Fixing both ends of a beam to its supports stiffens the

beam against bending induced stresses just as it does for

columns.  Fixing the ends complicates detailed analyses

of the stresses and reactions occurring in the beam in

comparison to a simply supported beam.  However, in

general, fixed beams behave similarly in how factors

such as the moment of inertia, modulus of elasticity, and

(demonstration models)

bending moment affect their load bearing characteristics.

Fig. 143 - Fixed end beams

Loaded in middle

Uniformly loaded

.

Simply supported beam

              M_max = P L

               M_max = P L²

                            4

                             8

.

              M_max = P L

               M_max = P L²

                            8

                            24

            where M_max = maximum bending moment,   P = load,   L = length of beam

.

Notice that simply fixing the ends of a beam reduces

the bending moment by a factor of two to three.  The

graph to the right shows that M_max is the greatest in

the middle of a uniformly loaded, simply supported

beam since this is the farthest point from the supports.

From there it gradually reduces to zero at the ends,

which can rotate slightly and thus do not experience a

bending moment.  Of course a beam can be loaded

Fig. 144 - Bending moment

non-uniformly which will affect the bending moment.

diagram of a uniformly loaded,

Only beams loaded in the middle or uniformly are

simply supported beam

treated in this lesson since they are the simplest cases.

Page 94 - Building stability - Beam bending moment