Duration of load effects in lumber. Part I: A fracture mechanics approach

1982 ◽  
Vol 9 (3) ◽  
pp. 502-514 ◽  
Author(s):  
Kenneth Johns ◽  
Borg Madsen

In Part I of this paper, the deterioration of the strength of lumber with continued application of constant stress, called the duration-of-load effect, is treated using a viscoelastic, limited ductility fracture mechanics model. The model is explained and developed in a general way, then modified for use with commercial lumber. The problems of assigning correct creep function parameters and values of stress ratio for use in calculations involving the model are discussed. The evident weakening of boards surviving a long-term test can be used to project a failure time that is longer than the test period. Numerical results are shown and compared with the Madison curve, the basis for current design codes. Parts II and III of this paper demonstrate experimental verification and discuss design implications.

1986 ◽  
Vol 13 (2) ◽  
pp. 188-195 ◽  
Author(s):  
R. A. Spencer ◽  
Borg Madsen

The strength of wood falls with time under load, and in current design codes the short-term strength of wood is reduced by about 40% to account for duration of load effects. This figure is based on tests made on small bending specimens. In this paper are described tests made on wooden torque tubes to investigate the effect of duration of load on shear strength. A control sample was tested to establish a curve for short-term strength, and four groups of 80 specimens each were then tested under various levels of constant long-term load. Stress ratio at failure was estimated by assuming that the short-term strength of each group could be represented by the control curve, and that under long-term loading specimens would fail in the order of their short-term strength. In each group the stress ratio at failure fell with time under load, and this reduction appears to be related to that predicted by a viscoelastic plastic model. It is concluded that the Madison curve presently used to predict duration of load effects may be conservative at normal levels of applied stress. Key words: wood, shear, long-term loading, duration of load.


1982 ◽  
Vol 9 (3) ◽  
pp. 515-525 ◽  
Author(s):  
Borg Madsen ◽  
Kenneth Johns

The viscoelastic fracture mechanics model developed in Part I is calibrated using a 70-day duration of load test on commerical lumber. The model is then verified using another similar test on a different population of boards, and on a unique 6-year test just terminated. All three test programs are described. The model is used to tentatively project results beyond the period of testing. The strength predictions of the model compare well with those obtained experimentally during the tests, the coefficient of correlation being 0.95. Implications for design practice are outlined in Part III of this paper.


1982 ◽  
Vol 9 (3) ◽  
pp. 526-536 ◽  
Author(s):  
Borg Madsen ◽  
Kenneth Johns

The implications for practical structural design with wood of a visco-elastic fracture mechanics model, recently developed and verified experimentally by the authors, are presented. These are compared with those of the presently used Madison concept, and with those of the cumulative damage models. Following discussion of present practice and the consequences of the fracture mechanics model, specific design recommendations are made as to how this more complicated model might be incorporated into design codes.


Author(s):  
Pieter van Beek ◽  
Richard Pijpers ◽  
Kenneth Macdonald ◽  
Johan Maljaars ◽  
Knud Lunde ◽  
...  

In the process systems of offshore installations, welded small-bore side branches can prove vulnerable to high-cycle fatigue failure due to vibrations. This is especially the case for welded connections at tie-in points to the main pipe which are often critical details. International standards and guidelines therefore provide maximum acceptable vibration levels to ensure long term safe operation. In some guidelines, however, these acceptable vibration levels are phrased in terms of screening levels and in practice can be unduly conservative. Process pipework might then unjustly be regarded as unsafe based on measured vibrations in the field. This is especially true for offshore systems, which are characterized by low mechanical damping in the structure. This may result in overdesigned piping or over-conservative operational limits in order to keep vibration levels within the acceptable range. Furthermore, the screening methods and any detailed fatigue assessments typically use established stress-life (S-N) based fatigue design methods where uncertainty exists in the very high-cycle regime. This paper describes a novel and advanced tailor-made fatigue assessment method whereby acceptable vibration levels are based on maximum acceptable stress ranges for individual side branches. The acceptable stress ranges for each critical welded connection are based on a fracture mechanics analysis of fatigue crack growth. This method also minimizes the cantilevered (overhung) mass of small-bore side branches, whilst remaining safe for long-term operation. To illustrate the strength of the assessment methodology in practice, this paper describes the application of the procedure to a 2″ side branch connected to a main piping system. A fracture mechanics model and a detailed 3D finite element model are made. By comparing the stress ranges from the fracture mechanics model with the normalized stress ranges obtained from the dynamic FE analysis, maximum acceptable vibration levels for this particular side branch have been derived. The method is validated with experimental modal analysis and strain gauge measurements.


