As often seen when reviewing residential building plans..........most often by architect-only...............there is no design for hip and valley beams.......nada.
"Reasons" for this result, in general order of importance, include; (1) Basic lack of knowledge, (2) Typical safety margin for usual design methods, and (3) Lack of adequate code provisions.
Typical safety margin often amounts to "luck". Yet, most important is that safety margin does not necessarily apply at all when basic concept is completely missed.........which is that hip beam and valley beam will act as beam element for conditions that may not be easy to control.......and may only occur after many years of service........especially for heavy snow load.
Hip beam tends to be less likely to act as beam element as long as connections at low ends of supported rafters have adequate design shear capacity to resist outward lateral thrust force, especially with snow on roof. Hip beam will then tend to act as ridge board in compression.......not as beam-element. However, even small slippage at low ends of rafters can change this condition very quickly......such that conservative design is important for long-term performance. Also wind uplift force reverses effects.......so that for wind uplift, hip beam essentially acts like valley beam for downward force!
Valley beam should always be designed as beam-element since, for downward force (load) rafters are trying to pull away from valley beam...........and, risk of heavy snow load is much, much greater as snow tends to collect in valley. Also, roof leaks tend to occur in valleys, resulting in decay at low ends and loss of shear capacity for nailed connections.
Other than conceptual issue..........difficulty for effective design is need to consider variable distributed load instead of uniform (constant-value) loading. However, relatively standard design methods are of course available.
Most important are the following issues for design of hip beam and valley beam;
(1) Provision of supports. All-too-often, no support is provided at or near high end of beam. Intermediate supports may also be required.
Each support ...........typically in attic space........must of course also have adequate support.........provided by attic floor framing and elements below.......down to adequate foundation elements.
(2) Consideration of wind uplift force...........which requires adequate connections between hip beam or valley beam and each support.............as well as adequate connection between each support and elements below. For wind uplift force, bottom edge of beam has NO LATERAL BRACING..........which can greatly reduce design bending capacity compared to conditions for downward force. Load Duration Factor of 1.6 (allowable for wind-load case) mitigates this factor somewhat.........but may not be enough, especially for long beams.
For conservative approach...........which is of course warranted............all hip and valley members should be designed as beam-elements.........with adequate strength, stiffness and.........supports!! Horizontal length is applicable for typical design as beam.
