Question

The member is supported by a pin at A and cable BC. Determine the components of reaction at these supports if the cylinder has a mass of 75 kg. 0.75 m 1.5 m D 1.25 m 1.25 m 3.5 m

Answer 1

Given data"- . m = 75 kg - I 3.5m v 1 .2.5 m The weight of the cylinder Ps. sử - -75 x 4.8) x < ü =-6135.75 ND Â The coordinate of the point A is A(4,9,,?,) = (0,0,0) The coordinate of the point B as B ( 72, , 3) = 6 -0.753, 15) At paint i es c ( 43, 93,73) = (3.5, + 1.25, 0)

At point ő as 0(94, 94,24) = (3.5, -125,0) The position vector along es is 7ce = (0-3.5) Î +(-0.75 -1.25) À + (1.5-0) Ê = -3.5 î +6-2°) + 15 € -35 † +2i +15 Â the unit Vector û ca e -3.5 to zſ +15e V 6-3.5) + (-2)* +(1.5) ? = -3,5 î ŷ tis R ... 4.3 = -0.813 ^ - 0.465 f + 0.348 is The force in member BC is tec = Tec (-0.813 † -0.465 +0.348 €)

The position vector Pite = (3.5-0) along AC is + (1.25-0) Î + (0-0). The position vector along as is VAD = (3.5-0) ŷ + (-1.25-0) } t (0-0) f The expression for the force equilibrium is Ranit Ray ŷ + Raz être two son Ranî + Ray ĵ + Razê + Toc (+0.813 î+ 0.465 ? A tougue ') + (-735.75 )=0 the compare coefficient of î in above equations Ⓡ Ron = Compare the Ray = 0.813 TBC + coefficient of Î 0:465 Tec - ③ $tmi) 1 ) RA + 0.3% 8 Tac = 725.75 > 8 . The expression for the moment about point A is (Mala i + (Mm)Ê + one x Pac) +one xw) = 0.

Ti i R.1 (Male +(maz êt. * 3.5 1.75 0 Tento -0.813 -0.405 0.348] * 101 3.5 -1.25 01 O Ö -735.15] Marft emnQ @ + roues plave +(-1.275 +.03] ] Tec .+ [925-13 î • +255 v2 +of] =0 (Ma) ft Man) 2 + Covarî -iznî -0.6176 ] Tee + [ 136.75 1 + 575.129.] =0 → Compare the col triciens Î, Ê, ê Tec (+1.218 ) +2575.12 = 0 Tec = +2575.12 + 1.218 TBC = 2114.2 N/ . (MA-) = 0.017s Tau (Malz= 0.6195 ( 214.2) IMA) = 1305.5 Nim

(MA) = -0.435 TBC 0.435 TBC - 735.75 = -0.435 ( 2-114.2) - 735095 A) -1655.5 N-m From the ese Rana 0.813 Toc = 0.813 ( 21462) TRAM = 1718.8 N) from the es Ray = 0.465 Tec = 0.465. (219412) Ray = 983.1 ~] the es o Ret 0.348 Trc = 735.75 . RAZ = 735175 -0.348 TBC Raz = 735,75. - 0.348 12134,2) RAZ= 84xion Razno Result: RAM = 111s.sn Ray = 983.1 N Razno