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Questions and Answers
The body is in equilibrium when the resultant force and couple moment are both equal to zero.
The body is in equilibrium when the resultant force and couple moment are both equal to zero.
True
In the condition of equilibrium, σ __ = 0.
In the condition of equilibrium, σ __ = 0.
Fx
Which of the following is NOT a type of support reaction?
Which of the following is NOT a type of support reaction?
What is the first step in solving equilibrium problems?
What is the first step in solving equilibrium problems?
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When a support prevents rotation, a couple moment is __.
When a support prevents rotation, a couple moment is __.
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What are the equilibrium equations used in 2D?
What are the equilibrium equations used in 2D?
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What is the maximum number of unknown reactions at a fixed support?
What is the maximum number of unknown reactions at a fixed support?
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What is the resultant equilibrium condition for three-dimensional systems?
What is the resultant equilibrium condition for three-dimensional systems?
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Match the supports with their unknown reactions:
Match the supports with their unknown reactions:
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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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