This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Influence Lines for Statically Indeterminate Beams-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.
1. What will be the value of Ray in the above figure?
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.
2. What will be the difference between magnitudes of Fad and Fda?
Explanation: Due to validity of Maxwell’s reciprocal theorem, magnitudes of Fad and Fda will be equal.
3. What is the relation between Fad and Fda?
a) Fad = -Fda
b) Fad = Fda
c) Fad = -2Fda
d) Fad = 2Fda
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.
4. Which of the following is equal to Ray?
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.
5. The relationship between Ray,Fda and Faa is valid only for point A.
State whether the above statement is true or false.
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.
6. What is the DSI for this structure?
Explanation: Total 4 unknowns are there and 3 equations are there.
7. How many redundant forces are there in the above structure?
Explanation: 1 redundant force is there as it is equal to DSI.
We have taken the horizontal force at point A as redundant force.
8. Which support should replace fixed support at point A for above condition?
d) slider mechanism
Explanation: Only slider will give both moment and vertical reaction.
9. What will be the value of Ray for ILD?
Explanation: Since redundant force is applied at point A, Fda/Faa will be the result unity.
10. What will be the value of Δaa?
Explanation: Applying a redundant load of unity on point A and applying conjugate beam method will give the answer easily.
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