Sophie CAMBREA Jérémie DEIANA Kévin TOUATIVisiting students 2013

Technical reportStructural Mechanics

Technical report

SummaryIntroduction............................................................................................................21. Presentation of structure....................................................................................3

1.1 Engineering model:.......................................................................................31.2 Analysis model :............................................................................................3

2. Presentation of results.......................................................................................42.1 Deformed mesh.............................................................................................42.2 Forces and moments diagrams.....................................................................6

3. Validation of the model:.....................................................................................83.1 Linear elasticity:............................................................................................83.2 Euler buckling effect of a small deformation:................................................83.3 Bending theory, shear deformation...............................................................83.4 Loading.........................................................................................................8

4. Results verification.............................................................................................84.1 Data check OK.........................................................................................84.2 Check restraints............................................................................................84.3 Symmetry......................................................................................................94.4 Equilibrium noddle 1.....................................................................................94.5 Form of results: Deformation......................................................................104.6 Checking model – Internal forces................................................................104.7 Checking model – Deformation...................................................................104.8 Stress on the model....................................................................................114.9 Effects of moment connection.....................................................................11

5. Sizing verification.............................................................................................125.1 For element A (one element at the bottom):...............................................125.2 For the element B (one diagonal):...............................................................12

Conclusion............................................................................................................13

University of Strathclyde | 1

Technical report

IM comments in red

IntroductionRefer to the requirments of the project

In this report we will validate a simple model and verify the results obtained with the LUSAS software.

To do this, you will find an overview of the structure used, secondly the presentation of the results obtained with the software LUSAS, thirdly the validation model, fourthly the validation results and finally the sizing verification.

University of Strathclyde | 2

Technical report

1. Presentation of structureThe structure used for the work is a bridge composed of 27 elements IPE 220 steel mesh like.

The steel used is a S235.

1.1 Engineering model:

Specify the material, give details of the supports and the connections

1.2 Analysis model :The bridge is subjected to a distributed 10 kN/m.

Noddle 1 = Pin

Noddle 22 = Roller

University of Strathclyde | 3

1.5

4@2

Figure 1 Elevation of bridge truss

Dimensions - metres

Technical report

Noddle 1 (X, Y, Z) = (0, 0, 0)

Noddle 2 (X, Y, Z) = (1, 1.5, 0)

Noddle 4 (X, Y, Z) = (2, 0, 0)

Noddle 7 (X, Y, Z) = (3, 1.5, 0)

Noddle 10 (X, Y, Z) = (4, 0, 0)

Noddle 13 (X, Y, Z) = (5, 1.5, 0)

Noddle 16 (X, Y, Z) = (6, 0, 0)

Noddle 19 (X, Y, Z) = (7, 1.5, 0)

Noddle 22 (X, Y, Z) = (8, 1.5, 0)

Show node coordinates in a table

Material properties? section properties? Element types?

2. Presentation of resultsAll the results are in kN and m cxz\cxz\c.

2.1 Deformed mesh

University of Strathclyde | 4

Node DX DY1 0 02 0,0004109 -0,00039453 1,619E-05 -0,00132944 6,478E-05 -0,00074155 3,239E-05 -0,00194756 4,858E-05 -0,00140537 0,0002875 -0,00092668 0,000365 -0,00140539 0,0003812 -0,0019475

10 0,0002068 -0,00101811 0,0003974 -0,001329412 0,0001003 -0,001381713 0,0001261 -0,000926614 0,0001358 -0,001916415 0,0001713 -0,001561116 0,0003488 -0,000741517 0,0002423 -0,001561118 0,0002778 -0,001916419 2,688E-06 -0,000394520 0,0003133 -0,001381722 0,0004136 0

Technical report

University of Strathclyde | 5

Technical report

2.2 Forces and moments diagrams

Fx

Mz

Fy

University of Strathclyde | 6

Element Node Fx Fy Mz13 19 -38,1 -1,3 0,613 22 -38,1 -1,3 -1,714 5 22,2 3,5 -2,314 6 22,2 3,5 -0,615 6 22,2 8,5 -0,615 4 22,2 8,5 3,716 16 22,2 -8,5 3,716 8 22,2 -8,5 -0,617 8 22,2 -3,5 -0,617 9 22,2 -3,5 -2,318 9 22,2 1,5 -2,318 11 22,2 1,5 -1,619 11 22,2 6,5 -1,619 22 22,2 6,5 1,720 4 48,6 -7,6 3,320 12 48,6 -7,6 -0,621 12 48,6 -2,6 -0,621 14 48,6 -2,6 -1,922 14 48,6 2,4 -1,922 15 48,6 2,4 -0,723 15 48,6 7,4 -0,723 10 48,6 7,4 3,024 10 48,6 -7,4 3,024 17 48,6 -7,4 -0,725 17 48,6 -2,4 -0,725 18 48,6 -2,4 -1,926 18 48,6 2,6 -1,926 20 48,6 2,6 -0,627 20 48,6 7,6 -0,627 16 48,6 7,6 3,3

Element Node Fx Fy Mz

1 2 -42,2 -0,2 0,31 7 -42,2 -0,2 -0,22 7 -55,3 0,0 -0,12 13 -55,3 0,0 -0,13 13 -42,2 0,2 -0,23 19 -42,2 0,2 0,34 1 22,2 -6,5 1,74 3 22,2 -6,5 -1,65 3 22,2 -1,5 -1,65 5 22,2 -1,5 -2,36 1 -38,1 1,3 -1,76 2 -38,1 1,3 0,67 4 36,7 -0,4 0,37 2 36,7 -0,4 -0,48 7 -11,6 0,0 0,08 4 -11,6 0,0 -0,19 7 11,9 0,1 -0,19 10 11,9 0,1 0,0

