# # Force

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

Using these and integrating over the element gives

The load intensity is a linear function in the range

Or

where

Substituting equation 3 in 1 for end 0

so

Substituting equation 3 in 2 for end 1

so

Roark Formulas for Stress and Strain, Table 3 (1.e)