with solid elements NO


Draft Calvi 268335015-image1.jpg

01_INT_PERICOLOSITA

Draft Calvi 268335015-image2.jpg

01_INT_SPETTRI_ELASTICI_O

Draft Calvi 268335015-image3.jpg

01_INT_VISTA_SOLIDA_001

Draft Calvi 268335015-image4.jpg

01_INT_VISTA_SOLIDA_002

Draft Calvi 268335015-image5.jpg

01_INT_VISTA_SOLIDA_003

Draft Calvi 268335015-image6.jpg

01_INT_VISTA_SOLIDA_004


SIMULATION OF MATERIALS

LEGEND OF MATERIAL DATA TABLE

The program allows to utilize various materials. The material types foreseen by the program are listed below:

1 material of r.c. type
2 material of steel type
3 material of masonry type
4 material of wooden type
5 material of general type


The materials utilized in the present simulation are identifiable by means of identification symbol and numerical code (the latter is actually indicated in the description of the structural elements). The table shows the following data for each material:

Young modulus of normal elasticity
Poisson transversal shrinkage factor
G modulus of tangential elasticity
Gamma specific weight
Alfa thermal expansion factor


The above stated data are utilized to simulate the static performance and to determine inertial and thermal loads.

Following data are indicated for the materials of type:

1 r.c.
Rck cubic specific strength
Fctm average simple tensile strength
2 steel
Ft breaking tensile strength
Fy yield tension
Fd estimated strength
Fdt estimated strength for thickness t>40 mm
Sadm allowed tension
Sadmt allowed tension for thickness t>40 mm
3 masonry
Resist. Fk characteristic compression strength
Resist. Fvko characteristic shear strength
4 wood
Resist. comp. compression allowed strength
Resist. traz. tensile allowed tension strength
Resist. fless. bending allowed strength
Resist. tau shear allowed strength
Lamellare lamellar or massive


The report shows both the characteristic and mean values ​​using one and/or the other in relation to the requests for legislation in use and the type of verification.


MATERIAL DATA TABLE

Id Type / Notes V. charact. V. mean Young Poisson G Gamma Alpha Others
kN/ m2 kN/ m2 kN/ m2 kN/ m2 kN/ m3
1 Calcestruzzo Classe C25/30-Calcestruzzo Classe C25/30 3.145e+07 0.20 1.310e+07 25.0 1.00e-05
Strength Rc 3.000e+04
Strength fctm 2558.0
Ratio R cracked/uncracked stiffness ratio; for non-linear analysis 1.00
Coefficient ksb 0.85
Ratio HRDb 1.00e-05
Ratio HRDv 1.00e-05
2 poroton 700-muratura E = 2.740e+04 2.740e+06 0.25 1.096e+06 15.0 0.0
Strength f 2740.0
Strength fh 400.0
Strength fv0 100.0
Strength fv0h 100.0
tau0 strength 100.0
Strength fvlim 300.0
Strength fb 5480.0
Strength fbh 1096.0
Strength fbt 548.0
Ratio R cracked/uncracked stiffness ratio; for non-linear analysis 1.00
Coefficient ksb 0.85
Coefficient mu tilda 0.50
Coefficient phi 0.50
Ratio HRDb 1.00e-05
Ratio HRDv 1.00e-05


Draft Calvi 268335015-image7.jpg

11_MOD_MATERIALI_D2

Draft Calvi 268335015-image8.jpg

11_MOD_MATERIALI_D3

R.C. Walls 1/7/.. 2/8/.. 3/9/.. 4/10/.. 5/11/.. 6/12/..
General data
Reinforcement design Single element Single element FOUNDATION Single element NON DISSIPATIVE Single element Single element Single element FOUNDATION
Reinforcement
Av inclination [ degrees ] 90.00 90.00 90.00 90.00 90.00 90.00
Av-Ah angle [ degrees ] 90.00 90.00 90.00 90.00 90.00 90.00
Minimum tension reinforcement 0.25 0.25 0.25 0.25 0.25 0.25
Maximum tension reinforcement 4.00 4.00 4.00 4.00 4.00 4.00
Central reinforcement only NO NO YES NO NO NO
single vertical layer NO NO NO NO NO NO
single horizontal layer NO NO NO NO NO NO
Rebar cover [ cm ] 2.00 2.00 2.00 2.00 2.00 2.00
Vertical reinforcements
Diameter 10 10 12 10 10 10
spacing 25 25 12 25 25 25
additional reb. diameter 12 12 12 12 12 12
Horizontal reinforcements
Diameter 10 10 0 10 10 10
spacing 25 25 0 25 25 25
additional reb. diameter 12 12 0 12 12 12
Ultimate limit states
yield strength fy [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
Steel Type C type C type C type C type C type C type
Gamma s coefficient 1.15 1.15 1.15 1.15 1.15 1.15
Gamma c coefficient 1.50 1.50 1.50 1.50 1.50 1.50
Check with constant N YES YES YES YES YES YES
Allowable stresses
Allowable stress concrete [kN/ m2 ] 9750.00 9750.00 9750.00 9750.00 9750.00 9750.00
Allowable stress steel [kN/ m2 ] 260000.00 260000.00 260000.00 260000.00 260000.00 260000.00
Homogenization ratio N 15.00 15.00 15.00 15.00 15.00 15.00
Maximum compressed/tensile reinforcement ratio 1.00 1.00 1.00 1.00 1.00 1.00
Large lightly reinforced wall
Shear factor magnification 0.0 1.50 1.50 0.0 0.0 1.50
Hcrit. par. 7.4.4.5.1 [ cm ] 0.0 0.0 0.0 0.0 0.0 0.0
Hcrit. par. 7.4.6.1.4 [ cm ] 0.0 0.0 0.0 0.0 0.0 0.0
Shear envelope diagram NO NO NO NO NO NO
Edge constraints no side no side no side no side no side no side
Check as masonry spandrel NO NO NO NO NO NO
Extreme diameter 0 0 0 0 0 0
Confined zone
Minimum tension reinforcement 1.00 1.00 1.00 1.00 1.00 1.00
Maximum tension reinforcement 4.00 4.00 4.00 4.00 4.00 4.00
Rebar spacing [ cm ] 2.00 2.00 2.00 2.00 2.00 2.00
Spacing 2 2 2 2 2 2
Inclined reinforcement
Rebars area [ cm2 ] 0.0 0.0 0.0 0.0 0.0 0.0
Horizontal angle [ degrees ] 0.0 0.0 0.0 0.0 0.0 0.0
Bottom distance [ cm ] 0.0 0.0 0.0 0.0 0.0 0.0
Fire resistance
Inner surface 3- NO NO NO NO NO NO
Outer surface 3+ NO NO NO NO NO NO
Exposure time R 15 15 15 15 15 15


