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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS AND MATERIALS II QUIZ I SOLUTIONS Distributed : Wednesday, March 17, 2004 This quiz consists of four (4) questions. A brief summary of each question’s content and associated points is given below: 1. (10 points) This is the credit for your (up to) two (2) pages of self-prepared notes. Please be sure to put your name on each sheet , and hand it in with the test booklet. You are already done with this one! 2. (20 points) A lab-based question. 3. (40 points) A multi-part question about a linear elastic boundary value problem. 4. (30 points) A ‘design for yield’ question. Note: you are encouraged to write out • your understanding of the problem, and • your understanding of “what to do in order to solve the problem”, even if you find yourself having “algebraic/numerical diﬃculties” in actually doing so: in short, • let me see what you are thinking, instead of just what you happen to write down.... The last page of the quiz contains “useful” information. Please refer to this page for equa- tions, etc., as needed. If you have any questions about the quiz, please ask for clarification. Good luck! Problem 1 (10 points) Attach your self-prepared 2-sheet (4-page) notes/outline to the quiz booklet. Be sure your name is on each sheet. Problem 2 (20 points) (Lab-Based Problem) In your own words, describ e the following terms used in the description of linear elastic stress concentration, and brieﬂy illustrate (with schematic figures, simple equations, etc.) how these features are used, measured, or are otherwise identified: • (5 points) stress concentration factor A stress concentration factor, K t , can be defined as the ratio of the [peak] value of a stress component, σ local , at a highly-stressed location (e.g., a notch root) to a nominal, or far-field value of a stress component, σ nom , that is [typically] readily associated with overall loading: σ local K t ≡ σ nom ≥ 1 . • (5 points) St. Venant’s principle St. Venant’s principle states that the perturbation in a nominally homogeneous stress state introduced by a [geometric/material] hetero- geneity (e.g., a hole, notch, cut-out, or reinforcement) of characteristic linear dimension “ ” decays rapidly with distance from the heterogeneity. In practice, the effects of the perturbation in the stress field are negligible for distances greater than ∼ 3 . (10 points) Describ e “best practice” in the location of a resistance strain gauge to measure stress concentration at the root of a through-thickness notch in a planar body subjected to in-plane loading. (1 page, maximum)....
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.002 taught by Professor Davidparks during the Spring '04 term at MIT.
- Spring '04
- Mechanical Engineering