The River Clyde Bridge

(Structural Mechanics) (The River Clyde Bridge) (Françoise GOUGHSimon ROYERArnaud THOLLETFriday, 26th July 2013)

IntroductionComments by IM in red

The Introduction should state that the report is a response to the requirements in the course document.You are not required to design a bridge but to carry out the tasks listed in the course document.

This project is about the construction of a new bridge over the River Clyde in New Lanark. After the first meeting these specifications have been pointed out:

- Design

- Respectful of the environment

- Enough resistance for 30 persons

Situation of New Lanark

Summary

1 -Introduction22 -Summary33 -Structural system44 -Engineering model55 -Analysis model with LUSAS66 -Model run67 -Model Validation and Results Verification77.1Model Validation77.1.1Connection eccentricity77.1.2Bending theory, shear deformation87.1.3Small deformations including Euler buckling effect87.1.4Loading10Sum of reactions10Displacement11Symmetry11Equilibrium12Form of results - Internal forces and Deformations138 -Check the sizes of 2 members148.1First Members: Element 4 beam steel in tension148.2First Members: Element 14 timber beam in compression14

Structural system

We selected a bridge made of Steel and Timber, which associates a beautiful design and an excellent resistance.

Sketch of the structural system

The bridge is made of two steel I-beams, and a wood bracing structure.

The elements in tension are made of steel whereas the elements in compression are made of timber.

This is the best compromise because the timber is better than steel in compression.

For people security we propose strips of wood with nonslip bands on them. The requirements does not mention this issue. Do what is required. Nothing more.

Engineering model

Sketch of the engineering model Show dimensions to centre lines

Analysis model of truss for a footbridge

Counter braces have several roles. The first one is about the structure, they brace the bridge. The second one is about the security, they protect people from falling in the water with railing. The third role is a nice design. This information not required.

About loading, 50 people can walk on the bridge at the same time.

50 x 100 = 5000 Kg = 50 000 N

Dimensions of model?

Element types used?

Geometric properties?

Material properties?

Information is needed so that the work can be independently checked.

Analysis model with LUSAS

We drew the engineering model on LUSAS software with the load of 50 KN:

The model on LUSAS software

On one side of the bridge we put a pin, on the other side a roller.

Model run

Deformed mesh

Model Validation and Results VerificationModel Validation

The model needs to be validated against the objectives of the analysis.

Connection eccentricity

The structure has concurrent axes, so there isn't any eccentricity.

beam axial of the engineering model

beam axial of the analysis model

Bending theory, shear deformation

Table 1 - Ratio Span/Depth

Span of the bridge : 10,3m

Depth of the bridge : 2m

Shear deformation less insignificant but normally neglected

Small deformations including Euler buckling effect

This assumption is normally valid due to use of code of practice rules for member sizing. For no-sway buckling of members results can be tested using the criterion = N/Ncr < 0.1 where N is the axial load and Ncr,euler is the Euler buckling load.

Ncr,euler = 2EI/(kL)2 where I is the minor axis I value, L is the length between connections

Typical values of the factor k are given in Table 2.

Table 2 - k Values for Euler Buckling

· Beam 1 (section 0.15 x 0.3 [m]):

Diagrams Fx (Force/Moment - Thick 2D beam)

The beam selected (in grey) is in compression, N=289 E3 [N]

Euler buckling load:

E = Young's Modulus of glued-laminated timber = 10 [Gpa]

I = Moment of inertia = = 405000 [cm4]

Length of the beam = 2 [m]

· Beam 2 (section 0.05 x 0.2 [m]):

Diagrams Fx (Force/Moment - Thick 2D beam)

The beam selected (in grey) is in compression, N=188 E3 [N]

Euler buckling load:

E = Young's Modulus of glued-laminated timber = 10 [Gpa]

I = Moment of inertia = = 3333 [cm4]

Length of the beam = 2 [m]

The structure won't buckle. Validate the supports? Validate the use of moment connections in the model?

Loading

The structure is in a standard situation, so the loading is valid.

Results Verification This should be Section 7.2

Verifying the results implies an attempt to answer the question “Has the model been correctly implemented?” The following items may be checked if relevant:

· Sum of reactions

Diagramme of the beam

Fundamental principle of the static

Sum on X: RAx = 0

Sum on Y: RAy + RBy - P x L = 0

=> RAy = RBy = P x L / 2 = 50 E3 x 10 / 2 = 250 E3 [N]

