Chapter 4 Shaft Design Objectives: At the end of this chapter, the students/ readers shoulg be able to: 1. Define shaft; 2. Derive formulas and apply it in solving problems; and 3. Practice exam in the multiple choice test to Master the usual questions and problems in the licensure examination. Shaft is a rotating or stationary member having a Circular cross section much smaller in diameter than the shaft length and having mounted on it such power-transmitting elements as pulleys, gears, belts, chains cams, flywheels, cranks, sprockets, and rolling element bearings. Shaft could be main shaft, line shaft, transmission shaft, machine shaft and other similar form. Main Shaft is the shaft receiving its power from the engine or motor and transmitting power to other parts. Line Shaft is a shaft used to transmit power from a central source to individual machines. Transmission Shaft is the shaft transmitting power between the source and the machines absorbing the power. 328machine Shaft is the shaft used as an integral part of th I tre itself. axle is a stationary member of primaril i nee pulleys and wheels rotating on it. Me eee vi Countershaft is a secondary shaft that is dri ; it is driven by i wt and from which power is supplied to a machine part. ees vo as spindle. shaft is 2 countershaft, especially when used ili ween two other shafts. as an auxiliary shaft ead shaft is the shaft driven by a chain and mounted at the delive end of chain conveyor. It serves as the mount for a sprocket which gives the drag chain. ic Formula: 1. For Main Power Transmitting Shafts Where: P = power transmitted D = shaft diameter N rotative speed 80 = constant value 3292. For Line Shafts Carrying pulley Where: P = power transmitteg D = shaft diameter N = rotative speed 53.5= constant value Small, Short Shafts and Counter Shafts 3. Fol Where: P= power transmitteg D shaft diameter N = rotative speed 38 = constant value 4, Power Transmitted Where: P = power transmitteg N = rotative speed P= 2nTN T = torque 5. Twisting moment for shafts of any cross section Where: T = torque transmitted S; = torsional shear stress Zp = polar section modulus 6. Torque transmitted for solid circular shaft Where:T = torque transmitted D = shaft diameter Ss; = torsional shear stress 5.1 = constant value 7. Pure Torsional Shear Stress (Solid) Where: T = torque transmitted D = shaft diameter Ss = _ torsional shear stress J = polar moment of inertia c = distance from the neutrd axis to the outer most fiber 8. Pure Flexural or Bending Stress (Solid) 330ee _| Where: M = Mc_32M Seige bending moment distance from the neutral axis to the outer Most fiber shaft diameter rectangular moment of inertia = flexural or bending stress cos D = 1 9 ¢_ pure Torsional Stress (Hollow) Where: T = twisting moment D, = outside diameter D, = inside diameter S. = torsional stress 10. Pure Flexural or Bending Stress (Hollow) Where: M = bending moment D, = outside diameter D) = inside diameter S; = torsional stress Sy = flexural or bending stress 11, Combined Torsion and bending Stress Where: M_ = bending moment D_ = shaft diameter Stmax= maximum tensile stress Semax= maximum shearing stress T = twisting moment 12. Combined Torsion and Bending Considering Shock and Fatigue Factors 331in etKs7? | 16 [x M+ = m Sw 93 Ssmax a KT 16 M)2+(KsT) 18k y+(Ks: xD bending moment ee 5 shaft diameter Sima = maximum tensile stress Serax * maximum shearing stress T = twisting moment Kn = numerical combined shock and fatig factor to be applied in every case to the computed bending moment kK, = numerical combined shock and fatigue factor to be applied in every case to the computed torsional moment Shock And Fatigue Factors For Shafts Nature of Loading k Ka Stationary Shafts Gradually Applied loads 1.0 Lo Suddenly Applied Loads 15-20 | 15-20] Rotating Shafts Gradually Applied or Steady Loads 15 1.0 Suddenly Applied Loads Minor Shock Only 15-2.0 | 15-20 Suddenly Applied Loads, Heavy Shocks 2.0-3.0 | 15-30 13. Vertical Shear Where: V = vertical load A cross-sectional area D = diameter “14. Angular Deformation (Solid shaft) 332Where: 9 oora gular Deformation (Hollow Shaft) isan Where: Qo T L De D, G angular deformation torque length diameter Modulus of elasticity angular deformation torque length Outside diameter inside diameter Modulus of elasticity Standard Sizes of Transmission Shafts, ty 11. 15. 3, 15 3 ile, tein, |. 28in, eA [Sp Wein. 16 | 6 n, igi a6 in ht | ots, in. | 318i, aZin. | 438 6 | 746!" | 355 16 te | Aagin | in. a 1, 1, — 5— in. 6— in. 7 in. | 16 2 Tin. 2 Bin, | in,Test 36 Choose the correct answer j rin the probl check your answers whether you Be crerieerie ae and then answer it again until you master it. Ne ipstrvction® , ME Bese ieee 2003 A torque 0! foot-pounds is applied to one end of it ical shaft fastened a a solid pula a caskio it the other end. The maximum shearing ‘A. 2500 psi g. 3500 psi c.