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All questions of Determinacy & Indeterminacy of Structures for Civil Engineering (CE) Exam
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?
Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is
a)
12
b)
14
c)
20
d)
22
|
Engineers Adda answered |
j = 11; r=8; m=11
Dk = 3j-r-no. of inextensible members = 3(11) – 8 -11 = 14
Dk = 3j-r-no. of inextensible members = 3(11) – 8 -11 = 14
Which one of the following statements is correct? The principle of superposition is applicable to- a)nonlinear behaviour of material and small displacement theory.
- b)nonlinear behaviour of material and large displacement theory.
- c)linear elastic behaviour of material and small displacement theory.
- d)linear elastic behaviour of material and large displacement theory.
Correct answer is option 'C'. Can you explain this answer?
Which one of the following statements is correct? The principle of superposition is applicable to
a)
nonlinear behaviour of material and small displacement theory.
b)
nonlinear behaviour of material and large displacement theory.
c)
linear elastic behaviour of material and small displacement theory.
d)
linear elastic behaviour of material and large displacement theory.
|
Lavanya Menon answered |
The principle of superposition states that the displacements resulting from each of a number of forces may be added to obtain the displacements resulting from the sum of forces. This method depends upon the linearity of the governing relations between the load and deflection, The linearity depends upon two factors.
(i) the linearity between bending moment and curvature which depends upon the linear elastic materials In non-linear material superposition of curvatures is not possible.
(ii) the linearity between curvatures and deflection depends upon the assumption that the deflections are so small that the approximate curvature can be used in place of true curvature.
(i) the linearity between bending moment and curvature which depends upon the linear elastic materials In non-linear material superposition of curvatures is not possible.
(ii) the linearity between curvatures and deflection depends upon the assumption that the deflections are so small that the approximate curvature can be used in place of true curvature.
For a simply supported beam, the moment at the support is always __________- a)Maximum
- b)Zero
- c)Minimum
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
For a simply supported beam, the moment at the support is always __________
a)
Maximum
b)
Zero
c)
Minimum
d)
Cannot be determined
|
Sudhir Patel answered |
As the moment is a product of force and perpendicular distance, the flexural moment at the support is zero because there is no distance at the support.
The degree of freedom of a joint for the rigid jointed joint plane frame is _____- a)0
- b)2
- c)3
- d)6
Correct answer is option 'C'. Can you explain this answer?
The degree of freedom of a joint for the rigid jointed joint plane frame is _____
a)
0
b)
2
c)
3
d)
6
|
|
Sudhir Patel answered |
Number of degree of freedom of a joint for the rigid jointed plane frame is 3 i.e. Horizontal sway, Vertical sway, and Rotation.
Find the degree of static indeterminacy, for a two dimensional truss (or frame) shown in the figure above.- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
Find the degree of static indeterminacy, for a two dimensional truss (or frame) shown in the figure above.
a)
1
b)
2
c)
3
d)
4
|
Pioneer Academy answered |
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:
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
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
A simple support offers only _______ reaction normal to the axis of the beam.- a)Horizontal
- b)Vertical
- c)Inclined
- d)Moment
Correct answer is option 'B'. Can you explain this answer?
A simple support offers only _______ reaction normal to the axis of the beam.
a)
Horizontal
b)
Vertical
c)
Inclined
d)
Moment
|
Rithika Reddy answered |
Support Reactions in Beams
In structural engineering, beams are commonly used to support loads and transfer them to the supports. The supports play a crucial role in providing stability and balance to the beam. There are different types of supports, each offering specific reactions depending on the nature of the load and the structural configuration. One of the most basic types of supports is a simple support.
Definition of a Simple Support
A simple support is a support that allows rotation but prevents translation in the horizontal and vertical directions. It is typically provided by a pin or a roller at the support location. This means that a simple support can resist vertical forces but cannot resist horizontal or inclined forces.
Reaction Normal to the Axis of the Beam
The reaction normal to the axis of the beam refers to the vertical component of the support reaction. In the case of a simple support, the only reaction it can offer is a vertical reaction. This reaction is normal (perpendicular) to the axis of the beam. Therefore, the correct answer to the given question is option 'B' - vertical.
Other Types of Reactions
While a simple support offers only a vertical reaction, other types of supports can offer additional reactions. Let's briefly discuss them:
1. Fixed Support: A fixed support prevents both translation and rotation. It can offer vertical, horizontal, and moment reactions.
2. Roller Support: A roller support allows translation but prevents rotation. It can offer only a vertical reaction.
3. Hinged Support: A hinged support allows rotation but prevents translation. It can offer only a vertical reaction.
4. Pinned Support: A pinned support allows rotation but prevents translation. It can offer vertical and horizontal reactions.
Conclusion
In summary, a simple support offers only a vertical reaction normal to the axis of the beam. It cannot provide horizontal, inclined, or moment reactions. Understanding the type of support and its reactions is essential for engineers to design and analyze beam structures accurately.
