Skip to content
Try ZeroTell

ZeroTell Pro is an auto-renewing subscription, billed weekly, monthly or yearly. Cancel anytime in Dashboard → Subscription. See plans and prices.

Built for students, writers and researchers

Statics AI Solver in equilibrium

Beams, trusses, frames and particles: the tutor lists every force and moment, explains its choice of moment point and solves the equilibrium equations with units.

Photo of the question
Optional · PNG, JPG or WebP up to 5 MB — choose, drop or paste a screenshot
Fill in the required fields to start.

Result

Your result will appear here.

The equilibrium method behind every statics problem

A body in static equilibrium has no net force and no net moment. In two dimensions that gives three independent equations: ΣFx = 0, ΣFy = 0 and ΣM = 0 about any point. Three equations means a single rigid body can have at most three unknown reactions you can solve for; with more, the structure is statically indeterminate.

Know your supports. A pin provides two reaction components, horizontal and vertical. A roller provides one, perpendicular to the surface it rolls on. A fixed support provides two forces and a moment. A cable or a two-force member can only pull or push along its own line.

Pick the moment point to eliminate unknowns. Summing moments about the point where two unknown forces act removes both from that equation, leaving a single unknown you can solve for directly.

Worked example: a simply supported beam

A 4 m beam, pinned at A, on a roller at B, with a 10 kN load 1.5 m from A.

  • Free-body diagram in words

    At A: unknown Ax (horizontal) and Ay (vertical). At B, 4 m from A: unknown By, vertical. A downward 10 kN force acts 1.5 m from A.

  • Moments about A

    Taking counterclockwise as positive, ΣMA = 0 gives By × 4 m − 10 kN × 1.5 m = 0, so By = 3.75 kN upward.

  • Vertical forces

    ΣFy = 0 gives Ay + 3.75 kN − 10 kN = 0, so Ay = 6.25 kN upward.

  • Horizontal forces and a check

    ΣFx = 0 gives Ax = 0. Moments about B confirm it: 10 kN × 2.5 m − 6.25 kN × 4 m = 25 − 25 = 0 kN·m.

How the statics tutor works

  • Describes the FBD

    Every force and moment with its point of application and direction, since the solver cannot draw the diagram for you.

  • Explains the moment point

    It says why summing moments about one particular point removes unknowns and shortens the algebra.

  • Writes all three equations

    ΣFx = 0, ΣFy = 0 and ΣM = 0 appear explicitly in math notation, then the system is solved one step at a time with units.

  • Tension or compression

    In trusses and frames, each member force found is labeled as pulling or pushing.

  • Reads your figure

    Attach an image of the figure from your textbook; dimensions it cannot read are flagged instead of assumed.

  • Checks the reactions

    A second moment equation or a quick reasonableness test confirms the support forces add up.

Solving a statics problem here

  1. Describe or upload the structure

    Give dimensions, supports and loads, or attach the figure as a PNG, JPG or WebP file of up to 5 MB.

  2. Keep college level or adjust

    College / university is preselected; change the level or the style, for example exam revision for a quick review.

  3. Follow FBD to equations

    Read the forces, the chosen axes and moment point, then each equation solved in turn.

  4. Practice one more

    Confirm the reactions with the suggested test, solve the practice problem, and ask a follow-up in AI Chat if a sign convention trips you up.

Frequently asked questions

Yes. It explains which method suits the question, writes each joint or cut as a set of equilibrium equations, and labels each member force as tension or compression.

Upload it and compare the transcription at the start of the answer with your figure. Distances, angles or loads it cannot read clearly are flagged; retype them so the solution uses the right numbers.

It can set up 3D equilibrium with six equations and cross products for moments. Long 3D problems are where errors creep in most, so check every component yourself.

Statics problems are covered by the Pro plans* (*fair use: up to 300 runs a day across the writing, study and code tools). Without one, a problem uses 2 credits, rising to 3 when a photo of the figure is attached. Signed out, you can read the first part of a solution for free.

Treat it as a way to understand the approach and test your own attempt. Engineering courses often set rules for AI help, so follow yours — see Academic Integrity.

They are usually close, but a sign error or a misplaced distance is easy to make. Verify with a second moment equation before you trust any number.

Related engineering and math tools

Reactions not balancing?

Get the free-body diagram in words and every equilibrium equation, then try another beam on your own.

Solve my statics problem
  • ΣF and ΣM written out
  • Tension or compression labeled
  • Moment point explained