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2.3 STATIC AND MODAL ANALYSIS-Robot Structural Analysis-

2.3.1 Static Analysis

a. Computation Model:

Structure geometry:

Figure a.1 – XY Plan View of the structure

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Figure a.2 – ZX Frontal View of the structure – Hfloor = 3.00 m

Figure a.3 – ZY Frontal View of the structure – Hfloor = 3.00 m

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Figure a.5 – 3D View of the structure

Cross-sections of the elements and materials used:

Data – Cross-sectionsSection name Bar list AX (cm2) AY (cm2) AZ (cm2)

C R60x60 Rectangular columns – Floors 1, 2 3600.00 3000.00 3000.00C C_60 Circular columns – Floors 1,2 2827.43 2385.65 2385.65

B R30x50 Rectangular beams – whole structure 1500.00 1250.00 1250.00C R50x50 Rectangular columns – Floors 3,4,5 2500.00 2083.33 2083.33C C_50 Circular columns – Floors 3,4,5 1963.50 1656.70 1656.70

Section name IX (cm4) IY (cm4) IZ (cm4)C R60x60 1821956.82 1080000.00 1080000.00C C_60 1272345.02 636172.51 636172.51

B R30x50 281631.13 312500.00 112500.00C R50x50 878644.30 520833.33 520833.33C C_50 613592.32 306796.16 306796.16

Data - MaterialsMaterial E (kPa) G (kPa) NI LX

(1/°C)RO

(kN/m3) Re (kPa)

1 C20/25 30000000.00 12900000.00 0.17 0.00 24.53 20500.00

Data - SupportsSupport name List of nodes List of edges List of objects Support conditions

Fixed Ground Floor Columns UX UY UZ RX RY RZUZ_RX_RY Base of the Columns UZ RX RY

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b. Loading assumption:

b.1 Permanent loading assumptions (P) :

b.2 Live loading (L) :

b.3 Snow load (S) :

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Loads - CasesCase Label Case name

1 DL1 Attic2 DL2 Roof3 DL3 Floor4 DL4 Curtain Wall5 DL5 LL Roof6 LL2 LL Floor7 LL3 LL Stair8 LL4 Snow9 DL0 Structure

Loads - ValuesCase Load type List Load values

1 uniform load Attic PZ=-1.52(kN/m)2 (FE) uniform Roof PZ=-3.60(kN/m2)3 (FE) uniform Floor PZ=-2.17(kN/m2)4 uniform load Curtain Wall PZ=-2.00(kN/m)5 (FE) uniform LL Roof PZ=-0.75(kN/m2)6 (FE) uniform LL Floor PZ=-1.50(kN/m2)7 (FE) uniform LL Stair PZ=-3.00(kN/m2)8 (FE) uniform Snow - Roof PZ=-2.00(kN/m2)9 self-weight Structure PZ Negative Factor=1.00

2.3.2 Modal Analysis :

2.3.2.1. Input data in Robot Structural Analysis :

i) Modal Analysis parameters (10 modes of vibration):

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ii) conversion of loads to masses (DL+0.4LL):

2.3.2.2 Output data in Robot Structural Analysis :

i) Modes of vibration – SRSS – deformed shape :

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ii) Modes of vibration – eigenvalues:

Case/Mode Frequency (Hz) Period (sec) Rel.mas.UX (%) Rel.mas.UY (%)12/ 1 1.50 0.67 0.00 78.3412/ 2 1.58 0.63 76.98 78.3412/ 3 1.67 0.60 78.96 78.3412/ 4 4.69 0.21 78.96 90.5112/ 5 4.91 0.20 90.79 90.5112/ 6 5.21 0.19 90.94 90.5112/ 7 7.94 0.13 90.94 90.5312/ 8 7.95 0.13 90.94 90.5312/ 9 8.07 0.12 90.94 90.53

12/ 10 8.10 0.12 90.96 90.5312/ 11 8.51 0.12 90.96 95.3612/ 12 8.78 0.11 95.54 95.3612/ 13 9.11 0.11 95.54 95.3812/ 14 9.12 0.11 95.54 95.3812/ 15 9.19 0.11 95.54 95.3812/ 16 9.21 0.11 95.56 95.3812/ 17 9.26 0.11 95.59 95.3812/ 18 9.30 0.11 95.61 95.3812/ 19 9.33 0.11 95.63 95.3812/ 20 9.35 0.11 95.63 95.3812/ 21 9.36 0.11 95.63 95.3912/ 22 9.37 0.11 95.65 95.3912/ 23 9.37 0.11 95.65 95.4312/ 24 9.39 0.11 95.65 95.4512/ 25 9.42 0.11 95.65 95.4512/ 26 9.46 0.11 95.66 95.4512/ 27 9.51 0.11 95.69 95.4512/ 28 9.59 0.10 95.69 95.4612/ 29 9.60 0.10 95.70 95.4612/ 30 9.60 0.10 95.70 95.4612/ 31 9.63 0.10 95.70 95.4612/ 32 9.76 0.10 95.70 95.4612/ 33 9.77 0.10 95.70 95.4612/ 34 10.50 0.10 95.70 95.4712/ 35 10.71 0.09 95.70 95.4712/ 36 10.72 0.09 95.70 95.4712/ 37 10.72 0.09 95.70 95.4712/ 38 10.73 0.09 95.70 95.4712/ 39 10.78 0.09 95.70 95.4812/ 40 10.92 0.09 95.70 95.49

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2.3.3 Seismic analysis according to P100 – 1 – 2013:

Seismic Parameters according P100 – 1 – 2013 :

Seismic Directions Definition

2.3.4 Group of loads:

Combinations of actions according SR – EN 1990 : 2004 / NA 2006

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2.3.5 Effort diagrams:

Maximum values

The studied frame – most loaded frame

Columns C R60x60 :

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Columns C R50x50 :

C R60x60– designefforts

NEd,max VEd,max,y VEd,max,z MEd,max,x MEd,max,y MEd,max,z

Diagrams- scheme

Values(kN) 1796 94 68 1.13 168 201

C R50x50– designefforts

NEd,max VEd,max,y VEd,max,z MEd,max,x MEd,max,y MEd,max,z

Diagrams- scheme

Values(kN /kNm)

1097 87 46 1.21 98 138

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Girders B R30x50 – The Studied Girder – Most Loaded Girder

Shear force diagram Vz

The maximum shear force will be : Vz,Ed = 119 kN

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Moment diagram My

The bending moment in the support will be My,Ed = 176 kNm (superior part)

The bending moment in the span will be My,Ed = 94 kNm (inferior part