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Questions and Answers

The body is in equilibrium when the resultant force and couple moment are both equal to zero.

True (A)

In the condition of equilibrium, σ __ = 0.

Fx

Which of the following is NOT a type of support reaction?

  • Magnetic support (correct)
  • Rocker
  • Roller
  • Fixed support

What is the first step in solving equilibrium problems?

<p>Draw the Free Body Diagram</p> Signup and view all the answers

When a support prevents rotation, a couple moment is __.

<p>exerted</p> Signup and view all the answers

What are the equilibrium equations used in 2D?

<p>All of the above (D)</p> Signup and view all the answers

What is the maximum number of unknown reactions at a fixed support?

<p>Three</p> Signup and view all the answers

What is the resultant equilibrium condition for three-dimensional systems?

<p>Both the resultant force and resultant couple moment are equal to zero.</p> Signup and view all the answers

Match the supports with their unknown reactions:

<p>Roller = One unknown Pin or Hinge = Two unknowns Fixed Support = Three unknowns Ball and socket = Three unknowns</p> Signup and view all the answers

Flashcards

Equilibrium of a Rigid Body (2D)

A state where the resultant force and couple moment acting on a rigid body are both zero.

Resultant Force

The single force that represents the combined effect of all forces acting on a rigid body.

Resultant Couple Moment

The single couple moment representing the combined tendency of all forces about a point to rotate a rigid body.

Free Body Diagram

A diagram isolating a body, showing all external forces and moments acting on it.

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Support Reactions

Forces or moments exerted by supports on a rigid body to keep it in equilibrium.

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Roller/Rocker Support

Supports that allow translation in one direction but prevent translation in other directions and rotation.

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Pin/Hinge Support

Supports that allow translation in two directions and prevent rotation.

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Fixed Support

Supports that prevent translation and rotation in all directions.

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Equilibrium Equations (2D)

ΣFx = 0, ΣFy = 0, ΣMO = 0

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ΣFx = 0

The sum of all horizontal forces acting on a body equals zero.

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ΣFy = 0

The sum of all vertical forces acting on a body equals zero.

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ΣMO = 0

The sum of all moments about any point O on a body equals zero.

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Weight (w)

The force exerted by gravity on a body.

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Applied Force

External force acting on a rigid body.

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Procedure to Solve Equilibrium Problems (2D)

Draw a free body diagram, resolve forces into components, apply equilibrium equations, solve for unknowns.

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Equilibrium of a Rigid Body 3D

A state where the resultant force and the resultant moment about any point are zero.

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Equilibrium Equations (3D)

ΣFx = 0; ΣFy = 0; ΣFz = 0; ΣMo = 0

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Study Notes

Course Information

  • Course Title: Mechanics
  • Course Code: GEN 0004
  • Part: Static
  • Chapter: Equilibrium of a Rigid Body
  • Instructor: Dr. Mohamed Salah
  • University: Helwan National University
  • Faculty: Engineering

Equilibrium of a Rigid Body (2D)

  • Equilibrium occurs when the resultant force and couple moment are both zero.
  • Σfx = 0
  • Σfy = 0
  • ΣMo = 0

Support Reactions

  • Supports prevent translation or rotation.
  • Translation prevention results in a force.
  • Rotation prevention results in a couple moment.
  • Different support types (roller, rocker, smooth surface, pin, hinge, fixed support) produce different reaction types.

Equilibrium of a Rigid Body (2D) - Procedure

  • Step 1: Draw the free body diagram.
    • Include weights and applied forces.
    • Include support reactions.
  • Step 2: Resolve forces.
  • Step 3: Apply equilibrium equations.
    • Σfx = 0
    • Σfy = 0
    • ΣMo = 0
  • Step 4: Solve equations.

Equilibrium of a Rigid Body (3D)

  • For 3D, resultant force and couple moment must both be zero.
  • ΣMx = 0; ΣMy = 0; ΣMz = 0
  • ΣFx = 0; ΣFy = 0; ΣFz = 0

Procedure for Solving (3D)

  • Step 1: Draw free body diagram (includes weights, tension forces, spring forces and support reactions).
  • Step 2: Represent forces as vectors.
  • Step 3: Apply the equilibrium equations.
    • ΣFx = 0
    • ΣFy = 0
    • ΣFz = 0
    • ΣMx = 0
    • ΣMy = 0
    • ΣMz = 0
  • Step 4: Solve resulting equations.

Additional Notes

  • Example problems (various scenarios like beams, plates, and assemblies with different supports and loads) are presented and analyzed.
  • Support reactions for various support types (roller, rocker, smooth surface, pin, hinge, fixed support, ball and socket) and their effects are outlined.
  • Cartesian vectors are used to represent forces and tensions.

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