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GLAST LAT Project

1x4 Grid Lift Fixture Weld Analysis1x4 Grid Lift Fixture Weld Analysis1x4 Grid Lift Fixture Weld Analysis1x4 Grid Lift Fixture Weld Analysis

September 19, 2003

Youssef IsmailYoussef Ismail

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ContentsContents

• Fixture Description

• Loading and BCs

• Analysis and Models Used

• Description of Analyses and Methodology

• Material Properties and Allowables

• Results

• Conclusions

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Component Design DescriptionComponent Design Description

• 1x4 Grid Lift Fixture• Unreleased Check Print• Frame constructed of 1144 Fatigue Proof Steel. Typical 1144 Steel has a Yield Strength of 276 MPa (40

ksi), - ASM Metals Reference Book, 1981. Fatigue Proof Steel is quoted as having a Yield Strength of 690 – 778 MPa (100 – 113 ksi), but no reference has been found to substantiate that strength.

• Fixture Structural members are 3 in square box beams with 0.25 in wall thickness.

• Two 0.25 in gusset plates on top and bottom are also welded at each member junction.

• Central lift point on center cross member.

• All members are butt welded with an assumed 80% penetration weld.

• 1x4 Grid lifted by four pickup points, one on each corner via a bar connected to Grid and Fixture at its ends by spherical bearings (rod ends).

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Loads and Boundary ConditionsLoads and Boundary Conditions

• The fixture is analyzed for lifting the 1x4 Grid and all four bays filled with flight components.

• The assumed mass of the filled 1x4 Grid:

– Grid: 150 lb (330.75 kg)

– Interface Plates (GSE): 50 lb (2 @ 25 lb) (110.25 kg)

– TKR: 280 lb (4 @ 70 lb) (617.4 kg)

– Cal: 880 lb (4 @ 220lb) (1940.4 kg)

– Eboxes: 60 lb (4 @ 15 lb) (132.3 kg)

– Lift Fixture: 180 lb (396.9 kg)

• Total load applied to Fixture during quasi static lift: 1600 lb (7116.8 N)

• Assumption: each corner carries equal amount of load.

• Three forces applied at each corner which are the component loads transferred from the lift fixture to the 1x4 Grid. Values determined from lift link orientation shown in Fixture drawing on pg 3.

– Z: 400 lb (1779.2 N)

– X: 58 lb (258 N)

– Y: 108 lb (480.4 N)

– Resultant Load on each corner 418.5 lb (1861.5 N)

• Boundary Condition: Frame held pinned in X, Y, and Z at the center of the center cross member.

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Analysis Model ConfigurationAnalysis Model Configuration

• Two models used:

– Simple Bar Model

– 3D shell model, modeling the actual box beams using shells

• Gusset plates were not modeled in either model under the reasoning that if the frame can sustain the applied loads without them, then it could sustain the loads with them.

• Model metrics

– Simple Beam Model• 88 Bar elements• 87 Nodes

– Shell Model• 20736 Quad4 elements• 20644 Nodes

• Comparison of FEA model with flight design

– Mass of FEA model: 185.88 lb (84.28 kg), slightly higher than prediction.

– Model simplifications• Gussets not modeled• Shell and beam elements are same material throughout, not accounting for different weld material

– Under the premise that in a penetration weld the strength of the weld is equivalent to the parent material. Stresses will be analyzed under this premise.

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Description of Analyses and MethodologyDescription of Analyses and Methodology

• Hand Calculations for load path analysis.

• Initial Stress calculation by hand.

• Initial FEM analysis via Bar Model

• Secondary FEM analysis via Shell model

• Assumptions made:

– 80% penetration welds understood as effective beam wall thickness is at 0.20 in (5.08 mm) vs. 0.25 in (6.35 mm)

– Both beam elements and shell elements modeled using the reduced thickness.

• Factors of safety used in the analyses

– Safety factor of 1.25 used on loads due to possible occurrence of a sudden drop.

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Material Properties and AllowablesMaterial Properties and Allowables

• Frame to be constructed of ASTM A500 steel with a Tensile strength of 400 MPa (58 ksi) and a Yield strength of 317 MPa (46 ksi)

• Joints are Butt Welded penetration welds. Assumption on actual weld penetration is 80%. Typical penetration welds have the strength of the parent material. Stresses in the box beam wall are dependent on the box beam wall thickness and hence the weld strength. With the 80% penetration weld, the box beam wall thickness is reduced by 20% with a 100% penetration weld in determining stresses.

• Need to maintain a minimum M.S. of 5 for these welded joints.