R.C. slabs 1/7/.. 2/8/.. 3/9/.. 4/10/.. 5/11/.. 6/12/..
Reinforcement
Ax inclination [ degrees ] 0.0 0.0 0.0 0.0 0.0 0.0
Ax-Ay angle [ degrees ] 90.00 90.00 90.00 90.00 90.00 90.00
Minimum tension reinforcement 0.31 0.31 0.31 0.31 0.31 0.31
Maximum tension reinforcement 0.78 0.78 0.78 0.78 0.78 0.78
Central reinforcement only NO NO NO NO NO NO
Rebar cover [ cm ] 2.00 3.00 2.00 2.00 2.00 3.00
Reinforcement x direction
Diameter 10 12 10 10 10 12
spacing 20 20 20 20 20 20
additional reb. diameter 12 12 12 12 12 12
Reinforcement y direction
Diameter 10 12 10 10 10 12
spacing 20 20 20 20 20 20
additional reb. diameter 12 12 12 12 12 12
Ultimate limit states
yield strength fy [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
Steel Type C type C type C type C type C type C type
Gamma s coefficient 1.15 1.15 1.15 1.15 1.15 1.15
Gamma c coefficient 1.50 1.50 1.50 1.50 1.50 1.50
Check with constant N YES YES YES YES YES YES
Apply ULS as DIN NO NO NO NO NO NO
Allowable stresses
Allowable stress concrete [kN/ m2 ] 9750.00 9750.00 9750.00 9750.00 9750.00 9750.00
Allowable stress steel [kN/ m2 ] 260000.00 260000.00 260000.00 260000.00 260000.00 260000.00
Homogenization ratio N 15.00 15.00 15.00 15.00 15.00 15.00
Maximum compressed/tensile reinforcement ratio 1.00 1.00 1.00 1.00 1.00 1.00
Fire resistance
Inner surface 3- NO NO NO NO NO NO
Outer surface 3+ NO NO NO NO NO NO
Exposure time R 15 15 15 15 15 15


Reinforced concrete beams 1/7/.. 2/8/.. 3/9/.. 4/10/.. 5/11/.. 6/12/..
General data
Design for support face NO NO NO NO NO NO
Lower As: from q*L*L / 0.0 0.0 0.0 0.0 0.0 0.0
Reinforcement
Minimum tension reinforcement 0.31 0.31 0.31 0.31 0.31 0.31
Minimum compressed reinforcement 0.31 0.31 0.31 0.31 0.31 0.31
Maximum tension reinforcement 0.78 0.78 0.78 0.78 0.78 0.78
As section YES YES YES YES YES YES
Use theoretical reinforcement area NO NO NO NO NO NO
Ultimate limit states
yield strength fy [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
fy stirrups strength [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
Steel Type C type C type C type C type C type C type
Gamma s coefficient 1.15 1.15 1.15 1.15 1.15 1.15
Gamma c coefficient 1.50 1.50 1.50 1.50 1.50 1.50
Check with constant N YES YES YES YES YES YES
Redistribution factor 0.0 0.0 0.0 0.0 0.0 0.0
Confinement model
Stress-strain law Mander Mander Mander Mander Mander Mander
Steel hardening 5.000e-03 5.000e-03 5.000e-03 5.000e-03 5.000e-03 5.000e-03
Lambda factor 1.00 1.00 1.00 1.00 1.00 1.00
epsilon max,s 4.000e-02 4.000e-02 4.000e-02 4.000e-02 4.000e-02 4.000e-02
epsilon cu2 4.500e-03 4.500e-03 4.500e-03 4.500e-03 4.500e-03 4.500e-03
epsilon c2 0.0 0.0 0.0 0.0 0.0 0.0
epsilon cy 0.0 0.0 0.0 0.0 0.0 0.0
Allowable stresses
Allowable stress concrete [kN/ m2 ] 9750.00 9750.00 9750.00 9750.00 9750.00 9750.00
Allowable stress steel [kN/ m2 ] 260000.00 260000.00 260000.00 260000.00 260000.00 260000.00
Homogenization ratio N 15.00 15.00 15.00 15.00 15.00 15.00
Maximum compressed/tensile reinforcement ratio 1.00 1.00 1.00 1.00 1.00 1.00
Stirrup
Stirrups diameter 10.00 0.0 0.0 0.0 10.00 0.0
Min spacing [ cm ] 10.00 4.00 4.00 4.00 20.00 4.00
Max spacing [ cm ] 15.00 30.00 30.00 30.00 20.00 30.00
Critic zone spacing [ cm ] 10.00 15.00 15.00 15.00 20.00 15.00
Critic zone length [ cm ] 50.00 50.00 50.00 50.00 50.00 50.00
Ctg(Theta) Max 2.50 2.50 2.50 2.50 2.50 2.50
Bent rebars shear percentage 0.0 0.0 0.0 0.0 0.0 0.0
Span length for CD [ cm ] 1.00 1.00 1.00 1.00 1.00 1.00
Average shear in zone NO NO NO NO NO NO
Unessential torsion included YES YES YES YES YES YES


Reinforced concrete columns 1/7/.. 2/8/.. 3/9/.. 4/10/.. 5/11/.. 6/12/..
General data
Reinforcement design Prefer edges Prefer edges Prefer edges Prefer edges Prefer edges Prefer edges
Design for support face NO NO NO YES NO NO
2nd order effects NO NO YES YES YES NO
2-2 beta 1.00 1.00 1.00 1.00 1.00 1.00
3-3 beta 1.00 1.00 1.00 1.00 1.00 1.00
Reinforcement
Maximum tension reinforcement 4.00 4.00 4.00 4.00 4.00 4.00
Minimum tension reinforcement 1.00 1.00 1.00 1.00 1.00 1.00
Ultimate limit states
yield strength fy [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
fy stirrups strength [kN/ m2 ] 450000.00 450000.00 450000.00 450000.00 450000.00 450000.00
Steel Type C type C type C type C type C type C type
Gamma s coefficient 1.15 1.15 1.15 1.15 1.15 1.15
Gamma c coefficient 1.50 1.50 1.50 1.50 1.50 1.50
Check with constant N YES YES YES YES YES YES
Confinement model
Stress-strain law Mander Mander Mander Mander Mander Mander
Steel hardening 5.000e-03 5.000e-03 5.000e-03 5.000e-03 5.000e-03 5.000e-03
Lambda factor 1.00 1.00 1.00 1.00 1.00 1.00
epsilon max,s 4.000e-02 4.000e-02 4.000e-02 4.000e-02 4.000e-02 4.000e-02
epsilon cu2 4.500e-03 4.500e-03 4.500e-03 4.500e-03 4.500e-03 4.500e-03
epsilon c2 0.0 0.0 0.0 0.0 0.0 0.0
epsilon cy 0.0 0.0 0.0 0.0 0.0 0.0
Allowable stresses
Allowable stress concrete [kN/ m2 ] 9750.00 9750.00 9750.00 9750.00 9750.00 9750.00
Allowable stress steel [kN/ m2 ] 260000.00 260000.00 260000.00 260000.00 260000.00 260000.00
Homogenization ratio N 15.00 15.00 15.00 15.00 15.00 15.00
Stirrup
Stirrups diameter 0.0 10.00 0.0 0.0 0.0 10.00
Min spacing [ cm ] 5.00 15.00 5.00 5.00 5.00 15.00
Max spacing [ cm ] 25.00 15.00 25.00 25.00 25.00 15.00
Critic zone spacing [ cm ] 15.00 15.00 15.00 15.00 15.00 15.00
Critic zone length [ cm ] 45.00 45.00 45.00 45.00 45.00 1.00
Ctg(Theta) Max 2.50 2.50 2.50 2.50 2.50 2.50
Span length for CD [ cm ] 1.00 1.00 1.00 1.00 1.00 1.00
Maximize capacity design YES NO YES YES YES NO


Masonry 1/7/.. 2/8/.. 3/9/.. 4/10/.. 5/11/.. 6/12/..
Buckling lengths
Interstory height [ cm ] 0.0 0.0 0.0 222.00 0.0 0.0
Rho 0.85 0.85 0.85 0.85 0.85 0.85
Slenderness limit 20.00 20.00 20.00 20.00 20.00 20.00
General data
Non-seismic gamma 3.00 3.00 3.00 3.00 3.00 3.00
Seismic gamma 2.40 2.40 2.40 2.40 2.40 2.40
Actions tolerance [kN/ m2 ] 0.0 0.0 0.0 0.0 0.0 0.0
Average values by elevation YES YES YES YES YES YES
Average values by element YES YES YES YES YES YES
Check as masonry spandrel NO NO NO NO NO NO
Use [7.8.3] formula YES YES YES YES YES YES



SIMULATION OF SECTIONS

LEGEND OF SECTION DATA TABLE

The program allows to use various sections. The following section types are provided:

1 section of general type

2 simple steel sections

3 special and coupled steel sections

The sections utilized for simulation are identifiable by means of reference symbol and numerical code (the latter is actually indicated in the description of the structural elements).