In structural engineering, beams are commonly used to support loads and transfer them to the supports. The supports play a crucial role in providing stability and balance to the beam. There are different types of supports, each offering specific reactions depending on the nature of the load and the structural configuration. One of the most basic types of supports is a simple support.
Definition of a Simple Support
A simple support is a support that allows rotation but prevents translation in the horizontal and vertical directions. It is typically provided by a pin or a roller at the support location. This means that a simple support can resist vertical forces but cannot resist horizontal or inclined forces.
Reaction Normal to the Axis of the Beam
The reaction normal to the axis of the beam refers to the vertical component of the support reaction. In the case of a simple support, the only reaction it can offer is a vertical reaction. This reaction is normal (perpendicular) to the axis of the beam. Therefore, the correct answer to the given question is option 'B' - vertical.
Other Types of Reactions
While a simple support offers only a vertical reaction, other types of supports can offer additional reactions. Let's briefly discuss them:
1. Fixed Support: A fixed support prevents both translation and rotation. It can offer vertical, horizontal, and moment reactions.
2. Roller Support: A roller support allows translation but prevents rotation. It can offer only a vertical reaction.
3. Hinged Support: A hinged support allows rotation but prevents translation. It can offer only a vertical reaction.
4. Pinned Support: A pinned support allows rotation but prevents translation. It can offer vertical and horizontal reactions.
Conclusion
In summary, a simple support offers only a vertical reaction normal to the axis of the beam. It cannot provide horizontal, inclined, or moment reactions. Understanding the type of support and its reactions is essential for engineers to design and analyze beam structures accurately.
Degree of kinematic indeterminacy of a pin jointed plane frame is given by where j is number of joints and r is reaction components.- a)2j - r
- b)j - 2 r
- c)3j - r
- d)2j + r
Correct answer is option 'A'. Can you explain this answer?
Degree of kinematic indeterminacy of a pin jointed plane frame is given by where j is number of joints and r is reaction components.
a)
2j - r
b)
j - 2 r
c)
3j - r
d)
2j + r
|
|
Shilpa Pillai answered |
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.
Dk = 3j –r for a rigid jointed frame
j number of joints and r number of reactions.
Degree of kinematic indeterminacy of a pin jointed plane frame is given by- a)2j – r
- b)j – 2r
- c)3j – r
- d)2j + r
Correct answer is option 'A'. Can you explain this answer?
Degree of kinematic indeterminacy of a pin jointed plane frame is given by
a)
2j – r
b)
j – 2r
c)
3j – r
d)
2j + r
|
Anjana Singh answered |
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
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
The degree of static indeterminacy of a pin- jointed space frame is given by- a)m + r - 2j
- b)m + r - 3j
- c)3m + r - 3j
- d)m + r + 3j
Correct answer is option 'B'. Can you explain this answer?
The degree of static indeterminacy of a pin- jointed space frame is given by
a)
m + r - 2j
b)
m + r - 3j
c)
3m + r - 3j
d)
m + r + 3j
|
Aditya Deshmukh answered |
Concept:
Static indeterminacy is the difference between a total number of unknowns (Total member forces+ reactions) and the total number of available equations from equilibrium conditions.
So for a pin-jointed frame total number of equations available at a joint = 2
So for j number of joints, equations available = 2j
So the degree of static indeterminacy of pin-jointed plane frame = m + r - 2j
Similarly, the DSI for pin jointed space frame = m + r - 3j
If the degree of static indeterminacy = 0, it is known as a statically determinate structure.
If the degree of static indeterminacy > 0, it is known as a statically indeterminate structure.
The kinematic indeterminacy of the following beam after imposing the boundary
- a)6
- b)8
- c)10
- d)12
Correct answer is option 'C'. Can you explain this answer?
The kinematic indeterminacy of the following beam after imposing the boundary
a)
6
b)
8
c)
10
d)
12
|
|
Pioneer Academy answered |
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.
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.
Total degree of indeterminacy (both internal and external) of the plane frame shown in the given figure is
- a)10
- b)11
- c)12
- d)15
Correct answer is option 'C'. Can you explain this answer?
Total degree of indeterminacy (both internal and external) of the plane frame shown in the given figure is
a)
10
b)
11
c)
12
d)
15
|
|
Swati Gupta answered |
The degree of indeterminacy,
Number of external reactions = re
= 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, rr = 3.
Number of external reactions = re
= 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, rr = 3.
The degree of freedom for the vertical guided roller is ________- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
The degree of freedom for the vertical guided roller is ________
a)
0
b)
1
c)
2
d)
3
|
Simran Dasgupta answered |
The degree of freedom for the vertical guided roller is 1.
Explanation:
A roller support allows for translation in only one direction, which is perpendicular to the axis of the roller. This means that the roller can move up and down vertically, but it cannot move horizontally or rotate. Therefore, it has only one degree of freedom.
