An umbrella has a shaft having upper and lower ends, a slide piece, and a head piece. One of the pieces has an upper part and a lower part having faces that are engaged together and that form a plurality of seats of predetermined diameter spaced angularly about the shaft. The parts are also formed at each seat with a radially outwardly open and axially extending notch of an angular width substantially smaller than the diameter of the respective seat. They are fixed together at the faces. Respective rib or strut elements each have a shaft of a width at most equal to the notch width and a head of a diameter greater than the seat diameter. The heads are received in the seats and the shafts project outward from the respective seats through the respective notches. A standard canopy is fitted over the ribs outside the head piece.