cee130-fa07-mt-Armero-soln

cee130-fa07-mt-Armero-soln - Problem #1 (40%) The bar...

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Unformatted text preview: Problem #1 (40%) The bar depicted in the figure below is made of a linear elastic material with Young’s modulus E, and has constant cross area A and length L. The bar is homogeneous and it is subjected to a constant distributed force n (force per unit length) along the left half. Determine: 1. The reactions at both (fixed) ends. 2. The distribution of the axial stress along the bar (draw a plot with the characteristic values). Specify carefully the part of the bar that is in compression. and the part of the bar that is in tension. 3. The displacement of the middle section of the bar (i.e., the section at a distance L/ 2 from both ends). IM~WWWWWW4 “““““““““ “mrwwmi m m a W» Mmmn W was ?|+RL+V\% 2:0 L/L ‘9 mm! In} Zannwwls/ /e?M/6‘d‘\ m (‘Wérm‘mi “ma 573.70 / .- Pe/ewe, 391/ fié/ra/ywié ’ W a; {Strife/,4 mei/r/ém [Max LfiA /a’)"ce £41) STEPg, 504»: /W A [a flo/uoélw 7/55/3/ L ) A 2.: flfiw 00¢ a £74 «Mummm, ....M.,.»W.”.WW.; 3w xMyanmantn«rwaxy:v¢mruvyawmw.~;«»fl'u’lde-MUWN-‘uxwLiww‘?»€«nrwmfi , 7;” Ofix «4 é: /jl::3~>~ww> WK; «W P km»: é» / W4 L . 2”" w? n {éwfla We 46 mm W g—wxfé— WW2: anmmm4 x "5% P:.: R2 47%) / % A”? d] 1’24 m? m - Wm - "4“ mm W DAmg g” dgwgz [EEQ X) 1-quka z )r mwgfl? m 4.» 04.“ KA [Ralf 3 WWKWW W 57?P$: .Zfl/coqs? Zack & ayaZ‘é/f MAIV7L m M 4 4 W I? a”. £5; Awowgfigwfim ~73 M: y WW “m” A E39 31.- HA Mm 9/944 é/nam I§+g #- 14: we P, 2:: égw, 3 A 8 flow a 7Z / «ac/am % / ” “Ea/flu “fig “[émxHQf n/%-x)m;‘* 5" 613"» W 4.. .... gm WWM m 3 am 3% flacm/ 51%;: 9%}: PKG) ; mmwmfim NEW“ Qwrremvm 7Z2 d‘J/LéCPMMILVé; (“v a» me? 407/ o} If: [00K azl % . ghee flawh/flvfé émfiW/‘Zé’m 4.14/42 “71/ Ma, [4xer 1.2 Mg) wax/AA Aflxw/m é 43/2?) ’74., “3" I142 "c "ya? 5”“ M M74“ WI 303 Problem #W A rectangular steel block 0.4 m by 0.3 m and thickness 0.02 m is subjected to uniformly distributed stresses along its edges. The total load is Pm 2:: 600 kN and Py 2: 1600 kN (see the figure). Let E x 200 GPa and 1/ tr:- 0.3. Find: 1. The normal and shear stresses acting on the diagonal d (see figure). 2. The relative change of thickness of the block. Py=1600kN KW'WWfi W“ me600kN C08 6" 2.2. Sin 8« :2. M}... 5” 5w A/orma/flme 0’» 013mm: 7?: Ema + geostQ" 3”” 600. .5. ., Mw-Eg’ m Arm/(M .5” fiC/Bk: M /J7~?wZ/E//47cg an Md/anaé‘cc/kh: x4: 057.02: 00/,»2 p a~= - Em§¢ gum»; t""6003 6 a “7%.. a o W.) 55mm: 5""‘7L/0 5* W KM 0;: mg..- /gy/7/2L ,4 ’ 0.0/ m2 23.1%.- mm ma [4 ~ 40/»!2 X N a ma #& A): 0.3 002 M2 721 #00 M/ U; .3; WM W”..me ; 200 flé. f? (24/ coma 264% M 0». 40 «9M. *3 5%- 3‘ wk “flaw act/1cm £5" 2: m ii...” {mowed/0°; -- 0-K“ /0 .3 200/9" m3 5% :1 MaQr/0~Z Problem #3 (30%) A shaft has a tubular cross section defined by an outer circle of radius c and an inner circle of radius c/ 2 (see figure). Determine the ratio Tun/Ty between the ultimate torque Tu“ and the maximum elastic torque Ty if the material response can be idealized by the stress-strain law depicted below. Sketch the distribution of the stresses on the cross section under Ty and Tu“, respectively. £4K2»&muwn'i~wr’5>§k\9yr¥v¥ may ...
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cee130-fa07-mt-Armero-soln - Problem #1 (40%) The bar...

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