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Test: Kinematic Indeterminacy - Civil Engineering (CE) MCQ


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10 Questions MCQ Test Structural Analysis - Test: Kinematic Indeterminacy

Test: Kinematic Indeterminacy for Civil Engineering (CE) 2024 is part of Structural Analysis preparation. The Test: Kinematic Indeterminacy questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Kinematic Indeterminacy MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Kinematic Indeterminacy below.
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Test: Kinematic Indeterminacy - Question 1

A single-bay, single-storeyed portal frame ABCD has its column ends fixed. If axial deformation is neglected, the kinematic indeterminacy is

Detailed Solution for Test: Kinematic Indeterminacy - Question 1

Concept: 
kinematic indeterminacy for Rigid jointed plane 2D framed, if axial deformation is neglected 

Dk = 3j - R
where j = Number of joints
R = Number of unknown support reactions
where j = 4 , R = 6 , m = 3
Dk = 3×4-6 = 6
If axial deformation is neglected,
Number of inextensible members (For which axial deformation is neglected) = 3
kinematic Indeterminacy = Dk - no of in extensible members = 6 - 3 = 3
Therefore kinematic indeterminacy of a single-bay, single-storeyed portal has its column ends fixed and if axial deformation is neglected is 3.

Test: Kinematic Indeterminacy - Question 2

The Kinematic Indeterminacy of a frame as shown is:

Detailed Solution for Test: Kinematic Indeterminacy - Question 2

Concept:
The degree of kinematic indeterminacy for the building frame is
DK = 3J – Re – m
Where,
m = number of the axially rigid member
Re = Support Reaction
J = Number of Joints

Calculation:
Given, 
m = 2, j = 3, Re = 2

DK = 3J – Re – m = 3 × 3 – 4 – 2
DK = 3

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Test: Kinematic Indeterminacy - Question 3

A continuous beam ABC with span AB = BC = L is shown in the figure. Supports A is fixed type, and supports B and C are roller type. The kinematic indeterminacy of the beam is:

Detailed Solution for Test: Kinematic Indeterminacy - Question 3

Concepts:
The kinematic indeterminacy is given as
Dk­ = 3j-r-m
j = no of joints
r = no of support reactions
m = no of axially rigid members 

Calculation:
No of Joints, j = 3
No of support reactions, r = 5 (3 at support A, 1 at each support B and C)
No of axially rigid members, m = 0 (assumed as not given in Question )
Dk­ = 3j-r-m
Dk = 3 × 3 – 5 – 0
∴ Dk = 4

Test: Kinematic Indeterminacy - Question 4


What is the degree of kinematic indeterminacy of the beam shown in figure above

Detailed Solution for Test: Kinematic Indeterminacy - Question 4

Concept:
Degree of Kinematic Indeterminacy:
Degree of kinematic indeterminacy (Dk) refers to the total number of independent available degree of freedom of all joints. The degree of kinematic indeterminacy may be defined as the total number of unrestrained displacement component of all joints.
Degree of kinematic indeterminacy for rigid jointed plane frame and beam is given by,
Dk = 3j - re
Where, j = Number of joint, re = Number of external recation

Calculation:
Degree of kinematic indeterminacy (Dk) = 3j - re
Here, j = 3 and re = 4
Dk = 3 × 3 - 4 = 5

Test: Kinematic Indeterminacy - Question 5

What is the number of kinematic indeterminacy for the building frame as shown in the figure when members are inextensible:

Detailed Solution for Test: Kinematic Indeterminacy - Question 5

Concept:
Static Indeterminacy: If the equilibrium equations are enough to analyze for unknown reactions, the structure is said to be statically indeterminate.
Ds = Dse + Dsi
Dse = r – S
Dsi = 3 × Number of closed loop (For portal frame)
Dsi = m- 2j+ 3 (For truss structure)
Kinematic Indeterminacy: It is the total number of possible degree of freedom of all the joints.
Dk = 3J - r (For portal frame)
Dk = 2J-r (For truss structure)
where, Dse = External Indeterminacy, Dsi = Internal Indeterminacy, Dk = Kinematic Indeterminacy, r = No. of unknown reactions, S = No. of equilibrium equation, m = No. of members & J = No. of joints

Given,
J = 9, r = 7, m = 10(inextensible)
∴ Dk = 3j - r = 27 - 7 = 20
For members are extensible, Dk = 20 - 10 = 10

Test: Kinematic Indeterminacy - Question 6

Degree of kinematic indeterminacy of a pin jointed plane frame is given by

Detailed Solution for Test: Kinematic Indeterminacy - Question 6

Concept:
If the number of unknown displacement components are greater than the number of compatibility equations, for those structures additional equations based on equilibrium must be written in order to obtain sufficient number of equations for the determination of all the unknown displacement components. The number of these additional equations necessary is known as degree of kinematic indeterminacy or degree of freedom of the structure.

