Past Year Questions: Determinacy and Indeterminacy | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

Q.1. The degree of static indeterminacy of the plane frame as shown in the figure is______    
[2019: 1 Mark, Set-II]

Solution. D_se = 7-3 = 4
D_si = (3 x 4)-(2--1)= 11
D_s = 15

Q.2.  Consider the frame shown in the figure

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematic indeterminacy would be equal to    [2017: 1 Mark, Set-II]
(a) 5
(b) 6
(c) 7
(d) 8
Ans. (b)
Solution. 
DOF of Joints:

When all members are extensible,

D_k (when extensible) = 14
D_k(when inextensible) = D_k (when extensible) - No. of axially rigid member
= 14 - 6 = 8
So, reduction in

Note : Shear deformation is not considered in calculation of D_K.

Q.3. A planar truss tower structure is shown in the figure.

Consider the following statements about the external and internal determinacies of the truss.
P. Externally Determinate
Q. External Static indeterminacy = 1
R. External Static Indeterminacy = 2
S. Internally Determinate
T. Internal Static Indeterminacy = 1
U. Internal Static Indeterminacy = 2
Which one of the following options is correct?    [2017: 2 Marks, Set-I]
(a) P-False; Q-True; R-False; S-False; T-False; U-True
(b) P-False; Q-True; R-False; S-False; T-True; U-False
(c) P-False; Q-False; R-True; S-False; T-False; U-True
(d) P-True; Q-True; R-False; S-True; T-False; U-True
Ans. (a)
Solution. D_se= r_e - 3 - s = 4 - 3 = 1
D_si = m -(2j - 3) = 15 - (2 x 8 - 3)
= 2
Trick : For a truss formed due to combination of simple triangles.
D_si = No. of double diagonal panels = 2
D_se = R - 3 = 4 - 3 = 1

Question for Past Year Questions: Determinacy and Indeterminacy

Try yourself:The kinematic indeterminacy of the plane truss shown in the figure is    
[2016: 1 Mark, Set-II]

• A.

  11
• B.

  8
• C.

  3
• D.

  0

Explanation

Kinematic indeterminacy,
D_k = 2j - r_e
= 2 x 7 - 3 = 11

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Question for Past Year Questions: Determinacy and Indeterminacy

Try yourself:A guided support, as shown in the figure below, is represented by three springs (horizontal, vertical and rotational) with stiffness k_x, k_y and ke respectively. The limiting values of k_x, k_y and k_e are   [2015: 1 Mark, Set-II]

• A.

  ∞, 0, ∞
• B.

  ∞,∞,∞
• C.

  0,∞,∞
• D.

  ∞,∞,0

Explanation

Guided roller support has 2 reactions:

For given support, kx = ∞, k_y = 0, k_{θ = ∞}

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Question for Past Year Questions: Determinacy and Indeterminacy

Try yourself:The static in determinacy of the two-span continuous beam with an internal hinge, shown below, is ____________.    [2014: 1 Mark, Set-II]

• A.

  0
• B.

  1
• C.

  2
• D.

  3

Explanation

Number of members, m = 4
► Number of external reaction, r_e = 4
► Number of joint, j = 5
► Number of reaction released, r_r = 1
► Degree of static indeterminacy, D_s = 3 m + r_e - 3j - r_r
= 3 x 4 + 4 - 3 x 5 - 1
= 0

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Question for Past Year Questions: Determinacy and Indeterminacy

Try yourself:The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in figure is    [2014: 1 Mark, Set-I]

• A.

  zero
• B.

  one
• C.

  two
• D.

  unstable

Explanation

D_s = D_se + D_si
= (r_e -3 ) + 3 C - r_r,
= (4-3)+ 3 x 0- 1
= 0
Hence, the structure is stable.

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Note: Stable for vertical loading unstable for horizontal loading.