A cooling tower is disclosed that is resistant to lateral displacement while minimizing the number and type of parts, and while limiting the amount of horizontal bracing. The cooling tower has a fiber reinforced material skeletal frame. Moment-transferring connections are provided in the connections between the elements of the skeletal frame and between the skeletal frame and the base on which it sits. Further cost savings may be realized by using separable parts made of wood instead of fiber reinforced material. The moment-transferring connections between the frame members are made by bonding the joined elements to a mounting plate. The moment-transferring connections between the frame and the base are made by bonding the frame members and the base to footings. A method of constructing such a cooling tower is also disclosed. Diagonal bracing may be provided at preselected joints.