For each section the following data are indicated in the table:

Area section area
A V2 section area/shear factor for shear in direction 2
A V3 section area/shear factor for shear in direction 3
Jt stiffness torsional factor
J2-2 moment of inertia of the section referred to axis 2
J3-3 moment of inertia of the section referred to axis 3
W2-2 section modulus referred to axis 2
W3-3 section modulus referred to axis 3
Wp2-2 plastic section modulus referred to axis 2
Wp3-3 plastic section modulus referred to axis 3


The above data are utilized to determine the inertia loads and to define the structural element stiffness; whenever the value of Area V2 (and/or Area V3) is zero, the deformation for shear V2 (and/or V3) is negligible.

The inertial section characteristics are estimated within element reference 2-3.

About the simple and coupled sections, reference axis 3 coincides with the axis x, according to the most widely known section reference charts.

About the general type sections (type 1):

the dimensional values labeled with B refer to the axis 2

the dimensional values labeled with H refer to the axis 3

Id Type Area A V2 A V3 Jt J 2-2 J 3-3 W 2-2 W 3-3 Wp 2-2 Wp 3-3
cm2 cm2 cm2 cm4 cm4 cm4 cm3 cm3 cm3 cm3
1 Rettangolare: b=60 h=40 2400.00 2000.00 2000.00 7.424e+05 7.200e+05 3.200e+05 2.400e+04 1.600e+04 3.600e+04 2.400e+04
2 Rettangolare: b=40 h=40 1600.00 1333.33 1333.33 3.599e+05 2.133e+05 2.133e+05 1.067e+04 1.067e+04 1.600e+04 1.600e+04
3 Rettangolare: b=50 h=20 1000.00 833.33 833.33 9.973e+04 2.083e+05 3.333e+04 8333.33 3333.33 1.250e+04 5000.00
4 Rettangolare: b=30 h=30 900.00 750.00 750.00 1.139e+05 6.750e+04 6.750e+04 4500.00 4500.00 6750.00 6750.00


Draft Calvi 268335015-image9.jpg

13_MOD_SEZIONI



LOAD CASE SCHEMATIZATION

LEGEND OF LOAD CASE TABLE

The program allows the usage of various load cases.

The following 11 load cases are considered:

Name Type Description
1 Ggk A load case including the structure dead weight
2 Gk NA load case including permanent loads
3 Qk NA load case including live loads
4 Gsk A load case including floor and roof permanent loads
5 Qsk A load case including floor and roof live loads
6 Qnk A load case including roof snow live loads
7 Qtk SA load case including structure temperature change
8 Qvk NA load case including structure wind loads
9 Esk SA seismic load case by the way of the equivalent static analysis
10 Edk SA seismic load case by the way of the dynamic analysis
11 Etk NA load case including forces due to earth pressure seismic increment
12 Pk NA load case including loads due to constraints subsiding, and prestressing.


The automatic (A) load cases (i.e. the user won't be asked to enter data) are labeled as:

1-Ggk, 4-Gsk, 5-Qsk, 6-Qnk;

The semi-automatic (SA) load cases (i.e. the user will be asked to enter a minimum part of data) are labeled as:

7-Qtk, (only the temperature change value has to be entered);

9-Esk, 10-Edk, (only the input earthquake direction angle value and the load case identification has to be entered.

The remaining load cases are said non-automatic (NA) load cases (i.e. the user will be asked to enter generic loads for the structural elements).

The below table shows the load cases affecting the structure and their related data, i.e.:

the Type Number, the Identification Code and the Load Case Reference Value (where requested).

For the non-automatic load cases, the loaded nodes and elements are listed (the load identification code is included).

For the seismic load cases (9-Esk and 10-Edk), the input angle values, the seismic intensity, the structure and foundation coefficients are shown; finally, the related mass rate, for each load case participating to the seismic mass definition, is shown.

Let us point out that in the load cases 5-Qsk and 6-Qnk, each floor or roof element in the model is assumed wholly participating to the seismic mass definition (see the Sksol value in the floor element chapter) and therefore, their participating mass rate is assumed to be 1.


LC Type ID code Notes
1 Ggk CDC=Ggk (peso proprio della struttura)
2 Qk CDC=Qk (variabile generico) ......... Applied actions:
Node: 13 Action  : CN:Fz=-208.90
Node: 14 Action  : CN:Fz=-208.90
D3 :from 2 to 4 Action  : P3:p=-4.000e-02
3 Edk CDC=Ed (dinamico SLU) alfa=0.0 (ecc. -) modal mass:1.00 for 1 CDC=Ggk (peso proprio della struttura)
4 Edk CDC=Ed (dinamico SLU) alfa=90.00 (ecc. +) as previous seismic LC
5 Edk CDC=Ed (dinamico SLU) alfa=90.00 (ecc. -) as previous seismic LC
6 Edk CDC=Ed (dinamico SLD) alfa=0.0 (ecc. +) as previous seismic LC
7 Edk CDC=Ed (dinamico SLD) alfa=0.0 (ecc. -) as previous seismic LC
8 Edk CDC=Ed (dinamico SLD) alfa=90.00 (ecc. +) as previous seismic LC
9 Edk CDC=Ed (dinamico SLD) alfa=90.00 (ecc. -) as previous seismic LC


Draft Calvi 268335015-image10.jpg

22_CDC_001_CDC=Ggk (peso proprio della struttura)

Draft Calvi 268335015-image11.jpg

22_CDC_002_CDC=Qk (variabile generico) .........

Draft Calvi 268335015-image12.jpg

22_CDC_003_CDC=Ed (dinamico SLU) alfa=0.0 (ecc. -)

Draft Calvi 268335015-image13.jpg

22_CDC_004_CDC=Ed (dinamico SLU) alfa=90.00 (ecc. +)

Draft Calvi 268335015-image14.jpg

22_CDC_005_CDC=Ed (dinamico SLU) alfa=90.00 (ecc. -)

Draft Calvi 268335015-image15.jpg

22_CDC_006_CDC=Ed (dinamico SLD) alfa=0.0 (ecc. +)

Draft Calvi 268335015-image16.jpg

22_CDC_007_CDC=Ed (dinamico SLD) alfa=0.0 (ecc. -)

Draft Calvi 268335015-image17.jpg

22_CDC_008_CDC=Ed (dinamico SLD) alfa=90.00 (ecc. +)

Draft Calvi 268335015-image18.jpg

22_CDC_009_CDC=Ed (dinamico SLD) alfa=90.00 (ecc. -)


LOAD COMBINATION DEFINITION

LEGEND OF LOAD COMBINATION DEFINITION TABLE

The program combines various load case types according to the regulations foreseen by the acting standards and norms currently in force.

