Ice Hockey Arena Milano-Cortina 2026 Winter Olympics Thesis [Section 7] by Elio Nassar

262

STRUCTURES

263

264

265 SUMMARY 1) STRUCTURAL COMPOSITION 2 66 2) VERIFICATIONS 289 2.2) TYPICAL SLAB STRUCTURES VERIFICATIONS 293 2.3) TYPICAL OPAQUE ROOF STRUCTURES 3 01 2.4) TRANSLUCENT ROOF STRUCTURES VERIFICATIONS 3 12 2.5) COLUMN STRUCTURES VERIFICATIONS 3 16 2.6) TENSION ROOF STRUCTURES VERIFICATIONS 3 22

1) STRUCTURAL COMPOSITION

1.1) REFERENCES FOR STRUCTURES

The structure settings of our building are a complex system that took reference from existing technologies to achieve static goals by simple, yet high-performing solutions. The outer rings of our layout are assembled with the same geometrical layout of typical alpine architecture, which uses a yuxtapsition of beams to end up distributing the snow heavy loads evenly through the element’s structural jerarchy. In this way, we used steel beams with the same philosophy of the wooden composition of this “chalets“, achieving high staticity, performance and lightness. The wooden planks that terminate the roof, in our case, are substituted by a technological compound called sandwich pannel, which uses two- sided steel laminates to cover a thick layer of rigid insulation. In this way we can, together with a density of tertiary beams , apply both rigidity to our roof and high-performing insulation coincidently. The arena, in the other hand, uses a complex steel roof that assembles a light upper series of beams with highly tensile resistant pre-tensioned cables lower body. This connection is made possible by connecting steel column thrusses entitled exclusively to bear compression. In order to understand this system, it was necessary to understand various similar systems, such as the Madison Square Garden and the wheel of a bike.

266

Figure 98. Typical alpine architecture Figure 99. Madison Square Garden under construction. New York City, USA. Year 1966. Figure 100. Cross-section of a modern bike wheel.

1.2) VERTICAL ELEMENTS

The structural grid is composed in all intersections by vertical elemtents is reinforced concrete. There is precense of stiffening elements along the grid such as bearing walls and distribution cores in strategic areas. These elements are jerarchically dimensioned and serve the sole purpose of transfer the loads from the horizontal structures All vertical elemnts are perpendicular to the ground as shown in the plans.

1.2.1) COLUMNS

The columns of our project are of two different diameters: 600mm and 800mm, and made of reinforced concrete.. The thickest one is to support the tensile structure roof and part of the translucent roof over the perimetral gallery ring, tgether with the two floors of the arena, where the entrances to the seating sections and the VIP section are.

The Selected one of 600mm is used on all spaces outside of the arena’s perimeter to be loaded by one floor and the outer opaque roof.

1.3) HORIZONTAL ELEMENTS

The horizontal and low-pitch inclinated rof elements are sustained mainly by bending (beams). In the case of the floors, a steel deck that combines corrugated steel with reinforced concrete is layed on top of beams spanning around 2m, letting a better load distribution. These beams, primary and secondary over all floors above the 0 level. These will be under the dead loads of a steel deck, nonstructural elements and live loads. As for roof beams The same principle is followed, although, it

267

D=800mm D=600mm

differs by an addition of terciary beams to turn by 90 degrees the lad flws on the composite pannel. This pannel is composed by an insulated inlay covered by steel sheet, making it structural.

268

RHS 100x180/5 RHS 150x250/10 RHS 300x500/165 HE550-A Floor slabs Opaque and transparent roof slabs 1:20

1.4) TENSION ROOF

The design of the tension roof is a complex set up of intersected beams bounded by an eliptical shape, from which is present a higly resistant compression beam to prevent as much as possible horizontal deformations.

These points of intersection will be a node composed by the hinge of the upper compression beams, the cable under tension loads of the structure plus pretension forces applied to diminish vertical deformation, and the pillars to sustain in height the whole system.

Compression arches in catenary tridimensional elipsoidal composition composition

Moment connection: All DOF fixed

Compression struts

Hinge connection: Rotation DOF Released

Pre-tensioned cables

HInge connection: Rotation DOF Released

Round cross section pre-cast R.C. pillars

Very first sketch of tension roof design.

269

94 118

GRASSHOPPER STEP-BY-STEP ROOF CODING: 1-4

1.4.1) TENSION ROOF GEMETRY GENERATION

GRASSHOPPER STEP-BY-STEP ROOF CODING: 1-4

Selection of nodes for connecting beams

LOD 300

Orthogonal composition of primary structure

LOD 300

270

Definition of the elipse

Equal subdivision of nodes

STEP-BY-STEP ROOF CODING: 6-10

GRASSHOPPER STEP-BY-STEP ROOF CODING: 6-10

STEP-BY-STEP ROOF CODING: 6-10

GRASSHOPPER STEP-BY-STEP ROOF CODING: 6-10

LOD 300

271

Adaptation in plan from spherical cap to elipsoidal cap Production of 4.5m sag catenary line Projection of primary structure to elipsoidal cap geometry Creation of spherical cap assembling geometry of catenary beam

GRASSHOPPER STEP-BY-STEP ROOF CODING:

272

Mirroring of catenary geometry. 9m max height. Primary structure, vertical struts and nodes definition.

Modification of surfaces t “Pillows“ assembling ETFE facade design

OPTIONS

273 CODING: 10-13 LOD 300

GRASSHOPPER STEP-BY-STEP ROOF CODING: 14.1 AND 14.2 Definition of skin in plane surrface NURBS

274

Perspective view of roof “disc“ together with addition of secondary structure and compression perimetral beam.

275

Top view of roof

An essential part of the primary structure are the cable diameter dimensioning, which will sustain high tension loads in order to prevent the high deformation of the building under self-weight, and the resistance of the structure under high level of live loads such as snow loads, which can be potentially challenging for the structure if not well dimensioned.

276

TENSION ROOF STRUCTURE ASSEMBLAGE

Facade

Double ETFE membranes and alluminium frames..

Top air ducts alluminium containers

Air ducts

Bottom air ducts alluminum container

Preliminary beam type SHS 200 / 10

Tension structure grid with ETFE membrane modular covering.

Thrust-guidance trusses. Cross-section type to be determined

Compression trusses.

Pre-tensioned cables in “x“ direction

Pre-tensioned cables in “y“ direction

Reinforced concrete columns supporting ring. Diameter: 80cm

277

Primary structure

Secondary structure

278

1.4.2) ROOF TENSILE ELEMENTS APPLICATION AND STRUCTURAL PRINCIPLE - SIMPLIFIED SCHEMES

The study of this solution is approached with a simply supported beam under an uniformly distributed load.

The following procedure will consist on understanding whether right half of symmetric structure has an outgoing (positive) or ingoing forces (negative). It is always considered that our structure is symmetric and is in every case over-ruled by Newton’s law of motion’s equilibrium condition:

279 x y +

��

�� >0 �� <0 �� ′ �� − �� ′ �� =+ �� ′ �� ↓

Free body diagrams for analogy between simply supported beam (above) and tension beam design (below)

Under structure’s self-weight and eventual applied forces, the response of the compressive forces may be in this case of higher impact on the boundaries, In the algebraic sum of these forces, being summarized between compression and tension resultants, the product might be a positive vector:

This reaction forces in the boundary, which allows horizontal translation, might result in elevated levels of deformation.

280 x y + x y + NO PRE-TENSION | HIGH DEFORMATION

�� =0 �� >0 �� <0 �� ′ �� − �� ′ �� =+ �� ′ �� ↓ ��≫ 0 ��′�� ′ �� ′ �� = ��′�� ,�� ↓ �� ≈ 0

On the other hand, applying and calibrating an acceptable level of pre-tension to the cables in both boundaries of the beam, the deformation will be reduced by the vertical inertia on the supports of the strut vertical structures., which connect the upper compression beams and the cables.

