By Parviz Ghavami
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Additional resources for Mechanics of Materials: An Introduction to Engineering Technology
As an example, the relations among three forces in equilibrium could be shown by forces F1 ¼ F2 ¼ 6,000 lb (Fig. 34). These forces are concurrent forces since their lines of action meet at point M. Then, what is the direction and magnitude of a horizontal force F3 exerted at the same point M such that F1, F2, and F3 will all be in equilibrium? F1=6 k F1 M F3 30º 30º R F2 F2=6 k Fig. 8 Mathematical Statement of Equilibrium 35 Force F3, called the equilibrant (or balancing force) of the two forces, is the closing line of the force triangle MNP shown in Fig.
1 Moment of a Force Moment of a force F about a given point O is the product of the force F and its perpendicular distance r from the line of action of the force to the center of rotation O. # Springer International Publishing Switzerland 2015 P. 1007/978-3-319-07572-3_3 51 52 3 Moment of a Force Point O is the O moment center ° r Mo m arm ent F 90 Line of action of force Fig. m. 2 Sign Convention of a Moment In the figure shown (Fig. 2), it is evident that the 100-lb force tends to rotate about point A in one direction, and about point B in the opposite direction.
52 46 2 Force Systems on Structures 7. F2=270 lb Y 45º F1=150 lb X 28º F3=320 lb Fig. 53 8. Using the law of cosines and the law of sines, find the resultant of the given force triangle (Fig. 54). F1=50 lb 65º F2=150 lb Fig. 54 9. Using the method of components, find the resultant of the force system shown (Fig. 55). F2=100 N Y F1=500 N 3 2 25º X F3=1200 N Fig. 55 Problems 47 10. Draw a force polygon diagram to show the resultant of the forces shown (Fig. 56). F1=100 lb F2=150 lb 6 Y 3 1 1 X F3=200 lb F4=350 lb Fig.