The foreseen combinations are provided for the structure safety control, in the course of which the structure resistance to displacements and stresses is checked.

The below presented load combination table shows the following data:

Type Number and Identification Symbol

The table below shows the load cases affecting the structure and involved in the load combination, each one with respective own weight.

Cmb Type ID code P-delta eff.
1 U.L.S. Comb. SLU A1 1
2 U.L.S. Comb. SLU A1 2
3 U.L.S. Comb. SLU A1 3
4 U.L.S. Comb. SLU A1 4
5 U.L.S. Comb. SLU A1 (SLV sism.) 5
6 U.L.S. Comb. SLU A1 (SLV sism.) 6
7 U.L.S. Comb. SLU A1 (SLV sism.) 7
8 U.L.S. Comb. SLU A1 (SLV sism.) 8
9 U.L.S. Comb. SLU A1 (SLV sism.) 9
10 U.L.S. Comb. SLU A1 (SLV sism.) 10
11 U.L.S. Comb. SLU A1 (SLV sism.) 11
12 U.L.S. Comb. SLU A1 (SLV sism.) 12
13 U.L.S. Comb. SLU A1 (SLV sism.) 13
14 U.L.S. Comb. SLU A1 (SLV sism.) 14
15 U.L.S. Comb. SLU A1 (SLV sism.) 15
16 U.L.S. Comb. SLU A1 (SLV sism.) 16
17 U.L.S. Comb. SLU A1 (SLV sism.) 17
18 U.L.S. Comb. SLU A1 (SLV sism.) 18
19 U.L.S. Comb. SLU A1 (SLV sism.) 19
20 U.L.S. Comb. SLU A1 (SLV sism.) 20
21 FO(seis.) Comb. SLE (SLD Danno sism.) 21
22 FO(seis.) Comb. SLE (SLD Danno sism.) 22
23 FO(seis.) Comb. SLE (SLD Danno sism.) 23
24 FO(seis.) Comb. SLE (SLD Danno sism.) 24
25 FO(seis.) Comb. SLE (SLD Danno sism.) 25
26 FO(seis.) Comb. SLE (SLD Danno sism.) 26
27 FO(seis.) Comb. SLE (SLD Danno sism.) 27
28 FO(seis.) Comb. SLE (SLD Danno sism.) 28
29 FO(seis.) Comb. SLE (SLD Danno sism.) 29
30 FO(seis.) Comb. SLE (SLD Danno sism.) 30
31 FO(seis.) Comb. SLE (SLD Danno sism.) 31
32 FO(seis.) Comb. SLE (SLD Danno sism.) 32
33 FO(seis.) Comb. SLE (SLD Danno sism.) 33
34 FO(seis.) Comb. SLE (SLD Danno sism.) 34
35 FO(seis.) Comb. SLE (SLD Danno sism.) 35
36 FO(seis.) Comb. SLE (SLD Danno sism.) 36
37 FO(seis.) Comb. SLE (SLD Danno sism.) 37
38 FO(seis.) Comb. SLE (SLD Danno sism.) 38
39 FO(seis.) Comb. SLE (SLD Danno sism.) 39
40 FO(seis.) Comb. SLE (SLD Danno sism.) 40
41 FO(seis.) Comb. SLE (SLD Danno sism.) 41
42 FO(seis.) Comb. SLE (SLD Danno sism.) 42
43 FO(seis.) Comb. SLE (SLD Danno sism.) 43
44 FO(seis.) Comb. SLE (SLD Danno sism.) 44
45 FO(seis.) Comb. SLE (SLD Danno sism.) 45
46 FO(seis.) Comb. SLE (SLD Danno sism.) 46
47 FO(seis.) Comb. SLE (SLD Danno sism.) 47
48 FO(seis.) Comb. SLE (SLD Danno sism.) 48
49 FO(seis.) Comb. SLE (SLD Danno sism.) 49
50 FO(seis.) Comb. SLE (SLD Danno sism.) 50
51 FO(seis.) Comb. SLE (SLD Danno sism.) 51
52 FO(seis.) Comb. SLE (SLD Danno sism.) 52
53 U.L.S.(live loads) Comb. SLU (Accid.) 53
54 U.L.S.(live loads) Comb. SLU (Accid.) 54
55 SLS(c) Comb. SLE(rara) 55
56 SLS(c) Comb. SLE(rara) 56
57 SLS(f) Comb. SLE(freq.) 57
58 SLS(f) Comb. SLE(freq.) 58
59 SLS(p) Comb. SLE(perm.) 59
60 SLS(p) Comb. SLE(perm.) 60


Cmb CDC 1/15... CDC 2/16... CDC 3/17... CDC 4/18... CDC 5/19... CDC 6/20... CDC 7/21... CDC 8/22... CDC 9/23... CDC 10/24... CDC 11/25... CDC 12/26... CDC 13/27... CDC 14/28...
1 1.30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 1.30 1.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4 1.00 1.50 0.0 0.0 0.0 0.0 0.0 0.0 0.0
5 1.00 0.80 -1.00 -0.30 0.0 0.0 0.0 0.0 0.0
6 1.00 0.80 -1.00 0.30 0.0 0.0 0.0 0.0 0.0
7 1.00 0.80 1.00 -0.30 0.0 0.0 0.0 0.0 0.0
8 1.00 0.80 1.00 0.30 0.0 0.0 0.0 0.0 0.0
9 1.00 0.80 -1.00 0.0 -0.30 0.0 0.0 0.0 0.0
10 1.00 0.80 -1.00 0.0 0.30 0.0 0.0 0.0 0.0
11 1.00 0.80 1.00 0.0 -0.30 0.0 0.0 0.0 0.0
12 1.00 0.80 1.00 0.0 0.30 0.0 0.0 0.0 0.0
13 1.00 0.80 -0.30 -1.00 0.0 0.0 0.0 0.0 0.0
14 1.00 0.80 -0.30 1.00 0.0 0.0 0.0 0.0 0.0
15 1.00 0.80 0.30 -1.00 0.0 0.0 0.0 0.0 0.0
16 1.00 0.80 0.30 1.00 0.0 0.0 0.0 0.0 0.0
17 1.00 0.80 -0.30 0.0 -1.00 0.0 0.0 0.0 0.0
18 1.00 0.80 -0.30 0.0 1.00 0.0 0.0 0.0 0.0
19 1.00 0.80 0.30 0.0 -1.00 0.0 0.0 0.0 0.0
20 1.00 0.80 0.30 0.0 1.00 0.0 0.0 0.0 0.0
21 1.00 0.80 0.0 0.0 0.0 -1.00 0.0 -0.30 0.0
22 1.00 0.80 0.0 0.0 0.0 -1.00 0.0 0.30 0.0
23 1.00 0.80 0.0 0.0 0.0 1.00 0.0 -0.30 0.0
24 1.00 0.80 0.0 0.0 0.0 1.00 0.0 0.30 0.0
25 1.00 0.80 0.0 0.0 0.0 -1.00 0.0 0.0 -0.30
26 1.00 0.80 0.0 0.0 0.0 -1.00 0.0 0.0 0.30
27 1.00 0.80 0.0 0.0 0.0 1.00 0.0 0.0 -0.30
28 1.00 0.80 0.0 0.0 0.0 1.00 0.0 0.0 0.30
29 1.00 0.80 0.0 0.0 0.0 0.0 -1.00 -0.30 0.0
30 1.00 0.80 0.0 0.0 0.0 0.0 -1.00 0.30 0.0
31 1.00 0.80 0.0 0.0 0.0 0.0 1.00 -0.30 0.0
32 1.00 0.80 0.0 0.0 0.0 0.0 1.00 0.30 0.0
33 1.00 0.80 0.0 0.0 0.0 0.0 -1.00 0.0 -0.30
34 1.00 0.80 0.0 0.0 0.0 0.0 -1.00 0.0 0.30
35 1.00 0.80 0.0 0.0 0.0 0.0 1.00 0.0 -0.30
36 1.00 0.80 0.0 0.0 0.0 0.0 1.00 0.0 0.30
37 1.00 0.80 0.0 0.0 0.0 -0.30 0.0 -1.00 0.0
38 1.00 0.80 0.0 0.0 0.0 -0.30 0.0 1.00 0.0
39 1.00 0.80 0.0 0.0 0.0 0.30 0.0 -1.00 0.0
40 1.00 0.80 0.0 0.0 0.0 0.30 0.0 1.00 0.0
41 1.00 0.80 0.0 0.0 0.0 0.0 -0.30 -1.00 0.0
42 1.00 0.80 0.0 0.0 0.0 0.0 -0.30 1.00 0.0
43 1.00 0.80 0.0 0.0 0.0 0.0 0.30 -1.00 0.0
44 1.00 0.80 0.0 0.0 0.0 0.0 0.30 1.00 0.0
45 1.00 0.80 0.0 0.0 0.0 -0.30 0.0 0.0 -1.00
46 1.00 0.80 0.0 0.0 0.0 -0.30 0.0 0.0 1.00
47 1.00 0.80 0.0 0.0 0.0 0.30 0.0 0.0 -1.00
48 1.00 0.80 0.0 0.0 0.0 0.30 0.0 0.0 1.00
49 1.00 0.80 0.0 0.0 0.0 0.0 -0.30 0.0 -1.00
50 1.00 0.80 0.0 0.0 0.0 0.0 -0.30 0.0 1.00
51 1.00 0.80 0.0 0.0 0.0 0.0 0.30 0.0 -1.00
52 1.00 0.80 0.0 0.0 0.0 0.0 0.30 0.0 1.00
53 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
54 1.00 0.80 0.0 0.0 0.0 0.0 0.0 0.0 0.0
55 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
56 1.00 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0
57 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
58 1.00 0.90 0.0 0.0 0.0 0.0 0.0 0.0 0.0
59 1.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
60 1.00 0.80 0.0 0.0 0.0 0.0 0.0 0.0 0.0



