Simply supported beam

A beam that is supported at both ends with moveable joints is said to be simply supported.

One end of the beam can rotate slightly around a support with a hinge joint, called the

fixed node.  The other end rests on some sort of roller or bearing surface, called the rolling

node.  Fig. 141 shows how it is diagrammed.  Although the fixed node allows that end of the

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 fixed node                      rolling node ( demonstration model) Fig. 141 - Simply supported beam

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beam to rotate slightly it cannot move vertically or horizontally.  The rolling node allows the

other end to move horizontally and rotate slightly but it cannot move vertically.  Examples

of simply supported beams include beam bridges, truss bridges, gangways, etc.

The following shows an idealized model of a simply supported beam before and after a

load has been applied to it.  The load is seen to impart a bending moment to the beam that

 subjects its upper edge to compressive stresses that tend to shorten it and subjects its lower edge to tensile stresses that tend to lengthen it.  In between there is a gradual shift from compressive to tensile stresses.  Notice that the purple line passing through the middle of the beam, called the neutral axis, remains the same length, which indicates the absence of these stresses there. The shift in stresses from compression to tension (training aid) causes the upper section of the beam to tend to Fig. 142 - Idealized model of slide past the lower section.  This induces another a simply supported beam stress in the beam called shear.  This horizontal shear stress is greatest along the neutral axis.

Solid beams have very high shear strengths.  Therefore shear stress is not a major factor in

beam design except for very tall, thin beams.

The importance of providing a rolling node for one end of the beam is demonstrated by

the model as that end of the beam moves in and out when the load is applied and removed.

If that end is not allowed to move additional stresses are placed on the beam and it will

no longer behave as a simply supported beam.

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