Structural Report: Calamarata

STRUCTURAL REPORT ARCHITECTURAL DESIGN STUDIO FOR COMPLEX CONSTRUCTIONS 1 2021/2022 prof. Grigor Angjeliu

Group 7 Julia Wisniewska Tyler Bakhtiari Teodora Matei

School: AIUC AY 2021/2022 Programs: Msc Architecture - Building Architecture Course: Architectural Design Studio for Complex Constructions 1 Professors: Angjeliu Grigor | Belloni Francesca Claudia Maria | Diez Medina Carmen | Mirarchi Claudio

Page 1

10842910 10876309 10816072

Julia Wisniewska 10842910 Tyler Bakhtiari 10876309 Teodora Matei 10816072

TABLE OF CONTENT:

Project description p. 3 Structural load calculations p. 8 Slab design p. 16 Continious beam design p. 22 Column design p. 35 Load analysis - Testing p. 38 Case Study p. 43 Structural drawings p. 45 Bibliography

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p. 47

1. PROJECT DESCRIPTION

Page 2

Project description Per our studio brief, we had the task of designing a lower secondary school. Based on the size and the structural needs we performed a structural analysis for the building concept (as an overview of the whole volume) and chose a specific area of focus to run tests and do the required pillar, beam and slab load calculations.

Due to its peculiar shape, there have been a couple of issues encountered during our analysis process, such as: the loads of the circular volume upper levels proved to be too heavy for the auditorium to carry, the structural grid clash between the radial grid and rectangular/standard grid and also there was the question on which material would be better suited for the project from a structural eficiency point of view.

Our structural analysis of the school project indicates that the solutions work and the proposed structural elements have passed the safety checks.

•Project location Via Pescarenico, 2, 20142 Milano MI, Italy •Surface/volume information Site surface: 6, 252 m2 Volume surface: 2,794 m2 Volumes height: - Main building: 14.70 m - Gymnasium: 11.10 m - Canteen: 3.63 m - Auditorium: 5.13 m - Library: 4.33 m •Typical dimensions Span between the shear wall and square column: approx. 6.1m Span between the square column and round column: approx. 3.9m Span between beams - outer circle: approx. 8.3m Span between beams - middle circle: approx. 6.1m Span between beams - inner circle: approx. 4.6m

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Drawings •Axonometry drawing

•Perspective - Auditorium

Page 4

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50

1

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26 30 567

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450

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Key

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1 50 0

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15

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264

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450

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15

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264

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D1 C4

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B3 A4

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2

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854

B5

495

1

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413

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413

758 P5

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613

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758 1 612

P5

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A 537 P4

B

A18

B1

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P4

P4

P4

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537 P4

A

P4

A2

P6

A1

Programme Main building Library Auditorium Canteen Gymnasium

Structural elements A1 ‐ A17 B1 ‐ B6 C1 ‐ C9 D1 ‐ D8 E1 ‐ E5

P6

466 1 783

A10

1 171

D6

A11

P6

466

A9

P6 P6

D7

510

P6 P6

D6 D5

510

Plan at 7000mm

P6 P6

377

P6

788 1 653

D1

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488

D5

D2 D3 D4

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B2

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537 P4

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758

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495

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P6

P4

P4

P4

604

P3

P2 P1

195

P2

466

604

317

317

D6

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11

510

P1

P2

P2

P3

195

490

510

466

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P6

466 1 783

P1

P6

P2

1 171

P6

P2

P2

P6

788 1 653

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P6

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488

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P1

510

P6

P1

Structural elements A1 ‐ A17 B1 ‐ B6 C1 ‐ C9 D1 ‐ D8 E1 ‐ E5

510

P6

95

Programme Main building Library Auditorium Canteen Gymnasium

P1

P6

P6

377

50

D7

P6

P3

P3

P6

P6

45

P2

Class Dimension No. Purpose I A7 H: 900 mm A13 1 H D6 Reinforced concrete C35 Helps 10 resist against lateral loads, such as the force from wind D5 8 W: 500 mm 9 H H: 500Gmm 2 D5 Reinforced concrete C35 Transmits the load of the structure above through compression D1 D2 W: 500A8 mm A12 D3 D4 G D: 500 mm 3 Transmits the load of the structure above through compression Reinforced concrete C35 F H: 500 mm 377 4 Transfer primarily vertical loads (offering resistance to forces and A11 A9 Reinforced concrete C25 788 A10 W: 300 mm bending under said loads) to the compressive element, in this case columns ffer 1 653 488 F 9 9 H: 500 mm 5 Transfer primarily vertical loads (offering resistance to forces and 9 Reinforced concrete C25 9 W: 300 mm bending under said loads) to the compressive element, in this case columns ffer A1 A2 A3 A4 H: 600 mm 6 Transfer primarily vertical loads (offering resistance to forces and Reinforced concrete 2 080 C25 A1 A3 A4 W:821400 mm bending under saidA2loads) to the compressive element, in this case columns ffer 537 722 2 080 A A B1 H: 600 mm 7 Transfer primarily vertical loads821(offering resistance to forces and 537 722 Reinforced concrete C25 A A D bending B1 case columns W: 400 mm underB1said loads) ffer A18 to the compressive element, in this 613 D H: 600 mm 8 Transfer primarily vertical loads (offering resistance to forces andB1 E1 B1 E5 613 848 Reinforced concrete C25 2 95 2 W: 400 mm bending under said loads) to the compressive element, in this case columns ffer B B1 B E2 848 565 A1 1 H: 600 mm 9 B B E3 Reinforced concrete C25 One way slab, transfering loads B1 to Beams 926 A2 1 W: 400 mm 7

