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Analysis of Static Equilibrium in Rigid Frames and Structures

This document explores the principles of static equilibrium for rigid frames, rods, and beams, focusing on graphical conditions of equilibrium and the application of force diagrams. Through detailed solutions to various exercises, we examine the behavior of structures subjected to different loading conditions, ensuring they meet the criteria for stability and balance. We cover the study of forces, couples, and the role of constraints, aiming to determine equilibrium equations and analyze the safety and structural integrity of mechanical systems like cranes.

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Analysis of Static Equilibrium in Rigid Frames and Structures

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  1. B C a A D form of a balanced force system. 2a B C A D 2-3 Solution take the rigid frame as object to study 习 题（静力学） According to the graphical condition of equilibrium: By the geometrical relation: Therefore:

  2. B C a A D 2a B C A D y x 2-3 Solution take the rigid frame as object to study 习 题（静力学） Solving them, we obtain:

  3. D C l According to the character of two couples in equilibrium, and make up a new force A B l l l couple. C B D C y A x 2-6 Solution 1.Study the rod CB 习 题（静力学） 2.Take the rod DC to study

  4. B 4m 3m y M q x A 2-12Solution: 1. take the rigid structure as object to study 习 题（静力学） 2. draw force diagram (make analysis of force) 3. set equilibrium equation. MA free from constraints Solving them, we obtain:

  5. y x 2-14(a)Solution: M B 1. take beam AB to study A C 2. draw force diagram 习 题（静力学） a 2a 3. set equilibrium equation. Solving them, we obtain:

  6. q M A B D a a 2a y x 2-14(b) 1. take beam AB to study 习 题（静力学） 2. draw force diagram 3. set equilibrium equation. Solving them, we obtain:

  7. 10 m 1.5m x (It should be under the action of which the crane can not turn over 3 m around point B.) 2-16Solution: take crane to study, it is acted upon by a C.P.F.S. 习 题（静力学） 1. Firstly, let us examine the full-loaded position of the crane. free from constraints A B set equilibrium equation

  8. due to 10 m 1.5m x (The crane will turn over around point A unless we can ensure .) 3 m we get 习 题（静力学） ① 2. Secondly, let us examine the empty position of the crane. A B set equilibrium equation we get due to ②

  9. ① ② From ① and ②, we find the range of equilibrium 习 题（静力学） Hence

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