This reaction forces in the right boundary, in this case negative, will maintain the level of deformation near to zero. This operation is dependent of a very resistant to compression boundary restraint.

281 x y +

PRE-TENSION | LOW DEFORMATION

�� =0 �� >0 �� <0 �� ′ �� ′ �� =+ �� ′ �� ↓ ��≫ 0 ��′�� − �� ′ �� − �� ′ �� = − ��′�� ,�� ↓ �� ≈ 0

1.5) OVERALL COMPOSITION

Tension structure grid with ETFE membrane modular covering.

Tempered Glass panels attached to non-structural mullions.

Secondary and terciary steel beams type RHS 250x150 / 10 supporting glass mullions

Perforated steel sheet pannels facade.

Facade pannels anchorage

Sandwich corrugated steel double-layer pannels

Terciary steel beams type RHS 180x100 / 5.

Primary and Secondary steel beams type RHS 500x300 / 16.

Primary steel beams type RHS 500x300 / 16.

Opaque roof hanging ceiling. Reinforced concrete upper seating grades with seatings attached laterally

Reinforced concrete “fingers“ (Beams).

Reinforced concrete columns (D = 800mm).

Reinforced concrete columns (d=600mm)

282

axonometry

Exploded

Primary structure

Terciary structure

283

Secondary structurestructure

Detailed layout spotlighting vertical and roof structures General layout spotlighting vertical and roof structures

General layout spotlighting hrizontal, diagonal and vertical structures exclusively in the arena area

284

285

Primary, secondary and terciary beams loading a column out of the arena’s perimeter.

286

Primary, secondary and terciary beams loading a column out of the arena’s perimeter.

287

Primary and secondary beams loading a 800mm column in the arena’s perimeter.

288

Series of primary and secondary beams loading tension roof’s perimetral compression beam.

2) VERIFICATIONS

2.1) LIVE LOADS

2.1.1) SNOW LOADS

We have calculated snow loads for our two geometrically different roofs: The one composed by the tension structure and the one with a pitch on the N-S axis of 8.9º and in the W-E axis of 10.95º. In the following tables it is possible to fins the values:

289 Source Specification Classification Symbol ValueUnit Google Earth Altitude from sea levelItaly: Milan: Santa Giulia A 108m Figure C.2 Z3Annex C:Table C.1 Altitude - Snow Load Relationships Alpine Region: [0.642Z+0.009][1+A/728²] Sk 1.98kN/m² 5.3.2 Snow load shape coefficien: Monopitch roofs-no parapet (5.5) 0º ≤ α ≤ 30º: α=8.9 ÷ 10.95 μ1 0.85.2: Table 5.1 Expousure coefficientWindswept Ce 0.85.2 (8) Ct 15.2: (3): (a) Snow load on the roofS = μ3 Sk Ce Ct S 1.3 kN/m² Source Specification Classification Symbol ValueUnit Google Earth Altitude from sea levelItaly: Milan: Santa Giulia A 108m Figure C.2 Z3Annex C:Table C.1 Altitude - Snow Load Relationships Alpine Region: [0.642Z+0.009][1+A/728²] Sk 1.98kN/m² 5.3.5 (1) Snow load shape coefficient: Cylindrical Roofs; no fences (5.5) 0.2+10h/b; h=4.5; b=91.5 μ3 0.6925.2: Table 5.1 Expousure coefficientWindswept Ce 0.85.2 (8) Ct 15.2: (3): (a) Snow load on the roofS = μ3 Sk Ce Ct S 1.1 kN/m² EN 1991-1-3 (2003):

Alpine Region Thermal coefficient Snow loads:

EN 1991-1-3 (2003):

on structures

Alpine Region Thermal coefficient Snow loads:

Actions on structures - Part 1-3: General actions

functions roof and glass roof

Actions

- Part 1-3: General actions

ETFE

Although the values differ of 0.2kN/m², we are going to use 1.3kN/m² values for our snow loads values in our location.

2.1.2) EUROCODE IMPOSED LOADINGS FOR SLABS

For our building typology, of which very occasionally we will be in presence of large crowds of spectators, we have decided to use the Category C5 of the Eurocode 1, Table 6.2. In the table 6.1 this category is defined as “Areas susceptible to large crowds, e.g., in buildings for public events like concert halls, sports halls including stands, terraces and access areas and railway platforms.

290

Figure 101. Eurocode 0: Snow loads map for the alpine region.

In our verifications Q1=5kN/m2

2.1.3) EUROCODE IMPOSED LOADINGS FOR ROOFS

The project’s roofs of all types will possibly be subjected to maintenance by a limited number of operators. We are then applying the recommended values of the Table 6.10 of Eurocode 1 of 0.4 kN/m2.

In our verifications Q2=0.4kN/m2

291

Figure 102. Eurocode 1: Table 6.2- Imposed loads on floors, balconies and stairs in buildings

292

Figure 103. Eurocode 1: Table 6.10 - Imposed loads on roofs of category H Figure 104. Eurocode 1: Table 6.9 - Categorization of roofs

2.2) TYPICAL SLAB STRUCTURES VERIFICATIONS

293

Typical slab contribution area (Scale 1:250)

2.2.1) LOAD COMBINATIONS AND DIMENSIONING

Project's TYPICAL SLAB loads

We can observe from the drawings that we have between secondary beams a span of 2.07m. Considering this, together with the ULS design area load of 8.7kN/m2, we verify the slab’s resistance from the producer.

294

Thickness Specific weight Linear load m kN/m³ kN/m Epoxi FinishingMapefloor I 900 - -Screed Tarmac 110/01 0.05 12.0Membrane MAPELASTIC AQUADEFENSEHorizontal structureComposite slab 0.1 -Hanging ceiling THERMATEX® SF Acoustic Dn,f,w = 38 dBPrimary and secondary beam HE550A - - 1.66 1.66 EN 1991-1-1:2002 Serviciability Limit StateTable A2.6 Secondary Primary 2 6.9 Area loadLinear loadLinear load kN/m²kN/mkN/m Serviciability Limit StateTable A2.6 8.318.358.9 γGj=1.35; γQi=1.50 Gj + Q1 + SW Load combinations for beams under one-way elements Horizontal slab's longest contribution span [m] Combination EN 1991-1-1:2002 Ultimate Limit StateTable A1.2 (B) (STR) γGjG1 + γQ1Q1 1226.284.7 Gj + Q1 5.9 Q1 5 Load combinations for composite slab Combination EN 1991-1-1:2002 Area load kN/m² Ultimate Limit StateTable A1.2 (B) (STR) γGjG1 + γQ1Q1 8.7 γGj=1.35; γQi=1.50 0.5-Table 6.2: Category C5: congregation areas G1 3.3 0.6 1.9 0.3 HVAC Live Loads Eurocode reference Area load kN/m² 5

Dead Loads Layer Product Name Area load kN/m²

TIPO A 55/P 600

HI-BOND

TYPE A 55/P 600

Caratteristiche della lamiera - Properties of the trapezoidal sheets

Peso - Weight

Sovraccarico utile uniformemente distribuito KN/m2 - Useful overload evenly distribuited KN/m2 Surcharge utile uniformement repartie KN/m2 - Nutzlast gleichmassig verteilt KN/m2

I valori in colore non prevedono limitazione di freccia f < l/240 (1a fase) - Values indicated in color are calculated without deflection limitation f < l/240 (1st phase) - Les valeurs emprimées en couleur sont sans limitation de flèche f < l/240 (1ère phase) - Die in Farbe angegebenen Werte sehen keine Begrezung der Durchbiegung vor f < l/240 (1. phase).