50

P4

P6

P6

466 1 783

1 171

35

A14

490

A11 P6

A10 P3

P3

P1

D8

95

A9

P1

P1

A12

P6

P3

P6 P6

P2

D1

Material

469

P1

P3

P3

P2

P2

P1

J

12 24 00

P6

P2

D7

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P5

P2

5 56

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A6

45

P6 P3

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P2

P1

P2

6

S

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45

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95P1

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0 39

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14 40

565

390

1 350

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P3

P1

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P3 E6

E4

95 60

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P2

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L

S

5 56

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P2

P2

US

A15 A13

P1

01

P2

834

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P3

P3

P3 A7

TR

P4

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P2

0 39

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P1

13

02

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A5

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24 00

0 35

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M

03

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1

US

834

604 P3

67

469

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P2

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50

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2

1 50 0

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50

14 P2

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Key

E

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0

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0 A4 P3 A6

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02 P3

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4

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450

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02 A17 P3

469

450

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01

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03

15

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N

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P6

P6

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495

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P3

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854

264

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2 96 7

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849 P2

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TR

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1 612

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0

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758

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15

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E

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16 E5

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565

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854

O B3

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722

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2

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P1

537

16

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1 612

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1

2 95 2

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565 P4

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413

854

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758

613

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2 96 7

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1 612

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35

A B5

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P4

P4

A

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P4

413

821

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P4

628

P4

2 080 722

537

1 50 0

A3

834

A2

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A1

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P6

P6

Plan at 10450mm P4

P4

P4

P4

P4

P5

P5

P4

P6

P1

P1 P2

P3

P3

4

P2

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P3 P4

P1 P3

P3

P3

P2

P2

P1

24 00

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5

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1

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13

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95 1

P1

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P2

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317

11 Class DimensionA8 No. PurposeA12 I 7 11 H: 900 mm 1 H forced concrete C35 Helps I 10 resist against lateral loads, such as the force from wind 8 W: 500 mm A11 H A9 9 10 A10 H 8 H: 500Gmm 2 9 forced concrete C35 Transmits the load of the structure above through compression H W: 500 mm G G 3 Transmits the load of the structure above through compression orced concrete C35 D: 500 mm F Page 7 to forces and G H: 500 mm 377 4 Transfer primarily vertical loads (offering resistance forced concrete C25 F 788 W: 300 mm bending under said loads) to the compressive element, in this case columns 1 653 488 F 377 9 9 H: 500 mm 5 Transfer primarily vertical loads (offering resistance781 658to forces488and 3 9 F forced concrete C25 9 9 9 W: 300 mm bending under said loads) to the compressive element, in this case columns P6

195

P6

P6

466

P6

466 1 783

P6

1 171

466 1 783

P6

490

P6

P6

P6

317

P1

490

P1

195

466

P6

P6

P6

P1

P1

P6

1 171

P1

P1

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510

P6

P6

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7

45

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95

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6

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Material

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45

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60

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565 390

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469

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Key

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P4

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C

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15

B1

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1 50 0

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95

P2

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4 TR

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15 A1

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1 612

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2

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628

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413

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P5

758

413

1 612

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P1

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P4

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P4

758

P4

P6

P6

P6

Programme Main building Library Auditorium Canteen Gymnasium

Structural elements A1 ‐ A17 B1 ‐ B6 C1 ‐ C9 D1 ‐ D8 E1 ‐ E5

Plan at 10600mm A2

A3

A4

2 080 722

821 P4

P4

A

B1 B1 613

P4

758

D

A18

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2 95 E12

628

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495

1

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16

564

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02 P2

01 P2

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03

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P1

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P3

P2

P2

P1

P1

P1

P2

P2

P2

D1

P1

Programme Main building Library Auditorium Canteen Gymnasium

317

11 Class Dimension No. Purpose I A8 mm A12 H: 900 1 H Reinforced concrete C35 Helps 10 resist against lateral loads, such as the force from wind 8 W: 500 mm 9 HA11 H: 500Gmm 2A9 Reinforced concrete C35 Transmits the load of the structure above through compression A10 W: 500 mm G 3 Transmits the load of the structure above through compression Reinforced concrete C35 D: 500 mm F H: 500 mm 377 4 Transfer primarily vertical loads (offering resistance to forces and Reinforced concrete C25 788 W: 300 mm bending under said loads) to the compressive element, in this case columns ffer 1 653 488 F 9 9 H: 500 mm 5 Transfer primarily vertical loads (offering resistance to forces and 9 Reinforced concrete C25 9 W: 300 mm bending under said loads) to the compressive element, in this case columns ffer H: 600 mm 6 Transfer primarily vertical loads (offering resistance to forces and Reinforced concrete C25 A1 A3 A4 W: 400 mm bending under saidA2loads) to the compressive element, in this case columns ffer 2 080 H: 600 mm 7 Transfer primarily vertical loads821(offering resistance to forces and 537 722 Reinforced concrete C25 A A W: 400 mm bending under said loads) to the compressive element, in thisB1 case columns ffer D H: 600 mm 8 Transfer primarily vertical loads (offering resistance to forces andB1 613 Reinforced concrete C25 W: 400 mm bending under said loads) to the compressive element, in this case columns ffer 848 H: 600 mm 9 B B Reinforced concrete C25A2 One way slab, transfering loads to Beams A1 A3 A4 1 W: 400 mm 7

P1

Material

35

P6 A13

95

A7

P1

P3

P2

P2

J

12

5 56

P1

14 40

45 P2

P5 P2

K

6

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P1

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US

P4

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24 00

P2

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L

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490

P1

P1

195

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P6

466

P6

466 1 783

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1 171

60

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US

45

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P2

TR

P3

13

P3

50

0 35

24 00

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1

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604

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1 350

M P3

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50

P2

390

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E6

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95 565

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N

S

604

US

469

67

A5 P2 TR

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50

14

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50

0

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S

45

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35

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P2

Key

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95

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450

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P3

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450

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P3

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P3

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P2

N

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P3

P2

P3

P4

264

P2

P3

P3

A4

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P1

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15

B1

D1 TR

TRUS S

P4

P2 P2

E5 E6

P1

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P1

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854

B1

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2

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413 P5

1 612

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P4

P4

P4

537 P4

A

P4

A1

P6

P6

510

P6

P6

510

P6

Structural elements A1 ‐ A17 B1 ‐ B6 C1 ‐ C9 D1 ‐ D8 E1 ‐ E5

P6

P6

P6

P4

P4

P4

P5

P5

P5

P5

P4

C

E

P2

P1

P2

P3

P3

P4

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P2

A18

B1

16 P4

03 P3

B1

P1

P6

P3

02

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C

P3

0

604

P2

469

P2

P3

12

P3

P2

P3

P2

9

1 171

5 56

P2

834

604

60

P6

P1

P6

P3

P6

P1

95

P2

45

P5

466 1 783

466

P3

P3

P3

P2

P2

P2

P1

317

I 10 P6

A13

35

H

P6

35

P3

P6 P2 P6

P6

G

P4

45

195

H

8

490

P1 P1

P1

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P6

P2

P2

510

P6

G

P2

D1

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510

317

P1

P1

F

11

P1

Class Dimension No. Purpose 377 I 788 A12 H: 900 mm 1 H A8 488 653 F 9 Reinforced concrete C35 Helps such1as the force from wind 10 resist against lateral loads, 9 8 W: 500 mm 9 9 9 H A11 H: 500Gmm 2 A9 Reinforced concrete C35 Transmits the load of the structure above through compression A10 W: 500 mm G 3 Transmits the load of the structure above through compression Reinforced concrete C35 D: 500 mm Page 8 F H: 500 mm 377 4 Transfer primarily vertical loads (offering resistance to forces and Reinforced concrete C25 788 W: 300 mm bending under said loads) to the compressive element, in this case columns ffer 1 653 488 F 9 9 H: 500 mm 5 Transfer primarily vertical loads (offering resistance to forces and 9 P6

