Structural Analysis - Relazione tecnica del progetto

COLUMNS SHEAR FORCE (3 COMBINATION)

16000

14000

12000

[mm] 10000

8000

Lenght 6000

4000

2000

0

-300000 -200000 -100000 0 100000 200000 300000

Shear Force [N]

COLUMN 1 COLUMN 2 COLUMN 3

COLUMN 4 LEFT LIMIT RIGHT LIMIT

Figure 102 - Columns Shear Force (3 combination).

121 COLUMN 1, COMBINATION 3 (FIXED)

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 4.58E+03 254944.1 VERIFIED 220

10 -1.27E+04 254944.1 VERIFIED 220

14 -1.33E+04 254944.1 VERIFIED 220

COLUMN 2, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 9.29E+03 254944.1 VERIFIED 220

10 4.41E+03 254944.1 VERIFIED 220

14 7.85E+03 254944.1 VERIFIED 220

COLUMN 3, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 -9.86E+03 254944.1 VERIFIED 220

10 -1.45E+04 254944.1 VERIFIED 220

14 -3.09E+03 254944.1 VERIFIED 220

COLUMN 4, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 8.68E+03 254944.1 VERIFIED 220

COLUMN 5, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 -7.79E+03 254944.1 VERIFIED 220

10 -2.87E+03 254944.1 VERIFIED 220

14 -2.33E+03 254944.1 VERIFIED 220

COLUMN 6, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 -8.61E+03 254944.1 VERIFIED 220

10 9.17E+03 254944.1 VERIFIED 220

14 -9.38E+02 254944.1 VERIFIED 220

COLUMN 7, COMBINATION 3

Height [m] Vsd MAX [N] Vrd [N] verification HEA

6 -1.22E+04 254944.1 VERIFIED 220

10 -2.22E+04 254944.1 VERIFIED 220

14 1.83E+04 254944.1 VERIFIED 220

As shown in the chart above, the shear of the columns is verified for every combination at

the ULS.

122 8.2. SLS LIMIT VALUES

8.2.1 BEAMS VERTICAL DISPLACEMENT

BEAMS DISPLACEMENT (3 COMBINATION)

0 0 5000 10000 15000 20000 25000 30000 35000 40000

-10

[mm] -20

Displacement -30

-40

-50

-60 Lenght [mm]

FLOOR 1 ROOF FLOOR 2

LOWER LIMIT (ROOF) LOWER LIMIT (1 & 2 FLOORS)

Figure 103 - Beams vertical displacement at SLS (3 combination).

From the chart, it is clear that the vertical displacement for the beams, calculated with

the third combination at the SLS, doesn’t exceed the limits.

8.2.2 COLUMNS HORIZONAL DISPLACEMENT

The chart of the horizontal displacement for the columns, calculated at the SLS with the

third combination, it’s the same as for the one in Chapter x for the verification of the joint.

Even in this case, we calculated the displacement on ANSYS without considering the brac-

ings, but it was not verified since it exceeded the limits, so we did again the simulation add-

ing the bracings to the structure. The charts related to the horizontal displacement of the

columns, are reported below.

123 COLUMNS DISPLACEMENT (3 COMBINATION) WITHOUT BRACINGS

16000

14000

12000

10000

[mm] 8000

Lenght 6000

4000

2000

0 0 10 20 30 40 50 60 70 80 90 100

Displacement [mm]

COLUMN 1 COLUMN 4 LIMIT COLUMN 2

COLUMN 3 COLUMN 5 COLUMN 7

Figure 104 - Columns horizontal displacement at SLS (3 combination) without bracings.

COLUMN 1, COMBINATION 3 (FIXED)

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.729 20 VERIFIED 220

10 4000 17.805 13.3 NOT VERIFIED 220

14 4000 20.412 13.3 NOT VERIFIED 220

COLUMN 2, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.729 20 VERIFIED 220

10 4000 17.785 13.3 NOT VERIFIED 220

14 4000 20.468 13.3 NOT VERIFIED 220

COLUMN 3, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 15.767 20 VERIFIED 220

10 4000 18.054 13.3 NOT VERIFIED 220

14 4000 20.339 13.3 NOT VERIFIED 220

124 COLUMN 4, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.744 20 VERIFIED 220

COLUMN 5, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.817 20 VERIFIED 220

10 4000 19.162 13.3 NOT VERIFIED 220

14 4000 20.293 13.3 NOT VERIFIED 220

COLUMN 6, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.868 20 VERIFIED 220

10 4000 19.298 13.3 NOT VERIFIED 220

14 4000 20.866 13.3 NOT VERIFIED 220

COLUMN 7, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 4.20E+01 20 NOT VERIFIED 220

10 4000 2.62E+01 13.3 NOT VERIFIED 220

14 4000 1.54E+01 13.3 NOT VERIFIED 220

TOTAL COLUMN, COMBINATION 3 (FIXED)

Total Height (mm) δ δ verification HEA

MAX(mm) (mm)

14000 20.4 28 VERIFIED 220

125 COLUMNS DISPLACEMENT (3 COMBINATION) WITH BRACINGS

16000

14000

12000

[mm] 10000

8000

Lenght 6000

4000

2000

0 0 10 20 30 40 50 60 70 80 90 100

Displacement [mm]

COLUMN 1 COLUMN 2 COLUMN3 COLUMN 4

COLUMN 5 COLUMN 6 COLUMN 7 LIMIT

Figure 105 - Columns horizontal displacement at SLS (3 combination) with bracings.

