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A bracket as ...

Question

A bracket as shown in figure is welded to a plate. The welds have the equal size and the permissible force per mm of the weld length is 1 kN. The length $l_{1}$ and $l_{2}$ are

A

l_{1} = 45 m m, l_{2} = 80 m m

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B

l_{1} = 60 m m, l_{2} = 80 m m

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C

l_{1} = 80 m m, l_{2} = 40 m m

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D

l_{1} = 40 m m, l_{2} = 80 m m

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Solution

The correct option is D $l_{1} = 40 m m, l_{2} = 80 m m$
$l_{1} + l_{2} = \frac{120 \times 10^{3}}{1 \times 10^{3}} = 120 . . . . . . . . . (1)$
$Resisting force at l_{1} i s p_{1}$
$Resisting force at l_{2} i s p_{2}$
$P \times 100 = P (50)$
$(100 \times l_{1}) (100) = (100 \times l_{2}) (50)$
$2 l_{1} = l_{2} . . . . . . . (2)$
From eq.(1) & (2)
$l_{1} = 40 m m; l_{2} = 80 m m$

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