P6

195

P1

P6

P6

490

466

P6

466 1 783

1 171

P1

P6

P6

P6

P6

P6

510

P6

P6

P6

P6

P1

P1

P6

510

7

P1

Material

P1

0 39

K

P2

J

45

11

P6

P1

P3

P2

14 40

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P3

6

S

24 00

P2

7 P3

P1

US

469 P6

P1

P2 TR

50

469

604

P

P3

P2 A6

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95 1

P1

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67

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5 56

13

P3

P2

P2

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P2

1

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P3

P1

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0 39

P3

1 350

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50

12

P2

P2

US

P1

390

P2

5 TR

565

P3

P3

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95

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01

6

2

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P1

P3

A

N

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P2

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50

14

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P2

P3

50

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P3

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0

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Key

E

P3

US

13 P3

P4

B1 P2

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1 50 0

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P3

450

P6

P3 P3

P3

02A

24 00

0 35

P3

P1

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4

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03

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5

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264

P3

P3

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C P1

P1 S

15

P3

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14

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3 P2

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01

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P2

A3 A1

C P4

D1

P2

A3

P1

E 4

P1

C

1 50 0

15

B1 B1

P4

P4 P6

495 P1

A2

B1

565

P3

854

2 95 2

P1

A1

P1

O

2

B1

848

P3

1

P4

A2

P6

B 3

P3

P5

P2

1 612

P5

P4

A1 P5

P2

413

P2

A3

P4

P4

613

P4

P6

D

B1

P1

P1

758

16

P4

D

B1

926

P1

O

2 B1

C

P5

P4

P6

495

P4

P4

A

B

B1 565

P1

854

821

P4

A

P1

2 080 722

537 P4

B1 2 95 2

P6

1 612

Plan at 14300mm

P4

413

P4

758

P4

Programme Main building Library Auditorium Canteen Gymnasium

Structural elements A1 ‐ A17 B1 ‐ B6 C1 ‐ C9 D1 ‐ D8 E1 ‐ E5

2. STRUCTURAL LOAD CALCULATIONS

Plan of chosen load calculations Page 9

for Complex Constructions Module: Structures Prof. Grigor Angjeliu Academic Year 2021-2022

A. Single Load Case Structural/ Dead/ Live Load Calculations In the grey cells the numbers can be hard

In other the cellstotal there beam are already In order to start the analysis wetyped. calculated load firstly with consideration of the permanent dead load and secondly with consideration to live loads of classrooms and corridors.

Part 1: Single load calculation

Wall layering

Dead load: Beam self-weight Concrete rectangular beam B H Material density Linear load G1'

Layer Reinforced Concrete Slab Area load G1"

40 cm 60 cm 2500 kg/m3

Reinforced Concrete Slab B 100 cm H 20 cm Mater 2500 kg/m3 Linear load G1'

0.4 m 0.6 m 25 kN/m3 6.0 kN/m

Dead load: Floor self-weight (structural) Length Width Height Volumetric weight 1.0 m 1.0 m 0.2 m 25 kN/m3

Standard lightweight concrete/bricks (non structural) Layer Length Width Ceramic Finish 1.0 m 1.0 m Levelling 1.0 m 1.0 m Insulation 1.0 m 1.0 m Suspended Ceiling 1.0 m 1.0 m Divisory walls Area load G2

Height 0.02 m 0.06 m 0.08 m 0.02 m

Variable load: Schools Classroom Live Load Area load q

1.92

kN/m2

Corridor Live Load Area load q

4.79

kN/m2

Selection of g2 for divisory walls:

For the Gym:

Page 10

Dead load: Beam self-weight

Volumetric weight 17.65 kN/m3 20 kN/m3 0.118 kN/m3 20 kN/m3

1m 0.2 m 25 kN/m3 5.0 kN/m

Weight 5.0000 kN/m2 5.0000 kN/m2

Weight 0.4 kN/m2 1.2 kN/m2 0.0 kN/m2 0.4 kN/m2 2.0 kN/m2 4.0 kN/m2

For the Gym: Dead load: Beam self-weight Concrete rectangular beam B H Material density Linear load G1'

Layer Reinforced Concrete Slab Area load G1"

40 cm 60 cm 2500 kg/m3

0.4 m 0.6 m 25 kN/m3 6.0 kN/m

Dead load: Floor self-weight (structural) Length Width Height Volumetric weight 1.0 m 1.0 m 0.2 m 25 kN/m3

Standard lightweight concrete/bricks (non structural) Layer Length Width Ceramic 1.0 m 1.0 m Levelling 1.0 m 1.0 m Insulation 1.0 m 1.0 m Insulation 1.0 m 1.0 m Steel 1.0 m 1.0 m Divisory walls Area load G2

Page 11

Height 0.01 m 0.04 m 0.15 m 0.15 m 0.05 m

Volumetric weight 2.5 kN/m3 20 kN/m3 0.118 kN/m3 0.118 kN/m3 77 kN/m4

Weight 5.0000 kN/m2 5.0000 kN/m2

Weight 0.0 kN/m2 0.8 kN/m2 0.0 kN/m2 0.0 kN/m2 3.9 kN/m3 kN/m2 4.7 kN/m2

Prof. Grigor Angjeliu Academic Year 2021-2022

B. General Load Case

In the grey cells the numbers can be

Structural/ Dead/ Live Load Calculations

In order to start the analysis we calculated the total beam load firstly with consideration of the Part 2: Typical Beam Total Load Calculation permanent dead load and secondly with consideration to live loads of classrooms and corridors.

