20110901123955271 - CES 4605 Steei Design Homework #1 Aug...

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Unformatted text preview: CES 4605 Steei Design Homework #1 Aug 26, 2011 Due Date: Sep 2 2011 Part l (30 points) — Tension Test. A tensiie test was conducted on a solid, circular-section specimen with diameter 1.25 inch. The “gage length" (initiai, iongitudinai length of specimen) is Lu=5.50 inches. The deformation was measured within this length. The test data are shown below. Deformation of Externai force the coupon, AL applied to the Pfease : inches couon F kis 0.00000 0.00528 0.00924 0.01540 0.01892 0.01980 0.02112 0.02200 0.02640 0.03344 0.04400 0.10560 0.13200 0.18040 0.35200 0.52800 0.70400 0.79200 0.88000 .00000 3.49903 6.99806 1.72428 1.54175 5.22331 7.67768 8.90486 1.35923 2.58642 3.81360 8.72234 2.40389 73.63108 79.76700 83.44855 84.67574 84.67574 83.44855 a. Draw best-fit (least squares) line to obtain stress-strain curves, after determining the stress-strain curve from force/deformation table shown to the left (piease, use engineering stress and engineering strain). b. Estimate the proportionai limit. c. Use the slope of the best~fit tine to estimate the Modulus of Eiasticity. (1. Estimate the 0.2% offset yield strength. e. Estimate the ultimate stress. f. if a toad of 50.0 kips is applied and then removed, estimate the permanent deformation in inches (Hint: is the elastic/plastic iimit going to be exceeded?) Note (for Part l): Please use MS Excel to plot data and determine the best-fit line. Please submit your work in paper format, only. Submission should include the stressistrain data (tabular form), any plots that you have used, a summary oi your results, etc. Submission of the Excel tits is not needed. Part II (30 points) — Review of MechanicsiStatics. For each "built-up" section shown below: a) Compute the Total Area, A (inz); ' b) Indicate the strong and weak axes of inertia of the built—up section (strong: principal axis with maximum moment of inertia; weak: principal axis with minimum moment of inertia); 0) Compute the Strong—Axis Moment of Inertia of the built—up section, ix (in‘), about the centroid of the built-up section; d) Compute the Weak-Axis Moment of Inertia of the builtwup section, ly (in‘), ), about the centroid of the buiit—up section; Part li.1 Part ".2 Note 1: A W16 x 67 with a 8 in. x 0.75 Two side-by—side L5x5x1/2: An example of “W—shape with cover in. cover plate on each flange y' plates" is shown in Figure 1.8 of the textbook by Segui (with solution). .t" Note 2: QG For Areas, Moments of inertia of: .. .- —_l - Rectangular plates (part iii). please check AISC, Part 17. Table 17-27; - For W16x67 (part tit), L5x5x1i2 (part “2). please determine moment of inertias and areas from the tables in “ Part 1 of the NSC manual. Hint (to solve Part “2): Please, recall the following properties of moments of inertias: ' if the built—up section has an axis of symmetry, one of the two principal axes of inertia will coincide with the direction of this axis; (Please, turn the page) The AISC manual has information on inertias vaand ly‘of each L shape (about centroid CG). and the principal, minimum moment of inertia only, the direction of which is inclined with respect to x’ (or y‘). In the manual, there is no information on the maximum moment of inertia. which must be determined in question c; Please, review “the parallel-axis theorem" to transfer moment of inertias along parallel axes; | suggest that you also possibly review the chapter on inertias from the textbook by Gore and Goodno. utilized in Analysis 1 and Statics. In partioutar, you may review the methods to determine the centroictal moment of inertia about an inciined axis. given iv and ly. Also, please recait the following property for plane sections: Ix + [y = constant (for any x, y pair of axes, when directions are mutualty orthogonal, x J. y) Probiem 1 deformation of externai force appiied area(square (inches) strain to the cou on(ki 5 stress (ksi) len t11(inches) inches 0.00000 0.00000 0.00000 0.00000 . 1.22718 0.00528 0.00096 13 .49903 11.00000 5.5 1.22718 0.00924 0.00168 26.99806 22.00000 5.5 1.22718 0 01540 0.00280 41.72428 34.00000 5.5 1.22718 0.01892 0.00344 51.54175 42.00000 . 1.22718 0.01980 5.5 1.22718 0.02112 5.5 002200 5.5 1.22718 0.02640 5.5 1.22718 0.03344 5.5 1.22718 0.04400 0.00800 63.81360 52.00000 5.5 1.22718 0.10560 0.01920 68.72234 56.00000 . 