Tham khảo tài liệu 'mechanics of microelectromechanical systems - and part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 18 Chapter 1 For relatively short beams as already mentioned the shearing effects are important and the shearing stresses are given by the equation T s ịzdA wl A z where S is the shear force and the integral the statical moment of area is taken for the area enclosed by an arbitrary line parallel to the y-axis situated at a distance z measured from the cross-section center and one of the external fibers. The shear strain is y t G In this case the total strain energy is ub mI 1 dx 2E K S2 Adx 2G l Load Sign Conventions Because the loads acting on an elastic body might be directed one way or the other about a specified direction it is customary to follow some simple rules that define the positive direction for a particular load. For axial loading the normal force is considered positive when its action tends to extend the portion of the body under consideration. In the case of torsion selecting a positive direction is entirely arbitrary. Figure Load sign convention a generic fixed-free member under planar loading b axial force c shearing force d bending moment 1. Stiffness basics 19 In shearing the variant generally accepted is that the shear force is positive when it tends to rotate the portion of the structure in a clockwise direction whereas in bending a component of the bending moment either force or moment produces a positive bending moment if the analyzed structural segment deforms in a sagging manner by compressing the upper fiber . All these situations are sketched in Fig. . The normal force N shearing force S torsion moment Mị and bending moment Mb are defined at a specific point on the linear member by calculating the sum of all relevant components that are applied between one end point of the member the free end of Fig. is a convenient choice because it does not introduce any reactions which are usually unknown amounts and the specific point as given in the equations Example Determine the axial shearing and bending moment
