Engineering Fundamentals and Applied Mathematics
What the exam tests
Engineering fundamentals and applied mathematics is the toolkit domain: unit systems, dimensional consistency, basic statics and geometry, and the numerical discipline every later calculation depends on. Questions typically ask you to convert units, resolve forces, compute areas and volumes, or judge whether an answer is physically sensible.
Core rules and concepts
- SI force is the newton: 1 N = 1 kg·m/s². Pressure and stress are N/m² (Pa); 1 kPa = 1 kN/m² and 1 MPa = 1 N/mm².
- Useful unit weights: water 9.81 kN/m³ (density 1000 kg/m³), concrete about 24 kN/m³, steel about 78.5 kN/m³.
- An equation is valid only if both sides reduce to the same units; check this before substituting numbers.
- Carry full precision through the calculation and round only the final answer.
- For a body in equilibrium, ΣF = 0 and ΣM = 0 about any point.
Worked example
A simply supported beam spans 6.0 m and carries a 12 kN point load 2.0 m from support A. Taking moments about A eliminates R_A: R_B × 6.0 = 12 × 2.0, so R_B = 4.0 kN. Vertical equilibrium then gives R_A = 12 − 4.0 = 8.0 kN. Check with moments about B: R_A × 6.0 = 12 × 4.0, giving R_A = 8.0 kN, which agrees. Keeping kN and metres throughout avoids conversion error; had the span been stated as 6000 mm, converting to 6.0 m first is essential.
Traps that cost marks
- Treating kg as a force unit and omitting the factor g.
- Substituting diameter where radius is required in A = πr².
- Rounding reactions before checking equilibrium.
- Assuming a non-central load acts at midspan.