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.
 

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

Problem 10
In a triangle ABC, if   $\dfrac{2 \cos A}{a} + \dfrac{\cos B}{b} + \dfrac{2 \cos C}{c} = \dfrac{a}{bc} + \dfrac{b}{ca}$,   find the value of angle $A$.
 

Problem 1010
A stone is thrown vertically up from the ground with a velocity of 300 ft per sec (91.44 m/s). How long must one wait before dropping a second stone from the top of a 600-ft (182.88-m) tower if the two stones are to pass each other 200 ft (60.96 m) from the top of the tower?
 

Problem 1019
The motion of a particle is given by the equation $s = 2t^4 - \frac{1}{6}t^3 + 2t^2$ where $s$ is in meter and $t$ in seconds. Compute the values of $v$ and $a$ when $t = 2 \, \text{ sec}$.