Question

Q3. A designer proposed the detail of a section of a shaft below. The shaft has a reduction with a filleted shoulder and a groove as shownin in the sketch. This rotating shaft will carry a bending moment fluctuating between -250 Nm and + 250 Nm, a torque fluctuating between 0 Nm and 400 Nm and an axial force fluctuating between 400 N and 900 N. (20 points) a. Calculate the mean and alternating force, moment and torque values for these loadings. b. Draw the stress-time graphs of each loading type and characterize the nature of the loading. M R2.5 TM F 11 F R3 T

Answer 1

Ono - ANSWER -) GIVEN DATA i The reduction with Shoulder a filleted shaft has a and a groove. - -250 Nm and Taorm Bending moment fluaction Torque fluacting betwees ONm and 400 mm 4OON and 900 N. Axial force fleaction between Herce for * Mmin Mmar 250 Nm T'min 0 Tmax 400 Nm * Pron . 100 N Pmax - 900 N Meas Max & min Variable Min Mau (9 To calculate the meas and torque values and alterating force, moment for these loadings are explaired as Pmax & Prin force a CS

PAGE 2 900 + Ubo २ 13 00 Mean force GSON Variable force Pmax - Prin 2 900-400 SOO 2 Variable force 2 SON Meon moment - relmax train 2 Arnean as + -250 а variable moment Mmax - Rimin 250-(-250) SOO २ + Mvariable QSD N- Meas Torque Tmax + Tmin 2 000 +0 200 т. mean Roo A-m. » Variable Torque = Tmax - Trin 2 yoo - 200

PAGE • Tvariable 200 N-m (6) To draw stress-time graphs of each loading, type and of loading characterise the nature Mar A Mean variable min Time Generaliced axes (0-t) 37.50 иод pub 68 -sop- = % ). F R2.5 Critical SYOSS - Section at minimum cross- section It is given OP Area min 37.5 50 mm Pmax Smax A 900 2 1 u 375 Imax = 0.8148 mpa (Nimma) es Omin Prin 400 Tx 3705² Smin o. 3621 mla

SPAGE-4 mean - meon A O. 5885 mPa. » Svariable -0.2263 mPa. ofmpa) 6.8147 0.585 AAA Tome 1 Evariable 0.2263 Bwin time >> Therefore it indicates the factuating fatigue strenes. ose akifferest is magnitude & Likenatere flackerating → That stresses Tie Axial load stress. BEN DING STRESS- It is given worth equation Ob xy = 32 M Ta' TL is for a shaft Here having circular section Bending moment - Maximum at minimum 66 cross-section for a specified Bending moment. Given with diameter : Minimum de 37.5mm My s 250 mlo? N-mm 250 x 32 xlo? T* (375)3 48.268 Mia CS

- 32 x 250 x 10 (60 min RAGG-5 x 37.5 -48-288 mla (06) mean (56) variable 41 46.288 mPa. 8 48-20 Imax HAE + Omeen O 6-t t sot Graph PL indicates that Sot graph which is completeley revessed stress ie Same but nature unlike in magnitude Bending stres. TORSIONAL STRESS- Here it is given with equation 2 IGT nd For Tmax at miniman Cross section Tie dmin = 3-5mm *10 To 400 a max 16 T mar Tx 37.5 16 x 400 x 10 0x 103 Tx 37.5 38.63 mPa.

RAGE 6 Imin = 6 ? mean = 19.315 mia Evariable = 19.315 mpa olmpa) C man 38.63 19.315 TAA Tmean variable 2 min =0 time this is a repeated 7 This graph indicates That fatigue stress ile betwees to max. stress Factuating between : Torsion → Repeated fatigue. please upuote — CS Scanned with CamScanner