Author(s):  
Francisco L. Silva-Gonza´lez ◽  
Ernesto Heredia-Zavoni

Fluctuating stresses and strains due to wave forces cause accumulated fatigue damage in tubular joints of marine platforms. Considering the uncertainties in the loads, material properties, initial crack sizes, and stress intensity factors, etc., may affect significantly the reliability assessment of marine jacket platforms. In this paper, we assessed the effect of uncertainties about such fatigue variables on the time evolution of the reliability of series and parallel systems considering correlation between failure modes. The fracture mechanics Paris-Erdogan model is used to model crack growth and a FORM method is used for computing the safety index. The uncertain variables analyzed are: initial crack size, material parameters C and m in the fracture mechanics model and the shape and scale parameters of the Weibull density function used for the long-term distribution of stress range.


Author(s):  
Thomas B. Johannessen ◽  
Øistein Hagen

Offshore structures are typically required to withstand extreme and abnormal load effects with annual probabilities of occurrence of 10−2 and 10−4 respectively. For linear or weakly nonlinear problems, the load effects with the prescribed annual probabilities of occurrence are typically estimated as a relatively rare occurrence in the short term distribution of 100 year and 10 000 year seastates. For strongly nonlinear load effects, it is not given that an extreme seastate can be used reliably to estimate the characteristic load effect. The governing load may occur as an extremely rare event in a much lower seastate. In attempting to model the load effect in an extreme seastate, the short term probability level is not known nor is it known whether the physics of the wave loading is captured correctly in an extreme seastate. Examples of such strongly nonlinear load effects are slamming loads on large volume offshore structures or wave in deck loads on jacket structures subject to seabed subsidence. Similarly, for structures which are unmanned in extreme weather, the governing load effects for the manned structure will occur as extremely rare events in a relatively frequent seastate. The present paper is concerned with the long term distribution of strongly nonlinear load effects. Using a simple point estimate of the wave elevation correct to second order and a crest kinematics model which takes into account the possibility of wave breaking, the long term distribution of drag load on a column above the still water level is studied and compared with a similar loading model based on second order kinematics which does not include the effect of wave breaking. The findings illustrate the challenges listed above. Model tests are useful in quantifying strongly nonlinear load effects which cannot be calculated accurately. But only a relatively small number of seastates can be run in a model test campaign and it is not feasible to estimate short term responses far beyond the three hour 90% fractile level. Similarly, Computational Fluid Dynamics (CFD) is increasingly useful in investigating complex wave induced load effects. But only a relatively small number of wave events can be run using CFD, a long term analysis of load effects cannot in general be carried out. It appears that there is a class of nonlinear problems which require a long term analysis of the load effect in order for the annual probability of occurrence to be estimated accurately. For problems which cannot be estimated by simple analytical means, the governing wave events can be identified by long term analysis of a simple model which capture the essential physics of the problem and then analysed in detail by use of CFD or model tests.


Author(s):  
Thomas B. Johannessen ◽  
Øystein Lande

Offshore structures are typically required to withstand extreme and abnormal load effects with annual probabilities of occurrence of 10−2 and 10−4 respectively. For linear or weakly nonlinear problems, the load effects with the prescribed annual probabilities of occurrence are typically estimated as a relatively rare occurrence in the short term distribution of 100 year and 10 000 year seastates. For strongly nonlinear load effects, it is not given that an extreme seastate can be used reliably to estimate the characteristic load effect. The governing load may occur as an extremely rare event in a much lower seastate. In attempting to model the load effect in an extreme seastate, the relevant short term probability level is not known nor is it known whether the physics of the wave loading is captured correctly in an extreme seastate. Examples of such strongly nonlinear load effects are slamming loads on large volume offshore structures or wave in deck loads on jacket structures subject to seabed subsidence. The present paper is concerned with the long term distribution of strongly nonlinear load effects and a methodology is proposed which incorporates CFD analysis in a long term Monte Carlo analysis of crest elevations and wave kinematics. Based on a long term time domain simulation of a linear surface elevation, a selection of events is run in CFD in order to obtain a database of linear and corresponding fully nonlinear wave fields with the possibility of wave breaking included. In the subsequent long term analysis, a large linear event is then replaced by the closest matching event in the database. A technique is developed to Froude scale the database results and shift the origin in time and plane so that the database of typically only 100 events give a close match to all the events in the simulation. The method is applied to the simple case of drag loading on a cylinder which is truncated above the still water level such that only the largest waves impact with the structure. It is observed that whereas the Event Matching method agree well with a second order model for return periods lower than 100 years, the loading on the cylinder is significantly larger for longer return periods. The deviation is caused by the increasing dominance of wave braking in the largest crest and illustrates the importance of incorporating wave breaking in the analysis of wave in deck loading problems.


IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 17903-17915
Author(s):  
Peng Qi ◽  
Minjuan He ◽  
Mengwei Li ◽  
Xiuzhi Zheng ◽  
Zheng Li ◽  
...  

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