{3000 psi p, 3842 psi 1, MEBoard April 2003 Achromium SAE 4340 steel 6 in. diameter by 24 in. long shafting weight is 87.3 kgs. How about the weight in Ibs of an AISI 1030 steel shaft on the same dimension? A. 173.5 lbs B, 182.3 Ibs C. 192.5 Ibs D. 217.5 Ibs 3. ME Board April 2003 i Determine the power transmitted by a main power transmitting steel shaft with 2 7/8 inches in outside diameter. SAE 1040 driving conveyor head pulleys at a shaft speed of 150 rpm. A. 45hp B. 50hp C. 55hp D. 60hp 4. ME Board April 2003 Design the safe diameter fo! transmit 30 hp at a shaft speed of 180 rpm. A. 2.25 a power transmitting shaft to 337e 2 B. 2.50 C. 3.25 D. 2.38 il 2003 Me emul Pe the diameter in millimeters of a maj at We transmitting steel shaft SAE 1040 to transmit 100 KW at boone A. 67 B. 47 iG 76 D. 56 ME Board April 2003 Find the diameter of a main power transmitting shaft in mm t, transmit 100 kw at 400 rpm. A. 48 B. 67 Cc. 76 D. 84 ME Board October 2002 What power in watt would a short shaft 40 mm in diameter transmit a 300 rpm. A. 23,132 B. 13,880 Cc. 12,400 D. 27,750 ME Board October 2002 Compute the outside diameter in mm of a main power transmitting SAE low carbon steel shaft to transmit 200 kw at 800 rpm? A. 87 B. 97 C. 67 Di 77 ME Board October 2002 Compute for the diameter of a line shaft to transmit 25 hp in@ speed of 225 rpm design stress is 6 ksi. 33847/8in 2,00 in 15/8 in 0. 1,00 in Board October 2002 sr rermine the diameter in inches of i mse ane @ SAE 140 steel line shaft to a, 1.25 g 175 ¢. 2.00 p. 1.50 ME Board October 2002 compute for the diameter of a shaft to transmit 15 hp at 120 rpm with a torsional deflection not to exceed 0.80 deg ft length shaft is Aft. A. 3.60in. g, 2.75 in. ¢. 345in p. 2.25in $ 1. ME Board April 2002 Compute for the diameter of a steel long shaft to transmit 15 Kp at 120 rpm. The allowable torsional deflection limit is 0.08/foot of length. A 2.25 8, 2.75 Cc. 3.00 D. 3.25 13, ME Board April 2002 Compute for the power transmitted by a journal shaft 55 mm in diameter at a speed of 360. A 59 8 65 CG 72 0. 79 339ril 2002 ee eae diameter in millimeters of a mai a 0) . 1, ' | shaft to transmit 100 kw a ey transmitting SAE 1010 steel it 800 Dm, A, 41 B. 51 Cc 61 Di 7i . ME Board April 2002 Ne 15. What will be the ultimate length of a S-inth diameter steg] isti Shaft subjected to 28,000 in-Ib twisting moment to reach the makings allowable angular deflection 0.08 degree/ft. length. Use torsion modulus of elasticity of 12 x 10 Ib/in*. A. 31.2in. B. Sft Cc. 36.7in D. 48.7 in. 16. ME Board April 2002 If the weight of %” X 4” x 8’ plain carbon steel is 652 Ibs, what wil be the weight of a high chrome abrasion resistant steel of same size in kgs? A. 513 * B, 592 Cc. 2.96 D. 3.55 17. ME Board April 2002 Compute for the diameter of a power transmitting shaft in millimeters to transmit 200 kw at 600 rpm. A. 48 : B. 68 Cc. 84 D. 96 18. ME Board April 2002 Compute for the torsional deflection in degrees for a 3 7/8 in. 0D x 48 in. long steel shafting which is subjected to 28,000 in.b twisting moment. Use a torsional modulus of elasticity of 12,000,000 psi. 3400.29 i: 0.31 ¢, 038 p, 0:35 April 2002 mine the torsional deflection in degrees of a SAE 1040 steel g of 120 mm in diameter and 1.4 m long subjected to a ent of 3,000 N.m. The torsional modulus of elasticity w peter! shaftin twisting MoM js 0,000 MPa. _ 1.285 0.148 c 1.480 p, 0.285 ME October 2001 Aline shaft having a diameter of 2 inches rotates at 180 rpm and having maximum torsional deflection of 0.08 degree/ft length. find the horsepower developed. A 27 8, 30 c 38 D. 46 11,ME Board April 2001 Compute for the diameter in inches of a SAE 1030 steel shaft to transmit 12 hp at 120 rpm with torsional deflection below 0.08 degree/foot length as required. A 27/8 B. 25/8 c 21/4 D. 23/8 2, ME Board April 2001 Determine the diameter of the chain driven power transmitting steel shaft to transmit 200 hp at 400 rpm. A 4 B. 25/8 C3 341D. 3% . ME Board April 2001 : 23. ra the diameter of a SAE 1040 line shaft to transmit by 120 rpm with a torsional deflection not exceedin 1 B 0, ,/meter length o& 0.08 degree/foot length. Shaft allway. le degree, stress is 8000 psi. A. 68mm B, 60mm Cc. 55mm D. 75mm 24. ME Board April 2001 Determine the diameter of a steel line shaft to transmit 20h at a speed of 300 rpm with a torsional deflection Not fo exceed 0.08 degree/foot length. A. 2.34 in. B. 3.00 in. C. 1.89 in D. 2.70 in. 25. ME Board April 2001 Determine the horsepower transmitted by a pair of friction wheels with a driving wheel diameter of 12 in., revolves at 240 rpm. The face width of the wheel is 3 in. Given a force/inch width of face at 200 and the coefficient of friction at 0.20 thus C= 0.00032. A. 3.30 B. 2.80 C. 2.00 D. 2.22 342olution to Test 16 1c 3000 psi From Machinery’s Handbook D = o029\F Dp = 0.294/3142¢ Ioxtai D = 4.00in. From torsional strength equation Soe torsional shear stress 5 = 16T i xD? 3 Me 16(3142x12) . (4.00) Ss = 3000 psi ae 192.5 Ibs W o= weight 2.205ibs Wo= 87.3kgx SERBS W = 192.5|bs 3A 45hp Pp =~ power D?Nn i = © cor 3 (22) (150) JOO re Poo 45 hp 4D 2.38 in. 343TA shaft diameter D = 80P. Do= Vw _— efe0te) D r 18 D = 2.38 in. 67mm . D = shaft diameter '80P = AE aoe N D = Do o= 7yomm D = shaft diameter Ed = 3;—— . N 100 a (or) 400 D = 2,9929in D = 76mm 23,132 watts : = power transmitted Pos Pos . 