Question

For the frame shown below, the radius of pulley is 0.5 m. a) Draw the free body diagram of the entire frame and of each member, including a diagram for the pulley. Show all forces, including the directions, if known. b) Determine the components of the reactions at A and E. Specify the direction (→, ←, ↑, ↓) for each.

1m Зт Зт С 1m В 2m ОА Е 700 N

Answer 1

GOOD MORNING THERE,

IN THE PROBLEM GIVEN THE PULLEY IS ASSUMED TO BE FRICTIONLESS.

ALWAYS REMEMBER THE FACT THAT THERE ARE 3 EQUILIBRIUM EQUATION (SUM OF HORIZONTAL VERTICAL AND MOMENT), NOT ONLY FOR EACH MEMBER TAKEN SEPARATELY BUT ALSO FOR EACH COMBINATION OF MEMBERS AND FOR THE WHOLE FRAME OR STRUCTURE, THAT MEANS IF WE HAVE 3 MEMBERS AB BC AND CD ARE CONNECTED BY HINGE THEN EQUILIBRIUM CONDITIONS ARE TO BE APPLIED FOR AB BC CD SEPERATELY AND FOR AB BC SEPERATELY BC CD SEPERATELY AND WHOLE STRUCTURE AB BC CD AS A WHOLE

SEE THE SOLUTION FOR MORE UNDERSTANDING.

H3-3- -ਵਣਾਈ free body diagram a whole frame 7000 700N Í VA free body dia grams ... ABC Hjuc Tria HC Note: as all the joints are pinned the moments are taken to be zero and the load given by the pulley is 700 kn asuming friction less pully and weight a the rope to be zero free body diagram a pully . >R=0.5m R is the force on beam by pully it 700kn will be equal to 700KN

Now free dody body diagram acc o Heck 3 37 Būt tookn 'VE Take member CEO FBP Het 3 + 3 - VC 700 kr 1€ HE Vctve a Fookw -0 HC=HE: -2] Taking moment about C (3) - 700 x 3 EVE -HE) - 700.- Taking moment about € =0 Vc C6) +Hc(3) - 700x350 | 2Vc+ H = 100 4)

from ean ③, ④ o Ve - HC = 700 vc t&c=700 CƯe →v> Tooº . VetUC= 700 Taking moment about point a VE.C.3) - Hell!5) -VC (3) - Hc (M)=0 Taking memberi ABC" CHINULSO VA ZVC HA - HC + 70020 Tre to 5 >7004 À HATT HC-HA=700 - - Tua Taking moment about a HC (3) = 700(2)+ve - ©

considering the whole frame 6 HA _3-13- TH> 700 HE VAVE = 700 700- THA THE Taking moment about A. VE (3+3+1). HE CO) – 700(31) - 700(2) ve (X) = h 0 ( 3+1+2) VE = 600 JA = 100 (from ean 8) : from equation © Uc Floo from equation 7 3CHC) = 1400 + 100 HC 315.000 HC=500 H4-200

from ean a He= 700-200 He=500 Hez 700-200 ☺ forces ) VA = 100 N (T) HA = 200 N (C VE = 600N (1) HE = Soun.(5 y Reaction forces at 1 A & E. ) Vc = loom(a) on member.cot =100Nca) on member: ABC HC = 500 N (E) on :member ABC =500N (~). One.member. CDE

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