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Double cantilever beam (DCB) specimen under tensile load. J-integral path for the DCB specimen under tensile load. Consider the double cantilever beam specimen shown in the figure, where the crack centered in the beam of height has a length of , and a load is applied to open the crack. Assume that the material is linearly-elastic and that the ...
Eq. 2 is the cumulative Weibull distribution with scale parameter and shape parameter ; = [^ ()] = constant factor depending on the structure geometry, = structure volume; = relative (size-independent) coordinate vectors, ^ = dimensionless stress field (dependent on geometry), scaled so that the maximum stress be 1; = number of spatial ...
The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass. The deflected shape of a beam can be represented by the moment diagram, integrated (twice, rotated and translated to enforce support conditions).
Fig. 2: Column effective length factors for Euler's critical load. In practical design, it is recommended to increase the factors as shown above. The following assumptions are made while deriving Euler's formula: [3] The material of the column is homogeneous and isotropic. The compressive load on the column is axial only.
The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).
where the factors can be found from fits to stress intensity curves [7]: 6 for various values of . A similar (but not identical) expression can be found for tip B of the crack. Alternative expressions for the stress intensity factors at A and B are [10]: 175
In gas dynamics we are interested in the local relations between pressure, density and temperature, rather than considering a fixed quantity of gas. By considering the density ρ = M / V {\displaystyle \rho =M/V} as the inverse of the volume for a unit mass, we can take ρ = 1 / V {\displaystyle \rho =1/V} in these relations.
Consider a beam whose cross-sectional area increases in one dimension, e.g. a thin-walled round beam or a rectangular beam whose height but not width is varied. By combining the area and density formulas, we can see that the radius or height of this beam will vary with approximately the inverse of the density for a given mass.