SEISMIC ACTION

SEISMIC ACTION EVALUATION

Seismic action on building is computed from “seismic base hazard” for ideal condition of rigid soil and horizontal surface. Now seismic hazard, for a reference grid and for return periods, is available from website http://esse1.mi.ingv.it/. For points non-coincident with the reference grid and lacking return periods the code works as suggested in the attach of NTC (weight media for the first and interpolation for the latter).

Seismic action is defined for a reference period Vr (product of nominal life of the structure by use coefficent as reported in the table Structure Parameters). For the reference period Vr and the related probability Pver for limit states, the code obtains return period Tr and seismic hazard parameters (see following table):

ag: maximum ground orizontal acceleration;

Fo: maximum amplification factor for orizontal acceleration spectrum;

T*c: initial period for costant velocity in the orizontal acceleration spectrum;

Structure Parameters
Use class


Life Vn [year] Use Coeff. Period Vr [year]


Kind of soil Kind of surface
II 50.0 1.0 50.0 D T1


From the seismic hazard parameters the code computes:

S factor for soil and kind of surface as: S = Ss*St (3.2.3)

Fo maximum amplification factor for orizontal acceleration spectrum

Fv maximum amplification factor for vertical acceleration spectrum

Tb initial period for costant acceleration

Tc initial period for costant velocity

Td initial period for costant displacement

The horizontal acceleration spectrum, Se, is definied by the espressions below:

Draft Calvi 268335015-image19-c.png

Ss =1 and Cc =1 for type A subsoil category; while, for categories B, C, D, E the coefficients Ss and Cc are calculated using the expressions shown in the following table

Draft Calvi 268335015-image20.png

Values of the coefficient St are showned in the following table

Draft Calvi 268335015-image21.png

The vertical acceleration spectrum, Sve, is definied by the espressions below:

Draft Calvi 268335015-image22.png

Values of the coefficients Ss, TB, TC and TD are showned in the following table

Draft Calvi 268335015-image23-c.png
Id node Longitude Latitude Distance
Km
Loc. 7.964 45.042
14018 7.905 45.005 6.179
14019 7.976 45.008 3.884
13797 7.971 45.058 1.856
13796 7.901 45.055 5.139


LS Pver Tr ag Fo T*c
Anni g sec
SLO 81.0 30.0 0.018 2.620 0.160
SLD 63.0 50.0 0.022 2.605 0.190
SLV 10.0 475.0 0.042 2.703 0.280
SLC 5.0 975.0 0.050 2.755 0.300


LS ag S Fo Fv Tb Tc Td
g sec sec sec
SLO 0.018 1.800 2.620 0.476 0.167 0.500 1.672
SLD 0.022 1.800 2.605 0.523 0.182 0.545 1.688
SLV 0.042 1.800 2.703 0.750 0.220 0.661 1.769
SLC 0.050 1.800 2.755 0.832 0.228 0.685 1.800



SEISMIC ANALYSIS RESULTS

LEGEND OF SEISMIC ANALYSIS RESULTS

The program allows to analyze various seismic configurations.

Actually the following load cases are provided:

9. Esk seismic load case with an equivalent static analysis

10. Edk seismic load case with a dynamic analysis

Each load case is characterized by an input angle and a configuration of masses which determine the comprehensive seismic force (see the load case chapter).

The dynamic seismic analysis can deal with a vertical dynamic action simultaneous to the horizontal one, in this case the superposition of the is applied.

For each seismic load case the following data is indicated (masses are expressed in units of force):

1) equivalent static seismic analysis:
:* quote, application centre position and resulting horizontal action, gravity centre position of stiffness total horizontal action
:* total horizontal action
2) dynamic seismic analysis with response spectrum:
:* quote, mass centre position and resulting mass, stiffness centre position
:* frequency, period, mass excited in three global directions for all the modes
:* total mass and mass share excited

Finally the deformation level (etaT, etaP, etaD) of the vertical structural elements is indicated: for the sake of user's convenience the deformation level is expressed in the units of 1000*etaT/L to be compared with value 2 or 4.