3445D 10.B on 8 30.833 hp x 746watts ‘hp 23,132 watts shaft diameter ,[80P N 2.9929 in, x 254mm jin. 77mm torque transmitted P 2aN 25x33000x12 2n(225) 7002.82 in.Ib diameter 16T eee /16(7002.82) (6000) 1.81 in. 1 iin diameter 345a1. 12.B mc [53.5(20) oe) po . 200 D = 1.75 in. 2.75in From Machinery’s Handbook dD = __ shaft diameter P 4AfP 4640 Do = D = asd D = 2.74 in. 2.75 in From Machinery’s Handbook ye shaft diameter . = 4 4.6 N 120 D = 274in, 72kw P = power transmitted Bo ON 38 3 55 > = Gx) 38 P= 96.18 hp x.2:746kw thp Pos kw 34654 15.€ 16, c D = shaft diameter ‘sop = 3/80P : N 100 rae eo <2 ) “800 = 2.375 in x 254mm 1 = 60.34mm 36.7 in. L = length of the shaft [= ae. T Solving for 6 0 @ = | 008s ix ft “4800 @ = 0.001396 rad A Solving for polar moment of inertia 4 a 20a j 32 (ey 12 | 32 A J = 000295906 in’ ft Substituting the values 0.0001396(0.00295906)(12x1 08) _ 28,000 4b : ‘in. Lo = 3.06 fx 12H Los 367in. 296 kg 34717.€ 18.A 19. weight of a high chrome abrasion, resistant steel ‘kg 652 Ibs x5 50sibs 296 kg shaft diameter fe N 200° ) (78) 600 25.4mm 3.29 in. x tin. 84mm torsional deflection (28,000)(48) 180 torsional deflection Zz JG 348ao 27 (3000)(1.4) 180° = (220, i 2 “(1000 ) N_ \(1000mm ) > | 80,000—~. | 32 meine) 0.148° power transmitted on 53.5 ’ (2)° (180) 53.5 27 hp torque transmitted ft-lb (12h 33000 ie } 2nroy( 120% mi 525.21 ft.lb shaft diameter 526.21(12)(12) 0. 08)( 5; |gp(12:000.000) 34922.D ‘23.4 y /s ae shaft diameter De 80P co oe N _ _,[80(200) a 400 D = 3.42 in. or 3 % in. 68 mm T = torque transmitted . 10,000 " * jx(2) \ 60 T = 795.77 N.m Deis shaft diameter De Die 2.34 in, T = torque transmitted (20hp)( 33,000 a } tS hp.min 2h rev ) “(200% ) T = 350.141 ft.lb Solving for diameter based on rigidity D = shaft diameter 350___350.14(1) 30.08) 5212x108) 144) 2.353 in ns torque Fir. f (20042 (ain) 6inyo.20) 720 in.lb horsepower transmitted 22TN ; 1\(1)(1 2n(720)(240x35)(;5)(s) 2.74 hpInstruction: Choose the correct answer in the Problems A, Test 37 check your answers whether you PASS the Te elo and then answer it again until you master jg. 5! FN ME Board October 2000 Compute for the torsional deflection in degrees of a diameter, 1.4 m long shaft subjected to a twisting mo, i im 10° N.mm. The torsional modulus of elasticity is 83,000 a of 3y A. 0.27 a. B. 0.31 C. 0.20 D. 0.24 ME Board October 2000 Find the torsional moment in Newton-meter develo, shaft delivers 20 kw at 200 rpm. A. 0.85 x 10° B. 1.0x 10° C. 1.20x 10° D. 2.10x 10° Ped when the ME Board October 2000 Compute for the twisting moment in in.Ib developed when the shaft delivers 20 hp at 1200 rpm. A. 1166 B. 915 c. 1050 D. 945 ME Board October 2000 Find the torsional deflection in degrees of a solid steel shaft, 110 mm OD 1.4 m long subjected to’ 3.1 x 10° N.mm. The torsional modulus of elasticity is 80,000 MPa. A. 0.22 3528. 0.195 ia 0.28 D. 0.24 poard October 2000 short shaft transmits 200 hp at 3 giameter of the shaft in inches. AS (00 rpm. Determine the ean B C 0. Board April 2000 what power in kw would a 2 inches diameter short shaft tr i : ‘an: at 500 rpm. The torsional modulus of elasticity is at 12 oe psi A, 53 3, 58 c. 65 p. 78 ME Board April 2000 Compute for the diameter in inches of a conveyor head pulley SAE 4130 solid steel shaft being driven by a 20 hp drive motor through a gear reducer with 120 rpm output. The torsional deflection is 0,06 degrees/foot of shaft length and the modulus of elasticity is 30X 10° psi in tension. A. 2.25 B. 2.50 C 2.75 D. 3.25 ME Board April 2000 Compute for the diameter of an overhead crane. travel shaft that transmit 10 hp of the electric motor at gear reduced rpm of 150 and with torsional deflection of 0.06 deg/ft of shaft length. A 1% B 2% C 25/8 D. 3% 35310. 11. 12. Board October 1999 Ard the diameter of a SAE 1030 line shaft for 20 ft Overhead travel drive at 180 rpm. The drive motor used is 19 torsional modulus of elasticity of this shaft is at 11.5 195 si vith torsional deflection within the 0.08 degree per foot length limit in A. 1.25in B. 1.50in Cc. 1.75in. D. 2.27 in. Crane . The ME Board October 1999 Find the diameter in inches of an alloy steel shaft transmits 200 hp at 400 rpm. The ultimate strength of the shaft material is 110 igi and modulus of elasticity is 30 x 10” psi. A. 2% B. 27/8 C. 3% D. 37/16 ME Board April 1999 Find the torsional deflection in degrees of a solid steel shaft 110 mm OD X 1.4 m long, subjected to 3.1 X 10° N.mm. The torsional modulus of elasticity is 80,000 MPa. A. 0.18 B. 0.20 Cc. 0.22 D. 0.28 ME Board April 1999 Determine the diameter in inches of a small steel countershaft that delivers 13.31 hp at a speed of 15.7 rad/sec. The material allowable design stress is 8.5 ksi. A. 1.25 B. 1.50 Cc. 1.75 D. 2.00 . ME Board October 1998 Compute the speed of the gear mounted in a 52.5 mm diameter shaft receiving power from a Prime motor with 250 hp. 35471821pm 5 zoairem ¢, 2265"Pm D. 2341 1pm rd April 1998 ute the diameter of a solid shaft transmitting 75 hp at 1800 The nature of the load and the type of service is such that the able ss based on pure torsion is 6000 psi. a 17/8 in. g, 22/16in. c¢. 