It is easy and intuitive to imagine that a beam must resist tensile forces along the horizontal strength axis. It is also easy to imagine a beam must resist vertical compressive forces, but horizontal compressive forces are not normally a primary concern. Those compressive forces though, on the horizontal axis are a more important consideration.
It is not intuitive, in fact most builders do not think about the compressive forces on the horizontal strength axis of a beam. The weakest part of a beam, even in most cases where over-notched or over-bored, is in the horizontal center. That part is intuitive, but the reason a beam resists that downward force which tries to flex or break the beam, is because the top of the beam is conversely being put into compression. That strength to resist the flexural force downward from above comes from a combination of tensile and compressive resistance mating at the horizontal strength axis of a beam (or girder). The middle horizontal center of the beam becomes the point of transfer of the stress and resistance. The bottom and top of a horizontal beam carry the highest concentration of stress, that's why the building Code prohibits joist notching, in most cases.
The steel girder in the photo below spans over and between the column and footing centered bearing points. The weakest point in that span is about the middle.
You can see markings on top of the girder showing the general direction of these forces. The tensile forces push away from the center of the load or bearing force above. Meanwhile the girder horizontal axis resists that internal stress in the beam by transferring the tensile force and resisting the compressive force.
Tensile failure is common in wood or engineered lumber beams, where you can see splitting in the bottom of a joist, for example. Compressive failure can be seen in buckling of the top flange in undersized steel beams, for example. Failure of undersized beams or girders is somewhat common, especially in historic or market cost construction.
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