LC Type ID code Notes
3 Edk CDC=Ed (dinamico SLU) alfa=0.0 (ecc. -)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.206 g
angle, direction:0.0
additional eccentricity: negative
own period T1: 0.126 sec.
q factor: 1.000
amplification ND (not dissipative): 1.000
factor mu d for displ.: 1.000
ductility class CD: B
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 0.0 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 0.0 0.06 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.06 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.06 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.693 0.149 0.164 9.50e-03 2.58e-02 31.83 86.4 0.30 0.8 0.0 0.0
2 7.907 0.126 0.151 34.35 93.3 0.01 2.86e-02 1.46e-03 3.95e-03 0.0 0.0
3 16.638 0.060 0.112 3.34e-03 9.06e-03 0.93 2.5 2.48e-03 6.74e-03 0.0 0.0
4 25.792 0.039 0.099 0.01 2.77e-02 0.32 0.9 33.40 90.7 0.0 0.0
5 27.057 0.037 0.098 0.40 1.1 0.16 0.4 1.93 5.2 0.0 0.0
6 33.891 0.030 0.094 1.90 5.2 9.10e-03 2.47e-02 0.90 2.4 0.0 0.0
7 42.950 0.023 0.090 0.01 3.58e-02 2.49 6.8 0.16 0.4 0.0 0.0
8 59.723 0.017 0.086 0.02 6.27e-02 1.04 2.8 0.04 0.1 0.0 0.0
9 71.327 0.014 0.084 0.12 0.3 0.02 5.30e-02 0.10 0.3 0.0 0.0
10 86.671 0.012 0.083 7.02e-05 1.90e-04 1.71e-04 4.64e-04 5.26e-04 1.43e-03 0.0 0.0
11 121.276 0.008 0.081 4.86e-06 1.32e-05 0.03 7.11e-02 1.70e-04 4.62e-04 0.0 0.0
12 168.472 0.006 0.080 1.36e-04 3.70e-04 7.56e-04 2.05e-03 6.87e-06 1.87e-05 0.0 0.0
13 176.682 0.006 0.079 1.58e-04 4.30e-04 3.50e-05 9.52e-05 2.32e-04 6.29e-04 0.0 0.0
14 213.962 0.005 0.079 1.81e-04 4.93e-04 8.57e-04 2.33e-03 2.47e-05 6.70e-05 0.0 0.0
15 297.680 0.003 0.078 9.07e-05 2.46e-04 5.67e-04 1.54e-03 4.09e-05 1.11e-04 0.0 0.0
16 343.449 0.003 0.078 5.27e-05 1.43e-04 3.42e-04 9.29e-04 1.17e-04 3.19e-04 0.0 0.0
17 398.729 0.003 0.078 1.83e-04 4.96e-04 2.16e-05 5.87e-05 3.08e-05 8.37e-05 0.0 0.0
18 549.273 0.002 0.077 1.32e-06 3.59e-06 2.87e-06 7.79e-06 6.37e-05 1.73e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
4 Edk CDC=Ed (dinamico SLU) alfa=90.00 (ecc. +)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.206 g
angle, direction:90.00
Additional eccentricity: positive
own period T1: 0.149 sec.
q factor: 1.000
amplification ND (not dissipative): 1.000
factor mu d for displ.: 1.000
ductility class CD: B
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 0.06 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 0.02 0.0 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.0 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.0 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.692 0.149 0.164 7.10e-03 1.93e-02 31.81 86.4 0.30 0.8 0.0 0.0
2 7.919 0.126 0.151 34.33 93.2 6.10e-03 1.66e-02 1.57e-03 4.26e-03 0.0 0.0
3 16.816 0.059 0.111 9.17e-03 2.49e-02 1.01 2.7 2.58e-03 6.99e-03 0.0 0.0
4 25.792 0.039 0.099 7.43e-03 2.02e-02 0.31 0.8 33.21 90.2 0.0 0.0
5 26.979 0.037 0.098 0.43 1.2 0.15 0.4 2.15 5.8 0.0 0.0
6 33.890 0.030 0.094 1.90 5.2 0.02 5.48e-02 0.87 2.4 0.0 0.0
7 43.625 0.023 0.090 8.41e-03 2.28e-02 2.51 6.8 0.18 0.5 0.0 0.0
8 59.936 0.017 0.086 0.03 7.87e-02 0.96 2.6 0.03 9.08e-02 0.0 0.0
9 71.434 0.014 0.084 0.11 0.3 0.03 6.89e-02 0.10 0.3 0.0 0.0
10 87.992 0.011 0.083 1.66e-05 4.49e-05 1.30e-04 3.53e-04 4.96e-04 1.35e-03 0.0 0.0
11 121.164 0.008 0.081 2.99e-05 8.11e-05 0.03 7.03e-02 1.16e-04 3.16e-04 0.0 0.0
12 159.500 0.006 0.080 1.87e-05 5.07e-05 6.34e-04 1.72e-03 4.33e-05 1.18e-04 0.0 0.0
13 173.644 0.006 0.080 2.83e-04 7.67e-04 2.81e-04 7.64e-04 2.40e-04 6.52e-04 0.0 0.0
14 212.326 0.005 0.079 1.42e-04 3.84e-04 8.80e-04 2.39e-03 3.73e-05 1.01e-04 0.0 0.0
15 298.958 0.003 0.078 1.03e-04 2.80e-04 5.48e-04 1.49e-03 3.46e-05 9.39e-05 0.0 0.0
16 341.534 0.003 0.078 5.67e-05 1.54e-04 3.43e-04 9.31e-04 1.24e-04 3.37e-04 0.0 0.0
17 395.537 0.003 0.078 1.78e-04 4.82e-04 3.32e-05 9.01e-05 2.93e-05 7.94e-05 0.0 0.0
18 546.619 0.002 0.077 1.18e-06 3.20e-06 1.82e-06 4.93e-06 6.49e-05 1.76e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
5 Edk CDC=Ed (dinamico SLU) alfa=90.00 (ecc. -)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.206 g
angle, direction:90.00
additional eccentricity: negative
own period T1: 0.149 sec.
q factor: 1.000
amplification ND (not dissipative): 1.000
factor mu d for displ.: 1.000
ductility class CD: B
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 -0.06 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 -0.02 0.0 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.0 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.0 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.694 0.149 0.164 5.44e-03 1.48e-02 31.85 86.5 0.30 0.8 0.0 0.0
2 7.919 0.126 0.151 34.33 93.2 4.56e-03 1.24e-02 1.68e-03 4.56e-03 0.0 0.0
3 16.773 0.060 0.111 9.06e-03 2.46e-02 0.90 2.4 5.15e-03 1.40e-02 0.0 0.0
4 25.793 0.039 0.099 7.57e-03 2.06e-02 0.32 0.9 33.18 90.1 0.0 0.0
5 26.973 0.037 0.098 0.43 1.2 0.14 0.4 2.16 5.9 0.0 0.0
6 33.897 0.030 0.094 1.90 5.2 0.02 4.89e-02 0.87 2.4 0.0 0.0
7 42.343 0.024 0.090 9.40e-03 2.55e-02 2.46 6.7 0.17 0.5 0.0 0.0
8 59.749 0.017 0.086 0.02 6.75e-02 1.09 3.0 0.04 0.1 0.0 0.0
9 71.249 0.014 0.084 0.12 0.3 0.02 6.64e-02 0.10 0.3 0.0 0.0
10 87.082 0.011 0.083 6.31e-05 1.71e-04 5.70e-05 1.55e-04 7.55e-04 2.05e-03 0.0 0.0
11 122.091 0.008 0.081 2.58e-05 7.00e-05 0.03 6.83e-02 6.53e-05 1.77e-04 0.0 0.0
12 171.453 0.006 0.080 2.86e-04 7.77e-04 6.34e-04 1.72e-03 1.20e-04 3.26e-04 0.0 0.0
13 189.308 0.005 0.079 1.15e-05 3.14e-05 4.23e-05 1.15e-04 1.13e-04 3.06e-04 0.0 0.0
14 214.713 0.005 0.079 1.45e-04 3.94e-04 8.86e-04 2.41e-03 2.93e-05 7.96e-05 0.0 0.0
15 303.325 0.003 0.078 1.06e-04 2.87e-04 5.99e-04 1.63e-03 3.09e-05 8.39e-05 0.0 0.0
16 337.723 0.003 0.078 6.49e-05 1.76e-04 3.00e-04 8.15e-04 1.32e-04 3.59e-04 0.0 0.0
