q3m_sol - 9:00 - 10:00 NAME So (A) I’M/ms March 17, 2004...

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Unformatted text preview: 9:00 - 10:00 NAME So (A) I’M/ms March 17, 2004 @NDFUEED) @3332 3M§ (1-D 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 pin-ended 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 /// / 1,1 f, __ r ' PC] = ‘ —_ 4... '16]: f _ LL 1." -'— CAM»- - “LL w CMLA MM— beMJALKA M I} I v r. ,z 1 p - Tl 61L 5 +116? r // “’ A ’ ,_ LL U Unified Quiz 3M3 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> /L‘J’w°5\ (fa. '9 5/ (3(3ka Jail/jg»de a ” V5“ M F) P urea, P f) Mu, ., P A2“ + 1:; " 09,—— - 0J9 “3%) My» g7; 61’ — L ll/ L—l “page?” /CK%> Unified Quiz 3M8 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 I t=2mm O H T=1kNm/m 2R=100 mm a) Calculate the maximum shear stress in the shaft and state its location. TM oJ: hit-8" : 3x\ RNM/V— 1' 3 rc— ., TR , WEL‘E : M *' 21m“- e zmx 6M0" ) " 2“” J :. ‘15 Mpaé air OVLCN ruckus a}- mfl—. Unified Quiz 3M5 March 17, 2004 b) calculate the angle of twist of the tip of the shaft. T: T:3.--|9C (Lac. 3 1 3 7- ¢ ’ “Lo 3—36. Ace: 19r[39cv39_ '- W 6") 7, p T '> 0 (half M' 9‘50, ¢>0 .' C. 3 ¢ :; [O H - 03 Z A 27xt01xUTxL$oxlo >X xto NAME YZNM Unified Quiz 3M8 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. \ [Z ::J<7S,—->1 N A mm Mad-k2 3 LM ek kk .- \I— oil/J2: (rCcLA 0U) '0 “MSW W . (1w .—.. v- x S . , (r (a f A A z b w 5 ' F77 ’ C h 2 M Unified Quiz 3M8 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 K :YCI‘A'TTa. MUM-'- Y 3’ Z .3 a _ ‘ .4 Z r ( 46mm - WIS-7040 C T 3; f (IT 345x106 Unified Quiz 3MS March 17, 2004 NAME PROBLEM #4 (24%) Answer the following questions (brief, concise and accurate answers are required) i) Sketch the stress-strain 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 talujcM/ij (Mil/k LoudA JYLeA/s MAI—TM. CM WV. as wtocaliuat mamgcj Unified Quiz 3MS 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/ MQKIALD M g lot-MEL la Law! <O§LLA 0W Nixie UAcLWEjg 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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q3m_sol - 9:00 - 10:00 NAME So (A) I’M/ms March 17, 2004...

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