Moment

Point moment at position a

From Roark, the end rotations for a point load at are

Letting the distance from end 1 be these equations can be rewritten

Varying load from with intensity and .

Using the equations above from Roark the end rotations for a point moment at are

Using these and integrating over the element gives

As with the forces the moment intensity can be written as

where

Substituting equation 6 in 4 for end 0

so

Substituting equation 6 in 5 for end 1

so

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Roark Formulas for Stress and Strain, Table 3 (3.e)