A Ridge Beam and a Ridge Board are both located at the ridge but they serve very different purposes for very different applications.
A ridge beam is a structural member used to support the ends of the rafters at the ridge, transferring it's loads to posts or gable end walls. Ridge beams are required by code if the roof slope is less than 3 in 12 (IRC section R802.3). Ridge beam sizing is based on the span of the beam between supports, and the amount of roof load supported by the beam.
A ridge board is a non-structural member that serves as a prop for opposing rafters to rest against and connect to. Ridge boards can only be used in roofs with slopes from 3 in 12 up to 12 in 12. Ridge boards shall be at least 1 inch nominal thickness and not less in depth than the cut end of the rafter (IRC section R802.3).
Chapter 8 of the International Residential Code (IRC) prescribes the elements for a type of roof frame known as a 'compression roof'. The figure below shows selected code sections that must be considered when designing this type roof.
Figure R802.5.1 - Braced Rafter Construction
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