Sébastien MICHAL
1. LIFTING BEAM ANALYSIS:
1.1. Lifting beam drawing.
This drawing is available on CDD: CMSTKGET0104.
This lifting beam will be used to lower the TRACKER, including the carriage, into the CMS experiment
cavern. Then it will also serve to lift the TRACKER into the CMS magnet.
This lifting beam is designed for lifting a load of 6650 Kg. This total mass is composed by the tracker
(5350kg), the carriage (1000 kg) and the lifting beam (300 kg).
The four 2 tons shackles used at the lifting beam are the same as used at the lifting T profiles (see CERN
catalog page 46 with reference 45.82.70.012.7).
The reference of the central shackles which supports half of the total mass (2900 kg) of the assembly
each is 45.82.70.021.6 (certified for 6500 Kg).
The partial safety factors according to the EUROCODE 3 (table 1 page 2-18: « tableau synoptique des
valeurs de coefficients partiels de sécurité ») and the FEM 1.001(notebook 2 and 9.3) are:
-
1.5 for the variable loads.
-
1.6 for the dynamic loads.
Consequently, the minimal safety factor allowed for this type of structure is 2.4 with respect to the yield
stress.
CMS/TRACKER Carriage Analysis
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Sébastien MICHAL
1.2. Lifting beam calculations
All the calculations are made for a total load of 65170 N composed by the Tracker, the carriage and the
lifting beam mass.
-
Stress in the top eye
The total mass of 65170 N is distributed on the
two lifting eyes.
Since the lifting sling has a maximum angle with
the vertical axe of 30° (left part of the drawing),
the first static equation gives:
F  56840 / 2 cos 30
F  32817 N
A conservative approach is to consider than the maximum stress is located in the top of the hole with
the maximal load (right part of the drawing). The plate is 20 mm thick. The section is 31 mm high.
Consequently, the shear area on the both side of the hole is: S
 20  31  620 mm2
The shear load of the section is 30300 N. Consequently the maximal stress is:

32817
 26.5 MPa
2  620
The maximum stress is:
 VM  (3 2 )  (3  24 2 )  45.9 MPa
The safety factor is 5.1 with respect to the yield stress.
-
Weld calculation
The total length of the weld is 540 mm.
Since the weld is 10 mm, the total area is 5400 mm .
2
 VM  (3 2   2 )  (5.3 2  3  3.12 )  7.6 MPa
The Von MISES stress in the weld is below 10 MPa.
The safety factor is 27 with respect to the ultimate stress.
The length of this weld loaded in shear stress is 280 mm.
The corresponding effective area of this weld is A  140  2  5  1400mm

15600
 12 MPa
1400
 vm  (3  12 2 )  21 Mpa
The safety factor with respect to yield stress is 9.8.
CMS/TRACKER Carriage Analysis
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Sébastien MICHAL
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Stress in the bottom eyes
The plate is 15mm thick. The section with the higher stress is 21mm high. The
corresponding area is A  21 15  315mm

2
15600
 50 MPa
315
 vm  (3  502 )  87 Mpa
The safety factor with respect to yield stress is 2.7.
-
Stress in HEB profiles:
The central beam is a HEB 160 profile (see CERN catalog
44.47.23.160.5). The length of this beam on bending load is
635 mm and his weight is 100 kg.
The load applied on each extremity of this beam is 27930 N,
(half of the tracker mass: 22050N, half of the mass of the
carriage: 4900 N and the mass of one transversal beam of the
lifting beam: 980N).
The resulting moment according to the scheme above is:
ql2
 F l
2
or P  ql  900 N for the central beam.
P 900
q 
 0.5294 N / mm
l 1700
ql2
0.5294  635 2
Mf 
 F l 
 27930  635  17842284 N .mm
2
2
Mf 
Since the section modulus of this beam is:

Mf
W

W  311000mm3
17842284
 58 MPa.
311000
The safety factor is 4 with respect to the yield stress.
In the same way, the extreme beams (HEB 140: CERN catalog 44.47.23.140.9) are loaded with two forces
of 13475 N on each extremity composed by a quarter of the mass of the tracker (11025 N) and a quarter
of the mass of the carriage (2450 N).
P 1000

 0.3571N / mm for the transversal beams.
l 2800
ql2
0.3571  1400 2
Mf 
 F l 
 13475  1400  19214958N .mm
2
2
q
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Sébastien MICHAL
Since the section modulus of this beam is:

Mf
W

W  216000mm3
19214958
 89 MPa.
216000
The safety factor is 2.6 with respect to the yield stress.
-
Bolts calculation:
The bolts of the lifting beam are principally loaded in tension since they support the total mass of the
assembly including the carriage and the transversal beams of the lifting beam (5100 Kg).
Four bolts ISO 4014-M16x60-8.8 are chosen (CERN catalog: 47.62.81.517.6).
Hexagonal screws
DIN933 ISO4014
Material
Steel
Quality
8.8
Ultimate stress
800 N/mm2
Yield stress
640 N/mm2
Elongation at rupture
12 %
Hexagonal nuts (black alloy, steel) ISO 4032-M16-8 (CERN catalog: 47.43.81.160.3) are used.
Plain washers (steel) M16 (CERN catalog: 47.78.12.160.3) are used.

Tensile load on the bolt:
The pretension load is: F  0.9  Re  S eq .
S eq 157 mm2
F  0.9  640  157  90430 N .
The tensile stress area is:
These 8 bolts can support a maximum tensile load of 720000 N.
Since the maximal load applied is 56840 N, the safety factor is 12.6.
The bolts will be tightened with 200 N.m resulting in a preload of 90000 N corresponding to 90 % of the
elastic limit.
CMS/TRACKER Carriage Analysis
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Sébastien MICHAL
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Hypothesis with maximal load on two shackles :
With two shackles loaded with their nominal values of 2000kg (19600N), the two other shackles are
loaded at 1175 kg (11515N) which correspond to a total load for the tracker assembly of 6350Kg.
The corresponding moment along the central beam of the lifting beam is:
Mz  1400  8085  11319000 N .mm
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