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Structural Steel Designers Handbook Part 2

Tham khảo tài liệu 'structural steel designers handbook part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3.3 GENERAL STRUCTURAL THEORY FIGURE 3.2 a Force F resolved into components Fx along the x axis and Fy along the y axis. b Addition of forces Fx and Fy yields the original force F. FIGURE 3.3 Resolution of a force in three dimensions. 3.4 SECTION THREE Fx F cos 3.2a Fy F cos ay 3.2b Fz F cos az 3.2c F Ff x Fy2 F2 3.2d where ax ay and az are the angles between F and the axes and cos ax cos ay and cos az are the direction cosines of F. The resultant R of several concurrent forces F1 F2 and F3 Fig. 3.4a may be determined by first using Eqs. 3.2 to resolve each of the forces into components parallel to the assumed x y and z axes Fig. 3.4b . The magnitude of each of the perpendicular force components can then be summed to define the magnitude of the resultant s force components Rx Ry and Rz as follows Rx - -1 - F1x F2x F3x 3.3a Ry RR F1y F2y F3y 3.3b Rz Fz F1z F2z F3z 3.3c The magnitude of the resultant force R can then be determined from R R Ry2 R 3.4 The direction R is determined by its direction cosines Fig. 3.4c __ _ Fx __ _ F _ _ ZFz cos ax cos v -jr- cos az 3.5 where ax ay and az are the angles between R and the x y and z axes respectively. If the forces acting on the body are noncurrent they can be made concurrent by changing the point of application of the acting forces. This requires incorporating moments so that the external effect of the forces will remain the same see Art. 3.3 . FIGURE 3.4 Addition of concurrent forces in three dimensions. a Forces F1 F2 and F3 act through the same point. b The forces are resolved into components along x y and z axes. c Addition of the components yields the components of the resultant force which in turn are added to obtain the .