Spring Main Exam / STUDENT NUMBER: I I J.. ll I I I I SURNAME: (FAMILY NAME) OTHER NAMES: < trength of Engineering Materi.a.

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1 Spring Main Exam / iuts UNIVERSITY OF TECHNOLOGY, SYDNEY STUDENT NUMBER: I I J.. ll I I I I SURNAME: (FAMILY NAME) OTHER NAMES: ''''''''"'.;..,;..:.;..,,,,"_'"'''"'"'"''''"""''"'""'"'''''"'"''"'"'''''"'"'"'''''''"'''''''_'_''"'""''''"''"'"'''''"''''''''""""'"'''"'""'"'""""'"- " This paper and all materials issued must be rt)t~rned at the end of the examination. They are not to be remoyed from the exam centre. ExarrHnation Conditions: lt is your responsibility to fill out and complete your details in the space provided on all the examination material provided to you. Use the time before your examination to do so as you will not be allowed any extra time once the exam has ended. You are not permitted to have on y()ur > desk or on your person any unauthori$_~d < material. This includes butnotlimitlsdt6: Mobile phones Smart watches Electronic devices Draft papel"{~llli:!:;s provided) Textbook;s (unless specified) NotE?S (unless specified) You are notpetmitted to obtain assistance by improper means or ask for help from or give h~lp to any other person... You are not permitted to leave your seat (including to use the toilet): Until 90 mins has elapsed During the final 15 mins < trength of Engineering Materi.a.ls Friday, 14 1 h November :30am- 12:40pm Time Allowed: 3 hours and 10 mins. Includes 10 minutes of reading time. ~eading time is fo.r. reading only. You are not penmitb~dtowr~e, calculate or mark your paper in any way during reading time. ::- -:.:.. 0Mo000MOOOM.. M00MOH0.. 00""''"''"'-'0o0MOMOMOM... -.MOOM0MOMOMOM MOMOMOMOU000000MOO.. OOOMOMOMOMO-OO;......,... ;.,.,,,,,,,,...,... _,,,,,o.. MOM00.. _0M... M0MM0MooM.. _0_MooMOM... Mo00M0Mo This is a Restricted Open Book exam Please refer to the permitted materialsbelpw: Permitted materials for this exam:.... ' Calcul(3.tors(iholuding programmable).- :. -:::::. <.-: Drawing il'l$tr'uments LE;l~ Rulers, Set Squares and ~ompasses..... OnEf(1) revision sheet (A4 double-sided). They can be handwritten, photocopied or typed. During the examination you must first seek permission (by raising your hand) from a supervisor before: Leaving early (after 90 mins) Using the toilet Accessing your bag Disciplinary action will be taken against you if you infringe universityrules> Materials provided for this exam: This examination paper One (1) answer booklet (20-pages) Students please note: { < > A formula sheet for fatigue Pr99.1l9m is attached. Read all instructions carefully. Some questions may have more information given tb<ih Is r~quired to solve the problem. Present your wpr~jd a prbtessional manner including well drawn diagrams, units, neat presentation, detailed procedure, formulas and principles' All ahs~~rs.~reto be legibly written in ink. Questions written in. pencil will not be accepted. Pencil may only be used for.. dr~wvings, sketches and graphs. <-:: :-:>-:-. - -:.-:. :--:. Do not open your exam paper until instructed......, '~ ~- "..,/', '_..'....-"'-",'.,. /. ".:':":~ ~:""-~ _; :~.::o,.. v.-"'.",~ '.-" ' " ~. ' /'''......_.-,,. "-,A,"',... v"v"'.-" /,,,. - - "-/~ "'-,/' v'\,; _.-"'-;,;~."'.".' /'."',.-'... "v"'.~/,v "" _,", "-... '' ". -. " -~v Faculty of Engineering ancjit/ SCbool of EMMS Page 1 of 7

2 48642 Strength of Engineering Materials /" -,/'-. "' -, ~- ' '. Rough work space Do not write your answers on this page. Page 2 of 7 Spring 2014

3 48642 Strength of Engineering Materials ~. ' j '.j'o.. ".._".,-~-. ''\,/' -- '-_ ' ~ '.. _..,,"~-~-,/', Question 1 [Stress analysis and transformation] (10 Marks} The solid rod shown in the figure has a radius of 0.75 cm. If it is subjected to the combined loading shown, (a) determine the state of stress at point A, (6 marks) (b) show the results on a stress element located at point A, (1 mark), and (c) determine the principal stresses acting at point A. {3marks) Question2 [Shaft design] (10 Marks} The shaft shown is supported by two smooth journal bearings at A and B. Due to the transmission of power to and from the shaft) the belts on the pulleys are subjected to the tensions shown. Determine the smallest diameter of the shaft using the maximumshear-stress theory, with Tauow = 50 MPa. The radius of the shaft can be obtained usingc=( 2..JM2 +T 2 ) 113. TCTallow Spring 2014 Page 3 of 7

