Fixed beam

 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

The bending moment exerted by load placed in the middle of a simply supported or fixed

beam can be derived from the following equations:

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 Loaded in middle Uniformly loaded . Simply supported beam Mmax = P L Mmax = P L2 4 8 . Beam fixed at both ends Mmax = P L Mmax = P L2 8 24 where Mmax = maximum bending moment,   P = load,   L = length of beam
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 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 Mmax 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.

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 Page 94 - Building stability - Beam bending moment