Advanced Foundation Engineering: Beams on Elastic Foundation- IX

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What type of beam is being discussed in the text?

Cantilever beam

Free end beam (correct)

Fixed beam

Simply supported beam

At what position does the bending moment become 0 according to the text?

$x=L/2$

$x=L$ (correct)

$x=0$

$x=2L$

How many nodes are mentioned in the text for applying the equations?

5

4 (correct)

3

2

What type of boundary condition is valid for the discussed problem?

Symmetric boundary condition Signup and view all the answers

What is the purpose of dividing the beam into nodes in the context of the lecture?

To apply the beam equation at multiple points Signup and view all the answers

What is the significance of the boundary conditions mentioned in the lecture?

To determine the shear force at the centre Signup and view all the answers

Why are imaginary nodes used in applying the beam equation in this context?

To apply the equation directly Signup and view all the answers

What purpose do boundary conditions serve in analyzing beams on elastic foundations?

To calculate the shear force and bending moment Signup and view all the answers

What is the role of symmetry in establishing boundary conditions for beams on elastic foundations?

Restricting the shear force and bending moment at specific points Signup and view all the answers

How do imaginary nodes contribute to the analysis of beams on elastic foundations?

By allowing for direct application of the beam equation at specific points Signup and view all the answers

What is the purpose of the imaginary nodes mentioned in the text?

To apply boundary conditions for the beam Signup and view all the answers

How many imaginary nodes are being used in the discussed problem?

4 Signup and view all the answers

What is the significance of dividing the beam into 𝑛 − 1 equal parts?

It allows for the application of boundary conditions Signup and view all the answers

What is the role of the first two imaginary nodes in the boundary conditions?

Applying specific conditions at those points Signup and view all the answers

How is the settlement at node 2 related to the settlement at imaginary node 2?

They are equal to each other Signup and view all the answers

What does 𝐸𝐼 represent in the discussed context?

"E" times "I" Signup and view all the answers

Why is it necessary to convert the imaginary nodes to real nodes?

To establish relationships for solving the problem Signup and view all the answers

What is being expressed in the finite difference scheme at 𝑥 = 0 in the discussed context?

"E" times "I" Signup and view all the answers

What mathematical operation is performed to convert 𝑊 to 𝑊  in the text?

Multiplication by 2 and subtraction of 𝑊 Signup and view all the answers

What does 𝑊  = 𝑊 represent in relation to imaginary and real nodes?

"W" at imaginary node equals "W" at real node Signup and view all the answers