Load Paths and Tributary Area Examples © T. Bartlett Quimby, 2007 A Beginner’s Guide to Structural Mechanics/Analysis

Alaska State Fairgrounds Farm Exhibits Building Palmer, Alaska Long Span Roof Truss Girders Mezzanine Area Awning Roof Awning Roof with Hip Beam A large open exhibit building with long span truss girders.

Long Span Roof Load Path Roof deck transfers load to supporting joists. Each joist supports an area equal to its span times half the distance to the joist on either side. Load rests on roof deck The joists transfer their loads to the supporting truss girders. The pier supports half the area supported by the truss girder plus area from other structural elements that it supports. Each truss girder supports an area equal to its span times half the distance to the girder on either side. The truss girders transfer their loads to the supporting piers and columns. Long Span Roof Load Path

Mezzanine Floor System The girders are not single span so the tributary area for the columns cannot be graphically determined The area tributary to a joist equals the length of the joist times the sum of half the distance to each adjacent joist. The area tributary to a girder equals the length of the girder times the sum of half the distance to each adjacent girder. Columns Support Girders Girders Support Joists Metal Deck/Slab System Supports Floor Loads Above Joists Support Floor Deck Mezzanine Floor System

Exterior joist carried load to the supporting cantilever beam ends The point load consists of the reaction from the two supported joists which equals the tributary area (1/2 the cantilever span times the spacing of the cantilevers) times the pressure load on the floor plus the self weight of the joist. Exterior joist carried load to the supporting cantilever beam ends The load diagram for the cantilever (excluding self wt) consists of a single point load at the end of the cantilever. Deck carries load to edge joist and wall. Cantilever Loads

End Wall Framing The beam-columns do not support any roof load, they are here to resist lateral forces that they receive from the girts. They support an area that extends from locations half way to the adjacent beam-columns on each side and from floor to roof as shown. For lateral pressures, the siding spans between the horizontal girts (yet another fancy word for a beam!) The girts support half the siding to the adjacent girts. This is the tributary area for one girt. The girts transfer their lateral load to the supporting beam-columns. The beam-columns transfer their lateral loads equally to the roof and foundation.

Hip Beam This beam picks up load from joists of varying lengths. In this case the resulting load distribution would have a linearly varying component. The illustrated area is part of the tributary area at the roof deck level. The hip beam also picks up a point load reaction from a pair of the roof girders.