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Shearing Stresses in Beams
Published in Robert L. Mott, Joseph A. Untener, Applied Strength of Materials, 2016
Robert L. Mott, Joseph A. Untener
After completing this chapter, you should be able to do the following: Describe the conditions under which shearing stresses are created in beams.Compute the magnitude of shearing stresses in beams by using the general shear formula.Define and evaluate the first moment of the area required in the analysis of shearing stresses.Specify where the maximum shearing stress occurs on the cross section of a beam.Compute the shearing stress at any point within the cross section of a beam.Describe the general distribution of shearing stress as a function of position within the cross section of a beam.Understand the basis for the development of the general shearing stress formula.Describe four design applications where shearing stresses are likely to be critical in beams.Develop and use special shear formulas for computing the maximum shearing stress in beams having rectangular or solid circular cross sections.Understand the development of approximate relationships for estimating the maximum shearing stress in beams having cross sections with tall thin webs or those with thin-walled hollow tubular shapes.Specify a suitable design shearing stress and apply it to evaluate the acceptability of a given beam design.Define shear flow and compute its value.Use the shear flow to evaluate the design of fabricated beam sections held together by nails, bolts, rivets, adhesives, welding, or other means of fastening.
5-caffeoylquinic acid retention in spray drying of cocona, an Amazonian fruit, using hydrolyzed collagen and maltodextrin as encapsulating agents
Published in Drying Technology, 2021
Diana Patricia Vargas-Muñoz, Leticia Cardoso da Silva, Luiza Andreza Neves de Oliveira, Helena Teixeira Godoy, Louise Emy Kurozawa
Viscosity of feed solutions was determined by steady-shear flow curves (shear stress vs. shear rate). The assays were done in triplicate using a strain-controlled rheometer (AR 1500 ex, TA Instruments, England, UK) with an acrylic plate-plate geometry of 4.0 cm of diameter. Three flow ramps (up, down, and up-cycles) were obtained at shear rates that ranged from 0 to 1000s−1, at 25 °C, to eliminate thixotropy. The data from the third flow curve were fitted to the empirical models of Newtonian fluids and Power Law (Eq. 1 and 2). Where: σ is shear stress (Pa), is shear rate (s−1), µ is the viscosity (Pa.s), K is the consistency index (Pa.sn), and n is the behavior index.
Consistently formulated eddy-viscosity coefficient for k-equation model
Published in Journal of Turbulence, 2018
M. M. Rahman, K. Keskinen, V. Vuorinen, M. Larmi, T. Siikonen
Using Boussinesq approximation, the Reynolds shear-stress anisotropy in homogeneous shear flow can be given as Detailed comparisons of the anisotropies with the DNS and experimental data are shown in Table 1 for the channel flow of Kim [32] in the inertial sublayer at , and in Table 2 for the homogeneous shear flow of Tavoularis and Corrsin [33] at , respectively. Clearly, the present model provides reasonable anisotropy of Reynolds stresses for both the boundary layer and homogeneous shear flows, compared to the standard eddy-viscosity model with . Therefore, the current model is capable of predicting the turbulent driven secondary flows.
Elasto-inertial particle migration in a confined simple shear-flow of Giesekus viscoelastic fluids
Published in Particulate Science and Technology, 2021
Bingrui Liu, Jianzhong Lin, Xiaoke Ku, Zhaosheng Yu
Studies have focused on the behavior of rigid particles migrating in the shear-flow of a non-Newtonian fluid. Hwang, Hulsen, and Meijer (2004) used a new finite-element scheme to simulate two-particle interaction in an Oldroyd-B fluid (it presents one of the simplest constitutive models capable of describing the viscoelastic behavior of dilute polymeric solutions under general flow conditions) and revealed kissing-tumbling-tumbling phenomena. Hashemi, Fatehi, and Manzari (2011) simulated the motions of two interacting circular and non-circular cylinders in an Oldroyd-B fluid and found that particle trajectory is very sensitive to the cross-sectional shape for higher elasticity. Yoon et al. (2012) identified three distinct types of particle interaction (passing, tumbling, and returning) in an Oldroyd-B fluid. Chiu, Pan, and Glowinski (2018) proposed a novel distributed Lagrange multiplier/fictitious domain method to simulate particle interaction in an Oldroyd-B fluid, showing the same types of particle interaction as those of Yoon et al. (2012). Snijkers et al. (2013) studied experimentally the effects of the rheological properties of suspending media of Boger fluid (an elastic fluid with almost constant viscosity) and a wormlike micellar surfactant solution (a kind of solution which consists of water, salts and free surfactant. Such solution is encountered in a wide variety of applications, e.g., enhanced oil recovery and ink-jet printing) on the hydrodynamic interaction between two equally sized spheres in a shear-flow and observed particle returning and passing. They concluded that the key rheological parameter which determines the overall nature of particle behavior is shear-thinning.