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QUESTION: 1

Ray = reaction at support A in y direction.

Sign convention is as usual.

Beam is linear elastic.

Point A is a pin joint and point B and C are roller support. D is just an arbitrary point.

Unit load is applied at point D.

**Q.** What will be the value of Ray in the above figure?

Solution:

Answer: b

Explanation: If we remove the support at point A and replace it by force Faa. Due to sign convention, its direction will be initially considered upward.

QUESTION: 2

Ray = reaction at support A in y direction.

Sign convention is as usual.

Beam is linear elastic.

Point A is a pin joint and point B and C are roller support. D is just an arbitrary point.

Unit load is applied at point D.

**Q. **What will be the difference between magnitudes of Fad and Fda?

Solution:

Answer: b

Explanation: Due to validity of Maxwell’s reciprocal theorem, magnitudes of Fad and Fda will be equal.

QUESTION: 3

Ray = reaction at support A in y direction.

Sign convention is as usual.

Beam is linear elastic.

Point A is a pin joint and point B and C are roller support. D is just an arbitrary point.

Unit load is applied at point D.

**Q. **What is the relation between Fad and Fda?

Solution:

Answer: a

Explanation: Magnitudes will be same as stated above. Now, sign will be opposite as slope at B won’t change in deflection diagram and there won’t be and vertical deflection at point C.

QUESTION: 4

Sign convention is as usual.

Beam is linear elastic.

Point A is a pin joint and point B and C are roller support. D is just an arbitrary point.

Unit load is applied at point D.

**Q. **Which of the following is equal to Ray?

Solution:

Answer: c

Explanation: Just replacing the value of Fad in the answer of Q1 will give us the result. This relation will be the basic equation for ILD of indeterminate structures.

QUESTION: 5

Sign convention is as usual.

Beam is linear elastic.

Point A is a pin joint and point B and C are roller support. D is just an arbitrary point.

Unit load is applied at point D.

**Q. **The relationship between Ray,Fda and Faa is valid only for point A.

State whether the above statement is true or false.

Solution:

Answer: b

Explanation: It is valid for all supports like B and C, just replace all a’s by that point. We haven’t used any support conditions of point A while deriving this equation.

QUESTION: 6

A is a fixed support and B is roller.

AB = 18m.

C is a point at a distance of 6m from point A.

D is a point at a distance of 6m from point B.

Assume E and I to be given.

What is the DSI for this structure?

Solution:

Answer: a

Explanation: Total 4 unknowns are there and 3 equations are there.

QUESTION: 7

A is a fixed support and B is roller.

AB = 18m.

C is a point at a distance of 6m from point A.

D is a point at a distance of 6m from point B.

Assume E and I to be given.

**Q. **How many redundant forces are there in the above structure?

Solution:

Answer: b

Explanation: 1 redundant force is there as it is equal to DSI.

We have taken the horizontal force at point A as redundant force.

QUESTION: 8

A is a fixed support and B is roller.

AB = 18m.

C is a point at a distance of 6m from point A.

D is a point at a distance of 6m from point B.

Assume E and I to be given.

**Q. ** Which support should replace fixed support at point A for above condition?

Solution:

Answer: d

Explanation: Only slider will give both moment and vertical reaction.

QUESTION: 9

AB = 18m.

C is a point at a distance of 6m from point A.

D is a point at a distance of 6m from point B.

Assume E and I to be given.

**Q. **What will be the value of Ray for ILD?

Solution:

Answer: b

Explanation: Since redundant force is applied at point A, Fda/Faa will be the result unity.

QUESTION: 10

AB = 18m.

C is a point at a distance of 6m from point A.

D is a point at a distance of 6m from point B.

Assume E and I to be given.

**Q. **What will be the value of Δaa?

Solution:

Answer: d

Explanation: Applying a redundant load of unity on point A and applying conjugate beam method will give the answer easily.

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