15/16 in. p. 31/8in. 5 ME Board April 1998 Asmall counter shaft is 1 % inch in diameter and has an allowable stress of 8500 psi. Find the horsepower delivered by the shaft at a speed of 15.7 rad/sec. A. 7.20 B, 1.40 c 13.31 D, 14.72 ‘6, ME Board April 1998 The shaft is subjected to a steady load of 36,000 in.Ib at a shear stress of 10,000 psi. Compute the diameter of the said shaft in inches. A. 17/8 B 2% 17. ME Board April 1998 A 16 ft steel line shaft has no bending action except its own weight. What power in hp can the shaft deliver at a speed of 200 tpm. Consider that the torsional deflection will not exceed 0.008/ft of length. A. 13.2 8 15.8 C244 355D. 14.6 . ME Board April 1998 : 18. The torsional deformation of a SAE 1040 steel shaft is toog, length of % meter. The shear stress is 69 MPa, Com > diameter of the shaft in millimeter. Steel modulus of elastic i shear is 79,300 MPa. A. 50 B. 52 Cc. 62 OD. 75 19. ME Board October 1997 t If the weight of 6 in. diameter by 48 in. long SAE 1039 shafting jg 174.5 kg, then what will be the weight of chromium SAE 51416 of same size? A. 305.5 Ibs B. 384.8 lbs C. 426.4 Ibs D. 465.1Ibs 20. ME Board April 1997 Determine the torque received by the motor shaft running at 4250 rpm, transmitting 11 hp, through a 10 in. diameter, 20° involutes gear. The shaft is supported by ball bearings at both ends and the Bear is fixed at the middle of 8 in. shaft length. A. 163 in.Ib B. 167 in.Ib C. 132in.Ib D. 138in.Ib 21. ME Board April 1997 Determine the estimated volume of a %"x6"X 20’ steel plate. A. 1809 in? B. 1490 in? C. 1709 in? D. 1080 in? 356poard April 1997 2 wat power would a spindle 55 mm in diameter transmit at 480 ; mn, stress allowed for short shaft is 59 N/mm?, 95.00KW 50.61 kw : 61.37 kw p, 39.21 kw Board October 1996 compute the power transmitted in Hp by the shaft rotating 1200 rpm and subjected to torsional moment of 1200 N.m. a, 202 p, 252 c, 150 p. 171 4. ME Board October 1996 Compute the line shaft diameter to transmit 12 hp at 180 rpm with torsional deflection of 0.08 degrees per ft length. A, 3.0in b. 2.0in c. 1.53in. D. 1.23 in. 25, MEBoard October 1996 Compute the nominal shear stress at the surface in MPa for a 40 mm diameter shaft that transmits 7SOKW at 1500 rpm. Axial and bending loads are assumed negligible. Torsional shearing stress is 28 MPa. A. 218 B. 312 C. 232 D. 380 357Solution to Test 17 0.20 oe torsional deflection eee is JG (x108 (1400) a= 4 — = (110)* (83,000 3p(1"0), (83,000) 0 @ = 0,00352 rad 180 arad @ = — 0.20° 1.0 x 10° + = torque transmitted T = at 2aN 20(tx108) T 242 6 T = —(0.9549929 X 10° N.mm 1050 in. Ib = torque transmitted Tait secs 2aN T = 20(33,000)(12) 22(1200) T = 1050 in.lb 358 A4A 6 D g oF ails Ie (3:1x108 (1400) setae ed eal = (110)"(80,000) 3a") ( 00) g = 0.22° 3in. D = __ shaft diameter Do= Dp = 3.00in. 78 p = __ power transmitted _- DN tae ase p= 2X00) o 38 p= 105.26 hp x 2748Kw thp p= 78kw 3.25 T = torque poe HIN. 33,000 20 = 2aT20) 33,000 T = 875.35 ft-lbs Solving for the shaft diameter 359 = __ torsional deflection 180 "9 D = shaft diameter De. | aun (S)oe) ._ 4201.69(12) 6 = || ~~ |(0.06)(12x10 32 a i ) D = 253in. or 23 in, 2.27 in. T torque Pp 2nTN _ —_2aT(180) a 33,000(12) T == 3501.41 in.Ib D = __ shaft diameter TL D = al( x (3 jena) De 875.35(12)(12)__ a(x a 3 ($5 }(0.00)(;25 Jt2x10 ) D = —-:3.18'in. of 3.25 in. 2 8 T = torque P=) 2nTN . 2nT (150) a 33,000(12) T = 4201.69 in.Ib Solving for the shaft diameter 3600 D u.€ solving for the shaft diameter De shaft diameter TL : Jaro) 3501.41(12) (0.08) 4515x109) 1 = 2.27in.or 2 in. D in. o1 4 in, 7 346 D = shaft diameter (80P = 3}— . N (80(200) = 3/80(200) y 400 D = 342inor 3 in = 2 6 0.22 8 = torsional deflection TL 08% 0 = © == 0.0037742( ) @ = 0.22deg 1.50 be - torque 36113.C 14. C P Toe o 7 = 23.34(850)(12) 15.7 i = 5591.08 in.Ib De = diameter p =. 