Determine the force in each member of the Howe roof truss shown. State whether e

Question

Determine the force in each member of the Howe roof truss shown. State whether each member is in tension or compression. Express the magnitude of eachforce as a positive value.

Do not round intermediate calculations, however for display purposes report intermediate steps rounded to four significant figures. Give your final answer(s) to three significant figures. Determine the force in each member of the Howe roof truss shown. State whether each member is in tension or compression. Express the magnitude of each force as a positive value. 594 1b 594 lb 594 1b 270 lb 2701b 9 ft 9 ft CEG 12 ft 12 ft 12 ft12 ft

Explanation / Answer

The truss is symmetrically loaded and supported. Also, the truss itself is symmetric

Reaction at supports A and H = RA=RH=(270+594+594+594+270)/2=1161 lb

Equilibrium of joint A

1161-270+FAB(9/15)=0

FAB = -1485 lb = 1485lb(compressive) = FFH(from symmetry)

FAC+FAB(12/15)=0

FAC = 1188lb(tension)=FGH(from symmetry)

Equilibrium of joint C

FBC=0=FFG (from symmetry)

FCE=FAC=1188lb (tension) = FEG(from symmetry)

Equilibrium of joint B

FBD(12/15)+FBE(12/15)+1458*(12/15)=0

Or, FBD+FBE + 1458=0

FBD(9/15)-FBE(9/15)-594+1458*(9/15)=0

Or, FBD-FBE +468=0

Solving above 2 equations,we get

FBD = -963lb = 963lb(compression)=FFD (from symmetry)

FBE = -495lb=495 lb(compressive)=FEF(from symmetry)

Equilibrium of joint D

963*(9/15)+963*(9/15)-594-FDE=0

FDE = 561.6 lb(tension)

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