Question

A countershaft carrying two V-belt pulleys is shown in the figure. Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side at Bis 15 percent of the tension on the tight side. For the steel countershaft shown in the figure below, find the slope of the shaft at each bearing. Use superposition with the deflection equations in Table A-9. Assume the bearings constitute simple supports. In the figure shown below, Tx = 290 lbf, Ty= 50 lbf, and diameter of the shaft (dshaft) is 1.08 in. 6 dia T V Ty dshaft 8 dia The slope at bearing O is The slope at bearing Cis rad. rad

Answer 1

Giver T2 20.155, ET=0 => (290-50) x4 + (72-T)*3 = 0 240*4 + (0:15 T -TI)x3=0 0.85T, 240x4 $ 240x4 3x0.85 Ti - = 376.471bf T2 z 0.157, 629050) = 56.4715f A Roz -34015 Qoz Rey {mogao RCZ (12.77) =432.9416f- -432.94 x 16 - Rezx22 = 0 = Rcz = 432.944716 22 --314.86164 {aget Reztrozt 432-94 = 0 -432.94+314.86 Roz 3.-118.0816f

{MOZ BO Reyx 22 + 340x 8 = 0 Rega 340 X8 22 --123.8415f Efyzo Roy + 340 + Rey EO Roy = -340 + 123.64 2-216.36 lbf 340lbf 118.08166 432.94154 314.86157 & in Gin 8 in sin 21636int 123.6416f Vani van) 123.64 118.08 K O 0 B - 216.36 314.86 1889.28 M (166 in ) plofin) 944.64 0 B B 741.84 -1730 88

From Table A-9 F الح 346 l 14 Top = fbx (m2? +62-22) 0 6G12 A B Yac - Fall-w) (2+02-x2) GET I Yon 340x44** (2+62-21) 6 EI da slope dy dh 340x14 459-2+ ax 2X GEIXOA For steel E = 29800 ksi (doogpa) -0.90x 10psi Iz Tidy by Tlx 1.084 64 0.0667 in 6EI 2 6x2.9810²x0.0667 1.16x107 day du 340814 1-16x com xold dy] - 340714 1.16110xad 14² 22² dy dh 20o dr ato + 0.00537

slope in y direction at o 0.00537 YAC= 340 x 8% (dvd-) (x2+82-2xdayx) 6xETx 2 dy 340x 8 GGIl -1(x2+64-coun)+ (da-v}(22-44 che - - 340x8 llbxlox22 =x2-64+44x + 443-968 - 2x^+44 21° +42x] 7 = -106.58X10 -3x²+ 1320 1032 dy dx at . dy. da 1032 21 = -106 8810? [3x222-132x02 = -1065x17 2 ['1e52.43 g - 1042] :-106.58x10?x 420 --4.48x160.00448 zo.0045 Slipe in y directions at a

2 dlicctos 432.94 16 B 22 deflochen 432-94 x6x* (x2+b?_e?) Yoo GET I Slope dy da 432.94 x6 (3x2+62-29) 1.16x10x ad 101.78x16 (32++b?-? dy 2 32 dy don 2-0 101.76x10? (3x0 46?-am?) . ato 3 101.78x10' ( 36 -484) : -4.568103 Slope dy :-0.00456 2:0 slope In 2 divcering af o 2-0.00456 YAKE A32.94 x 16 x (ad -x) (x+256-442) 1.16x107x22 = 2.914 450 [22 -1) (zºad 56-408)] = 27144710'-(2+056-+*+ (29-») (ax - 44 [cat (az-kv) = 2.9144x18" (+34 +132x - 1224) dy ch

dy dre 271.44716% (-33+ +13 22–1224) 2 dy da dy' che, Nal 271.44x16x (-3x ad+132*22 – lady) 2 Z AL 201.44X10%(-1452+2904 - 1244 ) 2744x10' x 228 2 6.198103 0.00619 slope in y directions at ' 0.00537 at -0.0045 slope in a director ائمه =-0.00456 at ć 0.00619