3f6r xS 2 1.08) ae q (8500) D = = 150in. 2265 rpm N = rotative speed 80P eo euee Dp? N = 80(250) (za) 25.4 N = 2265rpm 15 in. 16 ai = torque B= i2niN _ 2nT (1800) 75 = 33,000(72) T = — 2626.056 in.Ib Solving for the shaft diameter D = diameter = yf6r 2 Vas D = -¥(6000) 362pd = lagin 13.31 hp He = rotative speed 2 157200 Qn N = 150 rpm Pp = power transmitted 3 a D°N ae 38 (1.5)9(150) pe (8/8180) 38 p= 13.32hp 16D 2% in. D = diameter 167 Do i= = 3 Ss DoS D = 2.636 in. 17.D 14.6 From Machinery’s Handbook 2/3 aula z 8.95 OS diameter 93/2 > = (8) 8.95. D = 2.39 in. From Machinery’s Handbook 363= 4 Wl) (as) 8 Hp = horsepower Hp = (222) coo Hp = 14.6 18.0 62 7 = torque ‘ tT. Se? 3 rs ae T = 13.54803 Solving for the shaft diameter D = diameter TL a. = Je 13.5400°(3) oa 5) =___\#/ 180) ~ = p4 D4(79,300 320 | ) D = 0.0623m D = 62.32mm 19.B 384.8Ibs W = weight of chromium - Ibs ee 174.5 kg x 2.205 kg W = 384.8 Ibs 20. A 163in.Ib T = torque transmitted 3641D A 23.A 24.0 7 0 on) 7 " 7 " p 2nN 1 4hpx33,000 "IDS y49in hp-min™ ft rev 224 (4250) rev min 163.12 in.Ib volume txwxl 0.75 in. x 6 in. x 20 ft x 127 1080 in® power transmitted kw 128.24 hp x 0.746 hp 95.67 kw i power transmitted 221N : rad rev ant) ae (1200N.m) (12002) one. tts x —P __ 150796.447 watts x Fee atts 202.14 hp 365 E_ = D = diameter 53.5P = 3 ee 180 25.D 380 = torque eo gue iste 2xN 750 3 2e( 122) 60 T == 4.7746 KN.m T = = 4,7746 x 10° N.mm Solving for torsional stress Ss = torsional stress 16T S. = gc : nD? 16(4.7746x108) S, = — —__,—+ (40) Ss, = 380 MPaTest 38 Choose the correct answer in the questions below and check your answers whether you PASS the TEST or NOT and then answer it again until you master it. jptruction® Abasic shaft is one whose A, lower deviation is zero gp. upper deviation is zero ¢. lower and upper deviations are zero p, none of the above the standard length of the shaft is A 5m B. 6m c 7m D. allof the above |. Two shafts A and B are made of the same material. The diameter ofthe shaft B. The power transmitted by the shaft A. twice 8, four times C. eight times D. sixteen times Two shafts A and B of solid circular cross-section are identical except for their diameters da and dy. The ratio of power” transmitted by the shaft A to that of shaft B is AoA 4B 3, (ale (8)? cal (dg) ) , 36710. (aay D. 4B)" Two shafts will have equal strength if ‘A, diameter of both the shafts is the same angle of twist of both the shafts is the same : i C._ material of both the shafts is the same D. twisting moment of both the shafts is the same A transmission shaft subjected to bending loads must be designey on the basis of A. maximum normal stress theory maximum shear stress theory maximum normal stress and maximum shear stress theories B. CG D. fatigue strength The residential compressive stress by way of surface treatment of a machine member subjected to fatigue loading. ‘A. Improves the fatigue life B. Deteriorates the fatigue life C. Does not affect the fatigue life D. Immediately fractures the specimen When a shaft is subjected to a bending moment M and a twisting moment T, then the equivalent twisting moment is equal to A. M+T B. M?+T? C. VMesr? D. VM?-72 The maximum shear stress theory is used for A. brittle materials B. ductile materials C. plastic materials D. non-ferrous materials The maximum normal i stress theory is used for A. brittle materials Y 368ductile materials Gc Jastic materials p, non ferrous materials ne design of shafts made of brittle materials is based on J. Guest’s theory * pankine’s theory st.venant’s theory p, Von Mises theory jooke’s aw holds well up to _ yield point i elastic limit C plastic limit p. breaking point we he ratio of linear stress to linear strain is called modulus of elasticity p, modulus of rigidity bulk modulus D. Poisson’s ratio gt A 4u.The modulus of elasticity for mild steel is approximately equal to A. 80KN/mm? 8, 110 KN/mm? ¢, 100 KN/mm? p. 210 KN/mm? 15, When the material is loaded within elastic limit, then the stress is_______ to strain. A. equal 8. directly proportional C. inversely proportional D. not equal 16, When ahole of diameter “d” is punched in a metal of thickness “ t jae the force required to punch a hole is equal to . dtSy 8. dts, 3691 go 18. 19. 20. 2: p oh M42. Si Cy m 42. D. dS . gt Su The ratio of the ultimate st A. elastic limit B. strain C factor of safety D. bulk modulus tress to the design stress js knows Mas The factor of safety for steel and steady load is A 2 poe one ‘An aluminum member is designated based on yield stress B. elastic limit stress C. proof stress D. ultimate stress > In a body, s thermal stress is one, which arises because of thy existence of A. latent heat 8. temperature gradient c. total heat D. specific heat A localized compressive stress at the area of contact between tw members is known as A. tensile stress B. bending stress C. bearing stress D. shear stress The Poisson’s ratio for steel varies from A. 0.2110 0.25 , B. 0.25 to 0.33 370i 14. 