Study guides
Mechanics of Materials
3 guides for this subject — how to prepare, what to practise, and how to know it has gone in.
A practice question
Choose an answer and it is marked, with the explanation. From Mechanics of Materials Practice Questions: Worked Answers.
A steel bar carries an axial tensile load of 20 kN. Its uniform cross-sectional area is 200 mm². What is the average normal stress?
Average normal stress is σ = P/A. Convert 20 kN to 20,000 N: σ = 20,000/200 = 100 N/mm² = 100 MPa. The strongest distractor is 10 MPa, which comes from a factor-of-ten error in dividing the load by the area.
A spoken answer, marked
An examiner's question, answered out loud and marked criterion by criterion. From Mechanics of Materials Viva Questions: Practice Guide.
Examiner
A 2 m steel bar has area 400 mm² and carries a tensile force of 40 kN. Find its average axial stress and elastic extension, then state your assumptions. Take E = 200 GPa.
Identified axial tension but did not clearly state that the bar is uniform and remains elastic.
ImproveName the uniform, prismatic, linear-elastic bar model before using the equations.
The stress and extension are correct, but the conversion from mm² and GPa was not shown.
ImproveShow 40 kN / 400 mm² = 100 N/mm² = 100 MPa, then calculate extension.
Recognised tensile stress but did not connect the result to strain or the deformation assumption.
ImproveState that strain is 100 MPa / 200,000 MPa = 0.0005 and the extension is 1.0 mm.
The answer did not say what could make the elastic calculation unsuitable.
ImproveMention yielding, non-uniform area or a local stress concentration as reasons to refine the check.
A strong answerI will model this as a uniform prismatic bar in uniaxial tension, with linear-elastic behaviour and small strain. The average stress is P/A = 40,000 N / 400 mm² = 100 N/mm², or 100 MPa. With E = 200,000 MPa, the strain is σ/E = 0.0005, so over 2,000 mm the extension is 1.0 mm. This is an average-stress calculation; a shoulder, hole or yielding would require a more detailed assessment.
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Guides
- Mechanics of Materials Flashcards: A 19-Card DeckStudy 19 mechanics of materials flashcards covering stress, strain, bending, torsion, columns and energy, with a practical review method.
- Mechanics of Materials Practice Questions: Worked AnswersTest mechanics of materials with 10 worked questions on stress, deformation, torsion, beams, buckling and failure criteria.
- Mechanics of Materials Viva Questions: Practice GuidePractise mechanics of materials viva questions on axial loading, beam bending and torsion, with worked answers and a repeatable speaking method.
Studying mechanics of materials? Build your mechanics of materials board from your own notes — the cards, papers and lectures are written from it. Free plan: 20 cards, a paper, a lecture and a viva to try.
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