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Force Resolution and Component Analysis in Structural Engineering Problems

This document outlines various engineering problems related to force resolution and vector analysis. It includes problems where forces are resolved into components acting along specific axes, determining the angles and magnitudes of resultant forces, and expressing forces in Cartesian vector form. Each problem is presented with specific parameters and requirements, reflecting common scenarios in structural analysis and mechanical engineering. Solutions are provided for the calculations necessary to achieve accurate results in force analysis, essential for engineers in the field.

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Force Resolution and Component Analysis in Structural Engineering Problems

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  1. Problem 2-12 (page 26) The cable exerts a force of 600 N on the frame. Resolve this force into components acting (a) along the x and y axes and (b) along the u and v axes. What is the magnitude of each component? Solution:

  2. Problem 2-16 (page 26) If the resultant FR of the two forces acting on the jet aircraft is to be directed along the positive x axis and have a magnitude of 10 kN, determine the angle  of the cable attached to the truck at B such that the force FB in this cable in a minimum. What is the magnitude of force in each cable when this occurs? Solution:

  3. Problem 2-29 (page 35) Three forces act on the bracket. Determine the magnitude and orientation  of F2 so that the resultant force is directed along the positive u axis and has a magnitude of 50 lb. Solution:

  4. Problem 2-29 continued

  5. Problem 2-42 (page 47) The pipe is subjected to the force F which has components acting along the x, y, z axes as shown. If the magnitude of F is 12 kN, and α = 120 deg and γ = 45 deg, determine the magnitudes of its three components. Solution:

  6. Problem 2-48 (page 55) Express the position vector r in Cartesian vector form; then determine its magnitude and coordinate direction angles. Solution:

  7. Problem 2-48 continued

  8. Problem 2-59 (page 57) Express each of the two forces in Cartesian vector form and then determine the magnitude and coordinate direction angles of the resultant force. Solution:

  9. Problem 2.59 continued 1

  10. Problem 2-59 continued 2

  11. Problem 2-65 (page 59) The cylindrical vessel is supported by three cables which are concurrent at point D. Express each force which the cables exert on the vessel as a Cartesian vector, and determine the magnitude and coordinate direction angles of the resultant force. Solution:

  12. Problem 2-65 continued 1

  13. Problem 2-65 continued 2

  14. Problem 2-65 continued 3

  15. Problem 2-78 (page 65) Determine the magnitudes of the projected components of the force F={-80i + 30j + 20k} lb in the direction of the cables AB and AC. Solution:

  16. Problem 2-78 continued

  17. Problem 2-95 (page 68) Express each of the three forces acting on the column in Cartesian vector form and determine the magnitude of the resultant force. Solution:

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