2B. 0.33 to 0.38 5, 0.38 to 0.45 he stress in the bar when load i ‘ vompared to the stress ad's applied s A. Same 8. double c, three times p. four times uddenly is as the energy stored in a bo . a dy when strained within elastic limit is A. resilience B. proof resilience C. strain energy D. impact energy The maximum energy that can be i loading up to the elastic limit is “a alien Temadiacal A. resilience 8. proof resilience C. strain energy D. impact energyAnswer to Test 38 N DAD ¢ c FOPSMOMBDOYFBDMEOO BBO a0 a upper deviation is zero all of the above eight times (dA % (ae)° twisting moment of both the shafts is the same maximum normal stress theory improves the fatigue life \M247? ductile materials brittle materials Rankine’s theory elastic limit modulus of elasticity 210 KN/mm? directly proportional mdtS, factor of safety 4 yield stress temperature gradient bearing stress 0.25 to 0.33 double strain energy proof of resilienceTest 39 tion! choose the correct answer in the problems below and st check your answers whether you PASS the TEST or NOT and then answer it again until you master it. strain enerey stored in a body, when suddenly loaded he fi a the strain energy stored when same load is applied i——— gradually. i equal to 8. one-half c, twice D. four times When @ machine member is subjected to torsion, the torsional shear stress set up in the member is yero at both the centroidal axis and outer surface of the member maximum at both the centroidal axis and outer surface of the member ¢. zero at the centroidal axis and maximum at the outer surface of the member D. none of the above ‘The torsional shear stress on any cross-section normal to the axis is, the distance from the center of the axis. directly proportional to . inversely proportional to . equal to not equal to The neutral axis of a beam is subjected to A. zero stress . maximum tensile stress maximum compressive stress maximum shear stress eos 3735. Atthe neutral axis of a beam. A. the layers are subjected to maximum bending Stress B. the layers are subjected to tension C. the layers are subjected to compression D. the layers do not undergo any strain 6. The bending stress in a curved beam is A. zero at the centroidal axis zero at the point other than centroidal axis C. maximum at the neutral axis D. none of the above 7. The maximum bending stress, in a curved beam having symmetri section, always occur, at the ical A. centroidal axis B. neutral axis C._ inside fiber D. outside fiber 8. If d= diameter of solid shaft and S = permissible shear in shear for the shaft material, then torsional strength of shaft is written as A. Za4s 32 B. dLog.S x 43 CG es D. Za's 32 9. If d, and d, are the inner and outer diameters of a hollow shaft, then its polar moment of inertia is A. Zl aot -d] B. Zao? -4)| C= [do?-0/? ]shafts are under pure torsion are of identical length and , ica weight and are made of the same materials, The shaft A i f and the shaft B is hollow, we can say that iss0! haft B is better than shaft A h on Ais better than shaft B 6 ath the shafts are equally good ; none of the above solid shaft transmits a torque T. The allowable shear stress is 5. I the diameter of the shaft is A WSs y.When @ machine member is subjected to a tensile stress St due to direct load or bending and a shear stress S s due to torsion, then the maximum shear stress induced in the member will be A ; [sj2+4857 B ; 524s? 1B Rankine’s theory is used for A. Brittle materials 8. Ductile materials C. Elastic materials D. Plastic materials 14 Guest's theory is used for A. Brittle materials 8. Ductile materials 375C. Elastic materials D. Plastic materials 15. At the neutral axis of a beam, the shear stress is A. zero B. maximum Cc. minimum D. constant 16. The minimum shear stress developed in a beam of ,, section is. the average shear stress. A. equal to Cctangle 4a times B. 3 C. 1.5 times D. 3 times 17. The stress which vary from a minimum value to a maximum Value of the same nature that is tensile or compressive is called A. repeated stress B. yield stress C. fluctuating stress D. alternating stress 18. The endurance or fatigue limit is defined as the maximum value of the stress which a polished standard specimen can withstand without failure, for infinite number of cycles, when subjected to A. static load B. dynamic load C._ static as well as dynamic load D. completely reversed load 19. Failure of a material is called fatigue when it is fails A. at the elastic limit . below the elastic limit C. at the yield point D. below the yield point 20. The resistance to fatigue of a material is measured by 376 :elastic limit young’s modulus ultimate tensile strength endurance limit poet _- yield point in static loading is_____—_as compared to th fatigue loading. higher lower same p, constant 6. afety for fatigue loading is the ratio of 2 elastic limit to the working stress Young's modulus to the ultimate tensile strength ¢c. Endurance limit to the working stress p. Elastic limit to the yield point op Factor of § aterial is subjected to fatigue loading, the ratio of the 1 When am limit to the ultimate tensile strength is endurance A 0.30 B, 0.40 c. 0.50 D, 0.60 14. The ratio of endurance limit in shear to the endurance limit in flexure is A. 0.35 B, 0.45 Cc. 0.55 D. 0.65 35, Ifthe size of a standard specimen for a fatigue testing machine is increased, the endurance limit for the material will A. have the same value B. increase C decrease D. constant 377Answer Key to Test 39 D four times 2) B maximum at both the centroidal axis and oute T Su member face of the directly proportional to zero stress the layers do not undergo any strain zero at the point other than centroidal axis NOUbW Oo O7OPrD inside fiber 8. Z yps 16 al 4 oA Ze -o/*| 10. A shaft B is better than a A 3f 167 Ss 12 A 3s?