295 16 Ws Compressione inf. - Bottom compression Wi Wc cm /m cm3/m cm3/m 14,52 16,75 18,04 17,63 20,46 21,02 24,34 28,41 27,04 31,50 36,72 33,07

statiche

slab

Caracteristiques statiques

la dalleStatische eingenschaften der decke 600 55 1000 y h H X1 XS T Kg/m Wi cm3/m Ws cm3/m J tot. cm4/m Xs cm H cm Spessore lamiera- Sheet thickness Epaisseur de la tôle - Blechstärke mm Peso soletta - Slab weight Poids de la dalle - Gewicht der Decke kg/m2 10 190 1130 11 215 1250 12 240 1360 13 265 1460 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 51,57 58,31 71,38 83,90 59,85 67,70 82,93 97,51 68,50 77,53 95,08 111,88 77,43 87,71 107,69 126,84 1368,98 1435,63 1550,71 1648,72 1624,49 1701,96 1834,79 1946,55 1905,23 1995,33 2149,20 2277,62 2209,28 2313,67 2491,55 2639,26 329,49 362,35 422,25 475,79 424,00 466,42 543,66 612,43 533,98 587,80 685,83 773,00 659,76 726,89 849,32 958,20 3,61 3,79 4,08 4,33 3,92 4,11 4,44 4,72 4,20 4,42 4,79 5,09 4,48 4,71 5,11 5,45 16

Caratteristiche

della soletta - Properties of the

HI-BOND

Caracteristiques du profil - Blecheigenschaften 150 55 680 88,5 61,5 88,5 61,5 600 150 Spessore - Thickness - Epaisseur - Stärke mm 1,20 1,00 0,80 0,70

- Poids - Gewicht Peso - Weight - Poids - Gewicht J totale - total yi Area tot. Compressione sup. - Top compression Jf Wi Ws Compressione inf. - Bottom compression Wi Wc kg/m kg/m2 cm4/m cm cm2/m cm4/m cm3/m cm3/m cm3/m cm3/m 5,50 9,16 53,32 2,44 11,0 47,42 20,70 14,52 16,75 18,04 6,28 10,47 61,44 2,44 12,66 56,57 24,12 17,63 20,46 21,02 7,85 13,08 77,56 2,44 16,00 75,84 31,05 24,34 28,41 27,04 9,42 15,70 93,72 2,44 19,33 93,72 38,05 31,50 36,72 33,07 Caratteristiche statiche della soletta - Properties of the slab - Caracteristiques statiques de la dalleStatische eingenschaften der decke 600 55 1000 y h H X1 XS T Kg/m Wi cm3/m Ws cm3/m J tot. cm4/m Xs cm H cm Spessore lamiera- Sheet thickness Epaisseur de la tôle - Blechstärke mm Peso soletta - Slab weight Poids de la dalle - Gewicht der Decke kg/m2 10 190 1130 11 215 1250 12 240 1360 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 51,57 58,31 71,38 83,90 59,85 67,70 82,93 97,51 68,50 77,53 95,08 111,88 1368,98 1435,63 1550,71 1648,72 1624,49 1701,96 1834,79 1946,55 1905,23 1995,33 2149,20 2277,62 329,49 362,35 422,25 475,79 424,00 466,42 543,66 612,43 533,98 587,80 685,83 773,00 3,61 3,79 4,08 4,33 3,92 4,11 4,44 4,72 4,20 4,42 4,79 5,09 17 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 4,294,144,013,893,783,673,533,413,303,21 3,042,912,502,08 3,093,022,942,872,812,752,702,642,592,552,462,38 2,242,13 3,333,253,173,093,022,962,892,842,782,732,642,55 2,402,27 3,773,663,573,483,403,333,253,193,133,072,962,86 2,692,27 4,154,043,933,833,743,653,573,503,433,363,243,13 2,722,27 2,992,932,872,812,762,712,662,622,582,532,462,39 2,272,16 3,223,153,093,032,912,912,862,812,772,722,642,56 2,432,31 3,653,563,493,413,353,283,223,163,113,062,962,882,72 2,43 4,033,933,843,763,683,613,543,483,423,363,253,152,92 2,43 12 13 mm H Soletta Slab Dalle Decke mm Spessore Thickness Epaisseur Stärke 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 0,70 0,80 1,00 1,20 3,593,433,293,173,06 2,962,872,782,712,642,512,402,221,88 3,863,683,533,403,28 3,173,072,982,902,822,692,572,261,88 4,344,143,963,813,67 3,553,433,333,243,153,002,832,261,88 4,784,554,354,184,023,88 3,763,643,543,443,232,832,261,88 3,493,373,253,153,052,97 2,892,812,752,682,572,472,301,88 3,763,623,493,383,283,183,10 3,022,942,872,752,642,452,08 4,244,073,933,803,683,573,47 3,383,293,213,072,952,502,08 4,674,484,324,174,033,913,803,70 3,603,523,363,132,502,08 3,393,293,203,113,032,962,892,82 2,762,712,602,512,352,22 3,653,543,443,343,253,173,103,03 2,962,902,792,692,522,27 4,123,993,873,763,663,563,483,403,32 3,253,123,012,722,27 4,554,404,264,134,023,913,823,723,643,56 3,423,292,722,27 3,293,213,133,062,992,932,872,812,76 2,712,622,532,392,26 3,553,453,373,293,213,143,083,022,962,91 2,812,712,562,42 4,013,903,803,713,623,543,463,393,333,26 3,153,042,862,43 4,424,304,184,083,983,893,803,723,653,583,45 3,332,922,43 1,502,002,503,003,504,004,505,005,506,007,008,0010,0012,00

10 11 12 13 l l l p p p

METECNO

HI-BOND

S.p.A. Catalog extract- Composite slab

TYPE A 55/P 600

Epoxi finishing

Screed 50mm

Composite slab

HE550A primary/secondary beam

False ceiling

296

Typical slab detail. Scale 1:20

2.2.2) SIMPLY SUPPORTED BEAMS UNDER UNIFORMLY DISTRIBUTED LOAD VERIFICATION

The calculation is carried out using free body diagrams with boundary conditions coherent with simply supported beams. Even though the connections of our construction are fixed, this procedure lets us understand and verify either way the resistance and deformation of the beams under UDL.

2.2.2.1) SECONDARY BEAM BENDING MOMENTS

T Y P I C A L S L AB

2 r y b e a m

��/�� × 12.5��2

B e n d i n g m o m e n t s

B e n d i n g m o m e n t s �� =

2 r y b e a m

B e n d i n g m o m e n t s

�� = ��2 8 = 26.2��/�� × 12.5��2 8 =

SHEAR FORCES

�� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8��

S h e ar f o r c e s

S h e ar f o r c e s ��1 = −��2 =±

��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4��

S h e ar f o r c e s

R e a c t i o n f o r c e s

��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5��

R e a c t i o n f o r c e s

��1,2 = ��1,2 � = 168.4��

REACTION FORCES

��1,2 = ��1,2 � = 168.4��

R e a c t i o n f o r c e s

��1,2 = ��1,2 � = 168.4��

U L S S t r e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y - y )

U L S S t r e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y - y ) C o n d i t i o n s f o r U l t i m a t e L im i t S t at e

U L S S t r e n g t h d e s i g n : B e a m

s b e n d i n g m o m e nt r e s i s t

C o n d i t i o n s f o r U l t i m a t e L im i t S t at e ��

y )

