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.
Numerous methods are available for the determination of beam deflections. These methods include:
1. Double Integration Method
where x and y are the coordinates shown in the figure of the elastic curve of the beam under load,
The first integration y'(dy / dx) yields the Slope of the Elastic Curve
Second Integration
EIy = ∫∫M
The second integration y gives the Deflection of the Beam at any distance x.
2. Area Moment Method
(i) Theorems of AreaMoment Method
3. Method of Superposition
The method of superposition, in which the applied loading is represented as a series of simple loads for which deflection formulas are available. Then the desired deflection is computed by adding the contributions of the component loads(principle of superposition).
1. Concentrated load at the free end of cantilever beam
2. Concentrated load at any point on the span of the cantilever beam
3. Uniformly distributed load over the entire length of the cantilever beam
4. Triangular load, full at the fixed end and zero at the free end
5. Moment load at the free end of the cantilever beam
6. Concentrated load at the midspan of simple beam
7. Uniformly distributed load over the entire span of simple beam
8. Triangle load with zero at one support and full at the other support of simple beam
9. Triangular load with zero at each support and full at the midspan of simple beam
33 videos27 docs29 tests

1. What is beam deflection and why is it important? 
2. How is beam deflection calculated? 
3. What factors affect the deflection of a beam? 
4. How can beam deflection be minimized? 
5. What are the limitations of beam deflection calculations? 

Explore Courses for Mechanical Engineering exam