Degree of freedom refers to the number of independent movements or rotations that a structure or mechanism can have. In the case of a roller support, it can only move vertically, so it has a single degree of freedom.
To understand this concept further, let's consider the different types of supports commonly used in structural engineering:
1. Fixed Support: A fixed support provides complete restraint against translation and rotation in all directions. It has zero degrees of freedom.
2. Pinned Support: A pinned support allows for rotation but restricts translation in all directions. It has one degree of freedom.
3. Roller Support: A roller support allows for translation in one direction, perpendicular to the axis of the roller. It restricts translation in all other directions and rotation. It has one degree of freedom.
4. Hinged Support: A hinged support allows for rotation but restricts translation in all directions. It has one degree of freedom.
By understanding the characteristics of each type of support, we can determine the number of degrees of freedom for a given support condition. In the case of the vertical guided roller, it can only move vertically, so it has a single degree of freedom.
In conclusion, the correct answer is option B - 1 degree of freedom for the vertical guided roller.
Explanation:
A roller support allows for translation in only one direction, which is perpendicular to the axis of the roller. This means that the roller can move up and down vertically, but it cannot move horizontally or rotate. Therefore, it has only one degree of freedom.
Degree of freedom refers to the number of independent movements or rotations that a structure or mechanism can have. In the case of a roller support, it can only move vertically, so it has a single degree of freedom.
To understand this concept further, let's consider the different types of supports commonly used in structural engineering:
1. Fixed Support: A fixed support provides complete restraint against translation and rotation in all directions. It has zero degrees of freedom.
2. Pinned Support: A pinned support allows for rotation but restricts translation in all directions. It has one degree of freedom.
3. Roller Support: A roller support allows for translation in one direction, perpendicular to the axis of the roller. It restricts translation in all other directions and rotation. It has one degree of freedom.
4. Hinged Support: A hinged support allows for rotation but restricts translation in all directions. It has one degree of freedom.
By understanding the characteristics of each type of support, we can determine the number of degrees of freedom for a given support condition. In the case of the vertical guided roller, it can only move vertically, so it has a single degree of freedom.
In conclusion, the correct answer is option B - 1 degree of freedom for the vertical guided roller.
The degree of freedom for a rigid jointed plane frame without axial deformation is given by 3j – m – r.- a)True
- b)False
- c)Cannot be determined
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
The degree of freedom for a rigid jointed plane frame without axial deformation is given by 3j – m – r.
a)
True
b)
False
c)
Cannot be determined
d)
None of the above
|
|
Gitanjali Chauhan answered |
The degree of freedom for a rigid jointed plane frame without axial deformation is given by 3j, where "j" represents the number of joints in the frame.
Hinge support is called as __________- a)Socket joint
- b)Swivel joint
- c)Ball joint
- d)Pin joint
Correct answer is option 'D'. Can you explain this answer?
Hinge support is called as __________
a)
Socket joint
b)
Swivel joint
c)
Ball joint
d)
Pin joint
|
|
Sudhir Patel answered |
Hinge support is one, in which the position is fixed but not the direction. In their words hinged support offers resistance against vertical and horizontal moments.it is fixed in such a way that it resembles like a pin joint.
“Hinged support offers resistance against rotation”.- a)True
- b)False
- c)Cannot be determined
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
“Hinged support offers resistance against rotation”.
a)
True
b)
False
c)
Cannot be determined
d)
None of the above
|
|
Sudhir Patel answered |
A hinged support offers resistance against horizontal and vertical movement but not against rotation. It support offers a vertical and horizontal reaction only.
Find the reaction at simple support A?
- a)6.5 kN
- b)9 kN
- c)10 kN
- d)7.5 kN
Correct answer is option 'D'. Can you explain this answer?
Find the reaction at simple support A?
a)
6.5 kN
b)
9 kN
c)
10 kN
d)
7.5 kN
|
Vertex Academy answered |
Total load = 10 kN
Taking moment at A = 0
4 × R @ B – 10 = 0
R @ B = 2.5 kN
Reaction at A = 10 – 2.5 = 7.5kN.
Taking moment at A = 0
4 × R @ B – 10 = 0
R @ B = 2.5 kN
Reaction at A = 10 – 2.5 = 7.5kN.
Roller support is same as _____- a)Hinged support
- b)Fixed support
- c)Simply support
- d)Roller support
Correct answer is option 'C'. Can you explain this answer?
Roller support is same as _____
a)
Hinged support
b)
Fixed support
c)
Simply support
d)
Roller support
|
|
Sudhir Patel answered |
The support reaction is normal to the axis of the beam. It facilitates the vertical support. It helps the beam to overcome the temperature stresses effectively. It is similar to simple support.
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- a)m + r + 2j
- b)m - r + 2j
- c)m + r-2'j
- d)m + r- 3j
Correct answer is option 'C'. Can you explain this answer?