· Displacement

Name of nodes

Node

DX

DY

THZ

RSLT

Node

DX

DY

THZ

RSLT

1

0

0

-0,0035433

0

36

0,00165094

-0,00281765

-0,00127166

0,0032657

2

0,0001574

-0,004615

-0,0013207

0,004617

37

0,00185169

-0,00360175

-0,00081726

0,00404986

3

3,935E-05

-0,001862

-0,0034848

0,001862

38

0,000452079

-0,00630744

-4,8714E-05

0,00632362

4

7,869E-05

-0,003327

-0,0022494

0,003328

39

0,00039056

-0,00629257

0,000191444

0,00630468

5

0,000118

-0,004123

-0,0011054

0,004125

40

0,00022096

-0,00616963

0,000383606

0,00617358

6

0,0003815

-0,00619

-0,0003369

0,006202

41

0,000110281

-0,00570739

0,000324629

0,00570845

7

0,0002134

-0,005469

-0,0016637

0,005473

42

0,000218606

-0,00548686

0,000389063

0,00549121

8

0,0002695

-0,006112

-0,0007687

0,006118

43

0,000426043

-0,00516721

0,000721074

0,00518475

9

0,0003255

-0,006242

9,624E-05

0,00625

44

0,000294234

-0,00452906

0,00100052

0,0045386

10

0,0006422

-0,00619

0,0003369

0,006223

45

-0,00015022

-0,00444345

0,000809881

0,00444598

11

0,0004467

-0,006585

-0,0008025

0,0066

46

-0,00053172

-0,00435783

0,000748749

0,00439015

12

0,0005119

-0,006822

-3,469E-18

0,006841

47

-0,00082793

-0,00360175

0,000817255

0,00369569

13

0,0005771

-0,006585

0,0008025

0,00661

48

-0,00062718

-0,00281765

0,00127166

0,00288661

14

0,0008664

-0,004615

0,0013207

0,004695

49

-8,566E-05

-0,00169278

0,00218034

0,00169494

15

0,0006983

-0,006242

-9,624E-05

0,006281

50

0,000729531

-0,00452906

-0,00100052

0,00458744

16

0,0007543

-0,006112

0,0007687

0,006158

51

0,00117398

-0,00444345

-0,00080988

0,00459592

17

0,0008103

-0,005469

0,0016637

0,005529

52

0,00155549

-0,00435783

-0,00074875

0,00462712

18

0,0010238

0

0,0035433

0,001024

53

0,000597722

-0,00516721

-0,00072107

0,00520167

19

0,0009057

-0,004123

0,0011054

0,004222

54

0,000805158

-0,00548686

-0,00038906

0,00554562

20

0,0009451

-0,003327

0,0022494

0,003458

55

0,000913483

-0,00570739

-0,00032463

0,00578003

21

0,0009844

-0,001862

0,0034848

0,002106

56

0,000802804

-0,00616963

-0,00038361

0,00622164

22

0,0019388

-0,004272

-0,0008171

0,004692

57

0,000633205

-0,00629257

-0,00019144

0,00632435

23

0,0010565

-0,005963

-0,0005278

0,006055

58

0,000571686

-0,00630744

4,87143E-05

0,00633329

24

0,0017182

-0,004719

-0,0009261

0,005022

59

0,000531699

-0,00613332

-0,0002812

0,00615632

25

0,0014977

-0,00519

-0,0009142

0,005402

60

0,000671277

-0,00607641

-0,00029446

0,00611338

26

0,0012771

-0,005624

-0,0007814

0,005768

61

0,000834717

-0,0060195

-0,00037665

0,0060771

27

-3,272E-05

-0,005963

0,0005278

0,005963

62

0,000189047

-0,0060195

0,000376652

0,00602247

28

0,0007842

-0,006161

-0,0002639

0,00621

63

0,000352488

-0,00607641

0,000294462

0,00608663

29

0,0005119

-0,006226

7,373E-18

0,006247

64

0,000492065

-0,00613332

0,000281201

0,00615303

30

0,0002396

-0,006161

0,0002639

0,006165

65

0,00151399

-0,00478722

-0,00102438

0,00502092

31

-0,000915

-0,004272

0,0008171

0,004369

66

0,0010401

-0,00535129

-0,00101342

0,00545143

32

-0,0002533

-0,005624

0,0007814

0,00563

67

0,00062624

-0,00585533

-0,00078425

0,00588872

33

-0,0004739

-0,00519

0,0009142

0,005211

68

0,000397525

-0,00585533

0,000784253

0,0058688

34

-0,0006945

-0,004719

0,0009261

0,00477

69

-1,6335E-05

-0,00535129

0,00101342

0,00535131

35

0,0011094

-0,001693

-0,0021803

0,002024

70

-0,00049023

-0,00478722

0,00102438

0,00481225

Table 3 - k Values for Euler Buckling

The truss deflection is OK.

· Symmetry

The structure is symmetric with a symmetrical loading each side of point 59.

· Equilibrium

Element

Node

Fx

Fy

Mz

1

1

206569

-48201

8348,36

33

1

-288760

3372,97

-8348,4

Table 4 - Forces on element nodal

(Element 1) (Element 33)

Equilibrium

Node

Fx (kN)

Fy (kN)

Mz (kN m)

1

0.00E+00

250E+00

0.00E+00

2

0.00E+00

0.00E+00

0.00E+00

3

0.00E+00

0.00E+00

0.00E+00

4

0.00E+00

0.00E+00

0.00E+00

5

0.00E+00

0.00E+00

0.00E+00

6

0.00E+00

250E+00

0.00E+00

7

0.00E+00

0.00E+00

0.00E+00

8

0.00E+00

0.00E+00

0.00E+00

9

0.00E+00

0.00E+00

0.00E+00

10

0.00E+00

0.00E+00

0.00E+00

Table 5 - Nodal reactions (cf. picture 4)

· Form of results - Internal forces and Deformations

Displaced shape

The deflected shape looks rounded (cf picture 14). This will be due to the effect of the uniformly distributed load and global bending of the truss global load and the posts contributing a significant shear mode component to the deformation.

Internal forces?

Checking model?

Check the sizes of 2 members

(15) (13) (14)

Analysis model of truss for a footbridgeFirst Members: Element 4 beam steel in tension

We use the Eurocode 3

NEd Nt,Rd

Nt,Rd

NEd = 16457N

NEd Nt,Rd so it's OK

This member is also in bending!

First Members: Element 14 timber beam in compression

We use the Eurocode 5

= 20 N/mm2

it's not valid, because the beam works at 150%, so the section has to be bigger.

Bending?

Françoise GOUGH

Arnaud THOLLET

Sandwich course – Design and management of the construction – CMC 5

Page 15

Simon ROYER

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