BEAM 1 LOAD Influence area width I

2.048 m

Area load: floor structural (G1") Dead load: Beam self weight (G1') Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 16.238 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 8.190 kN/m

Area load Q1 Linear load Q1

4.790 kN/m2 9.808 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1

16.2 kN/m 8.2 kN/m 9.8 kN/m 1.3 1.50 1.50 -

TOTAL BEAM LOAD Quls

48.1 kN/m

BEAM 2 LOAD Influence area width I

1.355 m

Area load: floor structural (G1") Dead load: Beam self weight (G1') Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 12.775 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 5.420 kN/m

Area load Q1 Linear load Q1

4.790 kN/m2 6.490 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight (G2) Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1

12.8 kN/m 5.4 kN/m 6.5 kN/m 1.3 1.50 1.50 -

TOTAL BEAM LOAD Quls

34.5 kN/m Page 12

BEAM 3 LOAD

TOTAL BEAM LOAD Quls

34.5 kN/m

BEAM 3 LOAD Influence area width I

1.355 m

Area load: floor structural (G1``) Dead load: Beam self weight (G1`) Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 12.775 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 5.420 kN/m

Area load Q1 Linear load Q1

4.790 kN/m2 6.490 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight (G2) Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1 This is in addition to: Influence area width I

12.8 kN/m 5.4 kN/m 6.5 kN/m 1.3 1.50 1.50 1.983 m

Area load: floor structural (G1``) Dead load: Beam self weight (G1`) Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 15.913 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 7.930 kN/m

Area load Q1 Linear load Q1

1.920 kN/m2 3.806 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight (G2) Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1

15.9 kN/m 7.9 kN/m 3.8 kN/m 1.3 1.50 1.50 -

TOTAL BEAM LOAD Quls

72.8 kN/m

BEAM 4 LOAD Influence area width I

3.250 m

Area load: floor structural (G1``) Dead load: Beam self weight (G1`) Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 22.250 kN/m

Area load G2 Page 13 Dead load: Permanent non structural (G2)

4.000 kN/m2 13.000 kN/m

Q��� � 1.3 𝐺𝐺1 � 1.5 𝐺𝐺2 � 1.5 𝑄𝑄

TOTAL BEAM LOAD Quls

72.8 kN/m

BEAM 4 LOAD Influence area width I

3.250 m

Area load: floor structural (G1``) Dead load: Beam self weight (G1`) Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 22.250 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 13.000 kN/m

Area load Q1 Linear load Q1

1.920 kN/m2 6.240 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight (G2) Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1

22.3 kN/m 13.0 kN/m 6.2 kN/m 1.3 1.50 1.50 -

TOTAL BEAM LOAD Quls

57.8 kN/m

BEAM 5 LOAD Influence area width I

1.983 m

Area load: floor structural (G1``) Dead load: Beam self weight (G1`) Dead load: permanent structural (G1)

5.000 kN/m2 6.000 kN/m 15.915 kN/m

Area load G2 Dead load: Permanent non structural (G2)

4.000 kN/m2 7.932 kN/m

Area load Q1 Linear load Q1

1.920 kN/m2 3.807 kN/m

Dead load: Beam self weight (G1) Dead load: Floor Self weight (G2) Linear load Q1 Coefficient for G1 Coefficient for G2 Coefficient for Q1

15.9 kN/m 7.9 kN/m 3.8 kN/m 1.3 1.50 1.50 -

TOTAL BEAM LOAD Quls

38.3 kN/m

Q��� � 1.3 𝐺𝐺1 � 1.5 𝐺𝐺2 � 1.5 𝑄𝑄

Q��� � 1.3 𝐺𝐺1 � 1.5 𝐺𝐺2 � 1.5 𝑄𝑄

Page 14

Part 3: Pillar Part 3:Total Pillar Load Total Calculation Load Calculation Central column Central column 48.100 kN/m 48.100 kN/m 4.158 m 4.158 m 100.000 kN 100.000 kN

oad Beam Load 3 and Beam 3' Quls2 3 and 3' Quls2 ength Beam Length 5 Beam 5

72.800 kN/m 72.800 kN/m 6.053 m 6.053 m

oad Support LoadBeam Support 2 Ruls2 Beam 2 Ruls2

440.658 kN 440.658 kN

oad Beam Load 3 Quls2 Beam 3 Quls2 ength Beam Length 4 Beam 4 oad Support LoadBeam Support 2 Ruls2 Beam 2 Ruls2

57.400 kN/m 57.400 kN/m 6.600 m 6.600 m 189.420 kN 189.420 kN

PILLAR LOAD PILLAR FROM LOAD BEAMS FROMPuls,beams BEAMS Puls,beams

730.078 kN 730.078 kN

Density Density Pillar BasePillar dimension Base dimension a a Pillar BasePillar dimension Base dimension b b Pillar Height Pillar H Height H PILLAR SELF-WEIGHT PILLAR SELF-WEIGHT Puls,self Puls,self Number of Number pillars of pillars otal loadTotal self weight load self pillars weight pillars

0.500 m 0.500 m 0.500 m 0.500 m 3.600 m 3.600 m 30.375 kN30.375 kN 4 4 121.500 kN 121.500 kN

oad on upper Load on Pillar upper 1 Pillar 1 oad on upper Load on Pillar upper 2 Pillar 2 oad on upper Load on Pillar upper 3 Pillar 3 oad on Ground Load onFloor Ground Pillar Floor Pillar OTAL PILLAR TOTALLOAD PILLAR Puls LOAD Puls

730.078 kN 730.078 kN 730.078 kN 730.078 kN 730.078 kN 730.078 kN 730.078 kN 730.078 kN 3042 kN 3042 kN 3.5

3

3

2.5

2.5

2

2

1.5

4000.0

3000.0 4000.0

2000.0 3000.0

1000.0 2000.0

Floor [n]

3.5

1.5

1

1

0.5

0.5

0 1000.0 0.0

0.0

Floor [n]

or Typical ForFloor Typical Beams Floor Beams oad Beam Load 1 Quls1 Beam 1 Quls1 enght Beam Lenght 1 Beam 1 oad Support LoadBeam Support 1 Ruls1 Beam 1 Ruls1

0

Axial ForceAxial [kN]Force [kN]

Page 15

Cumulative Cumulative Load in kN Load in kN 730.1 730.13 1460.2 1460.22 2190.2 2190.21 3042 30420

Drawings Typical plan with different categories of live load Key Classrooms: 1.92 kN/m2 Corridor: 4.79 kN/m2 Library: 5.27 kN/m2 Grand stand: 4.79 kN/m2

Floor Loads Key Dead Load Snow Load Live Load Wind Load Resistant Load

Page 16

3. REINFORCED CONCRETE SLAB DESIGN

Plan of chosen slab’s main reinforcement Page 17

Based on what is described in BS8110 for two-way simply supported slabs, the maximum moments per unit width are determined from (a Based on what is described in BS8110 for two-way simply supported slabs, the maximum moments per unit width are determined from

Calculations

Based on what is described in BS8110 forlengths two-way simply supported slabs, from the maximum moments per unit determined from (a The bending moment multipliers for the slab are referenced theslabs, source below, which arewidth fromare BS8110 Based on what is described inboth BS8110 foroftwo-way simply supported the maximum moments per The bending moment multipliers for both lengths of the slab are referenced from the source below, which are from BS8110

unit width are determined from (and show the tables and formulas below)

The bending moment multipliers for both lengths of the slab are referenced from the source below, which are from BS8110

o for Complex

Calculations for the course Architectural Design Studio for Comp Constructions 1

Ly in m Lx in m Ly/Lx in m Ly in8.333 m Lx in m Ly/Lx in m 6.125 1.4 8.333 6.125 1.4 Ly in m Lx in m Ly/Lx in m Module: Structures ped. In other cells 8.333there 6.125 1.4

Prof. Grigor Angjeliu Academic Year 2021-2022

SLAB A, Ly

In the grey cells the numbers can be hard typed. In other cells are already formulas.