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
a)
m + r + 2j
b)
m - r + 2j
c)
m + r-2'j
d)
m + r- 3j
|
|
Srestha Khanna answered |
The degree of static indeterminacy of a pin-jointed plane frame can be determined by considering the number of unknown member forces (m), unknown reaction components (r), and the number of joints (j).
The formula to calculate the degree of static indeterminacy is given by:
Degree of Static Indeterminacy = m + r - 2j
Let's break down the formula and understand each component:
1. Unknown member forces (m):
These are the forces acting on the various members of the frame, such as axial forces or bending moments. The number of unknown member forces represents the number of forces that we need to solve for.
2. Unknown reaction components (r):
These are the forces acting at the supports or connections of the frame. They include the horizontal and vertical components of the reactions. The number of unknown reaction components represents the number of forces that we need to solve for.
3. Number of joints (j):
A joint is a connection point where two or more members meet. The number of joints represents the number of connection points in the frame.
Now, let's apply the formula to the given options:
a) m + r - 2j
b) m - r + 2j
c) m + r - 2j (Correct Option)
d) m + r - 3j
Applying the formula to option C, we have:
Degree of Static Indeterminacy = m + r - 2j
Here, the number of unknown member forces (m) and unknown reaction components (r) are added, while the number of joints (2j) is subtracted.
This formula represents the number of unknowns that need to be solved for in order to determine the equilibrium of the frame. By subtracting 2j, we account for the fact that each joint contributes two unknowns (horizontal and vertical reactions) to the overall system.
Therefore, the correct answer is option C, which states that the degree of static indeterminacy of a pin-jointed plane frame is given by m + r - 2j.
The formula to calculate the degree of static indeterminacy is given by:
Degree of Static Indeterminacy = m + r - 2j
Let's break down the formula and understand each component:
1. Unknown member forces (m):
These are the forces acting on the various members of the frame, such as axial forces or bending moments. The number of unknown member forces represents the number of forces that we need to solve for.
2. Unknown reaction components (r):
These are the forces acting at the supports or connections of the frame. They include the horizontal and vertical components of the reactions. The number of unknown reaction components represents the number of forces that we need to solve for.
3. Number of joints (j):
A joint is a connection point where two or more members meet. The number of joints represents the number of connection points in the frame.
Now, let's apply the formula to the given options:
a) m + r - 2j
b) m - r + 2j
c) m + r - 2j (Correct Option)
d) m + r - 3j
Applying the formula to option C, we have:
Degree of Static Indeterminacy = m + r - 2j
Here, the number of unknown member forces (m) and unknown reaction components (r) are added, while the number of joints (2j) is subtracted.
This formula represents the number of unknowns that need to be solved for in order to determine the equilibrium of the frame. By subtracting 2j, we account for the fact that each joint contributes two unknowns (horizontal and vertical reactions) to the overall system.
Therefore, the correct answer is option C, which states that the degree of static indeterminacy of a pin-jointed plane frame is given by m + r - 2j.
If 4 reactions are acting on a beam, then the system is:-- a)Unstable & indeterminate
- b)Can’t say
- c)Stable & indeterminate
- d)Stable & determinate
Correct answer is option 'B'. Can you explain this answer?
If 4 reactions are acting on a beam, then the system is:-
a)
Unstable & indeterminate
b)
Can’t say
c)
Stable & indeterminate
d)
Stable & determinate
|
Kabir Verma answered |
4 reactions mean that the system is definitely indeterminate. But stability would depend upon the nature of forces acting on the planar structure.
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 indeterminacyWhich of these statements is correct?- a)1 and 3
- b)2 and 3
- c)1 and 4
- d)2 and 4
Correct answer is option 'D'. Can you explain this answer?
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
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?
a)
1 and 3
b)
2 and 3
c)
1 and 4
d)
2 and 4
|
|
Anagha Mehta answered |
Force method is useful when,
Ds < Dk
Displacement method is useful when,
Dk < Ds
Ds < Dk
Displacement method is useful when,
Dk < Ds
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?
Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is:
a)
12
b)
14
c)
20
d)
22
|
|
Shilpa Pillai answered |
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
The rigid-jointed frame shown in the figure is
- a)unstable
- b)stable and statically determinate
- c)stable and statically indeterminate by one degree
- d)stable and statically indeterminate by two degree
Correct answer is option 'B'. Can you explain this answer?
The rigid-jointed frame shown in the figure is
a)
unstable
b)
stable and statically determinate
c)
stable and statically indeterminate by one degree
d)
stable and statically indeterminate by two degree
|
Sanjay Gp answered |
For a rigid joined 2D frame structure. Degree of static indeterminacy
Ds=3m+r-3j
here
Ds=3x2+3-3x3=0.
Hence it is statically determinate.
And since reactions are not parallel or concurrent it is a stable member.
Ds=3m+r-3j
here
Ds=3x2+3-3x3=0.
Hence it is statically determinate.
And since reactions are not parallel or concurrent it is a stable member.