+48 2 13. A Brittle materials 14. B Ductile materials 15.; 8 maximum 16. C 1.5 times 17,6 fluctuating stress 18. D completely reversed-load 19. D below the yield point 20. D endurance limit 21. A higher 22) Cc endurance limit to the working stress 23. ¢ 0.50 24.C 0.55 decreaseTest 40 cor choose the correct answer in the questions below and st check your answers whether you PASS the TEST or NOT and then answer it again until you master it. Board October 1999 b sorsional deflection is a significant consideration in the design of shaft and the limit should be in the range of, degrees/foot of length. 1p, 0.004 to 0.006 g, 0.08to 1 ¢, 0.006 to 0.008 p. 0.008 to 1 1. MEBoard April 1999 For a universal joint shaft angle should be__degrees maximum and much less if in high rotational speed. A 12 8 16 C15 D. 14 3, ME Board April 1998 Itisa good design practice for steel line shafting to consider a limit tothe linear deflection of, inch/foot length maximum. A. 0,050 8. 0.010 C. 0,020 D. 0.060 4. Supplementary Question Itisa rotating machine member that transmits power. A. Cam 8. Plate ©. Shaft 379D. Flywheel Supplementary Question A stationary member carrying pulleys, wheels and ete that transmit power. A. Axle B, Propeller shaft C. Turbine shaft D. Machine shaft 6. Supplementary Question Aline shaft is also known as A. counter shaft B. jackshaft C, main shaft D. head shaft 7. Supplementary Question Which of the following shaft intermediate between a {i and a driven shaft? A. Counter shaft B. Jackshaft C. Head shaft D. All of the above ine shaft 8. Supplementary Question Short shafts on machines are called A. core shafts B. heads shafts C. medium shafts D. spindles 9. Supplementary Question For shafts, the shear due to bending is a maximum at the neutral plane where the normal stress is A. constant B. maximum Cc. minimum . zero 380' supplementary Question fA “criteria for the limiting torsional deflection v length for machinery shafts to 1° 2° 3° 4° ary from 0.08 per foot of ——__ Per foot. POSS ys.Supplementary Question for transmission shafts the allowable deflection is one degree in a length of diameters. a. 10 p. 15 c. 20 Dp. 25 12,Supplementary Question 7 An old rule of thumb for transmission shafting is that the deflection should not exceed of length between supports. = A. 0.01 in. per foot B. 0.02 in. per foot C. 0,03 in. per foot D. 0.04 in. per foot 13,Supplementary Question In general for machinery shafts, the permissible deflection may be closer to A. 0.02 in/ft B. 0.01 in./ft C. 0.002 in/ft i D. 0.030 in/ft 14,Supplementary Question : The speed at which the center of mass will equal the deflecting forces on the shaft with its attached bodies will then vibrate violently, since the centrifugal force changes its direction as the shaft turns. A. Critical speed 381B. & D. 15. Supple: y For shaft, the minimum val fati Geometrical speed Mean speed unit speed uestion mentary O Jue of numerical combined g ho ase to the computed pt 2d igue factor to be applied in every ¢ d bending moment is A. B. Cc. D. 1.0 13 15 18 16.Supplementary Question It is suggested that the design factor on the yield strength be about 1.5 for the smooth load, about 2 to 2.25 for minor shock A B. a D. loads, and. when the loading reverses during operation, 3.0. 4.0 3.5 45 17.Supplementary Question Acolumn is called short column when A B. — D. the length is more than 30 times the diameter slenderness ratio is more than 120 the length is less than 8 times the diameter the slenderness ratio is more than 32 18.Supplementary Question For a circular shaft subjected to torque the value of shear stress A. B. c. D. is uniform throughout has maximum value at the axis has maximum value at the surface is zero at the axis and linearly increases to a maximum value at the surface of the shaft 19.Supplementary Question The compression members tend to buckle in the direction of 382axis of load perpendicular to the axis of load minimum cross-section Jeast radius of gyration ooee plementary Question reinforced concrete beam is considered to be a, clad material 8. composite material c, homogeneous material p, heterogeneous material made up of supplementary Question the column splice is used for increasing a. strength of the column g, cross-sectional area of the column c. length of the column p. all of the above s.Supplementary Question ‘Asimply supported beam has a uniformly distributed load on it, the bending moment is A. triangle 8, pafabola c. semi-circle D. rectangle 13,Supplementary Question The power obtained by piston reaches flywheel through the A. countershaft B, crank shaft C. transmission shaft D. line shaft 4,Supplementary Question There are two types of crankshafts A. single piece and