Engineering Mechanics
What is Engineering Mechanics?
An influence that can change the motion of an object. It has magnitude and direction (vector quantity).
Key formula / rule: Resultant of two forces
Key points
- Analyze forces acting on static bodies.
- Determine the resultant of a system of forces.
- Apply equilibrium conditions to solve problems.
- Draw and interpret Free Body Diagrams.
Common exam trap
Incorrectly drawing Free Body Diagrams (missing forces, incorrect directions).
Definitions
- Term
Force
- Meaning
An influence that can change the motion of an object. It has magnitude and direction (vector quantity).
- Term
Moment
- Meaning
The turning effect of a force about a point or axis. It is the product of the force magnitude and the perpendicular distance from the point/axis to the line of action of the force.
- Term
Equilibrium
- Meaning
A state where the net force and net moment acting on a body are zero, resulting in no change in its state of motion (i.e., no acceleration).
- Term
Free Body Diagram (FBD)
- Meaning
A diagram showing a body isolated from its surroundings, with all external forces and moments acting upon it represented by vectors.
- Term
Centroid
- Meaning
The geometric center of a plane area or volume.
- Term
Center of Gravity (CG)
- Meaning
The point where the entire weight of a body can be considered to act. For a homogeneous body, CG coincides with the centroid.
Learning objectives
Analyze forces acting on static bodies.
Determine the resultant of a system of forces.
Apply equilibrium conditions to solve problems.
Draw and interpret Free Body Diagrams.
Calculate centroids and centers of gravity.
Analyze simple structures like trusses and beams.
Formulae
- Name
Resultant of two forces
- Note
Where P and Q are magnitudes of forces, and θ is the angle between them.
- Expression
R = √(P2 + Q2 + 2PQ cos θ)
- Name
Equilibrium Equations (2D)
- Note
Sum of forces in x-direction, y-direction, and sum of moments about any point are zero.
- Expression
ΣFx = 0, ΣFy = 0, ΣM = 0
- Name
Moment of a force
- Note
Where F is the force magnitude and d is the perpendicular distance from the pivot point to the line of action of the force.
- Expression
M = F * d
- Name
Centroid of a composite area
- Note
Summation over individual areas Ai with centroids (x̄_i, ȳ_i).
- Expression
x̄ = (Σ(Ai * x̄_i)) / (ΣAi), ȳ = (Σ(Ai * ȳ_i)) / (ΣAi)
- Name
Friction Force
- Note
Where μ is the coefficient of friction and N is the normal force. Static friction is Fs ≤ μs N, kinetic friction is Fk = μk N.
- Expression
Ffriction ≤ μN
Prerequisites
Basic algebra and trigonometry.
Vector algebra.
Understanding of forces and moments.
Common mistakes
Incorrectly drawing Free Body Diagrams (missing forces, incorrect directions).
Errors in resolving forces into components.
Algebraic mistakes when applying equilibrium equations.
Confusing centroid with center of gravity for non-uniform bodies.
Assuming members in a truss are only subjected to axial forces without verifying assumptions (e.g., rigid joints, no external loads on members).
Keywords
Statics
Equilibrium
Forces
Moments
Free Body Diagram
Newton's Laws
Friction
Centroid
Center of Gravity
Trusses
Beams
Reactions
Practice preview
Which of the following is a scalar quantity?…
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For a particle to be in equilibrium, the resultant of all forces acting on it must be:…
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A T-section has a flange of 100 mm x 20 mm and a web of 20 mm x 80 mm. The total depth of the section is 100 mm. Calculate the moment of inertia about the centroidal x-axis. (All dimensions are in mm)…
hard