A rib connector is provided that has a first arm, a second arm, and a transverse member. The first arm has an inner wall, a first recess in the inner wall, and an inclined surface that extends toward the first recess. The second arm has an inner wall and a second recess. The second recess is positioned opposite to the first recess. The transverse member is located between the first arm and the second arm. The transverse member connects the first arm and the second arm. The transverse member is disposed adjacent to a space located between the first and second arms. The space is configured to receive an umbrella rib. A varying distance is provided between the inclined surface and the inner wall of the second arm such that the distance is less at a first position along the inclined surface than at a second position along the inclined surface. The first position is between the first recess and the second position.