Abstract: An all-purpose frame 1 is provided which extends at an angle from a rear-wheel fork 5 attachable to the rear axle of a bicycle to swivelable steering connection 6 to a front-wheel 17 of the bicycle. The frame 1 can be a rectangular-tube beam 40, an I beam 42, a channel beam 44, a foam beam, a honeycomb beam or such other form of beam as provides a separation of top girders 2 and bottom girders 3 with a strucutral positioning member 4. Beam material can be ferrous alloy, aluminum alloy, titanium alloy, adhered fibers, and various combinations of foamed, honeycombed or otherwise porous materials in combination with relatively solid girders. Connection of the rear-wheel fork 5 to the frame 1 can be resilient vertically for a cushioning spring effect to decrease frame-weight requirement for absorbing impact and increasing rider comfort. The front-wheel fork 7 can be provided with resilient connection for the same reasons.