297 1 2 L ULS 1 L 2 SLS 1 2 L ULS 1 2 L ULS T Y P I C A L S L

AB 2 r y b e a m

��2 8

26.2

8 = 510.8��

��

2 =±163.4

2 =± 26.2��⁄�� × 12.5��

��

��,�� = ��

��,�� > �� = 4620 ��3 B d i i t h k

×1.05

510.8��

,�� =

��,�� > ��

�� ×1.05

= 4620 ��3

2 =±163.4��

a n

C o n d i t i o n s f o r U l t i m a t e L im i t S t at e ��

TYPICAL SLAB 2ry beam Bending moments �� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8�� Shear forces ��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4�� Reaction forces ��1 2 = ��1 2� = 168.4�� ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4620 ��3 Bending resistance check �� = 510.8�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 �� SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 50�� TYPICAL SLAB 2ry beam Bending moments �� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8�� Shear forces ��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4�� Reaction forces ��1 2 = ��1 2� = 168.4�� ULS Strength design: Beam s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4620 ��3 Bending resistance check �� = 510.8�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 �� SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 50�� TYPICAL SLAB 2ry beam Bending moments �� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8�� Shear forces ��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4�� Reaction forces ��1 2 = ��1 2� = 168.4�� ULS Strength design: Beam s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4620 ��3 Bending resistance check �� = 510.8�� ,�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 ��

’

c e ( y -

×1.05

MATERIAL AND CROSS-SECTION DESIGN

Material and cross-section design

Y P I C A L S L AB

B e n d i n g m o m e n t s

2 r y b e a m

B e n d i n g m o m e n t s

�� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8��

S h e ar f o r c e s

��

S h e ar f o r c e s

R e a c t i o n f o r c e s

��1,2 = ��1,2 � = 168.4��

R e a c t i o n f o r c e s

R e a

��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4��

t i o n f o r c e s

��1,2 = ��1,2 � = 168.4��

U L S S t r e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y - y )

ULS STRENGTH DESIGN: BEAM’S BENDING MOMENT RESISTANCE (Y-Y)

ULS Strength design: Beam’s bending moment resistance (y-y)

C o n d i t i o n s f o r U l t i m a t e L im i t S t at e

e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y - y )

ULS Strength design: Beam’s bending moment resistance (y-y)

C o n d i t i o n s f o r U l t i m a t

U L S S t r e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y - y )

C o n d i t i o n s f o r U l t i m a t e L im i t S t at e

Conditions for Ultimate Limit State

C o n d i t i o n s f o r U l t i m a t e L im i t S t at e

B e n d i n g r e s is t a n c e c h e ck

CONDITIONS FOR ULS BENDING RESISTANCE

B e n d i n g r e s is t a n c e c h e ck

�� × 103 ×1.05

SLS DESIGN: BEAM DEFORMATION

S L S d e s i g n : B e a m d e f l e c t i o n

C o n d i t i o n f o r S e r v i c e a b i l i t y L i m i t S t a t e

S L S d e s i g n : B e a m d e f l e c t i o n

SLS design: Beam deflection

S L S d e s i g n : B e a m d e f l e c t i o n

C o n d i t i o n f o r S e r v i c e a b i l i t y L i m i t S t a t e

Condition for Serviceability Limit State

298

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section:

Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3

HE 550A

��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 Bending resistance check �� = 510.8�� ,�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 √

�� = 5��4 384�� (@0.5��) < �� 250 = 50��

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section:

Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3

HE 550A

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 Bending resistance check �� = 510.8�� ,�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 50�� T Y P I C A L S L AB 2 r y b e a m B e n d i n g m o m e n t s �� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8�� S h e ar f o r c e s ��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4�� R e a c t i o n f o r c e s ��1,2 = ��1,2 � = 168.4�� U L S S t r

��,�� = �� ×1.05 ��,�� > �� = 4620 ��3

��

510.8�� ,�� = 510.8��

235 ��2 ⁄ = 2282��3

4620 ��3 ��

× 103 ×1.05

�� = 5��4 384�� (@0.5��) < �� 250 = 50�� D f l t i h k

��

> ��

��3

,�� =

×1.05

,��

= 4620

235 ��2 ⁄

2282��3 < 4620 ��3 ��

�� = 510.8�� ,�� = 510.8

�� = 5��4 384�� (@0.5��) < �� 250 = 50�� T Y P I C A L S L AB 2

r y b e a m

�� = ��2 8 = 26.2��/��

12.5��2 8 = 510.8��

��1 = −��2 =± �� 2 =± 26.2��⁄�� ×

�� 2 =±163.4

12.5

,�� = �� ×1.05 ��,�� > �� = 4620 ��3

��

�� = 510.8�� ,�� = 510.8��

235 ��2 ⁄ = 2282��3 < 4620 ��3 ��

× 103 ×1.05

�� = 5��4 384�� (@0.5��) < �� 250 = 50�� D e f l e ct i o n c he c k 5× 18.3 ��⁄�� ×(12.54 ��) 5× 18.3 �� ⁄ × (125004 ��) T Y P I C A L S L AB 2 r y b e a m B e n

n t s �� = ��2 8 = 26.2��/�� × 12.5��2 8 = 510.8�� S h

o r c e s ��1 = −��2 =± �� 2 =± 26.2��⁄�� × 12.5�� 2 =±163.4��

��1,2 = ��1,2 � = 168.4�� U L

)

d i n g m o m e

e ar f

S S t r e n g t h d e s i g n : B e a m ’ s b e n d i n g m o m e nt r e s i s t a n c e ( y

e L im i t S t at e ��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 B e n d i n g r e s is t a n c e c h e ck �� = 510.8�� ,�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 �� S L S d e s i g n : B e a m d e f l e c t i o n C o n d i t i o n f o r S e r v i c e a b i l i t y L i m i t S t a t e �� = 5��4 384�� (@0.5��) < �� 250 = 50�� D e f l e ct i o n c he c k

CHECK CONDITION FOR SERVICIALITY LIMIT STATE Verified Material Steel class Young’s Modulus Cross-Section Beam height Area Moment of inertia Plastic modulus Steel HE 550A

CONDITION FOR SERVICEABILITY LIMIT STATE

2.2.2.2)

3.1.2.2_Primary beam

3.1.2.2_Primary

beam

Material and cross-section design

MATERIAL AND CROSS-SECTION DESIGN: SAME AS PREVIOUS PAGE.

ULS Strength design: Beam’s bending moment resistance (y-y)

Cross-Section:

299 �� = 5��4 384�� (@0.5��) < �� 250 = 50�� D e f l e ct i o n c he c k �� = 5× 18.3 ��⁄�� ×(12.54 ��) 384 × 210�� × �� = 5× 18.3 �� ⁄ × (125004 ��) 384 × 210000 ��2 ⁄ × 112000 × 104 ≈ 25�� 25�� < 50�� = �� 500 < �� 250 �� 1 L 2 SLS ��,�� = �� > �� = 4620 �� Bending resistance check �� = 510.8�� = 510.8�� × 103 ×1.05 235 ��2 ⁄ = 2282��3 < 4620 ��3 �� SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 50�� Deflection check �� = 5× 18.3 ��⁄�� ×(12.54��) 384 × 210�� × �� = 5× 18.3 �� ⁄ × (125004��) 384 × 210000 ��2 ⁄ × 112000 × 104 ≈ 25�� 25�� < 50�� = �� 500 < �� 250 ��

Bending moments �� = ��2 8 = 84.7�� /�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7�� /�� ×6.9�� 2 =±262.7�� Reaction forces ��1,2 = ��1,2 � = 262.7��

Steel Class: S235 → ��,�� = 235�� Young’s

→ ��

��

Material:

Modulus

= 210

→ ℎ = 540�� Area → �� = 21176��2

→ �� =

��4

→ �� = 4620 ��3

beam Bending moments �� = Shear forces ��1 = −�� Reaction forces ��1 2 = �� Material and ��,�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 ��,�� > �� = 4620 ��3 Bending resistance check �� = 407.1�� = 407.1�� × 103 ×1.05 235 ��2 ⁄ = 1819��3 < 4620 ��3 √ SLS design: Beam deflection Condition for Serviceability Limit State kN 262.7kN

