For structures consisting of multi$-$level roofs, snow on the lower roofs often tends to drift toward the upper building structure, such CS Fig. $5\mathrm{.}1$ Enclosed parking structure with the design snowdrift roof load.

STRATEGY:

Because the beams are equally spaced, the load applied along the length of one beam will be the given roof load multiplied by the

$1\mathrm{.}2-$m beam spacing. $($In other words, this is the portion of the total roof load that acts on one of the beams.$)$ CS Fig. $5\mathrm{.}2$ shows

the resulting load, along with the support conditions to be assumed for the beam. The magnitude of this distributed load's resultant

is the area under the load curve, and its location is the centroid of the load area. The total load area can be broken up into smaller

areas of simple geometry and used to calculate the magnitude and location of the resultant. This resultant can then be

applied to a free$-$body diagram of the beam to determine the support reactions. MODELING AND ANALYSIS:

a$.$ Equivalent Concentrated Load. Divide the area under the load curve into a rectangle and a triangle $($ CS Fig. $5\mathrm{.}3),$ and

construct the table below.

The equivalent concentrated load $($ CS Fig. $5\mathrm{.}4)$ is

$W=34\mathrm{.}8kN$

Its line of action is located at a distance

$\stackrel{}{x}=5\mathrm{.}93mto$ the right $ofA$ CS Fig. $5\mathrm{.}3$ The load modeled as a triangular and a rectangular area.CS Fig. $5\mathrm{.}3$ The load modeled as a triangular and a rectangular area.

as is shown in $$ CS Photo $5\mathrm{.}1.$ ASCE Standard $7^{**},$ used by structural engineers in the U$.$S$.,$ addresses such drifting in its

requirements governing snow loads. For example, let's consider an enclosed parking structure located in Duluth, Minnesota, that

has a $10-$m$-$long flat roof attached to a taller building. The roof is supported by beams equally spaced at $1\mathrm{.}2m.$ Following the

provisions of ASCE $7$ as a guide, we will assume a combination of building geometry, wind exposure, roof thermal characteristics,

and function of structure that result in the drifting snow load shown in CS Fig. $5\mathrm{.}1.$ For this distributed loading, let's determine

the magnitude and location of the resultant load that acts on one of the beams. Then, treating the beam's connection at $B$ as a roller

and the connection at $C$ as a pin, we'll determine the support reactions at these locations.