Summary of mechanical calculation results

A. CatinaccioPH-DT Engineering Office, CERN

Page 1

CERN, May 27th 2015

Calculations model: global “box” beam

Page 2

• Max lateral deflection (@350 mbar) = 31.2 mm

• Max beam stresses (Von Mises) = 160 Mpa

• Full model confirms that a beam portal model of a unit cell (1.6 m pitch) is well representative

• Results in line with 3D beam Scia engineer EC3 results

• Results in line with portal beam model (when modelling perfect moment connections)

• See next slides for EC3 and ASME verifications

Calculation model: portal beam

Page 3

Model loading and boundary conditions

Summary of results from the above runs:

Pressure [mbar] Vertical Deflection [mm] Lateral Deflection [mm]

350 -14.6 39

20 -17.5 30

Stresses at 350 mbar top Max VM equivalent stress Max VM equivalent stress

Value [MPa] 160 1.4

ASME verification of results from the above runs:

Stresses at 350 mbar top Max VM equivalent stress Max VM equivalent stress

Value [MPa] 160 1.4

Location Vertical beam top flange Vertical beam web

Linearized stress category Pm+Pb Pm

ASME allowable (ref. 6.1) < 1.5 S = 331 MPa < S = 220 MPa

Factor 2.06 157

It should also be mentioned that the condition Pm < S is verified in all points of the main members of the frame, where the maximum membrane stress, detected on the bottom beam is Pm = 24.4 MPa.

• Sag conservative but in favour of safety: due to extra span in modelling beam length and height to centroid axis and from rotational stiffness treatment for corner connections.

• Selected following EC3 to obtain conservative predictions.

• Moment & force results used to design and check connections

• ASME verification OK with minimum safety factor of 2

• Eurocode 3 verification on beam bending, shear, normal force capacity OK –buckling verification OK (with bracings).

𝑃𝑚 < 𝑆𝑃𝑚 + 𝑃𝑏 < 1.5 ∙ 𝑆

𝑃𝐿 < 1.5 ∙ 𝑆𝑃𝐿 + 𝑃𝑏 < 1.5 ∙ 𝑆

√

Static and buckling of shell portal model

Page 4

Table 1. Maximum static deflections in the horizontal and vertical directions obtained for an over-pressure of 20 and 350mbar.

Maximum Deflection (mm)

Over-pressure (mbar)

Horizontal direction Vertical Direction

20 18.6 -12.7

350 22.7 -6.7

Height of the lowest point along the vertical beam with zero bending moment for the two support configurations under investigation. This information has been taken into account in the definition

of a suitable position for the splice connection.

Height for zero bending moment in vertical beam * (m)

Over-pressure (mbar) Support Condition 1 (i.e. inside corner)

Support Condition 2 (i.e. outside corner)

20 2.19 2.74

350 2.24 2.71

* The height is measured from the ideal bottom corner of the warm vessel

Figure 1. Geometry and dimensions of the shell model of the main portal employed in the static finite element analysis.

Figure 1. Geometry and finite element mesh used for the detailed analysis of the splice connection.

• Smaller sag (in line with beam models with reduced span and perfect M connections)

• Shell model results well suited to analyse buckling, identify optimum position of splice connection and sub-modelling of connections for ASME FEA verification

Static and buckling of shell portal model

Page 5

Table 1. Linearized equivalent stresses computed for the linear paths illustrated in Figure 5.