HE 550A Beam height

Moment of inertia

1120

Plastic modulus

3.1.2.2_Primary

Bending moments �� = ��2 8 = 84.7�� /�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7�� /�� ×6.9�� 2 =±262.7�� Reaction forces ��1,2 = ��1,2 � = 262.7�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 407.1kNm 3.1.2.2_Primary beam Bending moments �� = ��2 8 = 84.7�� /�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7�� /�� ×6.9�� 2 =±262.7�� Reaction forces ��1,2 = ��1,2 � = 262.7�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 407.1kNm 262.7kN -262.7kN

beam Bending moments �� = ��2 8 = 84.7�� /�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7�� /�� ×6.9�� 2 =±262.7�� Reaction forces ��1,2 = ��1,2 � = 262.7��

3.1.2.2_Primary

Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 407.1kNm 262.7kN -262.7kN 3.1.2.2_Primary beam Bending moments �� = ��2 8 = 84.7��/�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7��/�� ×6.9�� 2 =±262.7�� Reaction forces ��1,2 = ��1,2� = 262.7�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4620 ��3 Bending resistance check �� = 407.1�� 407.1�� × 103 ×1.05 3 3 √ 407.1kNm 11 3.1.2.2_Primary

Bending moments �� = ��2 8 = 84.7��/�� ×(6.9��)2 8 = 407.1�� Shear forces ��1 = −��2 =± �� 2 =± 84.7��/�� ×6.9�� 2 =±262.7�� Reaction forces ��1 2 = ��1 2� = 262.7�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3

Material:

Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4620 ��3 Bending resistance check �� = 407.1�� = 407.1�� × 103 ×1.05 235 ��2 ⁄ = 1819��3 < 4620 ��3 √ SLS design: Beam deflection Condition for Serviceability Limit State 407.1kNm 262.7kN -262.7kN

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210��

HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3 407.1kNm 262.7kN -262.7kN

Cross-Section:

Verified

PRIMARY BEAM

SHEAR FORCES

FORCES

BENDING MOMENTS

REACTION

ULS Strength design: Beam’s bending moment resistance (y-y)

ULS STRENGTH DESIGN: BEAM’S BENDING MOMENT RESISTANCE (Y-Y)

CONDITIONS FOR ULS

ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State

3.1.3_Computation in tabular form

form

3.1.3_Computation in tabular form

3.3_Inclinated structures: Roofs

300 11

��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 Bending resistance check �� = 407.1�� ,�� = 407.1�� × 103 ×1.05 235 ��2 ⁄ = 1819��3 < 4620 ��3 √

Beam deflection Condition for Serviceability Limit State 11

SLS design:

Conditions

for Ultimate Limit State

Conditions for

Limit

��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 Bending resistance check �� = 407.1�� ,�� = 407.1�� × 103 ×1.05 235 ��2 ⁄ = 1819��3 < 4620 ��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 50�� Deflection check �� = 5× 18.3 �� ⁄ ×(6.94 ��) 384 × 210�� × �� = 5× 18.3 �� ⁄�� × (69004 ��) 384 × 210000 ��2 ⁄ × 112000 × 104 ≈ 4.8�� 4.8�� < 50�� = �� 1380 < �� 250 √

Ultimate

State

3.1.3_Computation in tabular

�� < 50�� = �� 1380 < �� 250 √

4.8

SLS conputation Steel class Length Plastic module Moment of inertia ULS SLS Shear (0,L)Moment (0.5L) Displacement Displacement (1/250) Resistance check MPa (N/mm²) m cm³ cm4 kN/mkN/mkN kNm mm mm cm³ Primary beam 6.2 84.758.9 262.7407.1 4.8 24.8 1900 Secondary beam 12.5 26.218.3 163.4510.8 24.7 50 2384 1120 HE 550 A 225 4620 Cross Section Beam Beam properties ULS Computation Simply supported beam computation Checks Applied forces �� = 5��4 384�� (@0.5��) < �� 250 = 50�� Deflection check �� = 5× 18.3 �� ⁄ ×(6.94��) 384 × 210�� × �� = 5× 18.3 ��⁄�� × (69004��) 384 × 210000 ��2 ⁄ × 112000 × 104 ≈ 4.8�� 4.8�� < 50�� = �� 1380 < �� 250 √ 3.1.3_Computation in tabular form 3.3_Inclinated structures: Roofs 3.3.1_Opaque roof SLS conputation Steel class Length Plastic module Moment of inertia ULS SLS Shear (0,L)Moment (0.5L) Displacement Displacement (1/250) Resistance check MPa (N/mm²) m cm³ cm4 kN/mkN/mkN kNm mm mm cm³ Primary beam 6.2 84.758.9 262.7 407.1 4.8 24.8 1900 Secondary beam 12.5 26.2 18.3163.4 510.8 24.7 50 2384 1120 HE 550 A 225 4620 Cross Section Beam Beam properties ULS Computation Simply supported beam computation Checks Applied forces BENDING RESISTANCE CHECK CONDITION FOR SERVICEABILITY LIMIT STATE DEFLECTION CHECK Verified SLS DESIGN: BEAM DEFORMATION �� = 5��4 384�� (@0.5��) < �� 250 = 50�� Deflection check �� = 5× 18.3 �� ⁄ ×(6.94 ��) 384 × 210�� × �� = 5× 18.3 �� ⁄�� × (69004 ��) 384 × 210000 ��2 ⁄ × 112000 × 104 ≈ 4.8�� 4.8�� < 50�� = �� 1380 < �� 250 √

3.3.1_Opaque roof SLS conputation Steel class Length Plastic module Moment of inertia ULS SLS Shear (0,L)Moment (0.5L) Displacement Displacement (1/250) Resistance check MPa (N/mm²) m cm³ cm4 kN/mkN/mkN kNm mm mm cm³ Primary beam 6.2 84.758.9 262.7407.1 4.8 24.8 1900 Secondary beam 12.5 26.218.3 163.4510.8 24.7 50 2384 1120 HE 550 A 225 4620 Cross Section Beam Beam properties ULS Computation Simply supported beam computation Checks Applied forces Verified

2.3) TYPICAL OPAQUE ROOF STRUCTURES VERIFICATIONS

301 B12 D13

B13 10.95 10.00 8.04 3 .2 1 3 3 0 1.60

D12

Typical roof contribution area (Scale 1:250)

2.3.1) LOAD COMBINATIONS AND DIMENSIONING

Project's FUNCTIONS roof loads

accessible except for normal maintenance and

EN 1991-1-1:2002Table 6.10: Category H

Horizontal slab's longest contribution span [m]

302 ThicknessArea loadLinear load mm kN/m²kN/m Façade 3 0.07Insulation / covering 120+39 0.1365Hanging ceiling - 0.3 Primary (a) beams - 1.66 Primary (b) and secondary beams Cross-section: 16mm 1.91 Terciary beams Cross-section: 5mm 0.50653.57

EN 1991-1-3 Part 1-3 ψ value EN 1990:2002+A1 :2005 γGjGj + γQ1Q1 + γQiψ0Q2 γGj=1.35; γQi=1.5 Serviciability Limit State ψ0=0Table A2.6 G1 + Q1 + ψ0Qi TertiaryPrimary (b)/secondaryPrimary 1.6 3.2 ψ value Area loadLinear loadLinear loadLinear EN 1990:2002+A1 :2005 kN/m²kN/m kN/m γGjGj + γQ1Q1 + γQiψ0Q2 γGj=1.35; γQi=1.5 Serviciability Limit State ψ0=0Table A2.6 G1 + Q1 + ψ0Qi 1.82.8 5.7 Insulated sandwich panels

ΣQn Eurocode reference HE 550 A RHS 500x300 / 16 RHS 180x100 / 5 Live Loads 1.3 Area load kN/m² 0.4

[Marcegaglia PGB TD5]

