The truss shown below is

statically indeterminate to 2 degree

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statically determinate but unstable

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statically determinate and stable

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Statically indeterminate to 1 degree

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Solution

The correct option is C statically determinate and stable
$m = 14, j = 9, r_{e} = 4$
$D_{s} = (m + r_{e}) - 2 j$
$= (14 + 4) - 2 \times 9 = 0 i . e . s t a t i c a l l y d e t e r m i n a t e$
$L e t m_{m} = n u m b e r o f m e m b e r s r e q u i r e d f o r t h e s t r u c t u r e t o b e s t a b l e .$

$∴ m_{m} = 2 j - 3 = 2 \times 9 - 3 = 15 > (m = 14)$

Hence, the frame is internally unstable being deficient by one number. However the internal deficiency is compensated by the provision of one extra external reaction component $r_{e} = 4.$

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