17 402.375 0.002 0.078 1.64e-04 4.44e-04 1.98e-05 5.37e-05 2.44e-05 6.61e-05 0.0 0.0
18 556.505 0.002 0.077 2.06e-06 5.59e-06 4.61e-06 1.25e-05 6.14e-05 1.67e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
6 Edk CDC=Ed (dinamico SLD) alfa=0.0 (ecc. +)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.104 g
angle, direction:0.0
Additional eccentricity: positive
own period T1: 0.126 sec.
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 0.0 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 0.0 -0.06 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 -0.06 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 -0.06 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.693 0.149 0.092 3.75e-03 1.02e-02 31.83 86.4 0.30 0.8 0.0 0.0
2 7.926 0.126 0.084 34.31 93.2 1.92e-03 5.22e-03 1.79e-03 4.85e-03 0.0 0.0
3 17.003 0.059 0.060 0.02 4.63e-02 0.98 2.7 5.59e-03 1.52e-02 0.0 0.0
4 25.792 0.039 0.053 5.04e-03 1.37e-02 0.31 0.8 32.94 89.4 0.0 0.0
5 26.905 0.037 0.053 0.45 1.2 0.14 0.4 2.43 6.6 0.0 0.0
6 33.898 0.029 0.050 1.89 5.1 0.03 8.77e-02 0.84 2.3 0.0 0.0
7 42.995 0.023 0.048 5.51e-03 1.49e-02 2.46 6.7 0.18 0.5 0.0 0.0
8 60.032 0.017 0.046 0.03 8.41e-02 1.02 2.8 0.03 9.18e-02 0.0 0.0
9 71.343 0.014 0.045 0.11 0.3 0.03 8.74e-02 0.10 0.3 0.0 0.0
10 88.446 0.011 0.044 3.65e-04 9.91e-04 4.56e-05 1.24e-04 6.65e-04 1.81e-03 0.0 0.0
11 122.165 0.008 0.043 7.06e-05 1.92e-04 0.02 6.73e-02 3.03e-05 8.24e-05 0.0 0.0
12 168.668 0.006 0.042 1.59e-04 4.32e-04 7.34e-04 1.99e-03 9.64e-06 2.62e-05 0.0 0.0
13 176.281 0.006 0.042 1.44e-04 3.92e-04 1.73e-05 4.70e-05 2.60e-04 7.05e-04 0.0 0.0
14 213.859 0.005 0.041 1.10e-04 2.99e-04 9.05e-04 2.46e-03 4.49e-05 1.22e-04 0.0 0.0
15 298.948 0.003 0.041 8.36e-05 2.27e-04 6.03e-04 1.64e-03 1.35e-05 3.68e-05 0.0 0.0
16 335.081 0.003 0.041 8.54e-05 2.32e-04 2.32e-04 6.29e-04 1.52e-04 4.14e-04 0.0 0.0
17 395.332 0.003 0.041 1.72e-04 4.68e-04 5.67e-05 1.54e-04 2.87e-05 7.79e-05 0.0 0.0
18 567.562 0.002 0.040 0.0 0.0 0.0 0.0 4.98e-05 1.35e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
7 Edk CDC=Ed (dinamico SLD) alfa=0.0 (ecc. -)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.104 g
angle, direction:0.0
additional eccentricity: negative
own period T1: 0.126 sec.
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 0.0 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 0.0 0.06 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.06 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.06 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.693 0.149 0.092 9.50e-03 2.58e-02 31.83 86.4 0.30 0.8 0.0 0.0
2 7.907 0.126 0.084 34.35 93.3 0.01 2.86e-02 1.46e-03 3.95e-03 0.0 0.0
3 16.638 0.060 0.061 3.34e-03 9.06e-03 0.93 2.5 2.48e-03 6.74e-03 0.0 0.0
4 25.792 0.039 0.053 0.01 2.77e-02 0.32 0.9 33.40 90.7 0.0 0.0
5 27.057 0.037 0.053 0.40 1.1 0.16 0.4 1.93 5.2 0.0 0.0
6 33.891 0.030 0.050 1.90 5.2 9.10e-03 2.47e-02 0.90 2.4 0.0 0.0
7 42.950 0.023 0.048 0.01 3.58e-02 2.49 6.8 0.16 0.4 0.0 0.0
8 59.723 0.017 0.046 0.02 6.27e-02 1.04 2.8 0.04 0.1 0.0 0.0
9 71.327 0.014 0.045 0.12 0.3 0.02 5.30e-02 0.10 0.3 0.0 0.0
10 86.671 0.012 0.044 7.02e-05 1.90e-04 1.71e-04 4.64e-04 5.26e-04 1.43e-03 0.0 0.0
11 121.276 0.008 0.043 4.86e-06 1.32e-05 0.03 7.11e-02 1.70e-04 4.62e-04 0.0 0.0
12 168.472 0.006 0.042 1.36e-04 3.70e-04 7.56e-04 2.05e-03 6.87e-06 1.87e-05 0.0 0.0
13 176.682 0.006 0.042 1.58e-04 4.30e-04 3.50e-05 9.52e-05 2.32e-04 6.29e-04 0.0 0.0
14 213.962 0.005 0.041 1.81e-04 4.93e-04 8.57e-04 2.33e-03 2.47e-05 6.70e-05 0.0 0.0
15 297.680 0.003 0.041 9.07e-05 2.46e-04 5.67e-04 1.54e-03 4.09e-05 1.11e-04 0.0 0.0
16 343.449 0.003 0.041 5.27e-05 1.43e-04 3.42e-04 9.29e-04 1.17e-04 3.19e-04 0.0 0.0
17 398.729 0.003 0.041 1.83e-04 4.96e-04 2.16e-05 5.87e-05 3.08e-05 8.37e-05 0.0 0.0
18 549.273 0.002 0.040 1.32e-06 3.59e-06 2.87e-06 7.79e-06 6.37e-05 1.73e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
8 Edk CDC=Ed (dinamico SLD) alfa=90.00 (ecc. +)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.104 g
angle, direction:90.00
Additional eccentricity: positive
own period T1: 0.149 sec.
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 0.06 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 0.02 0.0 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.0 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.0 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.692 0.149 0.092 7.10e-03 1.93e-02 31.81 86.4 0.30 0.8 0.0 0.0
2 7.919 0.126 0.084 34.33 93.2 6.10e-03 1.66e-02 1.57e-03 4.26e-03 0.0 0.0
3 16.816 0.059 0.061 9.17e-03 2.49e-02 1.01 2.7 2.58e-03 6.99e-03 0.0 0.0
4 25.792 0.039 0.053 7.43e-03 2.02e-02 0.31 0.8 33.21 90.2 0.0 0.0
5 26.979 0.037 0.053 0.43 1.2 0.15 0.4 2.15 5.8 0.0 0.0
6 33.890 0.030 0.050 1.90 5.2 0.02 5.48e-02 0.87 2.4 0.0 0.0
7 43.625 0.023 0.048 8.41e-03 2.28e-02 2.51 6.8 0.18 0.5 0.0 0.0
8 59.936 0.017 0.046 0.03 7.87e-02 0.96 2.6 0.03 9.08e-02 0.0 0.0
9 71.434 0.014 0.045 0.11 0.3 0.03 6.89e-02 0.10 0.3 0.0 0.0
10 87.992 0.011 0.044 1.66e-05 4.49e-05 1.30e-04 3.53e-04 4.96e-04 1.35e-03 0.0 0.0
11 121.164 0.008 0.043 2.99e-05 8.11e-05 0.03 7.03e-02 1.16e-04 3.16e-04 0.0 0.0
12 159.500 0.006 0.042 1.87e-05 5.07e-05 6.34e-04 1.72e-03 4.33e-05 1.18e-04 0.0 0.0
13 173.644 0.006 0.042 2.83e-04 7.67e-04 2.81e-04 7.64e-04 2.40e-04 6.52e-04 0.0 0.0
14 212.326 0.005 0.041 1.42e-04 3.84e-04 8.80e-04 2.39e-03 3.73e-05 1.01e-04 0.0 0.0
15 298.958 0.003 0.041 1.03e-04 2.80e-04 5.48e-04 1.49e-03 3.46e-05 9.39e-05 0.0 0.0
16 341.534 0.003 0.041 5.67e-05 1.54e-04 3.43e-04 9.31e-04 1.24e-04 3.37e-04 0.0 0.0
17 395.537 0.003 0.041 1.78e-04 4.82e-04 3.32e-05 9.01e-05 2.93e-05 7.94e-05 0.0 0.0
18 546.619 0.002 0.040 1.18e-06 3.20e-06 1.82e-06 4.93e-06 6.49e-05 1.76e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


