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Meaning of equilibrium; drawing good FBD

Short answer

Equilibrium means zero net force and moment, keeping a body at rest or uniform motion; it is crucial for structural stability and to determine reactions. A good FBD isolates the body, shows all external loads and support reactions, and labels known and unknown forces with axes.

What is the physical meaning of equilibrium and why is it important in structure? How can we draw good Free Body Diagram? Explain with suitable examples.

Physical meaning of equilibrium

A body is in equilibrium when all the forces and moments on it balance (ΣF = 0, ΣM = 0). It then has no tendency to translate or rotate: it is at rest, or moves with constant velocity. Every action is balanced by an equal reaction.

Importance in structures

  • A structure must stay at rest under its loads, so the loads must be carried to the ground through supports. The equilibrium equations give the support reactions.
  • Applied to a cut part of a member, they give the axial force, shear force and bending moment needed to design the member.
  • They give member forces in trusses (method of joints and method of sections).
  • They are used to check overturning and sliding of walls, dams and foundations.
  • If equilibrium cannot be satisfied, the structure is unstable and would collapse.

How to draw a good free body diagram

  1. Isolate the body (or joint or part of structure) completely from its surroundings.
  2. Draw it clearly with its dimensions and angles.
  3. Show the weight at the centre of gravity and all the applied loads.
  4. Replace every support with its reaction (roller: one normal force; hinge: two components; fixed: two components and a moment; cable: tension away from the body; smooth contact: force normal to the surface).
  5. Mark known values and name the unknowns. Show only external forces, never the internal forces of the body.
  6. Show the axes and the dimensions needed for moments.

Example 1: a beam AB with a point load P and a UDL w, hinged at A and on a roller at B. The FBD shows P, the UDL (as its resultant wL at mid-span), H_A, V_A and V_B.

Example 2: a ladder against a smooth wall. The FBD shows the weight W at the middle, the wall reaction N_A (horizontal, pushing the ladder away from the wall), the ground reaction N_B (vertical) and the friction F_B at the foot (towards the wall, because the foot tends to slide away from it).

 |\ ---> N_A
 | \
 |  \
 |   o  W (down)        FBD of ladder
 |    \
 |     \
 +------\------ ground
  F_B <--*
         ^ N_B

✓ Answer checked by Claude Opus 5.5 (high effort)

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