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

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

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Long Span Roof Load Path Load rests on roof deck 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. The joists transfer their loads to the supporting truss girders. 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. The pier supports half the area supported by the truss girder plus area from other structural elements that it supports.

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Mezzanine Floor System Metal Deck/Slab System Supports Floor Loads Above Joists Support Floor Deck Girders Support Joists Columns Support Girders 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. The girders are not single span so the tributary area for the columns cannot be graphically determined

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Cantilever Loads Deck carries load to edge joist and wall. 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. 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.

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End Wall Framing 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 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. The beam-columns transfer their lateral loads equally to the roof and foundation.

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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.

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