Over-

pressure (mbar)

Linearized Equivalent Stress (MPa) Allowable Limit

(MPa)

Pm or PL Pb (Pm+Pb) or (PL+Pb) 𝑺 𝟏.𝟓 ∙ 𝑺

Ver

tica

l Bea

m

Path A 20 8.7 82.5 91.2 225 337.5

350 13.2 102.6 115.7 225 337.5

Path B 20 74.9 90.3 165.1 225 337.5

350 89.9 109.1 199.0 225 337.5

Path C 20 27.3 15.0 42.2 225 337.5

350 45.9 49.4 95.3 225 337.5

Ro

of

Bea

m

Path D 20 7.1 38.3 45.4 225 337.5

350 12.1 12.3 24.4 225 337.5

Path E 20 6.3 31.0 37.3 225 337.5

350 19.1 64.4 83.6 225 337.5

Flo

or

Bea

m

Path F 20 25.3 0.7 26.0 225 337.5

350 30.5 0.9 31.4 225 337.5

Path G 20 64.1 81.2 145.3 225 337.5

350 80.4 103.1 183.4 225 337.5

Schematic representation of the line paths used to perform the stress linearization in the different beams.

• Linearized stresses all OK for ASME for general and local categories

• Load multipliers (with bracings) well above 4 for eigen-buckling

𝑃𝑚 < 𝑆𝑃𝑚 + 𝑃𝑏 < 1.5 ∙ 𝑆

𝑃𝐿 < 1.5 ∙ 𝑆𝑃𝐿 + 𝑃𝑏 < 1.5 ∙ 𝑆

1.1.1.1 Buckling Analysis: Results

Table 1. Load multipliers obtained in the linear buckling analyses performed on the main portal. Both the results obtained with and without bracing have been included for comparison.

Buckling Mode Load Multiplier

No bracing Bracing

1 2.2 7.1

2 4.2 9.6

3 4.3 12.0

4 5.6 18.5

5 6.4 18.8

√

√

Calculations models: main connectionsVerification based on EC3 (with M,N,T diagrams as input from beam model)

Strength and stability of material, welds and bolts verified.

Page 6

Table 1

Connection type 1 Column to beam

2 Splice corner 3 Reduced splice

Moment Capacity [MN m] 5.107 3.514 3.07

Calculated Moment [MN m]

2 1.5 (as design margin)

0

Margin on M capacity 2.55 2.34 NA

Shear Capacity [MN] 2.02 3.704 2.52

Calculated Shear [MN] 0.1775 1.56 0

Margin on Shear capacity 11.38 2.37 NA

Normal force capacity [MN]

-12.15/+7.113 -10.1/+4.72 -9.8/+5.19

Calculated Normal force [MN]

1.24 ~0.01 1.9

Margin on N force capacity 5.73 471 2.73

M+N capacity factor < 1 0.57 0.43 0.366

105 200

410

16

01

60

16

01

60

16

0

4 r

ow

s t

en

sio

n +

sh

ea

r2

ro

ws s

hea

r

16

9

11

38

HL 1100*607 (Steel S355)

12*M48 bolts (class 10.9)tp=30 mm (Steel S 355)

30 30

105 200

410

164

55

400

1008

HL 1100*607 (Steel S355)

10*M48 bolts (class 10.9)tp=30 mm (Steel S 355)

170

170

170

4 r

ow

s te

nsi

on

+ s

he

ar

30 30

170

1 r

ow

sh

ear

HL 1100*607 (Steel S355)

12*M48 bolts (class 10.9)tp=30 mm (Steel S 355)

200

410

20

0

13

88

10

02

45

200

20

02

00

20

0

30

HL 1100*607 (Steel S355)

HL 1100*607 (Steel S355)

20

20

√

Calculations models: main connectionsVerification based on FEA sub-models

Strength of material, welds and bolts ASME verified.

Page 7

Corner welded connection linearized equivalent stresses computed for the paths

Over-pressure

(mbar) Linearized Equivalent Stress (MPa) Allowable Limit (MPa)

PL Pb (PL+Pb) 𝑺 𝟏.𝟓 ∙ 𝑺

Path A 20 135.0 83.2 218.2 225 337.5

350 169.2 103.5 272.7 225 337.5

Path B 20 132.6 83.2 215.8 225 337.5

350 166.5 103.4 269.9 225 337.5

Path C 20 13.4 8.4 21.8 225 337.5

350 15.6 11.1 26.7 225 337.5

Averaged equivalent stress (von Mises) in the cross section of the bolts of the top connection calculated for 20 and 350mbar of over-pressure.

