August 2009

Problem 612
Compute the midspan value of EI δ for the beam loaded as shown in Fig. P-612.
 

Problem 611
Compute the value of EI δ at midspan for the beam loaded as shown in Fig. P-611. If E = 10 GPa, what value of I is required to limit the midspan deflection to 1/360 of the span?
 

Problem 610
The simply supported beam shown in Fig. P-610 carries a uniform load of intensity w_o symmetrically distributed over part of its length. Determine the maximum deflection δ and check your result by letting a = 0 and comparing with the answer to Problem 606.
 

Problem 609
As shown in Fig. P-609, a simply supported beam carries two symmetrically placed concentrated loads. Compute the maximum deflection δ.
 

Problem 608
Find the equation of the elastic curve for the cantilever beam shown in Fig. P-608; it carries a load that varies from zero at the wall to w_o at the free end. Take the origin at the wall.
 

Problem 607
Determine the maximum value of EIy for the cantilever beam loaded as shown in Fig. P-607. Take the origin at the wall.
 

Problem 606
Determine the maximum deflection δ in a simply supported beam of length L carrying a uniformly distributed load of intensity w_o applied over its entire length.
 

Problem 605
Determine the maximum deflection δ in a simply supported beam of length L carrying a concentrated load P at midspan.
 

The double integration method is a powerful tool in solving deflection and slope of a beam at any point because we will be able to get the equation of the elastic curve.
 

In calculus, the radius of curvature of a curve y = f(x) is given by
 

Deflection of Beams
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.