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Unformatted text preview: 9:00  10:00 NAME So (A) I’M/ms March 17, 2004 @NDFUEED) @3332 3M§ (1D structures handout; calculators allowed)  Put your name on the cover page, and if you disassemble the quiz, also on each subsequent page of the exam. — Read all questions carefully.  Do all work on that question on that page. Use back of that page if necessary.  Show all your work, especially intermediate results. Partial credit cannot be given
without intermediate results. — Show the logical path of your work. Explain clearly your reasoning and what you are doing. In some cases, the reasoning is worth as much (or more) than the actual
answers.  Be sure to show the units as well (if necessary). intermediate answers and final
answers are not correct without the units. — Report significant digits only.  Box your final answers. EXAM SCORING #2 (25%) #4 (24%) FINAL SCORE Unified Quiz 3M8
March 17, 2004 NAME PROBLEM #1 (26%) A pinended rod of length L and flexural rigidity El is loaded with an axial compressive
load. Derive (i.e. set up) the governing differential equation that will allow you to calculate the critical buckling load (do not solve the equation). Note: simply stating the equation is
not sufficient to earn full credit. 2 Flexural Rigidity, El MCI PC LCALLUVKS likka Unified Quiz 3M3 March 17, 2004 NAME b) The rod is supported with an additional pin/roller support at its mid point. What is the
critical buckling load for this configuration? F lexural Rigidity, El L/2 L/2 7W /// /
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March 17, 2004 NAME 0) Discuss how your solution approach and resulting solution to part (a) would be modified if the 76X rod had an initial deformed shape given by W = W0 Sin(1‘) where this represents a small deviation from the straight rod of part (a). Do not solve for the deformed shape. , :. ﬁ9r>
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March 17, 2004 NAME PROBLEM #2 (25%) A thin walled shaft, length 3m, with a circular cross section of radius 50 mm and wall thickness 2
mm is subjected to a distributed torque of 1kNm/m acting along its length. The shaft is made
of an aluminum alloy, with a Young’s modulus of 70 GPa, a shear modulus of 27 GPa and a
tensile yield strength of 500 MPa. —b
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H T=1kNm/m 2R=100 mm a) Calculate the maximum shear stress in the shaft and state its location. TM oJ: hit8" : 3x\ RNM/V— 1' 3
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March 17, 2004 b) calculate the angle of twist of the tip of the shaft. T: T:3.9C
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March 17, 2004 NAME Unified Quiz 3MS March 17, 2004 NAME PROBLEM #3 (25%) a) i find that I can pull adhesive tape (e.g. Scotch Tape) off a roll with a constant force of
1 N. The tape is 10 mm wide. If the tape does not stretch significantly at this load
estimate the toughness (in J/mz) of the adhesive on the tape.
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March 17, 2004 NAME b) For 2024 T3 aluminum alioy the fracture toughness is 44 MPaw/m and the yield strength
is 345 MPa. What is the maximum crack size that can be tolerated for yield to occur rather
than fast fracture? 6
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March 17, 2004 NAME
PROBLEM #4 (24%)
Answer the following questions (brief, concise and accurate answers are required) i) Sketch the stressstrain curve for a metallic alloy and indicate the yield stress, the region
where work hardening occurs and the ultimate tensile strength. ii) What mechanism(s) is(are) responsible for causing work—hardening? Nut/L thj (3ch AN LS Aisha.“th _s
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March 17, 2004 NAME iii) Explain the experimental observation that low yield stress metals such as solders or
pure metals are much more susceptible to fatigue failure than high strength metal alloys. alga“; {/3 w t; LL3ch wmm‘kgugm/
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pLMKLJ—j MM (twig WAC/cw OWE/w «KL Do curt MM OwScWVEQ 'toWwe iv) Trusses are generally found to be the most structurally efficient configuration for carrying
a given load for a minimum mass structure — as can be seen by the fact that trusses are
often used for spacecraft structures where aerodynamic considerations are not a concern. Why are beams less structurally efficient than trusses?.
lV\ (Aid/MA WA LBW) cure. Lou—clJ_CL UWt’S/us/Mb [m 'WLM W CMWMLW l:9, W M vxdl’ WM UWA‘M 1W “Ml LMU‘D ...
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 Fall '05
 MarkDrela

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