Question
Download Solution PDF______ Method is used to find the deflection of beam.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Deflection of beam:
- The deformation of a beam is usually expressed in terms of its deflection from its original unloaded position.
- The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam.
- The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.
Methods of Determining Beam Deflections:
Method | Details |
---|---|
Double Integration Method | This method is best when there is continuity in the applied loading. |
Moment Area Method | The method is especially suitable when the deflection or angle of rotation at only one point of the beam is desired. |
Strain-energy method (Castigliano's Theorem) |
Castigliano's Theorem lets us use strain energies at the locations of forces to determine the deflections. The Theorem also allows for the determining of deflections for objects with changing cross-sectional areas. |
Conjugate Beam Method |
This method is based on the construction of a conjugate beam, defined as an imaginary beam of length equal to that of the original beam and loaded with an elastic weight M/EI, where M is the BM of the actual beam. This method is especially useful for simply supported and cantilever beams with varying flexural rigidities. |
Method of Superposition | The slope and deflection of the beam caused by several different loads acting simultaneously can be found by superimposing the slopes and deflections caused by the loads acting separately. |
Macaulay's Method | In Macaulay’s method differential equation for the elastic curve is equated with the bending moment at the required section and by integrating the equation slope and deflection can be obtained. |
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