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A Simplistic Look at Limit Stresses From Random Loading (NASA TM-108247, Lee, 1993)

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NASA stresses
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  N S Technical emorandum NASA T - 108427 NI\S \ National Aeronautics and Space Administration ;if -,3 9 j j 7 Jj { NASA-TM-IOB427) A SIMPLISTIC LOOK T LIMIT STRESSES FROM R NDOM LO DING NASA) 22 P A SIMPLISTIC LOOK AT LIMIT STRESSES FROM RANDOM LOADING ByH.M. Lee Structures and Dynamics Laboratory Science and Engineering Directorate October 1993 N94 1S710 Unclas G3/39 0190896 George C Marshall Space Flight Center MSFC· Form 3190 Rev. Mev 1983  T BLE O CONTENTS Page IN1 R.ODUCTION THE CONTINUOUS BE M 3 SSUMPTIONS . 5 C LCUL TION OF BEAM FREQUENCIES 6 PEAK ACCELERATION FOR EACH MODE 7 M XIMUM DISPLACEMENT FOR EACH MODE 8 THE STRESS EQUATION 8 COMP RISON WITH TEST SIMULATION 2 CONCLUSIONS............................................................................................................................ 4 REFERENCES .... 7 PPENDIX 18 iii PMeEOfN PAGE BLANK NOT Ftl Mi  Figure 1 2 3 4 5 6 7 8 9 1 11 12 LIST OF ILLUSTR TIONS Title Statistical philosophy flow .......................................................................................... . Continuous beam model Pinned pinned beam modes 1 to 4 .............................................................................. . Peak acceleration for each mode ................................................................................. . Mass loading effect on beam ...................................................................................... . Maximum displacement for beam modes ................................................................... . Beam stress with Mlln = 0 Beam stress with Mlm = 3.0 ...................................................................................... . Multiple mode stress versus test simulation ............................................................... . First mode stress versus test simulation ...................................................................... . AEPI flight instrument ................................................................................................ . AEPI static tests .......................................................................................................... . iv Page 2 4 7 7 9 1 11 12 13 15 15  TECHNICAL MEMORANDUM A SIM PLISTIC LOOK AT LIMIT STRESSES FROM RANDOM LOADING INTRODUCTION Since random loads play such an important role in the design, analysis, and testing of most space shuttle payload components and experiments, the structures and dynamics community has long desired to more fully understand the relationship between the random load environment and the actual stresses resulting from that environment. The current philosophy at MSFC for calculation of random load factors embraces a statistical philosophy which utilizes Miles equation: where pk = peak random load factor (limit) Q = esonant amplification fa,ctor fn = component natural frequency, Hz PSD j = input qualification criteria atfn, G 2 /Hz. This equation involves calculation of the loads based on (1) analytical or tested values for significant resonant frequencies lfn), (2) an historically based damping value of 5 percent (Q = 10) or component measured damping from testing, (3) the magnitude of the maximum expected flight environment at resonance (PSDj), and (4) a statistically 30 definition of peak load. f you remove the crest factor of 3 from the equation, the remaining expression, J 1' Q n . P S j represents the root mean square response (Grms) of the component. This assumes that the component is a single degree-of-freedom harmonic oscillator driven at all frequencies by a white noise environment at constant PSD level and that the component does not affect the input. From a statistical point of view, the Grms response can be set equal to the standard deviation (0 ) by assuming that the realized ensemble of random input time histories are best represented by a Gaussian distribution with a mean of zero. Under these conditions the Grms response is a 10 response. Multiplying the Grms by the crest factor 3 produces the well known 30 response value which has a 99.73-percent probability of being greater than any instantaneous random load encountered. In Miles equation, the other critical probabilistic term is the qualification input criteria value (PSDj) at the component s natural frequency lfn) From the historical data base, a 97.50-percent probability level is calculated (a 1.960 value). This level then becomes the basis from which the actual component criteria is developed (fig. 1). Statistically, the criteria assures the analyst that the flight loads have only a 2.5-percent probability of an exceedance. Further confidence in the analytically derived criteria s gained from the fact that the criteria is created from straight-line enveloping of the data, and from the requirement to hard mount components during vibration testing.
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