Dead Loads Layer Product Name Perforated steel sheets Combination EN 1991-1-1:2002 Ultimate Limit State ψ0=0Table A1.2 (B) (STR) Roofs not

repair. General actions - Snow loads Load combinations for beams 1.7 2.0 Ultimate Limit State ψ0=0Table A1.2 (B) (STR) 1.7 10.8 2.64.1 Area load kN/m²

Load combinations

Combination EN 1991-1-1:2002 ThicknessArea loadLinear load mm kN/m²kN/m Façade 3 0.07Insulation / covering 120+39 0.1365Hanging ceiling - 0.3 Primary (a) beams - 1.66 Primary (b) and secondary beams Cross-section: 16mm 1.91 Terciary beams Cross-section: 5mm 0.50653.57 EN 1991-1-1:2002Table

Category H EN 1991-1-3 Part 1-3 ψ value EN 1990:2002+A1 :2005 γGjGj + γQ1Q1 + γQiψ0Q2 γGj=1.35; γQi=1.5 Serviciability Limit State ψ0=0Table A2.6 G1 + Q1 + ψ0Qi TertiaryPrimary (b)/secondaryPrimary (a) 1.6 3.2 10 ψ value Area loadLinear loadLinear loadLinear load EN 1990:2002+A1 :2005 kN/m²kN/m kN/m kN/m γGjGj + γQ1Q1 + γQiψ0Q2 γGj=1.35; γQi=1.5 Serviciability Limit State ψ0=0Table A2.6 G1 + Q1 + ψ0Qi 1.82.8 5.7 17.7 Insulated sandwich panels [Marcegaglia

TD5] ΣQn Eurocode reference HE 550 A RHS 500x300 / 16 RHS 180x100 / 5 Live Loads 1.3 Area load kN/m² 0.4

for sandwich panels

6.10:

PGB

Dead Loads Layer Product Name Perforated steel sheets Combination EN 1991-1-1:2002 Ultimate Limit State ψ0=0Table A1.2 (B) (STR) Roofs not

maintenance

repair. General actions - Snow loads Load combinations for beams 1.7 2.0 Ultimate Limit State ψ0=0Table A1.2 (B) (STR) 1.7 10.8 2.64.1 Area load kN/m² 28.1 Horizontal slab's longest contribution span [m]Load combinations for sandwich panels Combination EN 1991-1-1:2002

accessible except for normal

and

303

Marcegaglia (c) PGB-TD5

Perforated steel sheet facade

Composite insulated pannel model PGB TD5

Terciary steel beam RHS 180x100 / 5

RHS 500x300 / 16

False ceiling

304

Typical roof detail. Scale 1:20

2.3.2) LOAD COMBINATIONS AND DIMENSIONING

3.3.1.2.1_Terciary beam

2.3.2.1) TERTIARY BEAMS

3.3.1.2.1_Terciary beam

BENDING MOMENTS

3.1.2.2_Primary beam

3.3.1.2.1_Terciary beam

3.1.2.2_Primary beam

SHEAR FORCES

REACTION FORCES

Material and cross-section design

Material and cross-section design Material:

Material and cross-section design

Material and cross-section

MATERIAL AND CROSS-SECTION DESIGN

design

Steel

Material Steel class

Young’s Modulus

Cross-Section: RHS 180x100 / 5

Cross-Section

Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11.53��4

Plastic modulus → �� = 157.3 ��3

Beam height Area

Moment of inertia

Plastic modulus

ULS Strength design: Beam’s bending moment resistance (y-y)

4.6

3.3.1.2.1_Terciary beam Bending

Steel RHS 180x100 / 5

ULS Strength design: Beam’s bending moment resistance (y-y)

Conditions for Ultimate Limit State

ULS Strength design: Beam’s bending moment resistance (y-y)

ULS Strength design: Beam’s bending moment resistance

ULS Strength design: Beam’s bending

Conditions for Ultimate Limit State

305

moments �� = ��2 8 = 4.1�� /�� ×(3��)2 8 =4.6��

forces ��1 = −��2 =± �� 2 =± 4.1�� /�� ×3�� 2 =±6.2��

forces ��1,2 = ��1,2 � =6.2��

Bending

Shear

Reaction

Material: Steel Class: S235 → ��,�� = 235��

Young’s Modulus → �� = 210��

��,�� = �� ×1.05 �� > �� = 157.3��3

moments �� Shear forces ��1 = Reaction forces ��1,2 Material and cross Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11.53��4 Plastic modulus → �� = 157.3 ��3 ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 157.3��3 Bending resistance check �� =4.6�� ,�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √ 6.2kN -6.2kN

Bending moments �� = ��2 8 = 4.1�� /�� ×(3��)2 8 =4.6�� Shear forces ��1 = −��2 =± �� 2 =± 4.1�� /�� ×3�� 2 =±6.2�� Reaction forces ��1,2 = ��1,2 � =6.2��

Material:

Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11.53��4 Plastic modulus → �� = 157.3 ��3

for Ultimate Limit State �� ×1.05

Conditions

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11.53��4 Plastic modulus → �� = 157.3 ��3

Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11.53��4 Plastic modulus → �� = 157.3 ��3

�� ×1.05

Bending moments �� = ��2 8 = 4.1�� /�� ×(3��)2 8 =4.6�� Shear forces ��1 = −��2 =± �� 2 =± 4.1�� /�� ×3�� 2 =±6.2 Reaction forces ��1,2 = ��1,2 � =6.2��

Material:

Steel

�� ×1.05 kN -6.2kN

Material:

Steel

moment resistance (y-y)

kN -6.2kN

(y-y)

407.1kNm

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3

Material and cross-section design

�� ×1.05 407.1kNm 262.7kN -262.7kN 15 3.3.1.2.1_Terciary beam Bending moments �� = ��2 8 = 4.1��/�� ×(3��)2 8 =4.6�� Shear forces ��1 = −��2 =± �� 2 =± 4.1��/�� ×3�� 2 =±6.2�� Reaction forces ��1 2 = ��1 2� =6.2�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11 53��4 Plastic modulus → �� = 157.3 ��3

Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 157.3��3 Bending resistance check �� =4.6�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √ 4.6kNm 6.2kN -6.2kN 15 3.3.1.2.1_Terciary beam Bending moments �� = ��2 8 = 4.1��/�� ×(3��)2 8 =4.6�� Shear forces ��1 = −��2 =± �� 2 =± 4.1��/�� ×3�� 2 =±6.2�� Reaction forces ��1 2 = ��1 2� =6.2�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 180x100 / 5 Beam height → ℎ = 180�� Area → �� = 2673��2 Moment of inertia → �� = 11 53��4 Plastic modulus → �� = 157.3 ��3 ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 157.3��3 Bending resistance check �� =4.6�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √

ULS

ULS Strength design: Beam’s bending moment resistance (y-y)

ULS STRENGTH DESIGN: BEAM’S BENDING MOMENT RESISTANCE (Y-Y)

for Ultimate Limit State

SLS design: Beam deflection

SLS

306 15

Conditions

��,�� = �� ×1.05 ��,�� > �� = 157.3��3 Bending resistance check �� =4.6�� ,�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √ 15 Plastic modulus → �� = 157.3 ��3

Conditions

��,�� = �� ×1.05 ��,�� > �� = 157.3��3 Bending resistance check �� =4.6�� ,�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √ 15

for Ultimate Limit State

Conditions

��,�� = �� ×1.05 ��,�� > �� = 157.3��3 Bending resistance check �� =4.6�� ,�� = 4.6�� × 103 ×1.05 235 ��2 ⁄ = 21��3 < 157.3 ��3 √

for Ultimate Limit State

Condition for

Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×2.8 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces �� 10.8�� /�� ×8�� 1.2mm 86.7kNm SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×2.8 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces 1.2mm 86.7kNm SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×2.8 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces 1.2mm 86.7kNm

Serviceability

BENDING RESISTANCE CHECK Verified Verified Condition for Serviciality Limit State DEFLECTION CHECK

