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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?
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Verified Answer
If there are m unknown member forces, r unknown reaction components an...
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
Ds for a rigid jointed frame = 3m+r -3j
m- No. of members, r- no. of reactions, j- no. of joints
Most Upvoted Answer
If there are m unknown member forces, r unknown reaction components an...
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.
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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 bya)m + r + 2jb)m - r + 2jc)m + r-2'jd)m + r- 3jCorrect answer is option 'C'. Can you explain this answer?
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