Question

Question (2) (15 Marks) The 500-kg large chandelier is suspended from the wall and ceiling using rods AB and BC, which have diameters of 8 mm and 10 mm, respectively. Determine the angle 8 so that the normal displacement d in both rods is the same. Both rods are made of Aluminum material of E = 70 GPA. Also, determine the force in each rod and the normal displacement. VU 2.0 m 30° 1.0 m B IVTYT TUT

Answer 1

비 - Given data m=500kg or soorg.al 4905 N DAB =8mm DBC a lomm To determine the angle o., As per given in the Question displacement of both rud ABABC are same (SBC) (8) AB PABXLAB AABY eX EAB 'By using the displacement PBC x LBC ABCX Eoc formula where EAB = EBC (both are aluminium rod) AAB PAB PBC LBC LAB -X ABC DARTZ x PAR PBC Lbc LAB 2 Docx x Where SinC 3o) - 1 TAB LAB 2m S I sinco) 2 Sin - 2 LBC LBC Since) 2 PAB PBC х8 Sin(e) 2x 10² 16 25 X sinio PAR 2 PBC

3) By using the sine law PAB Pes Sin (90+30) Joox 9181 Sin (180-30-0) - Sin (90+) CAR Poc sin(goto) sin(120) Cove) Sin(120) PAB TBC I Sin Goto) = cos(o) from equation ④ fo 16 Cos (0) sin (120) 25 since Sinco) Cos (G) 2 16 x Sin (120) 25 32x Sin (120) 2 sinca) COS(O) = 25 Sin(20) = 32 x sin(120) 25 sincao) = 1,108 N1 20 ago =45 And Po determine the force force on AB PAB sin (180-30-0) PAB 3590.70 And Soox9.8) X Sin (90+0) [ By using sine law relations)

PBC 그 * sin(120) 5oor 9.8) Sin(180-30-45) PBC 4397.7N Ane Normal displacement SAB = SBC = PABX LAB AABX EAB - 3590.7 X 2000 2 x 8² x 70xlo SAB= SBC = 2 mm And
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