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Advanced Engineering Mathematics

This study delves into the application of Laplace Transform in determining the deflection of beams based on elasticity theory. Analyzing problems involving linear transformation and inverse transform to evaluate various equations related to deflection curves.

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Advanced Engineering Mathematics

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  1. Advanced Engineering Mathematics LAPLACE TRANSFORM

  2. Laplace Transform

  3. Laplace Transform Problem 1:

  4. Linear Transform

  5. Laplace Transform Problem 2: Evaluate L{t}

  6. Transformation Laplace Problem 3: Evaluate L{e-3t}

  7. Transformation Laplace Problem 4: Evaluate L{sin2 t}

  8. Transformation Laplace Problem 2:

  9. Inverse Transform

  10. Linear Transform

  11. Inverse Transform Problem 1:

  12. Inverse Transform Problem 2:

  13. Inverse Transform Problem 3:

  14. Axis of symmetry Deflection of curve Applications Deflection of Beams Beam is assumed as a homogeneous, and has uniform cross sections along its length Deflection curve can be derived from differential equation based on elasticity concept.

  15. L 0 x y(x) y Applications Deflection of Beams Elasticity theory: bending moment M(x) at a point x along the beam is related to the load per unit length w(x)

  16. L 0 y(x) x y(x) y Applications Deflection of Beams

  17. L 0 x y(x) y Applications Deflection of Beams • y(0) = 0 at embedded end. • y’(0) = 0 (deflection curve is tangent to the x-axis at embedded end) • y”(L) = 0, bending moment at free end is zer0. • y”’(L) = 0, shear force is zero at a free end. EIy’’’ = dM/dx is the shear force.

  18. w0 Wall L y Applications Determining deflection of a Beam using Laplace Transform x A beam of length L is embedded at both ends. In this case the deflection y(x) must satisfy:

  19. Applications Determining deflection of a Beam using Laplace Transform

  20. Applications Determining deflection of a Beam using Laplace Transform

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