10 13 11,9 -0,1 0,110 10 11,9 -0,1 0,011 13 -11,6 0,0 0,011 16 -11,6 0,0 0,112 19 36,7 0,4 -0,412 16 36,7 0,4 0,313 19 -38,1 -1,3 0,6

Technical report

University of Strathclyde | 7

Technical report

3. Validation of the model:3.1 Linear elasticity: The bridge is design for strength and stiffness to code of practice

3.2 Euler buckling effect of a small deformation: Λ=N/Ncc < 0.1Ncr=π²*E*I/ (CeL) ² = π²*20*10^7*3*10^-5/ (2*8)² =231 for what member?N= 11.6 so N/Ncr=0.05λ<0.1

3.3 Bending theory, shear deformationSpan/depth = 8/2 = 4

So, the shear deformation is noticeable but not dominated.

3.4 LoadingThe loading satisfies the code of practice.

Supports? connections?

ok

4. Results verification4.1 Data check OKSum of reactions Applied vertical load = 10.0 kN/m x 8 m = 80 kN

Node Rx Ry1 0.0 40.05 0.0 40.0Sum 0.0 80.0

University of Strathclyde | 8

Technical report

4.2 Check restraintsDisplacements at restraints - Node 1 X, Y and Node 5 Y = 0.0000 OK

4.3 SymmetryThe output for vertical displacement at symmetrically placed nodes 12 and 20 quoted to 15 decimal places is:

Node 12: -0.001381673528098

Node 20: -0.001381673528098

These two values are exactly the same OK

4.4 Equilibrium noddle 1

Cos (β) * 38 = 32Sin (β) * 38 = 21

Projections of the forces

With shear force of 7.95 kN

University of Strathclyde | 9

β

1

40kN

21kN

38kN

32kN

22.1kN

40kN

21kN 1

1

40kN

21.07kN 22.2kN

39.95kN

Use a greater number of signicant figures in the calculation

Technical report

The sum of the force on the noddle is equal to 0. So the equilibrium is respected. OK

4.5 Form of results: Deformation

Refer to diagram

The deflected shape looks quite linear –figure different. Meanwhile, on the bottom he deflected shape is parabolic due to a distributed load. Deflection of the top chord is linear between panel points (no applied load therefore no bending) but curved over span- expected for loading type.

Comment on the form of the force diagrams

4.6 Checking model – Internal forcesWe treat the elements as beams, so M= WL2/4 =80*82/4 = 1 280 kN.m . ??Axial force in the element F = M/b = 1 280/1.5 = 853 kN. which element?With the software we obtained 830 kN the difference between the sotware and the calcul is quite neglegtive. OK

4.7 Checking model – Deformation

W=80kN

Ac=Acl=Ap=33.4*10^-4

E=20*10^7 b=1.5 a=2 c=8

Ld=√a2+b2=√22+1.52=2.5m

Cos (θ) =a/cd=0.5

Sin (θ) =b/cd=0.6

University of Strathclyde | 10

80kN

Explain the checking model

Technical report

Θ=a.cos(a/cd)=36.87

Lb=Ac b²/2 =33.4*10^-4*1.5²/2=3.76*10^-3m

Ks=1

1E× Ad× sin (θ )∗cos (θ )

+ 1E× Ap×cot (θ)

=158227.85

Δb=W.L^3/4Ko=80*8^3/(48*20*10^7*3.76*10^-3)

=1.13*10^-3 m

ΔS=W.L/4Ko=80*8/4*Ko=1.01*10^-3 m

Δ=ΔS+Δb=2.14*10^-3 m

Δcomputeur =0.0019475 m

%diff=9.58%. OK

4.8 Stress on the model

In red there is traction and in bleu there is compression.

State how does this helps to verifty the results.

University of Strathclyde | 11

No posts therefore no Ap

Technical report

4.9 Effects of moment connection The IPE sections are convicted. ?? So we don’t have any problem to moments on the connections. not clear!

5. Sizing verificationThe sizing verification is based on the Eurocode 2.

σmax=235MPa (maximum stress acceptable)

S=33.4cm² (Area of the element) which element?

I = 3*10^-5 (Inertia moment of the element)

H = 220mm (Height of the element)

N = Traction/compression in the element

M = Moment in the element

5.1 For element A (one element at the bottom): On this element there is composed bending (traction/compression + moment).

σ =NS

+

MI

∗H

2=22.18∗103

33∗10−4 + 2.34∗103∗10−5

3

∗110∗10−3=15MPa<235MPa OK

You were expected to use the rules from the code of practice given on the website.

That the stress is less than the yield value is not an acceptable criterion. A factor of safety is needed.

5.2 For the element B (one diagonal):On this element there is only traction/compression.

σ=NS

=11.56∗103

33.∗10−4 =3.46 MPa < 235 Mpa OK

University of Strathclyde | 12

Technical report

ConclusionValidation of the model OK

Results verification OK

Sizing verification OK

After checking the results obtained with the software LUSAS, we validate verify the calculations on the structure.

Written by: -Sophie CAMBREA

-Jérémie DEIANA

-Kévin TOUATI

University of Strathclyde | 13