Solution for Cantilever Propped with a Spring


When a cantilever is propped with a spring at its free end instead of a support, deflection may occur there. Nonetheless, the spring is still considered a support system and therefore, the beam is at first degree of indeterminacy.

By applying force method, we can derive the expression for the spring deformation in terms of beam properties, spring constant and loading. The displacement of free end with spring is calculated for two extreme cases: zero stiffness (cantilever) and infinity stiffness (cantilever propped by an non-deformable support), and the result obtained from force method is validated by the empirical formula for both cases.

The following shows the solution for a cantilever propped with a spring. Watch the video above for full details.
Beam overview
Compatibility equation for force method
Expression for support reaction By based on Hooke's Law
Solution for node B deflection under both analysis cases
Solution for By using compatibility equation
Solution for deflection at node B under actual condition

Post a Comment

0 Comments