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Analysis Results and InterpretationAnalysis Results and Interpretation

• Hand Calculation of Load Path

X

Y

Z

R

Rz

1600

400

400

400

400

Rx Ry Ry

Ry

Ry

Ry

Rx

Rx

• Assumptions:• Each corner carries ¼ of vertical lift load• = 75 degrees from X axis from page 3

• 82 degrees from X axis from page 3

Rx = Rcos Ry = RcosRz = Rcos

R = [(Rcos(75))2+(Rcos(82))2+(Rcos())2]1/2

Solving for cos(): cos() = 0.9558With cos() known, and Rz = 400lb R is known: R = 400/0.9558 = 418.498 lbWith R known, Rx and Ry can be found: Rx = 58.244 lb, Ry = 108.315 lb

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Analysis Results and InterpretationAnalysis Results and Interpretation

• Hand Calculations of Load Path Cont.

•Internal loads at center cross bar and long bar interface

400 lb

800 lb

400 lb

Loading along long bar

Shear along long bar

Moment along long bar

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Analysis Results and InterpretationAnalysis Results and Interpretation

• Hand Calculations of Load Path Cont.

Peak Moment and shear occurs at the center of the long beam

400 lb 16400 in-lb = M

41 in 400 lb

• Hand Calculations of Bending Stress.

Moment of Inertia of Beam cross section

3 in

3 in0.2 in

I1 = I2 = 1/12[bo(ho)3-bi(hi)3] = 3.49479 in4

= My/I = (16400)(1.5)/3.494979 = 8362 psi, M.S. = 4.5 under quasi-static M.S. = 3.4 under sudden drop

Beam Bending Stress Calculation

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Analysis Results and InterpretationAnalysis Results and Interpretation

• FEM Bar model predicts slightly lower stresses due to additional components of axial stress not accounted for in hand calculations

Maximum Beam Stress from BAR Model: NASTRAN Output given in MPa.

ELEMENT SA1 SA2 SA3 SA4 AXIAL SA-MAX SA-MIN

ID. SB1 SB2 SB3 SB4 STRESS SB-MAX SB-MIN

21256 5.20E+07 -5.20E+07 -5.20E+07 5.20E+07 -1.79E+05 5.18E+07 -5.22E+07

5.54E+07 -5.55E+07 -5.54E+07 5.55E+07 5.53E+07 -5.56E+07

21257 5.55E+07 -5.54E+07 -5.55E+07 5.54E+07 -1.79E+05 5.53E+07 -5.57E+07

5.20E+07 -5.20E+07 -5.20E+07 5.20E+07 5.18E+07 -5.22E+07

Maximum Bending Stress: 55.5 Mpa = 8049.59 psiMaximum Combined Stress: 55.3 Mpa = 8020.59 psi M.S. = 4.7 under quasi static M.S. = 3.6 under sudden drop

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Analysis Results and InterpretationAnalysis Results and Interpretation

• FEM Shell model predicts higher stresses due to continuum interaction not present in beam theory.

Maximum Von Mises Stress: 55.5 Mpa = 8049.59 psi M.S = 4.7 under quasi static M.S. = 3.6 under sudden drop

Area of Maximum stress with the exception of the loading point at the center of the cross member

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Welded Joint StressesWelded Joint Stresses

• FEM Beam model is used to determine the internal forces at the welded joints.

• Loads at the frame corners in the shorter cross beams at the weld joints: – Tensile: -481 N (-108.13 lb)– Shear: 0.0 in both planes– Moment: -6.67 N-m (-59.03 in-lb) vertical plane; .0578 N-m (0.512 in-lb) horizontal plane

• Loads at the center cross member:– Tensile: -0.802 N (-18 lb)– Shear: 3558.41 N (799.96 lb) vertical plane; 0.0 in horizontal plane– Moment: -269 N-m (2380.85 in-lb) vertical plane; 12.1 N-m (107.09 in-lb) horizontal plane

• Weld analysis by hand calculations. Welds treated as lines and allowable loads determined using an equivalent force/unit length of weld formula similar to actual stress calculations. The above loads are applied over the length, and section moduli of the line and the resulting load/ unit length are combined vectorially and compared against accepted allowable line loads for the various welds.

• Allowable weld line loads (Ref: Design of Weldments, O. Blodgett, 1963-1977, pgs 6.3-3 to 6.3-5)

Fillet WeldPenetration

Weld

Parallel Load

9,600 lb/in 13,600 lb/in

Transverse Load

11,200 lb/in 13,600 lb /in

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Welded Joint StressesWelded Joint Stresses

• Frame Corners Welds see tensile and bending loads.

For tensile loading the equivalent line load formula is fp = P/Aw

where P is the tensile load and Aw is the combined length of

welded joint, uniform over the whole weld line.

