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The flexibility matrix for the simply supported beam with reference to the coordinates, as shown below, is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The flexibility matrix for the simply supported beam with reference to...
Concept:
Flexibility matrix:
- The redundant forces are identified and assign one co-ordinate to each redundant.
- The redundant are released to obtained to obtain the primary structure.
- Due to external load, the displacements in the direction of various co-ordinate and at the location of co-ordinate are found out.
- Positive sign is taken when the direction of slope/deflection is the same as the original moment/force.
- Negative sign taken when the direction of slope/deflection is opposite as of original moment/force
Slope at the point A due to the moment at A is given by
θα = ML/3EI
Slope at point B due to moment at point A is given by
θb = ML/6EI
Calculation:
Given: EI = Constant
First, apply unit moment at A and draw its deflected shape
First, apply unit moment at A and draw its deflected shape
δ11 = L/3EI (Same as of original moment) and δ21 = L/6EI (same as of original moment)
Now apply unit moment at B and draw its deflected shape
δ21 = L/6EI(Same as of original moment) and δ22 = L/3EI(Same as of original moment)
So, The flexibility matrix will be
∴ The flexibility matrix is given by 
Most Upvoted Answer
The flexibility matrix for the simply supported beam with reference to...
Concept:
Flexibility matrix:
- The redundant forces are identified and assign one co-ordinate to each redundant.
- The redundant are released to obtained to obtain the primary structure.
- Due to external load, the displacements in the direction of various co-ordinate and at the location of co-ordinate are found out.
- Positive sign is taken when the direction of slope/deflection is the same as the original moment/force.
- Negative sign taken when the direction of slope/deflection is opposite as of original moment/force
Slope at the point A due to the moment at A is given by
θα = ML/3EI
Slope at point B due to moment at point A is given by
θb = ML/6EI
Calculation:
Given: EI = Constant
First, apply unit moment at A and draw its deflected shape
First, apply unit moment at A and draw its deflected shape
δ11 = L/3EI (Same as of original moment) and δ21 = L/6EI (same as of original moment)
Now apply unit moment at B and draw its deflected shape
δ21 = L/6EI(Same as of original moment) and δ22 = L/3EI(Same as of original moment)
So, The flexibility matrix will be
∴ The flexibility matrix is given by
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The flexibility matrix for the simply supported beam with reference to the coordinates, as shown below, isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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