The rafter. The member runs 6 m along X and 1.608 m up, so its length is,
L=cos15°6=0.96596=6.212 m Every distributed load here is given per metre of that length, so it's 6.212 m we multiply by, not the 6 m on plan.
The snow, in global Z. This is the trapezoid from the Beams and frames pathway, and the check is the same. The total load is the area of the trapezoid,
W=2w1+w and its resultant sits at the centroid, nearer the heavy end, which measured along the member from the eaves is,
sˉ=3(w Taking moments about the eaves pin, the load and the ridge reaction are both vertical, so their lever arms are horizontal distances and the cosines cancel. The ridge reaction is,
Rridge=LWs against the solver's 18.635 kN, and the eaves takes the other 43.48−18.63=24.85 kN against the solver's 24.847 kN. Remember that only the part of a vertical load that acts across the rafter bends it, cos15° of it. The rest, sin15°, acts along the rafter and shows up as an axial force that changes along the member.
The wind, in local y. The pressure is uniform and normal to the slope, so the total is simply,
W=5×6.212=31.06 kN acting at the midpoint of the rafter, perpendicular to it. Resolving it, the vertical part is 31.06cos15°=30.00 kN and the horizontal part is 31.06sin15°=8.04 kN. The ridge roller holds nothing along X, so the whole horizontal part goes to the eaves pin, and that's the 8.038 kN the solver reports there.
To split the vertical part between the supports, we take moments about the eaves pin. The resultant is normal to the member and acts 3.106 m along it, so its lever arm about the eaves is simply 3.106 m,
Meaves=31.06×3.106=96.46 kNm (the same answer comes from the components: 30.00×3=90.00 kNm from the vertical part, plus 8.04×0.804=6.46 kNm from the horizontal part acting half the rise above the eaves). The ridge reaction is vertical and 6 m away on plan, so,
Rridge=696.46=16.08 kN which is the solver's 16.077 kN, and the eaves takes 30.00−16.08=13.92 kN of the vertical part, against 13.923 kN. So the roller carries more than half of a uniform load. The horizontal part of the pressure acts above the eaves, so it tends to rotate the rafter about the pin, and the ridge reaction has to resist that rotation. Since the whole load acts across the member this time, all of it bends the rafter, and the peak moment is,
M=8wL2= against the solver's 24.115 kNm at the midpoint.
The sideways beam. The beam is level and the load is uniform and horizontal, so the reactions are wL/2=5×4/2=10 kN each, in Y, and the peak moment is wL kNm, both exactly what the solver reports. The difference from every beam so far is the axis the moment acts about. The load acts across the flanges, so the second moment of area that resists it is the minor one, cm m. The sideways deflection at midspan is therefore,
δ=384EIy against the solver's 10.388 mm. The same 5 kN/m acting downwards would be resisted by Iz=8,500 cm4 and deflect mm, eleven times less. So, a beam that is comfortably stiff enough under gravity loads still needs its own deflection check if it also carries a sideways load.
The self-weight. The catalogue lists a UB 305 x 165 x 40 at 40.3 kg/m, so its weight per metre is 40.3×9.81=395 N/m, or 0.395 kN/m. Along the rafter that's 0.395×6.212=2.45 kN, split equally, 1.23 kN at each end against the solver's 1.227 kN. Along the beam it's kN, 0.79 kN at each end against 0.790 kN. The moments follow the same rules as the other cases. The beam's is kNm, and the rafter's is the vertical load's component across the member, kNm, against the solver's 1.840 kNm. In other words, self-weight is a global load in negative Z like any other, per metre of member axis, and it bends a sloping member by its cosine.