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Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is:
- a)12
- b)14
- c)20
- d)22
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Neglecting axial deformation, the kinematic indeterminacy of the struc...
Kinematic indeterminacy means degree of freedom of structure at various joints.
No rotation or translation is possible at A so degree of freedom at A is zero. There is a possibility of rotation at C but no translation so degree of freedom is one. At G both rotation and translation is possible so. degree of freedom is 2. At J no rotation but translation so d.o.f. is 1 . At B, D, H and K there are 4 rotations and 1 translation so d.o.f. is 5. At E, F and I three rotations and two translations so d.o.f., is 5.
So kinematic indeterminacy,
= 0 + 1 + 2 + 1 + 5 + 5 = 14
Alternate:
From direct formula
External reactions re = 3 + 2 + 1 + 2 = 8
Number of members (m) = 11
Number of rigid joints (j) = 9
Number of hinged joints (j') = 2
There are no internal hinges so number of releases is zero.
rr = 0
Degree of kinematic indeterminacy,
Dk = 3(j + j ' ) - re + rr - m
= 3 x (9 + 2 ) - 8 - 11
= 33 - 19 = 14
No rotation or translation is possible at A so degree of freedom at A is zero. There is a possibility of rotation at C but no translation so degree of freedom is one. At G both rotation and translation is possible so. degree of freedom is 2. At J no rotation but translation so d.o.f. is 1 . At B, D, H and K there are 4 rotations and 1 translation so d.o.f. is 5. At E, F and I three rotations and two translations so d.o.f., is 5.
So kinematic indeterminacy,
= 0 + 1 + 2 + 1 + 5 + 5 = 14
Alternate:
From direct formula
External reactions re = 3 + 2 + 1 + 2 = 8
Number of members (m) = 11
Number of rigid joints (j) = 9
Number of hinged joints (j') = 2
There are no internal hinges so number of releases is zero.
rr = 0
Degree of kinematic indeterminacy,
Dk = 3(j + j ' ) - re + rr - m
= 3 x (9 + 2 ) - 8 - 11
= 33 - 19 = 14
Most Upvoted Answer
Neglecting axial deformation, the kinematic indeterminacy of the struc...
Support C is fixed support so external reactions should be 3
Correct me if i am wrong
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Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is:a)12b)14c)20d)22Correct answer is option 'B'. Can you explain this answer?
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