Slab A, Ly n in kN/m^2 l in m Moment Multiplier (αsy) Slab15.4 Type: Two-Way Solid Slab 8.333 0.051 1. M_ED External Bending Moment Calculation Ly Moment Calculation For 2 Way Slabs αsx*n*Lx^2

29.46 kNm

2. Choose steel class Steel class S… fyk γs fyd

500 500 MPa 1.15 435 MPa

3. Choose concrete class Concrete class C… fck γc fcd

25 25 MPa 1.5 17 MPa Page 18

29464772 Nmm

Slab A, n in kN 15

fck γc fcd

25 MPa 1.5 17 MPa

4. Slab parameters b h c bar diameter d

1000 mm 200 mm 50 mm 8 mm 146 mm

usually 1/2 - 2/3 h usually 1/8 - 1/12 span effective depth

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏 𝐴𝐴� �

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 �

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

𝐾𝐾 1.134

0.055 � 0.167 OK �

138 mm 489 mm2

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

0.13% 189.8 mm2

4% 5840 mm2

8 mm 50.2 mm2

*suggestions: slab - fi 8 - fi12 mm concrete beam fi 14mm or more

6. Convert reinf. area into bars Bar diameter Bar area Provide bars Provided area

bars @

ro = A s /bd 7. Check Beam Dimension 1 row Minimum width "b"

10 per meter 502 mm2 OK 100 mm 0.34% OK

360

OK

8. Summary One way slab thickness Tension Steel Distribution Steel (min ratio)

200 mm 8 8

bars @ with As=

100 mm 502 mm2/m

bars @ with As=

200 mm 251 mm2/m

Source for the vertical spacing between bars https://paddyengineering.blogspot.com/2015/02/spacing-of-reinforcement-in-rcc-members.html Page 19

mm e

SLAB A, Lx Slab A, Lx n in kN/m^2 15.4

l in m Moment Multiplier (αsx) 6.125 0.099

1. M_ED External Bending Moment Calculation Lx 57.20 kNm

Moment Calculation For 2 Way Slabs αsy*n*Lx^2 2. Choose steel class Steel class S… fyk γs fyd

500 500 MPa 1.15 435 MPa

3. Choose concrete class Concrete class C… fck γc fcd

25 25 MPa 1.5 17 MPa

4. Slab parameters b h c bar diameter d

1000 mm 200 mm 20 mm 12 mm 174 mm

57196322 Nmm

usually 1/2 - 2/3 h usually 1/8 - 1/12 span effective depth

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏 𝐴𝐴� �

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 �

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

𝐾𝐾 1.134

0.076 � 0.167 OK �

162 mm 815 mm2

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

0.13% 226.2 mm2

4% 6960 mm2

12 mm 113.0 mm2

*suggestions: slab - fi 8 - fi12 mm concrete beam fi 14mm or more

6. Convert reinf. area into bars Bar diameter Bar area Provide bars Provided area

Page 20

8 per meter 904 mm2 OK

Slab A n in kN 1

Check minimum and maximum reinforcement

0.13% 226.2 mm2

4% 6960 mm2

Bar diameter Bar area

12 mm 113.0 mm2

*suggestions: slab - fi 8 - fi12 mm concrete beam fi 14mm or more

Provide bars Provided area

8 per meter OK 904 mm2 125 mm 0.52% OK

𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� , 6. Convert reinf. area into bars

bars @

ro = A s /bd 7. Check Beam Dimension 1 row Minimum width "b"

346

OK

8. Summary One way slab thickness Tension Steel

200 mm  12

Distribution Steel (min ratio)

8

Page 21

bars @ with As=

125 mm 904 mm2/m

bars @ with As=

200 mm 251 mm2/m

Drawings Section of designed slab with reinforcement - parallel to Lx 125 mm

12 mm

125 mm

12 mm 200 mm

8 mm

20018 mm mm 20 mm 18 mm 20 mm

8 mm 1000 mm 1000 mm

Section of designed slab with reinforcement - parallel to Ly 100 mm

8 mm

100 mm

8 mm 200 mm mm 20018 mm 20 mm 18 mm 20 mm

12 mm 12 mm 1000 mm 1000 mm

Example of a fully realised two-way slab

Page 22

4. CONTINIOUS BEAM DESIGN

3`

2

1

3

4

5

Plan of chosen beam with influence area Page 23

Minimum width "b"

300

OK

2 rows: if selected, recompute "d" Minimum width "b"

190

OK

A. Single Reinforced Beam Calculations

8.We Summary used the moment diagrams from the continuous beam analysis soft to verify our calculations. These

calculations use the various q values calculated for the beams earlier in the report, and the respective Beam dimension 300 x 500 mm lengths of said beams (l). Tension Steel Provide 4  20 bars with As=

1256 mm2

BEAM 1 Maximum bending moment and shear forces diagrams

Beam 1 q in kN/m 48.1

l in m 4.158

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value)

103.95 kNm

2. Choose steel class Steel class S… fyk γs fyd

500 500 MPa 1.15 435 MPa

3. Choose concrete class Concrete class C… fck γc fcd

25 25 MPa 1.5 17 MPa

4. Beam parameters b h c

300 mm 500 mm 50 mm

Page 24

103949896 Nmm

usually 1/2 - 2/3 h usually 1/8 - 1/12 span

B q

γc fcd

1.5 17 MPa

4. Beam parameters b h c bar diameter d

300 mm 500 mm 50 mm 20 mm 440 mm

usually 1/2 - 2/3 h usually 1/8 - 1/12 span

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 � 𝐴𝐴� �

0.072 <0.167 𝐾𝐾 1.134

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

OK

410 mm 583 mm2

0.13% 171.6 mm2

4% 5280 mm2

6. Convert reinf. area into bars Bar diameter Bar area

20 mm 314.0 mm2

Provid bars Provided area r = A s /bd

4 1256 mm2 0.95%

OK OK

7. Check Beam Dimension 1 row Minimum width "b"

300

OK

2 rows: if selected, recompute "d" Minimum width "b"

