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Exam1_Solution_MEEG374

Exam1_Solution_MEEG374 - 3 Ql(10 points Mt A steel beam...

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Unformatted text preview: 3 Ql. (10 points) Mt A steel beam, which is ﬁxed to the wall at A and simply support at B is carrying a distributed load of w = 10 kN/m. The beam of length L = 10 m has a triangular cross section as shown below. The design requirement is as such that the maximum deﬂection due to bending should not exceed 5",” = 5 mm. Based on this criterion, you are asked to design the cross section of the beam. Hence, determine s. Modulus of elasticity is E = 200 GPa. c. v [Hints use method of superposition] ‘3 we 0! “i 0” [Fifi I (A) =m>w A/aaoo w : e l ‘ >_y Shh/WM .- f Mac 1/» Wwe gm from #1 Afterth a; 77*: 5W... fly/Z {wafer/WW rue/ﬂaw! -' 0 ' w , a M'é/f/ : . ~ eh \ 3M 3M“ ; 5‘“? are :L (29??) (or; 2 (page) :9 a? z 35 L" “I 2?" 3' 3 .l i/Lfifiﬂfcjﬂw » 3) V21; z. 5 ML .m&s_‘_ <7+.+0<3 = 5%) - 5%) ' Z = é???- X-S’g) — My? [z/I’KHCL— él'e 561 981/ E: 9 _ - ﬁ~® ‘> ymx;-§’w% =,> 5:02.3gm‘“ Mil; ‘, aw]; r/Macfa ﬁwf/cr) w» "Mm awe May‘g‘ m m éuﬁ Z_ 1 L 3 : 0:? mama) = .32. fwd-3L M +1“) 4/8132 ‘ W52 ’3 L/ ZLLN '2— 3 - w {x L—(vaﬁx j .— m (@631, - 38L — 2x94 Zr, L) - W94 L699: 3 éKL’v) =.___U:>,-._ .K- (S,va gxz—étfl 9,3 z. w ' (15‘sz - 8K "' ' 9gEI W 98?: \‘MWDﬁfrﬁ-W-w ‘ - — .: Q __ 9 g 3 «7 > 7 a? if) ’3 r? = /\$" A“ “.3 - ~29»? 45 = - (>69 : W’fﬂ ~6>.€?74)/£«4S93L — 30 Saw, . 4/8' 5‘7: 7 i > W X‘fﬂcrfﬂrﬂn 9) 550N711 If 7’}, A ///7<47 3 4 __ 3. _ ‘ ___ tyifzés I:{p,/aﬁ/_Lz_§g./ 6-5., I: .25} 36 7 J > 3 ’ i 0 /é '/ M s “I 3) Q2. (25 points) The compressed-air tank AB has an outside diameter of d = 250 mm and a uniform wall thickness of t = 8 mm. It is ﬁtted with a collar by which a force F = 40 kN is applied at point B at an angle a = 45° as shown. Knowing that the internal pressure in the tank is Pi = 5 MPa (a) [15 points] Determine the principal stresses (0'; 2 0'2 2 0'3) at pointA (x = d/Z, y = z = O). [Hint.' stresses atA will arise due to bending, torsion and the internal pressure. You can consider the tank as a thin-walled vessel] (b) [10 points] The compressor-air tank is made of ductile hot-rolled AISI-lOlS (HR) steel. Determine the factor of safety against yielding at point A. [Hints you can ﬁnd material properties for AISI—1015 (HR) in Table A—18 in the textbook] 1/ , X, 150 mm d = 250% \‘F: 40kN 600 mm :4 L, t) x, (OupﬂES/VC— (a CL 2 pmM/ﬂw wild; P. mg) z .x [be/WW! 57M”? “1"” (a _ _,..,_ a...w.,.-.,-.. _.._.'_-—..‘—.——A—- ' fMi=-Hxv-2" ‘ Q N A 2:0") @MX O (N743 3 *3?“ J ° WWW >2 W? W WWW M; = 51, >9 @H‘L : ; ._ : X If M Z «’7— ,4 @PJ A K;'é’€‘ ’- ”’>' f4 : Filwxlm (:8 j I ﬁéewﬁ’cyvaw? 7é:-—‘é.£ J) 7: To - T~C ' _ a» '"_ ‘ Jr. _. ({C—rj 3-02 3-2;»? my}- fair JU- - + (asxﬁr K. :oL I‘ SP'L°’§}‘3E (OW-(\$299 = 1/9. mm, ) . d-Zt Wm}? 5% Ce? N 73*. To: Wiwwgﬁw 54m W'l'ww .__.‘:-; ¢ .NM “Mg w 0’ h . 0; cw A > a, 6'? ~ die: = 98’ WA —-~.._.A’- t i 5% E. M/ r g 63‘ 6:3 "' G * 03M? \ ~'O :CB3+_FWWLr:f&JW% T_ 2&— 7’ “ .zz " gg’ 5" (4) Fwd/2V5 57m ( "/5 ‘”°L‘> o’vzaojwc-t-Ej‘ 02%; 0:31.93 82.4% 7_ 4. ‘7 = o’ H. 1 'L K 37?} + 7w = 9 3 Wu (Ru €= £2!” 9.: : 8’69 W q = ﬂaw—E: ngLf'g‘:3= 9g.0 M’a i ‘91 L03 A; Cb} WM (Mk3 mama“: #15: m: (M) W ﬁe 3 F A" " ' 9 WW {Ma {8? > Maﬁa, 6w: m away «.f 7% WI; ﬁlm gab/cm, — (531.»M/9cs./Efvm¢) w - \$3 at I” _ __ MM“ . W 6'. _ 07 E[/c\$-o:)z+/c2vo‘=)z+(€e-o.)z 2'” 9? ' -J 4‘ ...
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Exam1_Solution_MEEG374 - 3 Ql(10 points Mt A steel beam...

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