For bending the equivalent line load formula is fm = M/Sw where

M is the bending moment on the joint and Sw is the section modulusof the welded joint, taken to be a maximum at either the top or the bottom and to right or left extreme position of the weld line relative to the weld line’s C.G.

fp

fm

For the weld line of a square beam to the side of a second beam of geometry shown on slide 10

Aw= 2 (3+3) = 12 in, then fp = P/Aw = 108.13/12 = 9.01 ib/in

The section modulus is given by Sw= bd + d2/3 where b is the width of the line pattern and d is the height

So Sw = 3*3 + (3*3)/3 = 12 in2, then fm = M/Sw = 59.03/12 = 4.92 ib/in

The Axial load is compressive, while the bending moment at the “top” is causing tension so the

Two loads are subtracted giving the resultant line load of fr = fp-fm = 4.09 lb/inwell below the allowable line load for either a fillet of penetration weld of 11,200 lb/in

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Welded Joint StressesWelded Joint Stresses

• Frame Cross bar Welds see tensile and bending loads.

For tensile loading the equivalent line load formula is fp = P/Aw

where P is the tensile load and Aw is the combined length of

welded joint, uniform over the whole weld line.

For bending the equivalent line load formula is fm = M/Sw where

M is the bending moment on the joint and Sw is the section modulusof the welded joint, taken to be a maximum at either the top or the bottom and to right or left extreme position of the weld line relative to the weld line’s C.G.

For the weld line of a square beam to the side of a second beam of geometry shown on slide 10

Aw= 2 (3+3) = 12 in, then fp = P/Aw = 18/12 = 1.5 ib/in and fv = 800/12 = 66.7 lb/in

The section modulus is given by Sw= bd + d2/3 where b is the width of the line pattern and d is the height

So Sw = 3*3 + (3*3)/3 = 12 in2, then fm = M/Sw = 2380.85/12 = 198.4 ib/in

The resultant force is the sum of the squares. fr = ([fm-fp]2 + fv2)1/2 = ([198.4-1.5]2+66.72)1/2 = 207.88 lb/in

Again well below the allowable 9600 lb/in for a loading when a parallel load is applied.

Setting the minimum M.S. based on allowable line load at: M.S. = 9600/207.88 -1 = 45.2

fp

fm

fv

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Preliminary SummaryPreliminary Summary

• Margins of safety for beam stresses are all found to be below 5.0 for the given beam geometry and material choice.

• The stresses recovered are for a frame without the proposed gusset plates. The nature of the stresses in the frame are primarily those due to bending and the additional gussets will not significantly reduce the bending stress.

• Suggest a different beam cross-section that will increase the bending stiffness of the beam.

• The welded joints of the lifting frame for the proposed beam geometry should be adequate to support the lifting operations it is designed for.

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Beam Cross-Section RedesignBeam Cross-Section Redesign

• The current beam cross-section depth is 3 inches. Increase the depth to 4 inches and reduce the width to 2 inches. This will maintain the same weld area and a 30% increase in mass over the current beam design but increases the bending stiffness by 51%.

• Resulting bending stresses from the updated beam geometry given below for the simplified beam FEA model

ELEMENT SA1 SA2 SA3 SA4 AXIAL SA-MAX SA-MIN

ID. SB1 SB2 SB3 SB4 STRESS SB-MAX SB-MIN

21288 2.88E+07 -2.87E+07 -2.88E+07 2.87E+07 -1.02E+05 2.87E+07 -2.89E+07

3.07E+07 -3.07E+07 -3.07E+07 3.07E+07 3.06E+07 -3.08E+07

21289 3.07E+07 -3.07E+07 -3.07E+07 3.07E+07 -1.02E+05 3.06E+07 -3.08E+07

2.88E+07 -2.88E+07 -2.88E+07 2.88E+07 2.87E+07 -2.89E+07

•Maximum beam stress reduced from 55.3 Mpa (8020.59 psi) to 30.6 MPa (4436.7 psi)

Maximum Combined Stress: 30.6 Mpa = 4436.7 psi M.S = 9.4 under quasi static M.S. = 7.3 under sudden drop

Bringing the required M.S. above 5 for the entire lifting frame.

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ConclusionsConclusions

• Margins of safety for beam stresses and welded joints found to exceed the requirement of 5.0 using the newly proposed beam cross section of 2 in wide by 4 in deep with a 3/8 inch wall thickness. Material choice of ASTM A500B is an adequate material for the frame. Although information regarding material property degradation due to welding was not found.

• Maximum stresses overall were found to be related to bending at the mid-span of the frame.

• Welded joints were not heavily loaded and are adequate.