Question

You are the project manager's assistant on a construction site. The project manager is off site for the day and you are responsible for the ongoing progress of the site in her absence. Two similar beams are delivered to a construction site. Each beam is a hollow box beam, constructed of A36 structural steel, (E=29.0 x 106 psi, density of 490 lbm/ft?), each beam having outside dimensions of 16" base and 18" height, 18 feet long. Beam A has top and bottom wall thicknesses of 0.5" and side wall thickness of 0.375". Beam B has top and bottom wall thicknesses of 0.4375" and side wall thickness of 0.3125". The structure to be constructed calls for a beam that will support a point load of 55,000 lbf at the mid- point of the span of the beam, 16 feet between supports, with a maximum allowable deflection at the mid-point of 0.20" 5. Beam D is delivered to the construction site by accident. Beam D is identical in dimensions to Beam B, except Beam D is made of aluminum (E=15.0 x 106 psi, density of 160 lbm/ft?). Will this beam support the design load without exceeding the allowable deflection? If so, what is the factor of safety of the beam as installed? If not, what is the actual deflection of beam at the design load? What is the maximum allowable load Beam D can support without exceeding the 0.20" deflection limit? What is the actual deflection of Beam D if loaded to the design load (55,000 lbt)? What is the weight of Beam D as installed? Document your work. If a problem exists based on your analysis, describe the problem and present a recommended solution to the problem, including any effects this may cause to the construction of the project (i.e., additional costs, delays to the schedule, performance of the structure compared to its design and intended purpose, etc.). Document this in a memo to your project manager and be prepared to make an oral presentation (2-3 minutes) to the project manager if needed to defend your solution.

Answer 1

X=16" 10.4345 x'-16- 16-260.3125) = 15.37514 S718.a 18" L = 18 feeth = 216 inch 16" Y-19 Y'= 18-2 (0.4375) = 11-0.875 7:125111 Ixx = xy² Xy? X'y 3 16 (1913 (15.345) ( 17.12993 12 h 12 12 7776-6434-66 - 1341-339 in ух'3 2 Tyy = Yx3 12 18(16)3 7125)( 1S-34592 12 12 6144 ។ 5186-74 = a57 25 in 1xx> Tyy The load should be loaded such that lyx Suppests the load. E = 15x106 psi volume of the beam ('= 160 lbm/sts L(xy-x4) Mass (lbon) = 1 (16X1P -15 375*17.125) -499.92 25335.87s in3 = 3.087 fif3 D . 160X 3.087 216 (24-703)

self weight = 493.92 x 32.17 lbf mg = 15889.40 15890 lbf 185,000 lbs j ng 16 feeth Ifo >> RATRE 55,000 +15890 70890 lbf TIMA 7 PB(16) - 70890(8) - - PB = 70 890 = 35445 lbf APA = 35 uus lbf MCX) = 2 BA 70sro b 8 feet El dy MY = 70890(2-8).- PA (X) = 70890 (2-8) 354450 Tosto (x-8) - 354450 =) El dy = 70890 (11 & Ely = 708 90 da² 2 3544s a ta ch १५) 2 fa - 4aly 3544523+04+CV 6

Applying Boundary Conditions da at =0 yoo CO and C2=0 y en frosqu (- 41035445x} Deflection 7 Ep = 15X10 psi = 2.16x109 Ps.fool Iy=1341.339 -O 0.06468 feet! 8 O ze xeletro-c4c270190(82-474 2.16X109x0.06468 35UMS ('83 6 ☆ 1.397088x 10 12-098568106 3:0.246810 15.1232 X 106 1.397088X108 = 0.10824 feet - 1.29 inch, 19170.204 Herce not suitable,

dergoing deflection of 0.20" Maximum load it can sustain withoup un -0.01667 feet Say. Ioad Susteinable - W lbf Thus. Mament Eq MCX) (2) Es dy = MC2) (wig) (x-8)- £1 dy = (wmd) -84) - Kvoting +G sery = {wtong (el - 42y- () 2 Applying Boundary Conditions (Wrmg)(x-P)– (wtma) 2 da? wting & 2 > El dy dyz wrong x 12 - I dy ch +Cix + C x 0 dyo at da at x=0 yoo Geoord (2=0 ,9 ㅗ ЕТ 8 ET = 1.397088 x 10' y=0.01667 mg = 15890 ebf we need to take y=-ve because dylection would be in axit

SEX :y {(29.40%- 리 13 - 40x² 23 (wtmg) EJ Wing /- 4.82 83 EI w ting 9 (-256- 85,34) ET EI f 0.01667 tootmgx 341-33 (wting) 0.01667 EL = 6829.752 lry, 341.33