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Statics: Forces, Equilibrium, and Free-Body Diagrams

Manual: General · Subject: Engineering

Develop the tools to analyze stationary structures and components using force balance and moments.

Forces in balance

Equilibrium conditions

A rigid body is in static equilibrium when the net force and net moment are both zero: ∑Fx=0,∑Fy=0,∑M=0.\sum F_x = 0, \quad \sum F_y = 0, \quad \sum M = 0. These conditions let engineers determine unknown reactions in supports, beams, and trusses.

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Free-body diagrams matter

A free-body diagram isolates one object and shows every external force and moment acting on it. If the diagram is wrong, the calculation will usually be wrong too.

Moments and leverage

The moment of a force about a point is M=FdM = Fd, where dd is the perpendicular distance from the point to the force's line of action. Moments explain why longer wrenches, levers, and beams can amplify or resist rotation.

How to solve a statics problem

  1. 1

    Step 1: Draw a clean free-body diagram.

  2. 2

    Step 2: Choose axes and a moment point wisely.

  3. 3

    Step 3: Write equilibrium equations.

  4. 4

    Step 4: Solve the unknown reactions or forces.

  5. 5

    Step 5: Check units, signs, and physical reasonableness.

What condition is required for a body in static equilibrium?

What quantity measures the turning effect of a force?

Why do engineers often take moments about a support point?