1.22718 0.13200 0.02400 72.403 89 59.00000 5.5 1.22718 0.18040 0.03280 73.63108 60.00000 5.5 1.22718 0 35200 0.06400 79.76700 65.00000 5.5 1.22718 0.52800 0.09600 83.44855 68.00000 5.5 1.22718 0.70400 0.12800 84.67574 69.00000 5.5 1.22718 0.79200 0.14400 84.67574 69.00000 5.5 1.22718 0.88000 0.16000 83.44855 68.00000 5.5 1.22718 U’I {J‘- Ln Ln (J1 LA 055 Lite? time 3: esteemed we; eat? 80 7o "‘ ""Zl‘il""""ui ""3." 50 A F: e, a a, 40‘ v 9 i3 2 E s a a 30- ------- w: ********* u: --------- --------- -- : : -------- ~ 20, ------ ---------- --------- -------------------- --------- ------------------- -- 10 gee—Test data : 1 0.2% offset ! 1M. ,, ‘Wfi—lm—U 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 strain 60 0 Test data _ y=12200*x(Filied line) 50 "‘y=10000*x _'“:"”""" y:14000*x 40 v .- +32 .8500 e a s : E a 5/1 g :3 so - ----- -- re-vav;93984ug---——--—-- :13 e s a g /2 e g M area =0.8523 ; 20 --------- --------- -------------- ------- 77777777 ---------- 4 -------- -- L. i 1.5 2 2.5 strain x 10'3 E (a) ""““““ 0‘! : a The coefficient of determination, R2, is nsnaily used in the statics to estimate the correiatien between the estimated data and real values. In the linear regression or curve fitting, this coefficient can be caiculated for the estimation of goodness of fitted curve. In the case at" simpic linear regression, the value ranges from 0 to 1. If the estimated values are much closed to the real value and the fitted line coincides very well with the real trend, the coefficient of determination will get much eiosed to 1. Please refer to the websites below about the conception of R-sqnare: l1ttp:l/en.wiltipedia.org/wiki/R-sguarul 'ass 4605Hw41 2)_ e. rag/.2 g [4.0!] ‘ xem Pehj [emf “(qua/12 Mal/ma] _ 7;?“ Milli/{£1381 - 01'” fl.) ) (11%;)? “H ,(Xn )3") rn 1: an *UAXnTLb) . a g ‘ g 2. 2. 15 retiw'red 1’70 .39, mira'flmrh. Par'b‘al Olflr‘fl/wtl'l/ei 4611/? to be Jan); :23; r; ‘ ($72 .2. 2 2‘, r,- ->(; :2 2M- " (M 1%)] {9(6): d? w "51;. F 0 93 :> art _. ,1 r- " 0 22mg;- :22n-(~--n 22>.EU.‘~(bxrbe]'(~U U, Celmmuj) MTM‘EzMTET #1. al A k A '3 Wm m | _;(n ,‘ nxl. 5" { ""* a] Li: :.' iii *1 I ~l . 12 I I ‘ "I *1 * l 3” } _ CtS‘ZfQQSJLWfijflZ—HA‘EJL _, J )L‘ ‘ FIRMIH’ __ mim&"§‘_fi_\ A 2X2 "“ ~ A 7 [2,; 2m : { :23“? STEEL DESIGN. (£34605 FW-Q 08:52:) am PM Probtoml 01> [00/2 a}! flu graphml I'm/xi‘ pfijfi’s b) H‘oporiaiimal (0,11% :3. #8 £15K; 0. Moms of mam-1 (1g- zzzoo 4.5.; L'} DEE m d7. 02% offmt yield Magi/t. 15 afloroxc'mufalg 5/115“; 43051 53 SH C 61332 100 SHE SCYE fiaflaflaflalafimfld 42-319 204; SHE SCYL 62> Mun-m ‘g‘z’l‘EI‘lsz/z A; (C? (‘5 . 11>. If a dead 91150123955 afflw,’ M_6;0;Q_ \_.. ‘ . \ firm M é$l~4ox71+ASL . Mm rm Par/71am Wmafion. '__Q_ESLI'6_05 HWMI f__§?8’[2~__6Z20_1L Fart 0.15; _: __;§;__ ', From "If/t2 1415K Manual, , for [IV/5X67: [161; 10 ml .ng i? W0 "at" [m ' /{?i;1."' (13am as slwwn in rig/d fly/’9) [Over Mm (@015) Aplaie fit 05/5“? :_ 6 in" 0> 70ml. area Atot ZJOflx 6:: .33. in‘ b) 701% Moment; (if 'z'me/“Xia , \ lmm :: $541))! JTiixS-‘x (05l5)3+0f15x8‘x ($31} 9:115):[ #,_,J \ Haul-£3113 r rpmutiei figment Tar each plat: : I 82 (17 in “' 155.10% :‘1 H‘? -I~ 3.x~,;~ xofiwxs-g ; 15:: W lmwt 7Ig‘fi0‘t‘ “Mm, >6 am is Me, 30'ij 60633 of warm M0153" mdn‘m ymzlis L5 HUI Luz-“M: (In; 0’]! Z/Lfll‘ftlt’t. Mfiafi ccnim‘é‘l 5‘ Pm- [lT/i, .2 from A156 Manual (form/1 15W): AL:JH5'U12 -LLIJ :3 N3 *1/14" Igy,.l.-'~' [3.4.111L3iu‘f X“X 60635 hubrizoiztai Faxing 1’3 centroid each 5221503, 6 ,- . ff 0x55 (wer'a‘cal), paw/:3 by centroid 59/ MA nggJGJ- dx : d5! 3- 7‘2 Lin ‘ d1: Clx1+dff132dxl Igaifizk 61": 1"- a \- [‘ 0M5” a) Tot-d area. .- Am "3 2 A]. =2XH~FI5 :- h5in‘ ' 55>. If My. [ym‘Zi-rujo mafia» Mg an M‘s (if ymmwg) 0/10.. 0f t/u Fri/lapr axes 'I'JLQNL‘Q. MM (xii/lad: MM f/moliredz'mi 07/ #55 [My .- from ‘Wé‘ Alli/"LL , m- m ax}; ,and mm axis are twO plyznzifml 61mg; lxxal— L : IrmnjL 11133))“ :(Inm’jfi i: 21%.; fl 13:331.: ’5' in I" :1}, Itnhn‘fb'i T‘. 2~ ‘Imnni. g r”- (3 “talk me ) J. ‘7: 11;? ,L [i] :- LI" :133553‘m‘” w ‘5 . , M—m am .< “ZS 't/uz. Mimi. an; Mme/T flu jlpbd CQJL'U'I‘JM , CG. YL-fl am“; is {M s-(mcj mm MM Um Jdpbai- (“fwd 7, p ‘ ...
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20110901123955271 - CES 4605 Steei Design Homework #1 Aug...

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