190

OK

8. Summary Beam dimension Provide Tension Steel

300 4

Page 25

x

 20 with As=

500 mm bars 1256 mm2

Provide Tension Steel

4

 20 with As=

bars 1256 mm2

BEAM 2 Maximum bending moment and shear forces diagrams

Beam 2 q in kN/m 34.5

l in m 4.603

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value)

103.95 kNm

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value) 2. Choose steel class Steel class S… fyk γs fyd 3. Choose concrete class Concrete class C… fck γc fcd 4. Beam parameters b h c bar diameter d 5. Section calculations 𝑀𝑀 𝐾𝐾 � � � 𝑏𝑏𝑏𝑏 𝑓𝑓��

2. Choose steel 91.37 class kNm Steel class S… fyk γs fyd

91371564 Nmm 500 500 MPa 1.15 435 MPa

500 500 MPa 3. Choose concrete 1.15class Concrete class C… 435 MPa fck γc fcd

25 25 MPa 1.5 17 MPa

25 25 MPa 4. Beam parameters 1.5 b 17 MPa h c bar diameter d 300 mm

300 mm 500 mm 50 mm 20 mm 440 mm

500 mm 50 mm 5. Section calculations 20 mm 440 mm𝑀𝑀 � 𝐾𝐾 � � 𝑏𝑏𝑏𝑏 𝑓𝑓�� 𝑧𝑧 � 𝑏𝑏

0.072 <0.167 𝐾𝐾 1.134 OK 𝑀𝑀

0.5 � 0.25 �

0.063 <0.167

Page 26

usually 1/2 - 2/3 h usually 1/8 - 1/12 span

𝐴𝐴� �

� �

410 mm 583 mm2

B q

usually 1/2 usually 1/8

OK

bar diameter d

20 mm 440 mm

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 � 𝐴𝐴� �

0.063 <0.167 𝐾𝐾 1.134

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

OK

414 mm 508 mm2

0.13% 171.6 mm2

4% 5280 mm2

6. Convert reinf. area into bars Bar diameter Bar area

20 mm 314.0 mm2

Provid bars Provided area r = A s /bd

4 1256 mm2 0.95%

OK OK

7. Check Beam Dimension 1 row Minimum width "b"

300

OK

2 rows: if selected, recompute "d" Minimum width "b"

190

OK

8. Summary Beam dimension Provide Tension Steel

300 4

Page 27

x

 20 with As=

500 mm bars 1256 mm2

Beam dimension Provide Tension Steel

400 6

x

600 mm bars 1884 mm2

 20 with As=

BEAM 3 Maximum bending moment and shear forces diagrams

Beam 3 q in kN/m 72.8

l in m 6.053

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value)

333.41 kNm

2. Choose steel class Steel class S… fyk γs fyd

500 500 MPa 1.15 435 MPa

3. Choose concrete class Concrete class C… fck γc fcd

25 25 MPa 1.5 17 MPa

4. Beam parameters b h c bar diameter d

400 mm 600 mm 50 mm 20 mm 510 mm

333413162 Nmm

usually 1/2 - 2/3 h usually 1/8 - 1/12 span

5. Section calculations 𝐾𝐾 �

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.128 <0.167

Page 28

OK

Be qi

bar diameter d

20 mm 510 mm

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 � 𝐴𝐴� �

0.128 <0.167 𝐾𝐾 1.134

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

OK

444 mm 1728 mm2

0.13% 265.2 mm2

4% 8160 mm2

6. Convert reinf. area into bars Bar diameter Bar area

20 mm 314.0 mm2

Provid bars Provided area r = A s /bd

6 1884 mm2 0.92%

OK OK

7. Check Beam Dimension 1 row Minimum width "b"

420

KO

2 rows: if selected, recompute "d" Minimum width "b"

260

OK

8. Summary Beam dimension Provide Tension Steel

400 6

Page 29

x

 20 with As=

600 mm bars 1884 mm2

Beam dimension Provide Tension Steel

400 6

x

600 mm bars 1884 mm2

 20 with As=

BEAM 4 Maximum bending moment and shear forces diagrams

q values calculated for the beams earlier in the report, and the respective lengths of said beams (l).

Beam 4 q in kN/m 57.8

l in m 6.6

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value)

333.41 kNm

Iteration 1 M_ED External Bending Moment Calculation 2. Choose steel class M_ED_ULS 314721000 Steel class S… 314.72 kNm 500Nmm (ql^2/8 or software value) fyk 500 MPa γs 1.15 fyd 435 MPa 2. Choose steel class Steel class S… 500 fyk 500 MPa 3. Choose concrete class γs 1.15 Concrete class C… 25 fyd 435 MPa fck 25 MPa γc 1.5 fcd 17 MPa 3. Choose concrete class Concrete class C… 25 fck 25 MPa 4. Beam parameters γc 1.5 b 400 mm fcd 17 MPa h 600 mm c 50 mm bar diameter 20 mm 4. Beam parameters d 510 mm b 400 mm usually 1/2 - 2/3 h h 600 mm usually 1/8 - 1/12 span c 50 mm 5. Section calculations bar diameter 20 mm 𝑀𝑀 d � 𝐾𝐾510 � mm� 0.128 <0.167 𝑏𝑏𝑏𝑏 𝑓𝑓�� 5. Section calculations 𝐾𝐾 �

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

𝑧𝑧 � 𝑏𝑏

0.5 � 0.25 �

0.121 <0.167 𝐴𝐴� �

Page 30

𝐾𝐾 1.134

OK 𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

444 mm

1728 mm2

Be qi

usually 1/2 usually 1/8 -

OK

bar diameter d

20 mm 510 mm

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 � 𝐴𝐴� �

0.121 <0.167 𝐾𝐾 1.134

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

OK

448 mm 1616 mm2

0.13% 265.2 mm2

4% 8160 mm2

6. Convert reinf. area into bars Bar diameter Bar area

20 mm 314.0 mm2

Provid bars Provided area r = A s /bd

6 1884 mm2 0.92%

OK OK

7. Check Beam Dimension 1 row Minimum width "b"

420

KO

2 rows: if selected, recompute "d" Minimum width "b"

