Application of Double Integration and Superposition Methods to Restrained Beams

Contents

  1. Superposition Method
  2. Double Integration Method
Contents 1 - Superposition Method 2 - Double Integration Method
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Superposition Method

There are 12 cases listed in the method of superposition for beam deflection.

  • Cantilever beam with...
    1. concentrated load at the free end.
    2. concentrated load anywhere on the beam.
    3. uniform load over the entire span.
    4. triangular load with zero at the free end
    5. moment load at the free end.
  • Simply supported beam with...
    1. concentrated load at the midspan.
    2. concentrated load anywhere on the beam span.
    3. uniform load over the entire span.
    4. triangular load which is zero at one end and full at the other end.
    5. triangular load with zero at both ends and full at the midspan.
    6. moment load at the right support.
    7. moment load at the left support.

See beam deflection by superposition method for details.
 

Restrained Beams

Restrained Beams
In addition to the equations of static equilibrium, relations from the geometry of elastic curve are essential to the study of indeterminate beams. Such relations can be obtained from the study of deflection and rotation of beam. This section will focus on two types of indeterminate beams; the propped beams and the fully restrained beams.
 

01 - Highest point of projectile as measured from inclined plane

Problem 01
A projectile is fired up the inclined plane at an initial velocity of 15 m/s. The plane is making an angle of 30° from the horizontal. If the projectile was fired at 30° from the incline, compute the maximum height z measured perpendicular to the incline that is reached by the projectile. Neglect air resistance.