For the plane frame as shown in the figure
The degree of kinematic indeterminacy, neglecting axial deformation, is- a)3
- b)5
- c)7
- d)9
Correct answer is option 'B'. Can you explain this answer?
For the plane frame as shown in the figure
The degree of kinematic indeterminacy, neglecting axial deformation, is
The degree of kinematic indeterminacy, neglecting axial deformation, is
a)
3
b)
5
c)
7
d)
9
|
|
Pioneer Academy answered |
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
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
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:
- a)5
- b)3
- c)2
- d)4
Correct answer is option 'D'. Can you explain this answer?
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:
a)
5
b)
3
c)
2
d)
4
|
|
Anjana Singh answered |
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
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
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
________ support develops support moment.- a)Hinged
- b)Simple
- c)Fixed
- d)Joint
Correct answer is option 'C'. Can you explain this answer?
________ support develops support moment.
a)
Hinged
b)
Simple
c)
Fixed
d)
Joint
|
|
Akanksha Tiwari answered |
Fixed support develops support moment.
Fixed support is a type of support that is commonly used in structural engineering. It restricts both translation and rotation of the supported element. When a load is applied to a fixed support, it resists both vertical and horizontal movement, as well as any rotation. This resistance to rotation leads to the development of a support moment.
Support moment refers to the bending moment that develops at a fixed support due to the applied load. It is a measure of the internal forces and stresses within a structure. The support moment is caused by the reaction forces at the fixed support, which counteract the external load.
The support moment can be calculated using the principles of statics and structural analysis. By applying equilibrium equations and considering the geometry and loading conditions, engineers can determine the magnitude and distribution of the support moment.
The support moment is an important consideration in the design of structures, as it affects the overall stability and strength of the system. It determines the maximum bending and shear stresses in the supported element and influences the selection of materials and dimensions for structural members.
The support moment also affects the deflection of the structure. Higher support moments result in larger deflections, which can impact the serviceability and functionality of the structure.
In summary, a fixed support develops a support moment when subjected to an applied load. This moment is caused by the reaction forces at the fixed support and is an important factor in the design and analysis of structures.
Fixed support is a type of support that is commonly used in structural engineering. It restricts both translation and rotation of the supported element. When a load is applied to a fixed support, it resists both vertical and horizontal movement, as well as any rotation. This resistance to rotation leads to the development of a support moment.
Support moment refers to the bending moment that develops at a fixed support due to the applied load. It is a measure of the internal forces and stresses within a structure. The support moment is caused by the reaction forces at the fixed support, which counteract the external load.
The support moment can be calculated using the principles of statics and structural analysis. By applying equilibrium equations and considering the geometry and loading conditions, engineers can determine the magnitude and distribution of the support moment.
The support moment is an important consideration in the design of structures, as it affects the overall stability and strength of the system. It determines the maximum bending and shear stresses in the supported element and influences the selection of materials and dimensions for structural members.
The support moment also affects the deflection of the structure. Higher support moments result in larger deflections, which can impact the serviceability and functionality of the structure.
In summary, a fixed support develops a support moment when subjected to an applied load. This moment is caused by the reaction forces at the fixed support and is an important factor in the design and analysis of structures.
A single-bay, single-storeyed portal frame ABCD has its column ends fixed. If axial deformation is neglected, the kinematic indeterminacy is- a)3
- b)2
- c)6
- d)4
Correct answer is option 'A'. Can you explain this answer?
A single-bay, single-storeyed portal frame ABCD has its column ends fixed. If axial deformation is neglected, the kinematic indeterminacy is
a)
3
b)
2
c)
6
d)
4
|
|
Anjana Singh answered |
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.
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.
The following methods are used for structural analysis:
1. Macaulay method
2. Column analogy method
3. Kani’s method
4. Method of sectionsThose used for indeterminate structural analysis would include- a)1 and 2
- b)1 and 3
- c)2 and 3
- d)2, 3 and 4
Correct answer is option 'C'. Can you explain this answer?
The following methods are used for structural analysis:
1. Macaulay method
2. Column analogy method
3. Kani’s method
4. Method of sections
1. Macaulay method
2. Column analogy method
3. Kani’s method
4. Method of sections
Those used for indeterminate structural analysis would include
a)
1 and 2
b)
1 and 3
c)
2 and 3
d)
2, 3 and 4
|
Rounak Mehta answered |
Macaulay's method is used for deflection and slope calculation due to point loads in prismatic beams. Method of sections is used for statically determinate trusses.
A uniform simply supported beam is subjected to a clockwise moment M at the left end. What is the moment required at the right end so that rotation of the right end is zero?- a)2M
- b)M
- c)M/2
- d)M/3
Correct answer is option 'C'. Can you explain this answer?
A uniform simply supported beam is subjected to a clockwise moment M at the left end. What is the moment required at the right end so that rotation of the right end is zero?
a)
2M
b)
M
c)
M/2
d)
M/3
|
|
Garima Kulkarni answered |
at left end
To keep rotation at right and zero a moment should be applied in anticlockwise direction. Let the moment in M'
What is the degree of kinematic indeterminacy of the beam shown in figure above- a)2
- b)3
- c)5
- d)9
Correct answer is option 'C'. Can you explain this answer?