built up 8, forged and turned C. rotary and stationary D. none of these 38325. Supplementary Question Engine valves get open by means of A. B. G D cam shaft rocker shaft crank shaft valve guardA Brera eeocen FP9OV9OFOSFOSoVVIA vO OOD >rPwawmagg nswer Key to Test 40 0.08 to 1 15 0.010 Shaft Axle main shaft All of the above spindles zero 1° 20 0.01 in per foot 0.002in/ft Critical speed 15 45 the length is less than 8 times the diameter is zero at the axis and linearly increase to a maximum value at the surface of the shaft least radius of gyration heterogeneous material length of the column parabola crank shaft single piece and built up cam shaftInstruction: Choos 3. Test 4] e the correct answer in the problems bey, check your answers whether you PASS the Test and then answer it again until you master it, OW ang OF Nor juestion Suppiemen ti Palowable stresses are generally used in practice for main transmitting shafts A. 282 kg/cm? B. 423 kg/cm? C. 599 kg/cm? D. 620 kg/cm? Supplementary Question The value of allowable stresses are generally, used in practice for line shafts carrying pulleys. A. 150 kg/cm? B. 282 kg/cm? C. 423 kg/cm? D. 550 kg/cm? Supplementary Question The value of allowable stresses are generally used in practice for small, short shafts, countershafts . A. 282 kg/cm? B. 599 kg/cm? C. 650 kg/cm? D. 750 kg/cm? Supplementary Question Torsional deformation in transmission shafts should be limited to___ in 20 diameters. AS 1s Bo 2 Cc. 3° D. 4° 386tementary Question ral deflection caused by bending should not exceed uO 001 in per foot of length 0,005 in. per foot of length "9.01 in. per foot of length p, 0.05 in per foot of length plementary Question Front axle should be live and A weak p. dead c. strong D. none of these supplementary Question The steering is coupled to the two front wheels by means ofa A. connecting rod B. tie rod Cc. push rod D. spindle g, Supplementary Question In the overdrive transmission system the rotation speed of. rest higher than that of engine’s speed. A. main shaft B. crank shaft C. propeller shaft D. machine shaft 9. Supplementary Question Aslip joint. the length of propeller shaft. A. increases B. decreases C. keeps appropriate D. none of the above 10.Supplementary Question The transmission system incorporates clutch, gear box, and Propeller shaft and 387A. brake B differential Cc. steering D. main shafting 1. Supplementary Question The lay shaft moves ____—— A. equal to B. more than C. less than D. inthe gear ratio the primary shaft. 12. Supplementary Question The main shaft is lifted A. before B. after C. parallel to D. adjacent to the lay shaft. 13.Supplementary Question In the top gear, the rotational speeds of = remain the same. A. primary and lay shafts B. main and lay shafts C. primary and main shafts * D. secondary and main shafts 14.Supplementary Question The primary and lay shafts rotate in. direction. A. inthe same B. different C. reverse D. none of the above 15.Supplementary Question It is an integral part of the machine . Spindle B. Axle C. Counter shaft D. Machine shaft > 388supplementary Question stresses in shafts are analyzed through A. torsional B. bending C. axial D. allof these s,Supplementary Question standard stock length is A. 16 ft B. 20ft C. 24ft D. all of the above 18. Supplementary Question Centrifugal separators that Operate at speeds these flexible shafts. A. 1,000 to 3,000 rpm B. 5,000 to 10,000 rpm C. 15,000 to 30,000 rpm D. 20,000 to 50,000 rpm also employ 19.Supplementary Question Which of the following material is used for shafting? A. AISI 3240 B. AISI3150 C. Als! 4063 D. Als! 33000 20.Supplementary Question The process of redistributing the mass attached to a rotating body in order to reduce vibrations arising froma centrifugal force. A. Shaft coupling B. Shaft balancing C. Shaft hooper D. Stator balancing 389Question ementary 21. Supp! of the shaft is an im Port dey, in many cases the, feature. A. deflections B. rigidity C. size D. strength 22.Supplementary Question Commercial shafting is made of A. low carbon steel B. castiron C. brass D. bronze 23.Supplementary Question The most common material for shafting is A. wrought iron B. cast iron C. mild steel D. aluminum 24.Supplementary Question Cold drawing produces a shaft that hot rolling, but with higher residual stresses. A. weaker B. stronger C. harder D. none of the above 25.Supplementary Question Allowable stresses in shear equal to are common in design of a shaft. A. 3000 to 5000 psi B. 4000 to 6000 psi C. 5000 to 8000 psi D. 6000 to 10000 psi 390guswer Key to Test 41 RRBRNRReeee een VE ESYMPE SSE ARARS Bee ernansene. i RE 282 kg/cm? 423 kg/cm? 599 kg/cm? 1° 0.01 in per foot of length dead tie rod propeller shaft keeps appropriate differential in the gear ratio parallel to primary and main shaft reverse Machine shaft all of these all of the above 20,000 to 50,000 rpm AISI 3240 Shaft balancing rigidity low carbon steel mild steel stronger 5000 to 6000 a