260

OK

8. Summary Beam dimension Provide Tension Steel

400 6

Page 31

x

 20 with As=

600 mm bars 1884 mm2

Beam dimension Provide Tension Steel

400 6

x

600 mm bars 1884 mm2

 20 with As=

BEAM 5 Maximum bending moment and shear forces diagrams

hese calculations use the various q values calculated for the beams earlier in the report, and the respective lengths of said be

We used the moment diagrams from the continuous beam analysis soft to verify our calculations. These calculatio

Beam 5 q in kN/m 38.3

l in m 8.333

Iteration 1 M_ED External Bending Moment Calculation M_ED_ULS (ql^2/8 or software value)

Iteration 1 M_ED External Bending Moment Calculation 2. Choose steel class M_ED_ULS Steel class S… 332.44 kNm (ql^2/8 or software value) fyk γs fyd 2. Choose steel class Steel class S… 500 fyk 3. Choose concrete500 classMPa γs Concrete class C…1.15 fyd 435 MPa fck γc fcd 3. Choose concrete class Concrete class C… 25 fck 4. Beam parameters25 MPa γc 1.5 b fcd 17 MPa h c bar diameter 4. Beam parameters d b 400 mm h 600 mm c 50 mm 5. Section calculations bar diameter 20 mm 𝑀𝑀 d � 𝐾𝐾 510 � mm 𝑏𝑏𝑏𝑏� 𝑓𝑓��

5. Section calculations 𝐾𝐾 �

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

𝑧𝑧 � 𝑏𝑏

0.5 � 0.25 �

314.72 kNm

332438681 500 Nmm 500 MPa 1.15 435 MPa

25 25 MPa 1.5 17 MPa

400 mm 600 mm 50 mm 20 mm 510 mm

usually 1/2 - 2 usually 1/8 - 1

usually 1/2 - 2/3 h usually 1/8 - 1/12 span

0.121 <0.167 𝐾𝐾 1.134

0.128 <0.167 OK 𝑀𝑀 � 𝐴𝐴� � 0.87 𝑓𝑓�� 𝑧𝑧

Page 32

Be qi

�

448 mm 1616 mm2

OK

bar diameter d

20 mm 510 mm

5. Section calculations 𝐾𝐾 � 𝑧𝑧 � 𝑏𝑏

𝑀𝑀 � 𝑏𝑏𝑏𝑏� 𝑓𝑓��

0.5 � 0.25 � 𝐴𝐴� �

0.128 <0.167 𝐾𝐾 1.134

𝑀𝑀 � 0.87 𝑓𝑓�� 𝑧𝑧

�

Check minimum and maximum reinforcement 𝜌𝜌��� � 𝜌𝜌 � 𝜌𝜌��� ,

OK

444 mm 1722 mm2

0.13% 265.2 mm2

4% 8160 mm2

6. Convert reinf. area into bars Bar diameter Bar area

20 mm 314.0 mm2

Provid bars Provided area r = A s /bd

6 1884 mm2 0.92%

OK OK

7. Check Beam Dimension 1 row Minimum width "b"

420

KO

2 rows: if selected, recompute "d" Minimum width "b"

260

OK

8. Summary Beam dimension Provide Tension Steel

400 6

Page 33

x

 20 with As=

600 mm bars 1884 mm2

Section of designed beam with reinforcement - Beam type 1

42 mm 42 mm

500 mm

78 mm

78 mm

20 mm

300 mm Section of designed beam with reinforcement - Beam type 2

42 mm

8 mm

42 mm

600 mm

78 mm

78 mm

20 mm

400 mm Page 34

Arrangement of the reinforcement - Beam type 1

Arrangement of the reinforcement - Beam type 2

Page 35

5. COLUMN DESIGN

Plan of chosen column with influence area Page 36

Calculations For the pillar calculation we chose to calculate the general axial force for the middle column (square column), the axial force applied to the roof and calculated for the middle column (square column) and the axial force for the roof calculated for the shear wall.

Pillar calculation - Square column

1. Obtain N_ED Axial force N_ED

3042 kN

3042000 N

2. Choose Pillar cross section dimensions B (width) x height H Pillar width H Pillar height H

0.5 m 0.5 m

3. Insert Concrete Class Concrete class Concrete fck αc γc Concrete fcd

35 35 MPa 0.85 1.5 19.8 MPa

500 mm 500 mm

45

4. Calculate Concrete Area Ac Required minimal Ac suggested edge dimension (for ratio 45%)

340,840 mm2 584 mm

5. Select Concrete Area Ac Dimensions a, b Choosen area

500 500 mm 250,000 mm2

6. Check that capacity NRd > demand NEd N_Ed N_RD 7. Calculate As Choose bar diameter Φ As (1.5% of concrete area Ac) Calculate Nbars

3042 kN 4958 kN

18 mm 3750 mm2 15

Note: Minimum number of bars 4

Page 37

check OK current ratio 61% suggested ratio 45% - 65%

Section of designed column with reinforcement

78 mm

42 mm

18 mm

42 mm

78 mm 500 mm

500 mm Arrangement of the reinforcement in the column

78

mm

8 mm

70 mm

50

0m

m

m

0m

50

Page 38

7. LOAD ANALYSIS - TESTING

Page 39

B. Specific Case Testing ITERATION 1(Initial Test) - Steel Cantilever Tested structural elements: Column type 1 - Reinforced concrete, round, 450mm Column type 2 - Reinforced concrete, square, 450x450mm Column type 3 - Reinforced concrete shear wall, rectangular, 450x450mm Floor slabs - Reinforced concrete, 500mm Beams - Steel, HEA 300x300mm Truss Beams - Steel, 190x200mm Cantilever Beams - Steel, 490x300mm Cantilever Columns- Steel, 490x300mm Evaluation The purpose of testing out 2 different iterations has been to asses potential of steel and concrete for the proposed cantilever solution. In both cases we made a model, input structural elements dimensions and load values in order to run the following simulations: self-weight analysis, beam deformation, dead load deformation and live load deformation.

