Hinged cantilever beam In the hinged cantilever design, only one end of the beam, the root, is attached to a support by some sort of hinge joint.  An external load applied to the free end of the beam causes it to rotate around the point where it is hinged.  In diagrams of this beam a triangle symbol is usually placed at the end of the beam that is hinged to denote that it can rotate about the support but it cannot move vertically or horizontally (Fig. 137 ). click image to enlarge

.

 click image to enlarge Fig. 136 - Hinged cantilever beam  (scale model) Fig. 137 - Diagram - hinged cantilever beam

.

Examples of hinged cantilever beams include hinged doors, draw bridges, ailerons, flaps,

bird wings, arms, etc.

.
 Fixed cantilever beam If one end of a beam is fixed to its support so that it cannot rotate it is called a fixed cantilever beam.  Examples include diving boards, airplane wings, posts, poles, masts,

trees, branches, etc.  When an external load is applied perpendicular to the free end of the

beam it will exert a force that will try to make the beam rotate in the direction of the force.

But because the root of the beam is fixed to a support it cannot rotate freely and the beam

will tend to bend instead.  The force will be distributed along the length of the beam as

tensile and compressive stresses and will be concentrated at the root..  The amount of force

exerted on the root depends on the size of the load and the distance from the root that it is

applied.  This is called the bending moment and can be expressed mathematically as:

M = P L                where   M = bending moment

P = load (expressed in Newtons or lbs.)

L = distance from the root (expressed in meters or feet)

.

Back to Knowhere

 Page 90 - Building Stability - Cantilever beams