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Engineering & design · University

Statics, free-body diagrams and design margins

A free-body diagram isolates a body and displays external forces and moments. Internal forces cancel only for the correctly chosen whole system.

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Prerequisites

Relevant school subject foundations and careful reasoning.

Study notes

Forces

A free-body diagram isolates a body and displays external forces and moments. Internal forces cancel only for the correctly chosen whole system.

Equilibrium

In planar statics, net force in two independent directions and net moment vanish. A balanced force sum alone may leave an unbalanced couple.

Reactions

Support models define which motions are constrained and which reaction components can occur. Do not invent reactions inconsistent with the support.

Engineering limits

Classroom equilibrium calculations do not certify a real structure. Materials, dynamic loads, codes and qualified review are additional requirements.

Worked examples

Horizontal forces are +10 N and −4 N. Find the additional horizontal force needed for equilibrium.

Their sum is +6 N, so add −6 N.

-6 N

A perpendicular force of 5 N acts at lever arm 2 m. Find moment magnitude.

Moment magnitude=force×perpendicular distance.

10 N m

Check your understanding

  1. Can zero net force coexist with nonzero net moment?

    1. Only in a vacuum
    2. Yes
    3. Only with zero mass
    4. No, never

  2. Why should a free-body diagram identify the isolated body clearly?

  3. A symmetric simply supported beam carries a central 20 N load with negligible self-weight. Find either upward support reaction.

  4. Does a correct classroom static calculation certify a real building design?

    1. Only if the answer is an integer
    2. Yes, universally
    3. No
    4. Only if printed

Answers and marking guidance

Answers and marking notes
  1. Yes

    A force couple can have zero resultant force and nonzero moment.

  2. It determines which interactions are external and which are internal, preventing double-counting or omitted reactions.

    Credit system boundary.

  3. 10 N

    Symmetry and vertical force balance split the load equally.

  4. No

    Real design needs additional load, material, code and professional checks.

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