What is the degree of kinematic indeterminacy of the beam shown in figure above
a)
2
b)
3
c)
5
d)
9
|
|
Anjana Singh answered |
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
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
Degree of kinematic indeterminacy (Dk) = 3j - re
Here, j = 3 and re = 4
Dk = 3 × 3 - 4 = 5
Hinged supports offers vertical and ________ reaction.- a)Horizontal
- b)Moment
- c)Rotation
- d)Couple
Correct answer is option 'A'. Can you explain this answer?
Hinged supports offers vertical and ________ reaction.
a)
Horizontal
b)
Moment
c)
Rotation
d)
Couple
|
|
Srestha Datta answered |
Hinged supports, also known as pinned supports or simply pins, are a type of support commonly used in structural engineering. They allow a structure to rotate freely around the pin connection, but they do not allow any horizontal movement or moment transfer. The only reaction offered by hinged supports is a vertical reaction, which can be either upward or downward depending on the load applied to the structure.
Vertical Reaction of Hinged Supports:
When a load is applied to a structure supported by hinged supports, the pins allow the structure to rotate freely. This rotation occurs around the axis of the pins, and the pins themselves do not resist this rotation. Instead, they provide a vertical reaction force to balance the applied load and maintain equilibrium.
Explanation of Options:
a) Horizontal: Hinged supports do not offer any horizontal reaction because they allow the structure to rotate freely without any resistance to horizontal movement.
b) Moment: Hinged supports do not offer any moment reaction because they do not resist the rotation of the structure around the pins. Moments are resisted by fixed supports or supports with moment connections.
c) Rotation: Hinged supports do allow rotation of the structure around the pins, as this is their primary function.
d) Couple: Hinged supports do not offer a couple reaction because they do not resist the rotation of the structure. Couples are resisted by fixed supports or supports with moment connections.
Conclusion:
In conclusion, hinged supports offer only a vertical reaction to balance the applied load and maintain equilibrium. They do not offer any horizontal reaction, moment reaction, or couple reaction. Hinged supports are commonly used in structures where rotation is desired, such as trusses, frames, and bridges.
Vertical Reaction of Hinged Supports:
When a load is applied to a structure supported by hinged supports, the pins allow the structure to rotate freely. This rotation occurs around the axis of the pins, and the pins themselves do not resist this rotation. Instead, they provide a vertical reaction force to balance the applied load and maintain equilibrium.
Explanation of Options:
a) Horizontal: Hinged supports do not offer any horizontal reaction because they allow the structure to rotate freely without any resistance to horizontal movement.
b) Moment: Hinged supports do not offer any moment reaction because they do not resist the rotation of the structure around the pins. Moments are resisted by fixed supports or supports with moment connections.
c) Rotation: Hinged supports do allow rotation of the structure around the pins, as this is their primary function.
d) Couple: Hinged supports do not offer a couple reaction because they do not resist the rotation of the structure. Couples are resisted by fixed supports or supports with moment connections.
Conclusion:
In conclusion, hinged supports offer only a vertical reaction to balance the applied load and maintain equilibrium. They do not offer any horizontal reaction, moment reaction, or couple reaction. Hinged supports are commonly used in structures where rotation is desired, such as trusses, frames, and bridges.
A horizontal fixed beam AB of span 6 m has uniform flexural rigidity of 4200 kN m2. During loading, the support B sinks downwards by 25 mm. The moment induced at the end A is- a)105 kN m (Anticlockwise)
- b)17.5 kN m (Clockwise)
- c)17.5 kN m (Anticlockwise)
- d)105 kN m (Clockwise)
Correct answer is option 'C'. Can you explain this answer?
A horizontal fixed beam AB of span 6 m has uniform flexural rigidity of 4200 kN m2. During loading, the support B sinks downwards by 25 mm. The moment induced at the end A is
a)
105 kN m (Anticlockwise)
b)
17.5 kN m (Clockwise)
c)
17.5 kN m (Anticlockwise)
d)
105 kN m (Clockwise)
|
Mehul Choudhury answered |
A pin-jointed plane frame is unstable if where m is number of members r is reaction components and j is number of joints- a)(m + r) < 2j
- b)m + r = 2j
- c)(m + r)> 2j
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
A pin-jointed plane frame is unstable if where m is number of members r is reaction components and j is number of joints
a)
(m + r) < 2j
b)
m + r = 2j
c)
(m + r)> 2j
d)
None of these
|
Sparsh Unni answered |
>j+2
Explanation:
For a pin-jointed plane frame to be stable, it must satisfy the condition of static equilibrium, which is that the sum of all forces and moments acting on the frame is zero. In other words, the number of unknown forces and moments must be equal to the number of equations of static equilibrium (i.e. three equations for a 2D frame).