Where
Dk = Kinematic Indeterminacy
J = number of joints
J’ = Number of hybrid joints
re = Number of external reactions
rr = Number of released reactions

Test: Kinematic Indeterminacy - Question 7

A singly-bay single-storeyed portal frame ABCD is fixed at A and D as shown in the figure. If axial deformation is neglected, the kinematic indeterminacy is

Detailed Solution for Test: Kinematic Indeterminacy - Question 7

Concept:
Static Indeterminacy: If the equilibrium equations are enough to analyze for unknown reactions, the structure is said to be statically indeterminate.
Ds = Dse + Dsi
Dse = r – S
Dsi = 3 × Number of closed loop (For portal frame)
Dsi = m- 2j+ 3 (For truss structure)
Kinematic Indeterminacy: It is the total number of possible degree of freedom of all the joints.
Dk = 3J - r (For portal frame)
Dk = 2J-r (For truss structure)
where, Dse = External Indeterminacy, Dsi = Internal Indeterminacy, Dk = Kinematic Indeterminacy, r = No. of unknown reactions, S = No. of equilibrium equation, m = No. of mombers & J = No. of joints
∴ Dk = 3j - r = 12 - 6 = 6
For axial deformation is neglected, Dk = 6 - 3 = 3

Test: Kinematic Indeterminacy - Question 8

For the plane frame as shown in the figure

The degree of kinematic indeterminacy, neglecting axial deformation, is

Detailed Solution for Test: Kinematic Indeterminacy - Question 8

Concept:
Static Indeterminacy: If the equilibrium equations are enough to analyze for unknown reactions, the structure is said to be statically indeterminate.
Ds = Dse + Dsi
Dse = r – S
Dsi = 3 × Number of closed loop (For portal frame)
Dsi = m- 2j+ 3 (For truss structure)
Kinematic Indeterminacy: It is the total number of possible degree of freedom of all the joints.
Dk = 3J - r (For beam & portal frame)
Dk = 2J - r (For truss structure)
where, Dse = External Indeterminacy, Dsi = Internal Indeterminacy, Dk = Kinematic Indeterminacy, r = No. of unknown reactions, S = No. of equilibrium equation, m = No. of mombers & J = No. of joints
Dk = 3J - r + H = 3 × 4 – 5 + 1 = 8
Dk = 8 - 3 = 5

Test: Kinematic Indeterminacy - Question 9

The kinematic indeterminacy of the following beam after imposing the boundary 

Detailed Solution for Test: Kinematic Indeterminacy - Question 9

Kinematic Indeterminacy (DK): 

  • Also known as the degree of freedom (DOF)
  • It refers to the number of independent components of joint displacement with the specified set of axes.
  • If the plane frame is extensible, the degree of kinematic indeterminacy = (3j - r)
  • If plane frame is inextensible & unbraced, Degree of kinematic indeterminacy = 3j - (r + m)
  • Here j = no. of Joints, r = No. of Unknown Equations, m = no. of Plastic hinges equation (m'-1), m' = No. of member meeting at hinges 

Calculation:
As per the above diagram:
No. of joints (j) = 7
No. of unknown Equation (r) = 3(Fixed end) +1 (Roller Support ) +2 (Hinged Support ) +1 (Spring as prop) = 7
No. of member meeting at hinges = 5
m = 5 - 1 = 4
Putting in formula Dk = 3j - (r + m)
Dk = 3 × 7 - (7 + 4)
Dk = 21 - 11
Dk = 10
So the Dk of the following beam is 10.

Test: Kinematic Indeterminacy - Question 10


Find the degree of static indeterminacy, for a two dimensional truss (or frame) shown in the figure above.

Detailed Solution for Test: Kinematic Indeterminacy - Question 10

Concept:
If the number of unknown reaction are more than the number of equilibrium equation available then structure is called indeterminate structure and degree of indeterminacy is given by static indeterminacy.
Some important cases are:

  • Pin jointed plane frame, Ds = m + r - 2j
  • Pin joined space frame, Ds = m + r - 3j
  • Rigid jointed plane frame, Ds = 3m + r - 3j
  • Rigid jointed space frame, Ds = 6m + r - 6j

Where,
m = number of members
r = number of external reactions
j = number of joints.
Data Given by the figure,
m = 7
r = 6
J = 5
We know that,
For pin jointed plane frame: Ds = m + r - 2J
Ds = 7 + 6 - 2 x 5
Ds = 3

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