For the traditional bicycle frame, the rear triangle that supports the back wheel is stable if it is treated as a pinned structure. The section bounded by the top, seat, down, and head tubes is not stable in this approximation and depends upon the welded joints being able to resist moments. With the frame dimensions shown in the diagram and considering a rider with a weight of 150 lbf enables determination of the reaction forces, R₁ and R₂.

Take W₁ as 120 lbf and W₂ as 30 lbf and use a moment balance about the point D:
(30 x 24.8) + (120 x 30.8) = (R₂ x 42)
so that: R₂ = 105.7 lbf.

Using the vertical force balance:
(R₁ + 105.7) = (120+ 30)
so that: R₁ = 44.3 lbf

All the forces acting on the structure are now known and the loads carried by the tubes can be determined.

From: McMahon & Graham,
"The Bicycle & the Walkman," Merion (1992)