For the first iteration where steel was tested and the Vierendeel cantilever was designed to have supports at the corners, the results were not satisfactory for beam stress deformation and dead load deformation, whereas the self-weight test and live load deformation maximum deflection points have not gone over 10mm deflection. midas Gen

Self-weight analysis

POST-PROCESSOR DISPLACEMENT

midas Gen

POST-PROCESSOR RESULTANT DISPLACEMENT 1.15121e+01 1.04655e+01 RESULTANT

9.41899e+00 1.15121e+01 8.37244e+00 1.04655e+01 7.32588e+00 9.41899e+00 6.27933e+00 8.37244e+00 5.23277e+00 7.32588e+00 4.18622e+00 6.27933e+00

3.13966e+00 5.23277e+00 2.09311e+00 4.18622e+00 1.04655e+00 3.13966e+00 0.00000e+00 2.09311e+00 SCALEFACTOR= 1.04655e+00 ST: DL

1.9644E+02 0.00000e+00

MAX : SCALEFACTOR= 151 1.9644E+02 MIN : 56 ST: DL FILE: 4_7_2022 UNIT: MAX mm : 151 : 56 DATE: MIN 07/04/2022 VIEW-DIRECTION FILE: 4_7_2022 X:-0.612 UNIT: mm DATE: 07/04/2022 Y:-0.612

VIEW-DIRECTION Z: 0.500 X:-0.612 Y:-0.612 Z: 0.500 Page 40

Beam Stress

Dead Load Deformation

Live Load Deformation

Page 41

ITERATION 2 (Solution)- Concrete Cantilever Tested structural elements: Column type 1 - Reinforced concrete, round, 450mm Column type 2 - Reinforced concrete, square, 450x450mm Column type 3 - Reinforced concrete shear wall, rectangular, 450x450mm Floor slabs - Reinforced concrete, 500mm Beams - Reinforced concrete 300x300mm Truss Beams - Steel, 190x200mm Cantilever Beams - Reinforced concrete 600x400mm Cantilever Columns - Reinforced concrete 490x300mm Evaluation For the second iteration the material changed to concrete, with slight increase in dimensions for the elements belonging to the cantilever system. Compared to the first iteration, here we simply the cantilever system by removing the supports at the joints. The same tests apply here as well: self-weight analysis, beam stress deformation, dead load deformation and live load deformation.

midas Gen

Self-weight analysis

POST-PROCESSOR DISPLACEMENT RESULTANT 1.29220e+01 1.17473e+01 1.05726e+01 9.39783e+00 8.22310e+00 7.04837e+00 5.87364e+00 4.69891e+00 3.52418e+00 2.34946e+00 1.17473e+00 0.00000e+00 SCALEFACTOR= ST: DL

1.7501E+02

MAX : 41 MIN : 56

midas G

POST-PROCE DISPLACEM

RESULTA

1.2922 1.1747 1.0572 9.3978 8.2231 7.0483 5.8736 4.6989 3.5241 2.3494 1.1747 0.0000

SCALEFACTOR= ST: DL

1.750

MAX : 41 MIN : 56 FILE: 6_7_22 FILE: 6_7_22 UNIT: mm DATE: 07/16/2022 UNIT: mm DATE: 07/16/ VIEW-DIRECTION VIEW-DIREC X:-0.612 X:-0.612 Y:-0.612 Y:-0.612 Z: 0.500 Z: 0.500 Page 42

midas Gen

Beam Stress

POST-PROCESSOR midas Gen

BEAM STRESS POST-PROCESSOR COMBINED BEAM STRESS

6.04759e-02 4.89901e-02 6.04759e-02 3.75043e-02 2.60185e-02 4.89901e-02 1.45327e-02 3.75043e-02 0.00000e+00 2.60185e-02 -8.43891e-03 1.45327e-02 -1.99247e-02 0.00000e+00 -3.14105e-02 -8.43891e-03 -4.28963e-02 -5.43821e-02 -1.99247e-02 -6.58679e-02 -3.14105e-02

COMBINED

SCALEFACTOR= -4.28963e-02 2.7762E+01 -5.43821e-02 CB: LCB1 -6.58679e-02 MAX : 57

MIN : 81 SCALEFACTOR=

FILE: 6_7_22

2.7762E+01 UNIT: kN/mm^2 CB: LCB1

DATE: 07/16/2022

VIEW-DIRECTION MAX : 57 MIN : X:-0.612 81

FILE: Y:-0.612 6_7_22 UNIT: Z:kN/mm^2 0.500 DATE: 07/16/2022 VIEW-DIRECTION X:-0.612

Dead Load Deformation

Y:-0.612 Z: 0.500

Live Load Deformation

Page 43

6. CASE STUDY

Image of the built work with colours that identify the deformations analyzed

Page 44

Vierendeel House ARCHITECTURE - Patricio Llordella, Juan Fostel STRUCTURAL ENGINEERING - Jorge Farez LOCATION - Hudson, Argentina STATUS - in construction, 2018 Content: The parametric modeling of the house was carried out to create an editable volume of all its elements allowing the study of the combination of the structural and architectural parameters. In this way the possibilities, advantages and disadvantages of each proposal are evaluated in real-time. The structural design is achieved through an interdisciplinary interplay between the architecture and the structure, obtaining the desired aesthetic and functional results for the house without compromising the stability.

•Main features: cantilever and use of concrete •Main structural characteristic: cantilevered structural system •Comparison with designed project: using the cantilevered main characteristic of the house and implement it as reinforcement for the auditorium, canteen and gym areas.

•Source: https://www.karamba3d.com/project/vierendeel-house/

Removal of Formwork not affected by the Vierendeel; Removal of Formwork below the Vierendeel

Tension diagram from Karamba3d are collated with the reinforcement indicated by the software Page 45

8. STRUCTURAL DRAWINGS

Warner truss solution for Auditorium

Page 46

Structural drawings Structural References - Warren Steel Struss

Structural Sketches

Page 47

Bibliography 1. Eurocode, ``Table of design material properties for structural steel``, EurocodeApplied.com. Accessed June 13 ,2022. https://eurocodeapplied.com/design/en1993/steel-design-properties 2. The Engineering TooldBox, `` Young’s Modulus, Tensile Strength and Yield Strength Values for some Materials``, www. TheEngineeringTooldBox.com. June 13, 2022. https://www.engineeringtoolbox. com/young-modulus-d_417.html 3. Indiana Government, `` MATERIAL PROPERTIES OF CONCRETE``, www.in.gov.com. Accessed June 13 ,2022. https://www.in.gov/dot/div/contracts/standards/dm-Archived/09Metric/Part6/Ch62/figures/ Fig62-1A.pdf 4. Eurocode, ``Table of concrete design properties``, EurocodeApplied.com. Accessed June 13 ,2022. https://eurocodeapplied.com/design/en1992/concrete-design-properties 5. Greyspace Engineering Services, ’’ What is two way slab || Solid slab reinforcement details || Two-Way Slab Animation’’, www.greyspace-es.com/blogs. Accessed July 15, 2022. https://www.youtube.com/ watch?v=A7LGJGayL8E&ab_channel=GreyspaceEngineeringServices

Page 48