COLUMN 1, COMBINATION 3 (FIXED)

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 12.831 20 VERIFIED 220

10 4000 13.078 13.3 VERIFIED 220

14 4000 13.234 13.3 VERIFIED 220

COLUMN 2, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 10.818 20 VERIFIED 220

10 4000 13.247 13.3 VERIFIED 220

14 4000 13.325 13.3 VERIFIED 220

COLUMN 3, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 11.202 20 VERIFIED 220

10 4000 13.109 13.3 VERIFIED 220

14 4000 13.109 13.3 VERIFIED 220

COLUMN 4, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 14.412 20 VERIFIED 220

COLUMN 5, COMBINATION 3

126 Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 10.863 20 VERIFIED 220

10 4000 13.05 13.3 VERIFIED 220

14 4000 13.219 13.3 VERIFIED 220

COLUMN 6, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 13.166 20 VERIFIED 220

10 4000 13.294 13.3 VERIFIED 220

14 4000 13.054 13.3 VERIFIED 220

COLUMN 7, COMBINATION 3

Height [m] h (mm) δ MAX [mm] δ [mm] verification HEA

6 6000 12.17 20 VERIFIED 220

10 4000 13.29 13.3 VERIFIED 220

14 4000 13.29 13.3 VERIFIED 220

TOTAL COLUMN, COMBINATION 3 (FIXED)

Total Height (mm) δ δ verification HEA

MAX(mm) (mm)

14000 14.8 28 VERIFIED 220

As shown in the charts, the beams’ horizontal displacements are always inside the dis-

placement limit given by the NTC thanks to the addition of circular bracings.

127

9. BB

CAPACITIES LIMIT VALUES SECTION

In order to analyse the data obtained on Ansys using the Finite Elements Method, it will be

needed to compare them with limit values. These limit values depend on the cross-section

size, class, and material (Steel S275). The verifications performed comparing the values from

the Ansys model and the resistant values calculated are here summarized:

Beams Bending Moment

• Beams Shear Force

• Beams Vertical Displacement

• Columns Axial Force

• Columns Bending Moment

• Columns Shear Force

• Columns Horizontal Displacement

•

The B-B section has been subjected to analysis. It is comprised, on the ground floor, of four

spans measuring 8.4 and 6.6 meters, while on the two upper floors, it assumes a similar con-

figuration with a cantilevered beam of 9.2 meters at one end.

The permanent and variable loads should be regarded as equivalent to the previously ap-

plied forces on the B-B section. Wind forces, on the other hand, have been recalculated to

align with the altered combination of the A-A section, both below and above the windward

facade. Figure 106 - Axonometric view of Section B-B

Additionally, the second section features a cantilevered volume and is equipped with an

external false ceiling as a finishing layer, filled with thermal insulation. Consequently, the

permanent load on this cantilevered part is slightly higher. The load combinations remain

consistent with those of the preceding section. In both the first and second combinations,

the forces acting on the beams alternate between favourable and unfavourable load. In

contrast, the third combination accounts for the maximum forces exerted on each span.

128

The structure is connected to the ground through simple remote connections, while the

joints between various beams and columns are fixed.

Figure 107 - Chessboard 1: first combination.

Figure 108 - Chessboard 2: second combination.

Figure 109 - Chessboard 3: third combination.

129 Figure 110 - Chessboard 3: third combination with bracing.

9.1. SLS LIMIT VALUES

9.1.1 BEAMS VERTICAL DISPLACEMENT

We start considering the worst values of the load combination 3 in SLS for each floor. As we

can see, the highest values are in the first span. We have a maximum vertical displacement

of 59,69 mm on the cantilever beam.

Vertical Displacement in each floor

0

-10

-20

[mm] -30

-40

Displacement -50

-60

-70

-80

-90

-100 0 5 10 15 20 25 30 35 40 45

Lenght [m]

LIMIT FLOOR 1 FLOOR 2 ROOF

Figure 111 – Beams Vertical Displacement of different slabs.

130 ROOF DISPLACEMENT WITH BRACING

Span Wed [mm] Wfloor, lim [mm] verification IPE

VERIFIED

W max 0 92 500

1 VERIFIED

W min -59,69 -92 500

VERIFIED

W max -0,56859 33,6 500

2 VERIFIED

W min -13,496 -33,6 500

VERIFIED

W max -6,6558 26,4 500

3 VERIFIED

W min -9,9461 -26,4 500

VERIFIED

W max -9,1646 33,6 500

4 VERIFIED

W min -24,777 -33,6 500

VERIFIED

W max 0 26,4 500

5 VERIFIED

W min -8,6618 -26,4 500

Table 50 - verification of the displacement in SLS

FLOOR 2 DISPLACEMENT WITH BRACING

Span Wed [mm] Wfloor, lim [mm] verification IPE

VERIFIED

W max -4,3267 92 500

1 VERIFIED

W min -59,69 -92 500

VERIFIED

W max -2,4172 33,6 500

2 VERIFIED

W min -10,745 -33,6 500

VERIFIED

W max -7,8444 26,4 500

3 VERIFIED

W min -11,09 -26,4 500

VERIFIED

W max -10,538 33,6 500

4 VERIFIED

W min -25,265 -33,6 500

VERIFIED

W max 0 26,4 500

5 VERIFIED

W min -9,8993 -26,4 500

Table 51 - verification of the displacement

131

Some verifications with other type of beams have been done. For the comparison we use

IPE 360, 300, 270 and 220 considering only the structure with bracings. The analysis has been

done for all the floors but here just the second floor and roof are shown because they are

the most significant since there is the cantilever.

FLOOR 2

Vertical Displacement SLS

0 5 10 15 20 25 30 35 40 45

20

0

[mm] -20

Displacement -40

-60

-80

-100 Lenght [m]

-120 Limit IPE 500 WITH BRACING IPE 500 WITHOUT BRACING

IPE 360 IPE 300 IPE 220

IPE 270

Figure 112 - IPE comparison for the Vertical Displace