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stress-moment equations

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Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001781
EISBN: 978-1-62708-241-9
... of the shaft, and I is the moment of inertia. This equation sets an upper bound for the ultimate stress, which was calculated as 389.74 MPa. Secondly, assuming an elastic-perfectly plastic material model, failure occurs once all the material has reached the ultimate stress. To calculate the failure...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
..., and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... sign. Contemporary models to predict plastic deformation utilize the “flow” (i.e., yield) surface via the plastic potential equation. Because any linear model to predict flow (e.g., the Tresca criterion) is discontinuous in principal stress space, it cannot predict plastic strains for several loading...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001810
EISBN: 978-1-62708-241-9
... torsion moment M tmax can be calculated using the equation, (Eq 2) M tmax = G ⋅ π ⋅ φ ⋅ d 4 32 ⋅ L f From Eq. 2 , the maximum torsion moment M tmax was calculated to be 905.5 Nm. Using Eq. 1 and Table 4 , the torsion stress τ t was calculated to be 671.4...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.bldgs.c9001618
EISBN: 978-1-62708-219-8
... to be the culprit, the initial cracks would appear at the top of the welded joint, where the longitudinal seam weld is located. However, the cracks always initiate at 45, 135, 225, and 315°. A simple moment calculation 3 using the following equation showed that the stress caused by gravity is 7.8 ksi: (Eq 1...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... in part by the publication of another paper by Freudenthal et al. ( Ref 2 ). In light of the practical difficulties in employing a probabilistic-statistical approach to design criteria development, C.A. Cornell ( Ref 3 ) suggested the use of a second-moment format (called mean value first-order second...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001851
EISBN: 978-1-62708-241-9
... Ω m t where I z is the mass moment of inertia of the receptor shaft, and B 2n = 2nA 2n . Equation of Motion The receptor shaft may be isolated and discretized by finite element methods, and the governing equations of each component in the receptor shaft may also be derived...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... 20 years because of the difficulty in employing a probabilistic-statistical approach to design criteria development. On the eve of the 1970s, Cornell ( Ref 6 ) developed a second-moment format and concept of a safety index. This safety index was used to account for uncertainties in the design process...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001797
EISBN: 978-1-62708-241-9
... that failure from contact stresses generally leads to localized deformation or fracture by progressive spreading of a crack. Pitting is a fatigue process that can also cause the initiation and propagation of cracks [ 14 ]. Rolling contact fatigue cracks can be classified into two groups depending on where...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.mech.c9001596
EISBN: 978-1-62708-225-9
... The increase in stress over the nominal value for laterally loaded springs can be estimated with: (Eq 5) C = 1 + δ x 2 r + F l 2 P r The torsion moment due to the axial load P will be Pr . The effective radius will be increased by an amount δ x /2. In addition...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001817
EISBN: 978-1-62708-241-9
... out to model the failure of the wire rope. For this, a finite element analysis was performed to compute the stress and deformation of the wires. Figure 9 shows the model of the wire rope. To model the sophisticated geometry of the wires, the parametric equations of the position of each wire...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... ( Fig. 3 ). The mean number of cycles, N 50 , for a failure probability of 50% and a total of m tests on the stress level S a i with single results N i is given by the equation: (Eq 6) lg N 5 0 = 1 / m Σ lg N i The scattering is defined by the standard...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006773
EISBN: 978-1-62708-295-2
... of a simple uniformly loaded cantilever beam shown in Fig. 2 (a). The stress and deflection profiles for this structural member are derivable from beam theory and are readily available in many engineering tests. Closed-form equations provide the results for any location desired in the beam, provided it meets...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003526
EISBN: 978-1-62708-180-1
... of the simultaneous set of equations provides the resulting displacements anywhere in the model while still providing continuity and equilibrium. Assuming various constitutive relationships allows the results to be expressed in strain or stress rather than displacement ( Ref 7 , 8 , 9 ). While FEA is a powerful...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.mech.c9001547
EISBN: 978-1-62708-225-9
... of approximately 30° to the wire axis. The cracking paths on Appendix — Method for Estimating Bending Stress at Critical Section in End Hook Resulting From Interference Fit 8 With it assumed that interference produces a deflection Δ at the top of the end hook, deflection can be related to a bending moment M...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006919
EISBN: 978-1-62708-395-9
... to bending moments. The notch serves to create a stress concentration and to produce a constrained multiaxial state of tension a small distance below the bottom of the notch. Both of these effects tend to make the test severe from the standpoint of early transition to brittle behavior as a function of both...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
...: σ a S e + σ m σ f = 1 Fig. 6 Comparison of mean stress equations from (a) Soderberg, (b) Goodman, (c) Gerber, and (d) Morrow. Adapted from Ref 6 Fatigue Damage Summation The Palmgren-Miner damage summation rule ( Ref 32 – 34 ), sometimes referred...
Book Chapter

Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003544
EISBN: 978-1-62708-180-1
...  for  R < + 0.1 where Δ K th is in units of ksi in. for both equations. These equations indicate that the fatigue-crack-propagation threshold for steels is primarily a function of the stress ratio and is essentially independent of chemical or mechanical properties. Region 2...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.9781627082952
EISBN: 978-1-62708-295-2
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.chem.c9001738
EISBN: 978-1-62708-220-4
..., the oxidation-cracks stopped. To determine the residual creep life of the sound (non-cracked) bottom manifold material, iso-stress creep tests were performed. It was found that tertiary creep started at 7% strain. The time-to-rupture was greater than 100,000 h. It was concluded that the bottom manifold...