Question

1. Problem Description A cage is to be operated in a vertical shaft in an underground mine. The cage lowers and lifts people, equipment or materials from ground level, to an underground, horizontal roadway 200 m below. The maximum load rating of the cage is 45,000 kg. The cage is lowered or lifted by a winch and cable system. The winch is powered by an electrically driven, winding engine located at the ground level. At the bottom of the shaft is a sump which removes water from the lower level of the mine. A sketch of the layout of the shaft is shown in Figure 1. pully block ground level (G/L) to winch shaft cage underground roadway 200 metres helow GUI Figure 1. Layout of the people, materials and equipment shaft. Figure 2 shows a schematic of the pulley block at the top of the cage shaft. The pulley shaft is made of a 6150 alloy steel and the load carrying members are made from a 1020 low carbon steel. Details of the eye bolts, used to attach 1) the members to the rigid plate; and 2) the pully block to the support structure are shown in Fig. 3. Support structure of lifting eye A (45 to x-direction) E.S.1.2L D 23 F E.S.1.2L 8,25, 20/3 -E2S Ff rigid plate to winch (x-direction) E 2 cage (rated mass 45,000 kg. y-direction) Figure 2. Cage shaft pulley block at the top of the Figure 3. Lifting eyes detail; bolt shaft; situation during hoisting operation; major diameter D = 64 mm, diameter at bolt components: neck d = 48 mm lifting eyes A-F (details Fig. 3), pulley shaft G (diameter DG = 60 mm), load carrying members AB, AC, AD, EG, FG (with different geometric properties based on length, L = 250 mm, and cross-sectional area, S = 900 mm)

Calculate the forces and stresses in the axial members, the lifting eye bolts and the pulley

shaft (the energy transfer pathway) and please discuss the results. Thank you!

Answer 1

Solution :- ป R = Jaw w 2w on the orlope ů - 45000 X 9.8) (45000 xg) N Assuming the mar is perpendicular to the ground the force cet exerts mg CN) 441450 Net form on the pally axle is Vener R- Vax 441450 624210N Assuming the Shaffi có con double sheas T pully shaft . shear stress T Force, R 2 Area 624210 2x to 4 624210 T8005~ 4 TG = 110.44mpa

Force in GiF= Force in GE=R va 624210 243 AF FGF = 243 ԿԵ՞ 12 441450N E Tensile stress in each of of Cor) GE R GE 4411450 FGE AGP N/mm 2x 900 BE GE = 245.25 Mpa Eye bolts & Erf will be looded as shown below the eye bort wo u Safter both Tensile Load and slicar load and therefore Tensile Shess and Shear stress The Tensile load= Shear load F TV FSF Fr ve 4 441450 va Fr 3/ 2200 N Falfe FF V2 heare 312200 shear stress on the bolt a eye Area of nedle of ече bolt EF TE = TE = 312200 Тачку 172.62 N/mm -

Tensile stress on the eye bolts E &F E = 312200 Tlu 480 = 172.62 mpa Resultant stress on. on eye bolts Ely - 1172-67 +172.62" Ette "244 - 11mpa - A 3oomn 1-2L 3com fasuee fc 250 mn Vio с Srce I B-624210 Fo For equilibrium of plate B CD R- Fc + FR Sino + Fo Sino By Symmetry FB = FD :, 624840 - Fc+2f. ( ) Tensile stress on eye bolt C Fc/Ac 312105 M4x48 (172-6mpa B- bolt Tensile stress on Tensile stress on ege bot eye 156053 Sia 56.44 to My x 48V 171.9mpa Shear stress on bott B ege 15603 COS 56.44 T/4 x 48" 14707mpa T to

bolt B Resultant stress on eye Tot To 71-99+47-49 86.28 mpa Member Force (N) Stress mpa 624210 345) Eye bolik A Eye bolt B Eye bolte Eye bolt 156053 86-28 312105 172.6 D 156053 86.28 Ege bout Eye bott 165 31 2200 244 ) F 31 2200 244.1 Shaft of fully a 624210 110.44 156053 173.4 Member AB member AD Member AC 156053 173.4 31210 173.4 Member GE 345.25 Member UF 441450 441450 aus. ar
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