Problem 657 | Beam Deflection by Conjugate Beam Method

Problem 657
Determine the midspan value of EIδ for the beam shown in Fig. P-657.
 

657-conjugate-beam-method.gif

 

Problem 656 | Beam Deflection by Conjugate Beam Method

Problem 656
Find the value of EIδ at the point of application of the 200 N·m couple in Fig. P-656.
 

656-conjugate-beam-method.gif

 

Problem 655 | Beam Deflection by Conjugate Beam Method

Problem 655
Find the value of EIδ under each concentrated load of the beam shown in Fig. P-655.
 

655-conjugate-beam-method.gif

 

Problem 654 | Beam Deflection by Conjugate Beam Method

Problem 654
For the beam in Fig. P-654, find the value of EIδ at 2 ft from R2.
 

654-conjugate-beam-method.gif

 

Problem 653 | Beam Deflection by Conjugate Beam Method

Problem 653
Compute the midspan value of EIδ for the beam shown in Fig. P-653. (Hint: Draw the M diagram by parts, starting from midspan toward the ends. Also take advantage of symmetry.
 

653-conjugate-beam-method.gif

 

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.
 

Conjugate Beam Method | Beam Deflection

Slope on real beam = Shear on conjugate beam
Deflection on real beam = Moment on conjugate beam

 

Properties of Conjugate Beam

Otto Mohr
Engr. Christian Otto Mohr
  1. The length of a conjugate beam is always equal to the length of the actual beam.
  2. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.

Strain Energy Method (Castigliano’s Theorem) | Beam Deflection

Alberto Castigliano (Catigliano's Theorem)
Engr. Alberto Castigliano

Italian engineer Alberto Castigliano (1847 – 1884) developed a method of determining deflection of structures by strain energy method. His Theorem of the Derivatives of Internal Work of Deformation extended its application to the calculation of relative rotations and displacements between points in the structure and to the study of beams in flexure.
 

1012 Train at constant deceleration | Rectilinear Translation

Problem 1012
A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its initial velocity and its constant acceleration.
 

02 Problem involving angle and median | Properties of a Triangle

Problem 02
From the figure shown below, angle CAD = angle BCD = theta and CD is a median of triangle ABC through vertex C. Determine the value of the angle theta.
 

02-median-angle-theta.gif

 

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