Over-pressure

(mbar) Averaged Equivalent Stress

(MPa) Allowable Limit,

𝟐

𝟑𝝈𝒚

(MPa)

Bolt 1 20 391.6 600

350 390.3 600

Bolt 2 20 390.4 600

350 388.6 600

Bolt 3 20 390.2 600

350 387.5 600

Bolt 4 20 389.8 600

350 388.3 600

Bolt 5 20 396.5 600

350 420.7 600

Bolt 6 20 430.9 600

350 454.6 600

Linearized equivalent stresses computed for the linear paths

Over-pressure

(mbar)

Linearized Equivalent Stress (MPa)

Allowable Limit (MPa)

PL Pb (PL+Pb) 𝑺 𝟏.𝟓 ∙ 𝑺

Path A 20 18.1 42.3 60.5 225 337.5

350 43.4 87.1 130.5 225 337.5

Path B 20 35.1 87.6 122.7 225 337.5

350 58.0 157.4 215.4 225 337.5

Path C 20 8.3 2.5 10.8 225 337.5

350 12.1 3.1 15.2 225 337.5

√

𝑃𝑚 < 𝑆𝑃𝑚 + 𝑃𝑏 < 1.5 ∙ 𝑆

𝑃𝐿 < 1.5 ∙ 𝑆𝑃𝐿 + 𝑃𝑏 < 1.5 ∙ 𝑆

welds

bolts

welds

Most stressed weld

Calculations models: main connectionsVerification based on FEA sub-models

Strength of material, welds and bolts ASME verified.

Page 8

Averaged equivalent stress (von Mises) in the cross section of the bolts of the splice connection calculated for 20 and 350mbar of over-pressure for different splice heights, Hsplice.

Over-pressure

(mbar) Averaged Equivalent Stress (MPa) Allowable Limit

(MPa) HSplice=2.25m HSplice =2.75m HSplice =3.25m

Bolt 1 20 422.0 422.0 421.6 600

350 422.3 422.4 422.0 600

Bolt 2 20 402.3 402.5 402.3 600

350 402.7 402.7 402.5 600

Bolt 3 20 401.8 402.1 401.8 600

350 402.1 402.2 401.8 600

Bolt 4 20 401.4 401.8 401.4 600

350 401.9 401.9 401.4 600

Bolt 5 20 401.1 401.6 401.1 600

350 401.9 401.6 401.0 600

Bolt 6 20 400.0 402.1 400.0 600

350 402.1 401.3 399.4 600

Linearized equivalent stresses computed for the linear paths illustrated (corresponding to a splice height of 2.75m measured from the bottom corner of the warm vessel).

Over-pressure

(mbar) Linearized Equivalent Stress (MPa)

PL Pb (PL+Pb)

Path A 20 44.7 33.1 77.8

350 52.0 37.8 89.8

Path B 20 13.1 7.8 20.9

350 12.9 9.0 21.9

√

welds

bolts

Calculations model: 3D beam (Scia eng)

Scia engineer full verification according to Eurocode 3:

Page 9

Figure 1 – Structure mesh

Figure 2 - Structure mesh (rendered geometry)

o All main members verified

according to EC3

o Connections modelled as

perfectly rigid connections

according to EC3 Mathcad

calculations (Annex H)

o All verifications OK

Steel Grades

• Steel S355 (EC properties for t>40mm)

– σy=335 MPa → σy/1.5=223 MPa

– UTS=470 MPa → UTS/3.5=134 MPa → UTS/2.4=195 MPa

• Baseline material S460ML (properties for t>40mm):

– σy=430 MPa → σy/1.5=286 MPa

– UTS=530 MPa → UTS/3.5=151 MPa → UTS/2.4 =220 MPa

Page 1024/04/2015