BEAM DEFORMATION

DESIGN:

3.3.1.2.2_Secondary beam

2.3.2.2)

3.3.1.2.2_Secondary beam

3.3.1.2.2_Secondary

BENDING MOMENTS

3.1.2.2_Primary beam

3.3.1.2.2_Secondary

3.1.2.2_Primary beam

3.3.1.2.2_Secondary beam

SHEAR FORCES

REACTION FORCES

Material and cross-section design

design

MATERIAL AND CROSS-SECTION DESIGN

and cross-section design

Material

Steel class

Young’s Modulus

Cross-Section

Beam height

Area

Moment of inertia

Plastic modulus

Steel

RHS 500x300 / 16

ULS Strength design: Beam’s bending moment resistance (y-y)

Conditions for Ultimate Limit State

307 16 1.2�� < 12�� = 2500 < 250 √

moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4��

Bending

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm 16 Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×2.8 ��⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = �� 8 Shear forces ��1 = −��2 =± Reaction force ��1 2 = ��1,2� Material and Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm kNm 43.4kN -43.4kN 16 1.2�� < 12�� = �� 2500 < �� 250 √

Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4��

beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm 16 384 × 210�� × �� 384 × 210000 ��2 ⁄ × 11.53 × 106 1.2�� < 12�� = �� 2500 < �� 250 √

beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm 16 �� = 384 × 210�� × �� = 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4��

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm -43.4kN 16 �� = 5×2.8 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×2.8 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √

Material

Bending moments �� = ��2 8 = 10.8�� /�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8�� /�� ×8�� 2 =±43.4�� Reaction forces ��1,2 = ��1,2 � = 43.4�� Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm -43.4kN

and cross-section

Material

Conditions

Ultimate

State ��,�� = �� ×1.05 �� > �� = 4620 ��3 407.1kNm

for

Limit

Material:

Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: HE 550A Beam height → ℎ = 540�� Area → �� = 21176��2 Moment of inertia → �� = 1120��4 Plastic modulus → �� = 4620 ��3

Steel

��,�� = �� ×1.05 ��,�� > �� = 4620 ��3 407.1kNm 262.7kN -262.7kN 16 SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34��) 384 × 210�� × �� = 5×2.8 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.2�� 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8��/�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8��/�� ×8�� 2 =±43.4�� Reaction forces ��1 2 = ��1 2� = 43.4�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 1.2mm 86.7kNm 43.4kN -43.4kN 16 SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 12�� Deflection check �� = 5×2.8 �� ⁄ ×(34��) 384 × 210�� × �� = 5×2.8 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.2 1.2�� < 12�� = �� 2500 < �� 250 √ 3.3.1.2.2_Secondary beam Bending moments �� = ��2 8 = 10.8��/�� ×(8��)2 8 = 86.7�� Shear forces ��1 = −��2 =± �� 2 =± 10.8��/�� ×8�� 2 =±43.4�� Reaction forces ��1 2 = ��1 2� = 43.4�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301�� Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��

SECONDARY BEAM

ULS Strength design: Beam’s bending moment resistance (y-y)

ULS STRENGHT DESIGN: BEAM’S BENDING MOMENT

ULS Strength design: Beam’s bending moment resistance (y-y)

Conditions for ULS

BENDING

SLS design: Beam deflection

SLS DESIGN: BEAM DEFORMATION

SLS design: Beam deflection

ULS Strength design: Beam’s bending moment resistance (y-y)

308

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3 Bending resistance check �� = 86.7�� ,�� = 86.7�� × 103 ×1.05 235 ��2 ⁄ = 405 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×5.7 �� ⁄�� × (30004 384 × 210000 ��2 ⁄ × 11 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces 1.8mm 86.7kNm

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3 Bending resistance check �� = 86.7�� ,�� = 86.7�� × 103 ×1.05 235 ��2 ⁄ = 405 < 4005��3 √

Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×5.7 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� × 11�� 2 =±154.3�� 86.7kNm 43.4kN

deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5×5.7 �� ⁄�� × (30004 ��) 384 × 210000 ��2 ⁄ × 11.53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces �� −�� =± �� =± 28.1�� /�� × 11�� =±154.3�� 86.7kNm 43.4kN 18

SLS design: Beam

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3 Bending resistance check �� = 424.5�� ,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 44�� Deflection check �� = 5× 17.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5× 17.7 �� ⁄�� × (110004 ��) 384 × 210000 ��2 ⁄ × 817.8× 106 ≈ 19.7�� 19.7�� < 44�� = �� 558 < �� 250 √ 20mm

Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4005��3 Bending resistance check �� = 86.7�� = 86.7�� × 103 ×1.05 235 ��2 ⁄ = 405 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34��) 384 × 210�� × �� = 5×5.7 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1��/�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1��/�� × 11�� 2 =±154.3�� Reaction forces ��1 2 = ��1 2� = 154.3�� 1.8mm 86.7kNm 43.4kN -43.4kN

RESISTANCE (Y-Y)

RESISTANCE CHECK Verified Verified

FOR SERVICIALITY LIMIT STATE

CHECK

CONDITION

DEFLECTION

3.3.1.2.3_Primary beam

MOMENTS

Material and cross-section design

MATERIAL AND CROSS-SECTION

ULS Strength design: Beam’s bending

Cross-Section: RHS 500x300

�� = 424.5�� ,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

SLS design: Beam deflection

State �� = 5��4 (@0.5��) < �� = 44��

309 17 1.8�� < 32�� = 4444 < 250 √

Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� × 11�� 2 =±154.3�� Reaction forces ��1,2 = ��1,2 � = 154.3�� 1.8mm �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34��) 384 × 210�� × �� = 5×5.7 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = Shear forces ��1 = −�� =± �� =± 28.1��/�� × 11�� =±154.3�� Reaction forces ��1,2 = �� 1.8mm 43.4kN -43.4kN 17 1.8�� < 32�� = 4444 < 250 √

Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� × 11�� 2 =±154.3�� Reaction forces ��1,2 = ��1,2 � = 154.3�� 1.8mm 86.7kNm 17 1.8�� < 32�� = �� 4444 < �� 250 √

Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� × 11�� 2 =±154.3�� Reaction forces ��1,2 = ��1,2 � = 154.3�� 1.8mm 86.7kNm 43.4kN -43.4kN 17 Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34��) 384 × 210�� × �� = 5×5.7 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1��/�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1��/�� × 11�� 2 =±154.3�� Reaction forces ��1,2 = ��1,2� = 154.3�� 1.8mm 86.7kNm 43.4kN -43.4kN 17 �� = 86.7�� = 86.7�� × 103 ×1.05 235 ��2 ⁄ = 405 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 32�� Deflection check �� = 5×5.7 �� ⁄ ×(34��) 384 × 210�� × �� = 5×5.7 ��⁄�� × (30004��) 384 × 210000 ��2 ⁄ × 11 53 × 106 ≈ 1.8�� 1.8�� < 32�� = �� 4444 < �� 250 √ 3.3.1.2.3_Primary beam Bending moments �� = ��2 8 = 28.1��/�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1��/�� × 11�� 2 =±154.3�� Reaction forces ��1 2 = ��1 2� = 154.3�� 1.8 86.7 43.4 17 384 × 210�� × �� 384 × 210000 �� ⁄ × 11.53 × 10 1.8�� < 32�� = �� 4444 < �� 250 √

Bending moments �� = ��2 8 = 28.1�� /�� ×(11��)2 8 = 424.5�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� × 11�� 2 =±154.3�� Reaction forces ��1,2 = ��1,2 � = 154.3�� 1.8mm 86.7kNm 43.4kN -43.4kN Material and cross-section design Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3

moment resistance (y-y) Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3 Bending resistance check �� = 424.5�� ,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

design: Beam deflection Condition

Conditions

State ��,�� = �� ×1.05 ��,�� > �� = 4005��3

resistance check �� = 424.5�� ,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

