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The Sizer analysis engine generates reactions that are assumed to be vertical, for transfer to supporting members.
For dead loads, which are directed vertically (see Direction and Intensity of Loads), it divides by the cosine of the slope angle to recover the full load intensity that was diminished for perpendicular shear and bending design. For wind loads the undiminished loads are multiplied by the cosine of the slope angle to take the vertical component of the reaction, the horizontal component being left for lateral design that is not part of the Sizer program. The example shown below is for dead loads.
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In summary:
Wind loads
These are assumed to be directed normal to the member, so the reactions generated are adjusted by multiplying by the cosine of the slope angle to to take their vertical component.
Dead, live, snow, (and earthquake for Canada) loads
These are assumed to be directed vertically, and the reactions are adjusted by dividing by the cosine of the slope angle so that they fully account for the vertical loading on the beam.
Total reactions vs. loads
In evaluating any member, it is useful to know what the total reactions will be on a sloped member compared to the total applied loads. The following applies to line loads:
Live loads, Snow Loads, (and Earthquake loads for Canada)
The program uses the input loads on the projected span lengths, adjusts the direction, then adjusts the reaction back again, so the reactions will equal the intensity times the projected length.
Dead loads
The program uses the input loads on the sloped length, adjusts the direction, then adjusts the reaction back again, so the reactions will equal the loads on the projected length divided by cosine of the slope angle.
Wind loads
The program applies the loads to the sloped length, makes no adjustment for direction, but adjusts the reactions so as to negate the sloped length. The reactions will equal the load intensity times the projected length (the vertical component of the wind load).
Therefore, if the same load intensity is applied for live, dead, and wind loads, the reactions will be greater for dead loads than for the other two types of loads.