LC Type ID code Notes
9 Edk CDC=Ed (dinamico SLD) alfa=90.00 (ecc. -)
soil category: D
Site factor S = 1.800
spectrum ordinate (range Tb-Tc) = 0.104 g
angle, direction:90.00
additional eccentricity: negative
own period T1: 0.149 sec.
number of vibrations mode considered: 18
modal combination: CQC


Quote Seismic mass x g Pos. GX Pos. GY E add X-X E add Y-Y Pos. KX Pos. KY (r/Ls)^2 ex/rx ratio ey/ry ratio
m kN m m m m m m
2.86 2.88 0.35 0.75 -0.06 0.0 0.31 0.75 2.218 0.091 0.0
2.68 8.39 2.19 1.38 -0.02 0.0 0.0 0.0 0.0 0.0 0.0
2.13 13.35 1.25 1.22 0.0 0.0 1.25 0.76 0.019 0.0 4.942
1.21 12.21 0.0 1.19 0.0 0.0 0.0 1.20 0.021 0.0 0.016
Result 36.83


Mode Frequency Period Spectral acceleration. M excited X x g  % M excited Y x g  % M excited Z x g  % Energy Energy x v
Hz sec g kN kN kN
1 6.694 0.149 0.092 5.44e-03 1.48e-02 31.85 86.5 0.30 0.8 0.0 0.0
2 7.919 0.126 0.084 34.33 93.2 4.56e-03 1.24e-02 1.68e-03 4.56e-03 0.0 0.0
3 16.773 0.060 0.061 9.06e-03 2.46e-02 0.90 2.4 5.15e-03 1.40e-02 0.0 0.0
4 25.793 0.039 0.053 7.57e-03 2.06e-02 0.32 0.9 33.18 90.1 0.0 0.0
5 26.973 0.037 0.053 0.43 1.2 0.14 0.4 2.16 5.9 0.0 0.0
6 33.897 0.030 0.050 1.90 5.2 0.02 4.89e-02 0.87 2.4 0.0 0.0
7 42.343 0.024 0.048 9.40e-03 2.55e-02 2.46 6.7 0.17 0.5 0.0 0.0
8 59.749 0.017 0.046 0.02 6.75e-02 1.09 3.0 0.04 0.1 0.0 0.0
9 71.249 0.014 0.045 0.12 0.3 0.02 6.64e-02 0.10 0.3 0.0 0.0
10 87.082 0.011 0.044 6.31e-05 1.71e-04 5.70e-05 1.55e-04 7.55e-04 2.05e-03 0.0 0.0
11 122.091 0.008 0.043 2.58e-05 7.00e-05 0.03 6.83e-02 6.53e-05 1.77e-04 0.0 0.0
12 171.453 0.006 0.042 2.86e-04 7.77e-04 6.34e-04 1.72e-03 1.20e-04 3.26e-04 0.0 0.0
13 189.308 0.005 0.042 1.15e-05 3.14e-05 4.23e-05 1.15e-04 1.13e-04 3.06e-04 0.0 0.0
14 214.713 0.005 0.041 1.45e-04 3.94e-04 8.86e-04 2.41e-03 2.93e-05 7.96e-05 0.0 0.0
15 303.325 0.003 0.041 1.06e-04 2.87e-04 5.99e-04 1.63e-03 3.09e-05 8.39e-05 0.0 0.0
16 337.723 0.003 0.041 6.49e-05 1.76e-04 3.00e-04 8.15e-04 1.32e-04 3.59e-04 0.0 0.0
17 402.375 0.002 0.041 1.64e-04 4.44e-04 1.98e-05 5.37e-05 2.44e-05 6.61e-05 0.0 0.0
18 556.505 0.002 0.040 2.06e-06 5.59e-06 4.61e-06 1.25e-05 6.14e-05 1.67e-04 0.0 0.0
Result 36.83 36.83 36.83
Per cent 100.00 100.00 100.00


REFERENCE BUILDING CODES

[1] D.Min. Infrastrutture Min. Interni e Prot. Civile 17 Gennaio 2018 e allegate "Norme tecniche per le costruzioni".

[2] Circolare 21/01/19, n. 7 C.S.LL.PP “Istruzioni per l’applicazione dell’aggiornamento delle Norme Tecniche delle Costruzioni di cui al decreto ministeriale 17 gennaio 2018”

[3] D.Min. Infrastrutture e trasporti 14 Settembre 2005 e allegate "Norme tecniche per le costruzioni".

[4] D.M. 9/01/96 "Norme tecniche per il calcolo, l'esecuzione ed il collaudo delle strutture in cemento armato, normale e precompresso e per le strutture metalliche".

[5] D.M. 16/01/96 "Norme tecniche relative ai <<Criteri generali per la verifica di sicurezza delle costruzioni e dei carichi e sovraccarichi>>".

[6] D.M. 16/01/96 "Norme tecniche per le costruzioni in zone sismiche".

[7] Circolare 4/07/96, n.156AA.GG./STC. istruzioni per l'applicazione delle "Norme tecniche relative ai <<Criteri generali per la verifica di sicurezza delle costruzioni e dei carichi e sovraccarichi>>" di cui al D.M. 16/01/96.

[8] Circolare 10/04/97, n.65AA.GG. istruzioni per l'applicazione delle "Norme tecniche per le costruzioni in zone sismiche" di cui al D.M. 16/01/96.

[9] D.M. LL.PP. 20 novembre 1987 "Norme tecniche per la progettazione, esecuzione e collaudo degli edifici in muratura e per il loro consolidamento".

[10] Eurocode n.2 – Common unified rules for concrete structures.

[11] Eurocode n.3 – Common unified rules for steel structures.

[12] Eurocode n.4 – Common unified rules for composite steel and concrete structures.

[13] Eurocode n.5 – Common unified rules for timber structures.

[14] Eurocode n.8 – Design of structures for earthquake resistance.

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