SLS

for Serviceability Limit State Material and cross-section design

ULS Strength design: Beam’s bending moment resistance (y-y)

for Ultimate Limit

Bending

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210��

Condition for Serviceability Limit State / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3

ULS Strength design: Beam’s bending moment resistance (y-y)

Bending resistance check

DESIGN

SLS design: Beam deflection Condition for Serviceability Limit

BENDING

SHEAR FORCES REACTION FORCES ULS STRENGHT DESIGN: BEAM’S BENDING MOMENT RESISTANCE (Y-Y) Verified

FOR ULS

2.3.2.3) PRIMARY BEAM

CONDITIONS

BENDING RESISTANCE CHECK

SLS design: Beam deflection

SLS DESIGN: BEAM DEFORMATION

SLS

SLS design: Beam deflection

ULS Strength design: Beam’s bending moment

3.3.1.3_Cantilever beam with UDL verification

2.3.2.4) CANTILEVER BEAM

3.3.1.3.1_Secondary beam

BENDING MOMENTS

310 18 ��,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 44�� Deflection check �� = 5× 17.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5× 17.7 �� ⁄�� × (110004 ��) 384 × 210000 ��2 ⁄ × 817.8× 106 ≈ 19.7�� 19.7�� < 44�� = �� 558 < �� 250 √ 18 ��,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 44�� Deflection check �� = 5× 17.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5× 17.7 �� ⁄�� × (110004 ��) 384 × 210000 ��2 ⁄ × 817.8× 106 ≈ 19.7�� 19.7�� < 44�� = �� 558 < �� 250 √ 18 ��,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

Limit

�� = 5��4 384�� (@0.5��) < �� 250 = 44�� Deflection check �� = 5× 17.7 �� ⁄ ×(34 ��) 384 × 210�� × �� = 5× 17.7 �� ⁄�� × (110004 ��) 384 × 210000 ��2 ⁄ × 817.8× 106 ≈ 19.7�� 19.7�� < 44�� = �� 558 < �� 250 √ 20mm Area → �� = 24301�� Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3

Condition for Serviceability

State

(y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4005��3 Bending resistance check �� = 424.5�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = 5��4 384�� (@0.5��) < �� 250 = 44�� Deflection check �� = 5× 17.7 �� ⁄ ×(34��) 384 × 210�� × �� = 5× 17.7 ��⁄�� × (110004 ��) 384 × 210000 ��2 ⁄ × 817.8× 106 ≈ 19.7�� 19.7�� < 44�� = �� 558 < �� 250 √ 20mm 18 ��,�� = 424.5�� × 103 ×1.05 235 ��2 ⁄ = 1897��3 < 4005��3 √

resistance

beam Bending moments �� = ��2 2 = 28.1�� /�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� ×6�� 2 =±168.38�� Reaction forces -168.38kN

beam with UDL verification

beam Bending moments �� = ��2 2 = 28.1�� /�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� ×6�� 2 =±168.38�� Reaction forces ��1,2 = ��1,2 � = 168.38.3�� -505.1kNm -168.38kN

3.3.1.3.1_Secondary

3.3.1.3_Cantilever

3.3.1.3.1_Secondary

Bending moments �� = ��2 2 = 28.1�� /�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� ×6�� 2 =±168.38�� Reaction forces ��1,2 = ��1,2 � = 168.38.3�� -505.1kNm -168.38kN 3.3.1.3_Cantilever beam with UDL verification 3.3.1.3.1_Secondary beam Bending moments �� = ��2 2 = 28.1��/�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1��/�� ×6�� 2 =±168 38�� Reaction forces ��1 2 = ��1 2� = 168 38.3�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus→ �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Verified

CONDITION FOR SERVICIALITY LIMIT STATE DEFLECTION CHECK

Material and cross-section design

3.3.1.3.1_Secondary

Material and cross-section design

ULS Strength design: Beam’s bending moment resistance (y-y)

SLS design: Beam deflection

Conditions for Ultimate Limit State

Condition for Serviceability Limit State

SLS design: Beam

Bending resistance check

311 19 �� = ��2 2 = 28.1�� /�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� ×6�� 2 =±168.38�� Reaction forces ��1,2 = ��1,2 � = 168.38.3��

Material and cross-section design

��,�� = �� ×1.05 ��,�� > �� = 4005��3

-505.1kNm -168.38kN 19 �� = ��2 2 = 28.1�� /�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1�� /�� ×6�� 2 =±168.38�� Reaction forces ��1,2 = ��1,2 � = 168.38.3��

Conditions for Ultimate Limit State

Bending resistance check

Material: Steel Class: S235 → ��,�� = 235�� Young’s Modulus → �� = 210��

Beam height → ℎ = 500�� Area → �� = 24301��2

→ �� = 817.8��4

→ �� = 4005 ��3

Cross-Section: RHS 500x300 / 16

Moment

inertia

Plastic modulus

��,�� = �� ×1.05 ��,�� > �� = 4005��3

-505.1kNm -168.38kN 19

beam Bending moments �� = ��2 2 = 28.1��/�� ×(6��)2 2 = 505.1�� Shear forces ��1 = −��2 =± �� 2 =± 28.1��/�� ×6�� 2 =±168 38�� Reaction forces ��1 2 = ��1 2� = 168 38.3�� Material and cross-section design Material: Steel Class: S235 → �� = 235�� Young’s Modulus→ �� = 210�� Cross-Section: RHS 500x300 / 16 Beam height → ℎ = 500�� Area → �� = 24301��2 Moment of inertia → �� = 817.8��4 Plastic modulus → �� = 4005 ��3 ULS Strength design: Beam’s bending moment resistance (y-y) Conditions for Ultimate Limit State �� = �� ×1.05 �� > �� = 4005��3 Bending resistance check 19

Conditions for Ultimate Limit State ��,�� = �� ×1.05 ��,�� > �� = 4005��3 Bending resistance check �� = 505.1�� ,�� = 505.1�� × 103 ×1.05 235 ��2 ⁄ = 2257��3 < 4005��3 √

deflection Condition for Serviceability Limit State �� = ��4 8�� (@��) < �� 180 = 33�� Deflection check �� = 28.1 �� ⁄ ×(34 ��) 8× 210�� × �� = 28.1 �� ⁄�� × (110004 ��) 8× 210000 ��2 ⁄ × 817.8× 106 ≈ 2.8�� = 505.1�� ,�� = 505.1�� × 103 ×1.05 235 ��2 ⁄ = 2257��3 < 4005��3 √ SLS design: Beam deflection Condition for Serviceability Limit State �� = ��4 8�� (@��) < �� 180 = 33�� Deflection check �� = 28.1 �� ⁄ ×(34 ��) 8× 210�� × �� = 28.1 �� ⁄�� × (110004 ��) 8× 210000 ��2 ⁄ × 817.8× 106 ≈ 2.8�� 2.8�� < 33�� = �� < �� √ 3mm �� = 505.1�� ,�� = 505.1�� × 103 ×1.05 235 ��2 ⁄ = 2257��3 < 4005��3 √

�� = ��4 8�� (@��) < �� 180 = 33�� Deflection check �� = 28.1 �� ⁄ ×(34 ��) 8× 210�� × �� = 28.1 �� ⁄�� × (110004 ��) 8× 210000 ��2 ⁄ × 817.8× 106 ≈ 2.8�� 2.8�� < 33�� < �� √ 3mm ULS STRENGHT DESIGN: BEAM’S BENDING MOMENT RESISTANCE (Y-Y) BENDING RESISTANCE CHECK

LIMIT STATE SLS DESIGN: BEAM DEFORMATION CONDITIONS FOR ULS SHEAR FORCES REACTION FORCES MATERIAL AND CROSS-SECTION DESIGN

CONDITION FOR SERVICIALITY