A Note on the Pure Bending of Unsymmetrical Prismatic Beams

1977 ◽  
Vol 44 (2) ◽  
pp. 344-345 ◽  
Author(s):  
V. K. Stokes
Keyword(s):  
Invariant Form ◽  
Pure Bending

It is shown that the equations governing the pure bending of unsymmetrical prismatic beams can be written in a coordinate-free invariant form.

A Simple Model for Cornering and Belt-edge Separation in Radial Tires

1986 ◽  
Vol 14 (1) ◽  
pp. 3-32 ◽  
Author(s):  
P. Popper ◽  
C. Miller ◽  
D. L. Filkin ◽  
W. J. Schaffers
Keyword(s):  
Simple Model ◽  
Transverse Shear ◽  
Mathematical Analysis ◽  
Pure Bending ◽  
Radial Tire ◽  
Optimum Angle ◽  
Shear Strains ◽  
Interlaminar Shear ◽  
Edge Separation ◽  
Shear Bending

Abstract A mathematical analysis of radial tire cornering was performed to predict tire deflections and belt-edge separation strains. The model includes the effects of pure bending, transverse shear bending, lateral restraint of the carcass on the belt, and shear displacements between belt and carcass. It also provides a description of the key mechanisms that act during cornering. The inputs include belt and carcass cord properties, cord angle, pressure, rubber properties, and cornering force. Outputs include cornering deflections and interlaminar shear strains. Key relations found between tire parameters and responses were the optimum angle for minimum cornering deflections and its dependence on cord modulus, and the effect of cord angle and modulus on interlaminar shear strains.

The stability of rectangular thin-walled profile with loading according to the scheme of pure bending

2020 ◽  
pp. 41-45
Author(s):  
V.B. Zylev ◽  
◽  
P.O. Platnov ◽  
I.V. Alferov ◽  
◽  
...  
Keyword(s):  
Pure Bending ◽  
Thin Walled ◽  
The Stability

Comparison study of crack propagation in rubberized and conventional prestressed concrete sleepers using digital image correlation

2021 ◽  
pp. 095440972110205
Author(s):  
Guoqing Jing ◽  
Du yunchang ◽  
Ruilin You ◽  
Mohammad Siahkouhi
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Prestressed Concrete ◽  
Mouth Opening ◽  
Image Correlation ◽  
Crack Mouth Opening Displacement ◽  
Experimental Program ◽  
Pure Bending ◽  
Opening Displacement ◽  
Rubber Concrete

Rubber concrete (RC) has been confirmed to be suitable for concrete sleeper production. This paper studies the cracking behaviour of conventional and rubber-reinforced concrete sleepers based on the results of an experimental program. The cracking behaviour in the pure bending zone was analysed up to a load of 140 kN. The crack mouth opening displacement (CMOD) was accordingly measured using a digital image correlation (DIC) method. The DIC results show that the rubber prestressed concrete sleeper (RPCS) has a resistance against crack initiation that is 20% greater than that of the conventional prestressed concrete sleeper (CPCS) under the same loading condition; however, due to the higher crack growth rate of the RPCS, the first crack detected by the operator forms at 60 kN, which corresponds to a strength approximately 9% lower compared with the 65 kN load at which the first crack is detected in the CPCS. Before the first crack (60 kN), the RPCS has a deflection 35% lower than that of the CPCS, but after cracking, at loads of 80 kN, 100 kN and 140 kN, the RPCS has a deflection 15%, 4% and 24% higher than that of the CPCS, respectively.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Investigation of Nanometric Thin-Film Bismuth Piezoresistors Deposited on Silicon Substrates

2012 ◽  
Vol 1477 ◽  
Author(s):  
Horacio V. Estrada
Keyword(s):  
Thin Film ◽  
Axial Strain ◽  
High Sensitivity ◽  
Metal Alloys ◽  
Silicon Substrates ◽  
Transverse Strain ◽  
Bending Stress ◽  
Pure Bending ◽  
Strain Fields ◽  
Strain Axis

ABSTRACTThin film bismuth piezoresistors, defined on oxidized silicon wafers, are investigated as a function of their orientation for their eventual integration on micro-electro-mechanical (MEMS) microsensors. Bismuth’s piezoresistance (or elasto-resistance) is experimentally investigated to accurately determine its longitudinal and transverse strain sensitivities. Whisker-shaped resistive elements defined on different orientations (from 0o, the beam’s main strain axis, to 90o, perpendicular to that axis) undergo changes of resistance (ΔR), associated with the induced strains on silicon cantilevers beam’s surface when these are mechanically loaded under pure bending stress conditions. For Bi-resistors, the traditional gage factor concept, (ΔR/Ro)/εl, is found to be equal to +16 and +33, for elements oriented along 0 and 90o, respectively, considerably larger than those for metals or metal alloys. These high sensitivity values and the “unusual” positive, higher value for the 90o (perpendicular) resistors can be of considerable interest for microsensors applications. The results of this study enable us to precisely determine the bismuth’s longitudinal and transverse strain sensitivities that are calculated to be equal to +26 and +40.5 respectively. This experimental study is extended to explore the Bi-films’ response to bi-axial strain fields.

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