Find the distance of weight ‘x’ from support, Mechanical Engineering

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Find the distance of weight ‘x’ from support:

The two weights C = 2000N and D = 1000N are located on horizontal beam AB as shown in the figure given below. Find the distance of weight 'C' from support 'A' that is, 'X' so that support reaction at A is twice that at point B.      (May-00-01)

Sol.: As given that RA  = 2RB

∑H = 0

RAH = 0                                                                                                                                      ...(i)

∑V = 0

1328_Find the distance of weight ‘x’ from support.png

RA  + RB  - 2000 - 1000 = 0

RA  + RB = 3000N

But RA = 2RB

That is

RB = 1000N

...(ii)

 

RA = 2000N

...(iii)

By taking moment about point A:

∑MA = 2000 × x + 1000 × (x + 1) - RB  × 4 = 0

2000 × x + 1000 × (x + 1) -1000 × 4 = 0

2000x + 1000x + 1000 - 4000 = 0

3000x = 3000

x = 1m                                  .......ANS


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