In a pin-jointed plane frame, each joint can provide two equilibrium equations (one for force in the x-direction and one for force in the y-direction). Therefore, the total number of equations of equilibrium is 2j.
On the other hand, each member can carry one unknown force (either tension or compression). Therefore, the total number of unknown forces is m.
Finally, the reaction components at the supports can be expressed using two equations of equilibrium (one for force in the x-direction and one for force in the y-direction). Therefore, the total number of unknown reaction components is r.
So, by applying the principle of statics, we can write the following equation for stability of a pin-jointed plane frame:
m + r = 2j
Simplifying this equation, we get:
m - 2j + r = 0
Therefore, for a pin-jointed plane frame to be stable, the expression (m - 2j + r) must be equal to zero. However, for instability, this expression must be greater than zero.
Hence, the condition for instability can be expressed as:
m - 2j + r > 0
or equivalently,
m > 2j - r
Adding 2 to both sides, we get:
m + 2 > 2j - r + 2
which can be rewritten as:
(m + r) > 2(j + 1)
or simply:
(m + r) > 2j + 2
Therefore, the condition for instability in a pin-jointed plane frame is:
(m + r) > 2j + 2.
Explanation:
For a pin-jointed plane frame to be stable, it must satisfy the condition of static equilibrium, which is that the sum of all forces and moments acting on the frame is zero. In other words, the number of unknown forces and moments must be equal to the number of equations of static equilibrium (i.e. three equations for a 2D frame).
In a pin-jointed plane frame, each joint can provide two equilibrium equations (one for force in the x-direction and one for force in the y-direction). Therefore, the total number of equations of equilibrium is 2j.
On the other hand, each member can carry one unknown force (either tension or compression). Therefore, the total number of unknown forces is m.
Finally, the reaction components at the supports can be expressed using two equations of equilibrium (one for force in the x-direction and one for force in the y-direction). Therefore, the total number of unknown reaction components is r.
So, by applying the principle of statics, we can write the following equation for stability of a pin-jointed plane frame:
m + r = 2j
Simplifying this equation, we get:
m - 2j + r = 0
Therefore, for a pin-jointed plane frame to be stable, the expression (m - 2j + r) must be equal to zero. However, for instability, this expression must be greater than zero.
Hence, the condition for instability can be expressed as:
m - 2j + r > 0
or equivalently,
m > 2j - r
Adding 2 to both sides, we get:
m + 2 > 2j - r + 2
which can be rewritten as:
(m + r) > 2(j + 1)
or simply:
(m + r) > 2j + 2
Therefore, the condition for instability in a pin-jointed plane frame is:
(m + r) > 2j + 2.
What is kinematic indeterminacy for the given figure considering axial deformation?
- a)0
- b)4
- c)6
- d)10
Correct answer is option 'A'. Can you explain this answer?
What is kinematic indeterminacy for the given figure considering axial deformation?
a)
0
b)
4
c)
6
d)
10
|
|
Sudhir Patel answered |
The given beam is supported by fixed support at both of it ends. Fixed support, if not considering axial deformation does not any degree of freedom. Therefore, the degree of freedom of the beam is 0.
What is the degree of static indeterminacy of the plane structure as shown in the figure below?
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'B'. Can you explain this answer?
What is the degree of static indeterminacy of the plane structure as shown in the figure below?
a)
3
b)
4
c)
5
d)
6
|
|
Raghav Mukherjee answered |
For plane truss degree of indeterminacy,
Ds = m + re - 2j
re = 4; m= 10; j = 5
Ds = 4 + 10 - 2 x 5 = 4
Ds = m + re - 2j
re = 4; m= 10; j = 5
Ds = 4 + 10 - 2 x 5 = 4
Which one of the following structures is statically determinate and stable?- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Which one of the following structures is statically determinate and stable?
a)
b)
c)
d)
|
|
Mahesh Nair answered |
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.
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.
What is kinematic indeterminacy for the given figure considering axial deformation?
- a)0
- b)2
- c)4
- d)6
Correct answer is option 'C'. Can you explain this answer?
What is kinematic indeterminacy for the given figure considering axial deformation?
a)
0
b)
2
c)
4
d)
6
|
|
Sudhir Patel answered |
The given beam is supported by roller support at both of its ends. Roller support, if considering axial deformation has two degrees of freedom i.e. Rotation and Horizontal sway. Therefore, the degree of freedom of the beam is 4.
