Dynamic Behavior of a Clamped Plastic Beam With Cracks at Supporting Ends Under Impact

1999 ◽  
Vol 121 (4) ◽  
pp. 406-412 ◽  
Author(s):  
F. L. Chen ◽  
T. X. Yu

This paper examines a projectile impact on a rigid-plastic beam with cracks at the fully clamped ends. By assuming the cracked sections yield immediately after impact, a three-hinge/two-hinge mechanism for the response process is constructed so that a complete solution considering the interaction between bending moment M and axial force N is derived. The key of the formulation is to find a complementary equation concerning the axial force N. To predict accurately the stability of the initial cracks, the J-integral criterion is extended to involve the contribution of the axial force. All the governing equations are nondimensionalized and rearranged, ready for Runge-Kutta integration procedure. The numerical results demonstrate that the mass ratio and the axial force have significant influence on the final deformation, energy partition, and the value of J-integral near the crack tip. The J-integral is not very sensitive to the depth of the initial cracks, but the presence of initial cracks in a beam may alter the failure behavior of the beam after impact, that is, from a strength-type failure to a fracture-type failure.

Author(s):  
Yinsheng Li ◽  
Kunio Hasegawa ◽  
Naoki Miura ◽  
Katsuaki Hoshino

When a crack is detected in a piping line during in-service inspections, failure estimation method provided in ASME Boiler and Pressure Vessel Code Section XI or JSME Rules on Fitness-for-Service for Nuclear Power Plants can be applied to evaluate the structural integrity of the cracked pipe. The failure estimation method in the current codes accounts for the bending moment and axial force due to pressure. The torsion moment is not considered. Recently, analytical investigations have been carried out by several authors on the limit load of cracked pipes considering multi-axial loads including torsion and two failure estimation methods for multi-axial loads including torsion moment with different ranges of values have been proposed. In this study, to investigate the failure behavior of cracked pipes subjected to multi-axial loads including the torsion moment and to provide experimental support for the failure estimation methods, failure experiments were performed on 20 mm diameter stainless steel pipes with a circumferential surface crack or a through-wall crack under combined axial force and bending and torsion moments. Based on the experimental results, the proposed failure estimation methods were confirmed to be applicable to cracked pipes subjected to multi-axial loads.


2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Yinsheng Li ◽  
Kunio Hasegawa ◽  
Naoki Miura ◽  
Katsuaki Hoshino

When a crack is detected in a piping line during in-service inspections, failure estimation method provided in ASME Boiler and Pressure Vessel Code Section XI (ASME Code Section XI) or JSME Rules on Fitness-for-Service for Nuclear Power Plants (JSME FFS Code) can be applied to evaluate the structural integrity of the cracked pipe. The failure estimation method in the current codes accounts for the bending moment and axial force due to pressure. The torsion moment is not considered. Recently, analytical investigation was carried out by the authors on the limit load of cracked pipes considering multi-axial loads including torsion. Two failure estimation methods for multi-axial loads including torsion moment with different ranges were proposed. In this study, to investigate the failure behavior of cracked pipes subjected to multi-axial loads including the torsion moment and to provide experimental support for the failure estimation methods, failure experiments were performed on 20 mm diameter stainless steel pipes with a circumferential surface crack or a through-wall crack under combined axial force, bending moment, and torsion moment. Based on the experimental results, the proposed failure estimation methods were confirmed to be applicable to cracked pipes subjected to multi-axial loads.


2011 ◽  
Vol 3 (4) ◽  
pp. 150-156 ◽  
Author(s):  
Vaidotas Šapalas ◽  
Gintas Šaučiuvėnas

