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CRC Press - Mechanical Engineering Handbook- Mechanics Of Solids Part 2

Tham khảo tài liệu 'crc press - mechanical engineering handbook- mechanics of solids part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-10 Section 1 Example 2 The torque wrench in Figure 1.2.10 has an arm of constant length L but a variable socket length d OA because of interchangeable tool sizes. Determine how the moment applied at point O depends on the length d for a constant force F from the hand. FIGURE 1.2.10 Model of a torque wrench. Solution. Using MO r X F with r Li dj and F Fk in Figure 1.2.10 Mo Li dj x Fk Fdi - FLj Judgment of the Result According to a visual analysis the wrench should turn clockwise so the -j component of the moment is justified. Looking at the wrench from the positive x direction point A has a tendency to rotate counterclockwise. Thus the i component is correct using the right-hand rule. Equilibrium of Rigid Bodies The concept of equilibrium is used for determining unknown forces and moments of forces that act on or within a rigid body or system of rigid bodies. The equations of equilibrium are the most useful equations in the area of statics and they are also important in dynamics and mechanics of materials. The drawing of appropriate free-body diagrams is essential for the application of these equations. Conditions of Equilibrium A rigid body is in static equilibrium when the equivalent force-couple system of the external forces acting on it is zero. In vector notation this condition is expressed as y F 0 yMo r X F 0 1.2.13 where O is an arbitrary point of reference. In practice it is often most convenient to write Equation 1.2.13 in terms of rectangular scalar components y F 0 y M 0 x x y F 0 y Mv 0 z J y z J y y F 0 y i. 0 z t z z t