For the beam and loading shown, determine the range of the distance a for which

Question

For the beam and loading shown, determine the range of the distance a for which the reaction at B does not exceed 50lb downward or 245lb upward.

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. For the beam and loading shown, determine the range of the distance a for which the reaction at B does not exceed 50 lb downward or 245 lb upward. 340 lb 340 lb 12 in DC 35 Ib 16 in. 8 in 24 in. in.

Explanation / Answer

Equivalent reaction force at B:

case 1 ) REACTION IS UPWARDS ( 245 lb max)

Fb = 340 + 35 + 340 - F <---------- F = reaction at fulcrum

For maximum value of Fb = 245 lb,

245 = 340 + 35 +340 - F

So, F = 470 lb

Equating torques about B:

470*32 = 340*(48 - a - 12) + 35*24 + 340*(48 - a)

So, a = 21.1 in

case 2 ) REACTION IS DOWNWARDS ( 50 lb max)

F = 340 + 35 + 340 + Fb <---------- F = reaction at fulcrum

For maximum value of Fb = 50 lb,

F = 340 + 35 +340 + 50

So, F = 765 lb

Equating torques about B:

765*32 = 340*(48 - a - 12) + 35*24 + 340*(48 - a)

So, a = 7.24 in

So, range of a : 7.24 in <= a <= 21.1 in

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