The statical indeterminacy for the given 3D frame is
- a)8
- b)6
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
The statical indeterminacy for the given 3D frame is
a)
8
b)
6
c)
9
d)
12
|
|
Swati Gupta answered |
Ds = Dse + Dsi
Dse = rE - 6
rE = 6 + 3 + 3 + 6 = 18
Dse = 12
Dsi = 6c - rR = 6 x 1 - 3
= 6 - 3 [(2 - 1) + (3 - 1)]
= 6 - 9 = -3
∴ Ds = 12 - 3 = 9
Dse = rE - 6
rE = 6 + 3 + 3 + 6 = 18
Dse = 12
Dsi = 6c - rR = 6 x 1 - 3
= 6 - 3 [(2 - 1) + (3 - 1)]
= 6 - 9 = -3
∴ Ds = 12 - 3 = 9
A loaded porta! frame is shown in figure. The profile of its Bending Moment diagram will be
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A loaded porta! frame is shown in figure. The profile of its Bending Moment diagram will be
a)
b)
c)
d)
|
|
Aditi Sarkar answered |
- The horizontal force will be distributed to both the supports.
- The bending moment at hinged end will be zero and fixed end will have some B.M.
- The B.M.D. for columns will be linear.
- The B.M.D. for beam will be parabolic.
The choice now remains between (b) and (d). In diagram (b) and (c) the Left column has negative B.M. in upper half or at top. The beam at left end in (b) shows negative B.M. while in (c) it shows a positive B.M.
- The bending moment at hinged end will be zero and fixed end will have some B.M.
- The B.M.D. for columns will be linear.
- The B.M.D. for beam will be parabolic.
The choice now remains between (b) and (d). In diagram (b) and (c) the Left column has negative B.M. in upper half or at top. The beam at left end in (b) shows negative B.M. while in (c) it shows a positive B.M.
The pin-jointed frame shown in the figure is
- a)a perfect frame
- b)a redundant frame
- c)a deficient frame
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
The pin-jointed frame shown in the figure is
a)
a perfect frame
b)
a redundant frame
c)
a deficient frame
d)
None of the above
|
|
Subham Unni answered |
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.
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.
What is kinematic indeterminacy for the given figure?
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
What is kinematic indeterminacy for the given figure?
a)
0
b)
1
c)
2
d)
3
|
|
Anjana Singh answered |
The given beam is supported by fixed supports at both of its ends and intermediary roller support. Fixed does not provide any degree of freedom. Whereas, roller support provides both rotation and horizontal sway. But horizontal sway is already restricted by the ends fixed support. Thus, the only degree of freedom is the rotation about roller support.
The plane pin joint structure shown in figure below is
- a)Externally indeterminate
- b)Internally indeterminate
- c)Determinate
- d)Mechanism
Correct answer is option 'B'. Can you explain this answer?
The plane pin joint structure shown in figure below is
a)
Externally indeterminate
b)
Internally indeterminate
c)
Determinate
d)
Mechanism
|
Satish Yadav answered |
Dsi= 3 C- rr
here
C is loop C=1
rr= restrain release
rr values for hinges are summation (m'-1)
here m' = no. of members to connect to the hinge joint
rr= (3-1)+(2-1)+(2-1)+(2-1)+(3-1)+(2-1)
rr= 8
Dsi= 3*1-8
Dsi= -5
then we called the structure internally indeterminate
here
C is loop C=1
rr= restrain release
rr values for hinges are summation (m'-1)
here m' = no. of members to connect to the hinge joint
rr= (3-1)+(2-1)+(2-1)+(2-1)+(3-1)+(2-1)
rr= 8
Dsi= 3*1-8
Dsi= -5
then we called the structure internally indeterminate
Name the support from following figure.
- a)Hinge support
- b)Fixed support
- c)Free support
- d)Roller support
Correct answer is option 'B'. Can you explain this answer?
Name the support from following figure.
a)
Hinge support
b)
Fixed support
c)
Free support
d)
Roller support
|
|
Sudhir Patel answered |
In the above figure we can observe that the beam is supported at both the ends so the beam is fixed at both ends. Hence the support is a fixed support.
What is the total degree of indeterminacy both internal and external of the plane frame shown below?
- a)10
- b)11
- c)12
- d)14
Correct answer is option 'A'. Can you explain this answer?
What is the total degree of indeterminacy both internal and external of the plane frame shown below?
a)
10
b)
11
c)
12
d)
14
|
|
Gauri Sarkar answered |
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
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
What is kinematic indeterminacy for the given figure without considering axial deformation?
- a)0
- b)6
- c)4
- d)2
Correct answer is option 'D'. Can you explain this answer?
What is kinematic indeterminacy for the given figure without considering axial deformation?
a)
0
b)
6
c)
4
d)
2
|
|
Anjana Singh answered |
The given set of frame consists of fixed end supports with two intermediate rigid joints. Each rigid joint allows horizontal sway, vertical sway, and rotation. Therefore, two rigid joints will have six degrees of freedom.
What is the number of kinematic indeterminacy for the building frame as shown in the figure when members are inextensible:
- a)8
- b)10
- c)12
- d)16
Correct answer is option 'B'. Can you explain this answer?
What is the number of kinematic indeterminacy for the building frame as shown in the figure when members are inextensible:
a)
8
b)
10
c)
12
d)
16
|
|
Anjana Singh answered |
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
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
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