Straipsnyje pateikta plieninių spragotinio skerspjūvio kolonų laikomųjų galių, apskaičiuotų vadovaujantis Lietuvoje galiojančių plieninių konstrukcijų projektavimo normų STR 2.05.08:2005 ir Eurokodo 3 nuostatomis, lyginamoji analizė. Skaičiavimai buvo atliekami vienodomis pradinėmis sąlygomis, tik naudoti skirtingi skaičiavimo metodai. Kai kuriais atvejais gautieji rezultatai yra labai prieštaringi ir reikalingi išsamesnės analizės ar eksperimentinių tyrimų. The paper presents the analysis of built-up laced axially loaded steel columns in light of Eurocode 3 and Lithuanian design code STR 2.05.08:2005. The theoretical part analyzes two design methods. Some cases indicate principal differences. According to STR, axial forces are equally divided into two parts for both chords. However, in Eurocode 3, axial force (formula 8) for one chord increases due to the additional bending moment (Formula 6) that depends on the shear stiffness of lacings (Formula 5). For very slender columns, the axial force of one chord, considering Eurocode 3, is 2.7 times bigger than that taking into account the STR method. Another big difference between the methods is that according to Eurocode 3 it is not necessary to check the overall stability of the built-up member round the z-z axis (only checking the stability of one chord round the z1-z1 axis is obligatory). Both methods require checking the stability of one chord round the y-y axis. In two cases, calculations referred to the same initial data (Table 1, 2) applying different design codes. The obtained results are presented in the diagrams. The first case shows that column slenderness in both planes equals λy = λz. The axially loaded column calculated with reference to the STR method has bigger bearing capacity reserve than that calculated considering the Eurocode 3 method. In this case, the stability of one chord round the y-y axis (Fig. 3) is the most dangerous. This example illustrates that the stability condition of the axially loaded column according to Eurocode 3 is not satisfied; thus, a necessity of increasing the column cross-section arises. The main reason for the latter situation is a different method used for calculating the axial force of one chord. This difference is greater for more slender columns. In the second case - column slenderness makes λy = λz/2. When slenderness is λz ≤ 100, the axially loaded column calculated according to the STR method has similar results compared to the Eurocode 3 method (Fig. 10). The most dangerous according to STR is the stability of the entire column round the z-z axis (Fig. 8), whereas in accordance with Eurocode 3 it appears to be the stability of one chord round the y-y axis (Fig. 9). In such a case, the stability condition of the axially loaded column according to Eurocode 3 has more reserve only when slenderness is λz > 100 (Fig. 10). Therefore, calculation according to Eurocode 3 is less safe if compared to the STR method. The main reason is that Eurocode 3 does not require checking the entire column stability round the z-z axis. Hence, for calculating slender columns according to Eurocode 3, some cases (λz > 100) are not very safe, which was also noticed in the numerical investigations provided by other authors Kalochairetis (2011). In some cases, results are controversial, and therefore it is necessary to perform additional analysis or experimental investigation.


Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1111
Author(s):  
Wei Fang ◽  
Gang Wang ◽  
Chang Wang

In this paper, we aim to reveal the influence of fault fracture zones on the stability of submarine tunnels and the surrounding rock under different water and drainage measures. Firstly, four typical working conditions of submarine tunnels intersecting with fault fracture zones were selected. On the basis of the typical cross section of the intersections of submarine tunnels and faults, they were divided into four working conditions. Then, the displacement and plastic zones of the surrounding rock of the tunnel were studied, and the stability of the rock surrounding the submarine tunnel was discussed. This research structure indicates that the bending moment and axial force of the lining structure of the submarine tunnel increase with increasing sealing degree, but the safety factor exhibits a downward trend. When the fault fracture zone goes through the section above the tunnel axis, the bending moment and axial force at the lining vault are greater than the other working conditions, and the displacement of the surrounding rock at the vault and spandrel is prominent. When the fault fracture zone completely passes through the tunnel, the safety factor of the lining structure is at its lowest, and the displacement of the surrounding rock at the arch waist develops laterally. When the fault fracture zone passes through the part below the tunnel axis, the arch foot displacement converges significantly, and the surrounding rock displacement exhibits a downward inclination. In addition, the plastic zone is mainly developed in the arch and the shoulder. These research results provide a reliable reference for tunnel design and excavation support.


2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Osama A. B. Hassan

Abstract This study investigates the stability of timber members subjected to simultaneously acting axial compression and bending moment, with possible risk for torsional and flexural–torsional buckling. This situation can occur in laterally supported members where one side of the member is braced but the other side is unbraced. In this case, the free side will buckle out of plane while the braced side will be prevented from torsional and flexural–torsional buckling. This problem can be evident for long members in timber-frame structures, which are subjected to high axial compression combined with bending moments in which the member is not sufficiently braced at both sides. This study is based on the design requirement stated in Eurocode 5. Solution methods discussed in this paper can be of interest within the framework of structural and building Engineering practices and education in which the stability of structural elements is investigated. Article Highlights This case study investigates some design situations where the timber member is not sufficiently braced. In this case, a stability problem associated with combined torsional buckling and flexural buckling can arise. The study shows that the torsional and/or flexural–torsional buckling of timber members can be important to control in order to fulfil the criteria of the stability of the member according to Eurocode 5 and help the structural engineer to achieve safer designs. The study investigates also a simplified solution to check the effect of flexural torsional buckling of laterally braced timber members.


2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.


2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xigui Zheng ◽  
Jinbo Hua ◽  
Nong Zhang ◽  
Xiaowei Feng ◽  
Lei Zhang

A limitation in research on bolt anchoring is the unknown relationship between dynamic perturbation and mechanical characteristics. This paper divides dynamic impulse loads into engineering loads and blasting loads and then employs numerical calculation software FLAC3Dto analyze the stability of an anchoring system perturbed by an impulse load. The evolution of the dynamic response of the axial force/shear stress in the anchoring system is thus obtained. It is revealed that the corners and middle of the anchoring system are strongly affected by the dynamic load, and the dynamic response of shear stress is distinctly stronger than that of the axial force in the anchoring system. Additionally, the perturbation of the impulse load reduces stress in the anchored rock mass and induces repeated tension and loosening of the rods in the anchoring system, thus reducing the stability of the anchoring system. The oscillation amplitude of the axial force in the anchored segment is mitigated far more than that in the free segment, demonstrating that extended/full-length anchoring is extremely stable and surpasses simple anchors with free ends.


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