ENGINEERING NOTES
Basics, units, forces, and equilibrium
1. What is Engineering?
Engineering involves the application of mathematics, science, and design to problem solving. Engineers study
force, material, energy, motion, and structure before using the findings in designing systems.
2. SI Units
● Length: metre (m)
● Mass: kilogram (kg)
● Time: second (s)
● Force: newton (N)
● Work / energy: joule (J)
● Power: watt (W)
● Pressure / Stress: Pascal (Pa)
Useful conversions
● 1 kN = 1,000 N
● 1 MPa = 1,000,000 Pa
● 1 GPa = 1,000 MPa
● 1 kW = 1,000 W
3. Basic Engineering Equations
● Force: F = m × a
● Work: W = F × d
● Power: P = W / t
● Density: ρ = m / V
● Pressure: p = F / A
● Efficiency is: η = useful output / total input × 100%
4. Equilibrium
Static equilibrium is achieved when all forces and couples acting on a body are balanced.
● ΣFₓ = 0 → equilibrium of forces horizontally
, ● ΣFy = 0 equilibrium of vertical forces
● ΣM = 0 → moments in both directions cancel out
Example
A 20 kg object is acted on by gravity. Using g ≈ 9.81 m/s²: W = mg = 20 × 9.81 = 196.2 N.
Statics, couples, beams and trusses
5. Moments
A moment is the measure of a force’s torque around a point.
● M=F×d
● Moment = M (in N·m)
● F = force in N
● d = Distance from the pivot point in m
Example
A 100 N force acts 0.5 m from a pivot: M = 100 × 0.5 = 50 N·m.
6. Free-Body Diagrams (FBDs)
The Free Body Diagram is the diagram of the object isolated from everything else showing the force(s) acting on
the object.
● Show the object clearly.
● Include all applicable external forces.
● Label unknown reactions.
● Select the x-axis and y-axis.
● Use ∑ F = 0 and ∑ M = 0 for statics.
7. Beams
Beams have to resist the load by bending and shear actions. Examples of support are pinned, roller and fixed.
Simply supported beam with a central point load
● In the case of a centrally applied load F for a span of L, each reaction will be F/2.
● Momen maksimum saat membengkokkan: M_max = Kekuatan x Panjang / 4.
Worked example
Given F = 10 kN and L = 4 m: Mmax = (10 × 4) / 4 = 10 kN·m.
Basics, units, forces, and equilibrium
1. What is Engineering?
Engineering involves the application of mathematics, science, and design to problem solving. Engineers study
force, material, energy, motion, and structure before using the findings in designing systems.
2. SI Units
● Length: metre (m)
● Mass: kilogram (kg)
● Time: second (s)
● Force: newton (N)
● Work / energy: joule (J)
● Power: watt (W)
● Pressure / Stress: Pascal (Pa)
Useful conversions
● 1 kN = 1,000 N
● 1 MPa = 1,000,000 Pa
● 1 GPa = 1,000 MPa
● 1 kW = 1,000 W
3. Basic Engineering Equations
● Force: F = m × a
● Work: W = F × d
● Power: P = W / t
● Density: ρ = m / V
● Pressure: p = F / A
● Efficiency is: η = useful output / total input × 100%
4. Equilibrium
Static equilibrium is achieved when all forces and couples acting on a body are balanced.
● ΣFₓ = 0 → equilibrium of forces horizontally
, ● ΣFy = 0 equilibrium of vertical forces
● ΣM = 0 → moments in both directions cancel out
Example
A 20 kg object is acted on by gravity. Using g ≈ 9.81 m/s²: W = mg = 20 × 9.81 = 196.2 N.
Statics, couples, beams and trusses
5. Moments
A moment is the measure of a force’s torque around a point.
● M=F×d
● Moment = M (in N·m)
● F = force in N
● d = Distance from the pivot point in m
Example
A 100 N force acts 0.5 m from a pivot: M = 100 × 0.5 = 50 N·m.
6. Free-Body Diagrams (FBDs)
The Free Body Diagram is the diagram of the object isolated from everything else showing the force(s) acting on
the object.
● Show the object clearly.
● Include all applicable external forces.
● Label unknown reactions.
● Select the x-axis and y-axis.
● Use ∑ F = 0 and ∑ M = 0 for statics.
7. Beams
Beams have to resist the load by bending and shear actions. Examples of support are pinned, roller and fixed.
Simply supported beam with a central point load
● In the case of a centrally applied load F for a span of L, each reaction will be F/2.
● Momen maksimum saat membengkokkan: M_max = Kekuatan x Panjang / 4.
Worked example
Given F = 10 kN and L = 4 m: Mmax = (10 × 4) / 4 = 10 kN·m.
