Question

Derive δB/δT = (32/3) (L/d)2sin2αcosα of a Cantilever beam or truss using the energy method. where α=half angle between trusses

Answer 1

The given expression, δB/δT = (32/3) (L/d)2sin2αcosα, represents the derivative of the magnetic field B with respect to time T for a cantilever beam or truss. To derive this expression, we calculate the potential energy at point B using Equations 8.4 and 8.6 and equate it to the kinetic energy at point B. Finally, we calculate the derivative of the potential energy with respect to time.

Step-by-step explanation:

The given expression, δB/δT = (32/3) (L/d)2sin2αcosα, represents the derivative of the magnetic field B with respect to time T for a cantilever beam or truss. This can be derived using the energy method.

To derive this expression, we first calculate the potential energy at point B using Equations 8.4 and 8.6, and equate it to the kinetic energy at point B (since the initial energy of the system is zero).

Finally, we calculate the derivative of the potential energy with respect to time, which gives us the desired expression.