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Introduction
Published in Ansel C. Ugural, Youngjin Chung, Errol A. Ugural, Mechanical Engineering Design, 2020
Ansel C. Ugural, Youngjin Chung, Errol A. Ugural
Distributed forces within a member can be represented by statically equivalent internal forces, so-called stress-resultants, or load resultants. Usually, they are exposed by an imaginary cutting plane containing the centroid C through the member and resolved into components normal and tangential to the cut section. This process of dividing the body into two parts is called the method of sections. Figure 1.2a shows only the isolated left part of a slender member. A bar whose least dimension is less than about 1/10 its length may usually be considered a slender member. Note that the sense of moments follows the right-hand screw rule and, for convenience, is often represented by double-headed vectors. In 3D problems, the four modes of load transmission are axial force P (also denoted F or N), shear forces Vy and Vz, torque or twisting moment T, and bending moments My and Mz.
Elastic Rods Subjected to General Loading
Published in Abdel-Rahman Ragab, Salah Eldin Bayoumi, Engineering Solid Mechanics, 2018
Abdel-Rahman Ragab, Salah Eldin Bayoumi
The ring is considered to have a rectangular cross section b × h and mean radius r¯. The stress resultants at any cross section is an axial force Ps, a shearing force Py, and a bending moment M.
Structural analysis modeling
Published in A. Ghali, A. M. Neville, T. G. Brown, Structural Analysis, 2017
A. Ghali, A. M. Neville, T. G. Brown
Structures deform under the action of forces. The column of Figure 1.21a is acted on by forces P and Q as shown. Figure 1.21b shows the deflected shape of the column. The applied forces cause internal forces that are stress resultants. The resultants of stresses at any section are bending moment, M, shear force, V and axial force, N. To show these internal forces, the structure must be cut (Figure 1.21c). Now we have two free body diagrams, with the internal forces shown at the location of the cut. Note that we must show the internal forces on both sides of the cut as pairs of arrows in opposite directions. Applying equilibrium equations to the upper free body diagram (part AC), we get:
Axisymmetric analysis of auxetic composite cylindrical shells with honeycomb core layer and variable thickness subjected to combined axial and non-uniform radial pressures
Published in Mechanics of Advanced Materials and Structures, 2022
Hamidreza Eipakchi, Farid Mahboubi Nasrekani
βo and βi are the angles of q1(x) and q2(x) with the horizon direction, respectively and they are equal to the slope of the external and internal radiuses. The stress resultants for the composite shell are defined as the following: where κ is the shear correction factor [36] and in this study, it has been considered κ = 5/6. The variations of the strain energy and external works are as the following:
A review on non-classical continuum mechanics with applications in marine engineering
Published in Mechanics of Advanced Materials and Structures, 2020
Jani Romanoff, Anssi T. Karttunen, Petri Varsta, Heikki Remes, Bruno Reinaldo Goncalves
The classical ship structural design approach is to consider the length scales for the primary (i.e. hull girder), secondary (i.e. bulkhead spacing) and tertiary (i.e. panel) responses separately, see Figure 1 [2]. This multi-scale structural modeling accounts for displacement compatibility and (stress resultant) equilibrium in the coupling between the consecutive length scales. Usually the structural models at larger length scales are based on classical continuum mechanics, e.g. Euler-Bernoulli beam modeling of the ship hull girder. The classical beam kinematics are assumed to be valid (e.g. curvature) and the resulting stress resultants (e.g. bending moment) are balanced by loads arising from the environment. The relation between the curvature and bending moment can be non-linear, with sources of non-linearity arising from buckling, plasticity or fracture of the structural elements (e.g. [3–12]), see Figure 2.
Simple first-order shear deformation theory for free vibration of FGP-GPLRC spherical shell segments
Published in Mechanics of Advanced Materials and Structures, 2023
Van-Loi Nguyen, Suchart Limkatanyu, Huu-Tai Thai, Jaroon Rungamornrat
The stress resultants of the FGP-GPLRC spherical shell segment can be defined by where is the shear correction factor (SCF) which is required in the case of S-FSDT. By substituting Eqs. (13) and (16) into Eq. (18), the stress resultants of the FGP-GPLRC shell can be expressed in the following forms: where