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QUESTION: 1

Total degree of indeterminacy (both internal and external) of the plane frame shown in the given figure is

Solution:

The degree of indeterminacy,

Number of external reactions = r_{e}

= 3 + 3 + 3 + 3 = 12

Number of rigid joints,

j= 10

Number of joints at which releases are located,

j= 1

Number of members,

m = 12

As the hinge is located at a point where 4 members meet. Hence it is equivalent to three hinges.

Therefore number of releases, r_{r }= 3.

QUESTION: 2

If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin-jointed plane frame is given by

Solution:

Ds for a pin jointed frame = m+r-2j

Ds for a rigid jointed frame = 3m+r -3j

m- No. of members, r- no. of reactions, j- no. of joints

QUESTION: 3

Degree of kinematic indeterminacy of a pin jointed plane frame is given by where j is number of joints and r is reaction components.

Solution:

Dk = 2j –r for a pin jointed frame

Dk = 3j –r for a rigid jointed frame

j number of joints and r number of reactions.

QUESTION: 4

A pin-jointed plane frame is unstable if where m is number of members r is reaction components and j is number of joints

Solution:

QUESTION: 5

The degree of static indeterminacy of a pin- jointed space frame is given by

Solution:

QUESTION: 6

The degree of kinematic indeterminacy of a pin-jointed space frame is given by

Solution:

QUESTION: 7

The degree of static indeterminacy of the pin- jointed plane frame shown in figure is

Solution:

External indeterminacy,

Internal indeterminacy,

No, of members, m = 21

Number of joints, j = 11

QUESTION: 8

The portal frame as shown in the given frame is statically indeterminate to the

Solution:

m=3; r= 3+3 =6 ; j=4

Ds = 3m+r-3j = 3(3) + 6 -3(4) = 3

QUESTION: 9

A perfect plane frame having n number of members and j number of joints should satisfy the relation

Solution:

A perfect plane frame means a determinate structure, so

QUESTION: 10

Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is

Solution:

j = 11; r=8; m=11

Dk = 3j-r-no. of inextensible members = 3(11) – 8 -11 = 14

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