Move a point load along a simply supported beam and watch its shear and bending moment diagrams redraw instantly — the direct, visual link between where load sits and where the beam is actually most stressed.
Structural analysis determines the internal forces (shear and bending moment) within a structural member as a function of position, given its loading and support conditions. Shear and moment diagrams are the standard tool for visualizing these internal forces along a beam's length — and they directly show where a beam experiences its highest internal stress, which is exactly where a design needs to be checked most carefully.
Shear force at any cross-section is the net transverse (perpendicular to the beam) force the material at that section must resist to stay in equilibrium — as shown above, it jumps abruptly at the point load location, since the internal force needed to carry the load to the supports changes discontinuously right where that load is applied.
Bending moment at a cross-section is the internal rotational (bending) effect the material must resist — mathematically, it's the integral of the shear force diagram up to that point, which is exactly why the moment diagram peaks precisely where the shear diagram crosses zero (directly beneath the point load). This peak moment location is where a beam experiences its highest bending stress and is the critical location a structural engineer checks against the material's allowable stress.
Moving the load along the span, as demonstrated above, redistributes the support reactions (a load closer to one support puts more reaction force on that support) and shifts where the maximum moment occurs and how large it is — a load at midspan produces a different, generally larger, maximum moment than the same load positioned near a support. This is exactly why structural design considers the full range of possible load positions (moving/live loads), not just one fixed case.
Mathematically, bending moment is the integral (running sum) of shear force along the beam, and a function's integral reaches a local maximum or minimum exactly where the function itself crosses zero — this is why, wherever the shear diagram crosses from positive to negative (as it does directly under a point load), the moment diagram reaches its peak at that same location.
The shear force diagram jumps discontinuously by an amount equal to the point load's magnitude — the internal force redistributes abruptly right at that point, unlike gradual changes seen with distributed loads, which produce a sloped (not stepped) shear diagram instead.
The full moment diagram shape shows how bending stress varies along the entire beam length, not just at one point — this matters for selecting where to place material efficiently (a beam can often be tapered or have reduced cross-section where moment is lower), and for checking multiple potentially critical sections, not just the single absolute maximum.
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