1.035 MECHANICS OF MATERIALS
Massachusetts Institute of Technology
Department of Civil and Environmental Engineering
Cambridge, MA 02139
Problem Set 1
Posted:
Due by 11:59pm, submitted on Canvas:
February 7, 2024
February 20, 2024
1. Concept questions. Provide brief answers (1-3 sentences or equations) to the following questions.
Hint: for parts (a)-(c), it will be helpful to read Appendix B (Elastic Bending of Beams) of the course
textbook.
(a) In words, explain the kinematic assumption behind the Euler-Bernoulli beam theory.
(b) Write down the relation between the transverse displacement of the neutral axis, v(x), at location
x along the axial direction and the curvature, κ(x), without making a small angle approximation.
Note that no derivation is required; just look up the result.
(c) Now simplify the displacement–curvature relation from part 1b with the small angle approximation, i.e. tan θ ≈ θ ≪ 1.
(d) A material with a yield strength of σy = 100 MPa is stiffer than a material with σy = 5 MPa.
True of False? Justify.
(e) The trace of the stress tensor varies under coordinate transformation. True or False? Justify.
(f) In one sentence, what is the physical significance of the stress deviator, σ ′ = σ − (1/3)(trσ)1?
The following problems come from the supplementary problem book, AKG_ExampleProblems_Student.pdf
on Canvas. Hereafter, a problem number starting with “AKG” will refer to that book.
2. Problem 2: AKG A.4
3. Problem 3: AKG 1.16
4. Problem 4: AKG 1.19
5. Problem 5: AKG 1.27
6. Problem 6: AKG 1.29
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