4 ~ Strength of Engineering Materials..,.~.. _,".... ~....,.,... '.,...,......_... Question 3 [Fatigue failure](12 Marks) The shaft shown is machined from AISI 1040 CD steel with the ultimate strength of 590 ::::: ::::. MP a and the yield strength of 490 MPa. The shaft rotates af1600-rpm and is supported.... in rolling bearings at A and B. The applied forces are F.1;;;.1Q 7 kn and F2=4-kN. Determine the fatigue factor of safety at the critical location based on achieving infinite life. If :- :... :. :: infinite life is not predicted, estimate the number of cycles to failure. The notch sep~itivity is found to be q = Ignore th~ shear stress caused by shear forces. Additional information (tables, figures andformulae) is given at the end of the e)(am paper. _...,.._192 mm-~- 30 A All fillet$ls1nrtl R. 8 Question 4 [Deflection and statically indeterminate problem] (10 Marks) Determine the reaction forces at the bearing supports A, 8, and C of the shaft. El is constant. Each bearing exerts orly vertical reactions on the shaft. Complet~procedure including FBD and defl!cfjqp diagrams is required for full marks. Page4of7 Spring 2014

5 -~-... ~-. ~-~/ ~-~-_.~. "'~ v'. / ~ '-.-"', -.,. -.."'-... ~ v "\..."v Y~-,./'.A... " /'-./v"~ "'. ",/'-v,/v"v''v",_-",/ v'' -.. -'-./',.''..-.. '. V". '"._/..._...,_."v' -... "'./'v"'... '" V"\...'"......,_."'-, "v"',. 'y"-,/"v-'" -~ '\.. "'v"'...a.,/,. 'v "" '. " "', "'-. '"'.,.,/"..-" Strength of Engineering Materials Question 5 [Strain energy and impact loading] (8 Marks)... The 2-kg block D. i$ droppec:ffrom the position shown onto the? >~ndpfa 16-mm-diameter rod. Knowing tht:~t.e = 200 GPa, determine the maximum deflection of end A. The moment of inertia of the circular is: I= ~rrr Spring 2014 Page 5 of?

6 '.~-_. v,j,.-,_ '"'.,_---'..-'._.--,/" '-._.-,_., ".''"< ~v.. ~ -J,_ Strength of Engineering Materials Tables, Figures and Formulae (with usual meanings) Fatigue stress-concentration factor: K1 = 1 + q(kt- 1) d f { O.SSut Sut $ 1400 MPa} The en urance llm1t or steels: Se = 700 MP a Sut > 1400 MP a The surface finish factor can be determined by formula: Csurf = as~t where a and b can be found in Table 6-2. The size factor for bending and torsion can be expressed as: ( d - (--) Csize l.sld-o.1s $ d $ 51 mm ) 51< d $ 254mm! 1 bending) The loading factor: Cst = axial 0.59 torsion Fatigue factorof safety: n 1 =(a~ +am J-' where a a= K 1 aao se su I S-N equation: S(N) = anb, where N is the number ofcycles, a and bare given by --..(fsut) 2 b _ 1/ (!Sut) a -----, --- og-. Se 3 Se For a completely reversed stress CTrev the number of cycles-to-failure can be expressed ( (J )1/b as: N = ;v. Stress-concentration factors Kt under bending: Page 6 of 7 Spring 2014

7 48642 Strength of Engineering Materials.. A'',.~.. /", ' ' _n,.r, '."-.,_ "\.,./"..._"'~ ",,./ v v.,_.,,..,"'-./'._ "\_/'V, ' ~.-..,{::',,/'v",/'v""v "v ".-.,..,.,_ " ~".. -~-..., '., ~./-,/,_.'.,/.-~'~ ".,_/'. '. 'v'\...",.'. "../'.,.. "'-,...",/",, ";,/' '' '"'.,<~. ~, 'v '-... 'v". ".,. "-. '-..-,,~,_.,,_.',/. /,,, '-,_. Two constants in the formula determing the surface factor Table 6-2 Parameters for Marin Surface Modification Factor, Eq. (6-'19) Factor a Exponent Surface Finish Svt, kpsi Sut/ MPa b Ground 1.34! Machined or cold-drawn Hot-rolled As-forged 3\1.9 ' From C.J. Noli and C. Lipson, "AIIr>wableWorking Stresses," Society.for f.~tperinu.mtal Stress Analysis. vof. 3, no. 2, 19<t6p/2,9,Reproduccd by O..T. Horgcr (ed.) MetaL~ Engin(~eting Design AS!>fE HarJdbqak; McGraw-Hill, New York. Copyright 1953 by "!11e McGraw-Hill Companies, Inc. Reprinted by permission. Fatigue stress fraction fused in constructing S-N equation: Figure 6-18 I o.9 Fatigue strength fntction,.f " '"''.... of s., at I 0 3 cycles for S, = s; = 0.5S,, at 10 6 cycles. o,s Conservation of energy Ue = Ui f.,.!l:fpa L M 2 The strain energy of the beam due to bending moment: Ui = f dx, ''':,, 1 External work done by a gradually applied force P: Ue = -P!J... <''..,,.,,. 2, Spring 2014 Page 7 of7