to its magnitude it can be derived that the slope of the shear diagram is equal to the magnitude of the distributed load. The relationship, described by Schwedler's theorem, between distributed load and shear force magnitude is: Some direct results of this is that a shear diagram will have a point change in magnitude if a point load is applied to a member, and a linearly varying shear magnitude as a result of a constant distributed load. Similarly it can be shown that the slope of the moment diagram at a given point is equal to the magnitude of the shear diagram at that distance. The relationship between distributed shear force and bending moment is: A direct result of this is that at every point the shear diagram crosses zero the moment diagram will have a local maximum or minimum. Also if the shear diagram is zero over a length of the member, the moment diagram will have a constant value over that length. By calculus it can be shown that a point load will lead to a linearly varying moment diagram, and a constant distributed load will lead to a quadratic moment diagram. Practical considerations In practical applications the entire stepwise function is rarely written out. The only parts of the stepwise function that would be written out are the moment equations in a nonlinear portion of the moment diagram; this occurs whenever a distributed load is applied to the member. For constant portions the value of the shear and/or moment diagram is written right on the diagram, and for linearly varying portions of a member the beginning value, end value, and slope or the portion of the member are all that are required. See also Bending Euler–Bernoulli beam theory Bending moment Singularity function#Example beam calculation References Further reading Cheng, Fa-Hwa. "Shear Forces and Bending Moments in Beams" Statics and Strength of Materials. New York: Glencoe, McGraw-Hill, 1997. Print. Spotts, Merhyle Franklin, Terry E. Shoup, and Lee Emrey. Hornberger. "Shear and Bending Moment Diagrams." Design of Machine Elements. Upper Saddle River, NJ: Pearson/Prentice Hall, 2004. Print. External links Continuum mechanics Diagrams Moment (physics) Structural analysis