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# Test: Determinacy & Indeterminacy -2

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## 10 Questions MCQ Test GATE Civil Engineering (CE) 2023 Mock Test Series | Test: Determinacy & Indeterminacy -2

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Test: Determinacy & Indeterminacy -2 - Question 1

### If 4 reactions are acting on a beam, then the system is:-

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 1

4 reactions mean that the system is definitely indeterminate. But stability would depend upon the nature of forces acting on the planar structure.

Test: Determinacy & Indeterminacy -2 - Question 2

### A prismatic beam is shown in the figure given below. ​Consider the following statements: 1. The structure is unstable. 2. The bending moment is zero at supports and internal hinge. 3. It is a mechanism, 4. It is statically indeterminate. Which of these statements are correct?

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 2

The degree of indeterminacy = 3 - 1 - 1 = -1 V So structure is deficient.and unstable. It is a mechanism,

Test: Determinacy & Indeterminacy -2 - Question 3

### The rigid-jointed frame shown in the figure is

Test: Determinacy & Indeterminacy -2 - Question 4

What is the degree of static indeterminacy of the plane structure as shown in the figure below?

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 4

For plane truss degree of indeterminacy,
Ds = m + re - 2j
re = 4; m= 10; j = 5
Ds = 4 + 10 - 2 x 5 = 4

Test: Determinacy & Indeterminacy -2 - Question 5

Consider the following statements:
1. The displacement method is more useful when degree of kinematic indeterminacy is greater than the degree of static indeterminacy,
2. The displacement method is more useful when degree of kinematic indeterminacy is less than degree of static indeterminacy.
3. The force method is more useful when degree of static indeterminacy is greater than the degree of kinematic indeterminacy
4. The force method is more useful when degree of static indeterminacy is less than the degree of kinematic indeterminacy

Which of these statements is correct?

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 5

Force method is useful when,
Ds < Dk
Displacement method is useful when,
Dk < Ds

Test: Determinacy & Indeterminacy -2 - Question 6

Which one of the following structures is statically determinate and stable?

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 6

A structure will be statically determinate if the external reactions can be determined from force- equilibrium equations. A structure is stable when the whole or part of the structure is prevented from large displacements on account of loading.
The structure in figure (b) is stable but statically indeterminate to the second degree.
The structure shown in figure (c) has both reaction components coinciding with each other, so the moment equilibrium condition wilt never be satisfied and the structure will not be under equilibrium. In figure'(a), the structure is stable and there are three reaction components which can be determined by two force equilibrium conditions and one moment equilibrium condition.

Test: Determinacy & Indeterminacy -2 - Question 7

How is a truss, which undergoes rigid body translation for an arbitrary load, classified as?

Test: Determinacy & Indeterminacy -2 - Question 8

The degree of static indeterminacy of the rigid frame having two internal hinges as shown in the figure below is

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 8

Ds=Dse+Dsi
Dss= rE- 3
= 4 - 3 = 1
Dsi = 3C - r= 3C - ∑(m1- 1)
= 3 x 2 -(2-1) +(2-1)
= 6 - 2 = 4
∴ Ds = Dss + Dsi = 5

Test: Determinacy & Indeterminacy -2 - Question 9

The pin-jointed frame shown in the figure is

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 9

Degree of indeterminacy,
n = (m + rE) - 2j
= (9 + 3 ) - 2 x 6 = 0
Since the degree of indeterminacy is zero and the frame is stable so it is a perfect frame.

Test: Determinacy & Indeterminacy -2 - Question 10

What is the total degree of indeterminacy both internal and external of the plane frame shown below?

Detailed Solution for Test: Determinacy & Indeterminacy -2 - Question 10

Ds = 3m + re- rr 3(j + j)
Number of members m=10
Number of external reactions re= 12
Number of interna! reaction components released
(rr) = 2
Number of rigid joints (j) = 8
Number of joints at which releases are located (j') = 2
∴ Ds = 3 x 10 + 12 - 2 - 3 x ( 8 + 2) = 10

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