DERIVATION OF AWWA D100 ROOF THICKNESS EQUATION AWWA D100, EQ 3-36 (D100-21) For supported roofs, this formula prescribes the maximum spacing of rafters or stiffeners for roof dead load combined with the greater of roof live load or snow load. (Eq 3-36) Fy t WD 36000 psi 0.1875 in. 7.66 psf WL 25 psf WD+L 32.66 psf published minimum yield strength of ASTM A36 plate standard minimum roof plate thickness for 3/16" roof plate standard roof live load unless reduction is allowed combined roof dead and standard live load This equation was empirically derived by analyzing a 1" strip of roof plate spanning between rafters as a bending member and considering partially fixity at the point of support by using a rule of thumb value for the bending moment = W·L²/10 and an allowable bending stress of 0.75·Fy for plate bent the easy way (AISC). M = W L² / 10 and Fb = 0.75Fy Coefficient, K = 2545.584 With the coefficient so calculated, it was then refined to match up to the historical spacing of L = 84 inches for 3/16" roof plate and a Live Load of 25 psf. Refined Equation Coefficient = 2560.272 Rafter spacing calculated with refined coefficient L = 84.00 in. So, the coefficient of 2,560 was rounded up to 2,575 so as not to imply a greater level of accuracy or analytical correctness than should be applied to an empirical formula. NOTE: Deflection associated with this structural model does not hold to the bending theory underlying the equation, but it is nonetheless useful to establish a practical limit for normal loading conditions. It would probably be considered reasonable to use a catenary analysis in lieu of this equation for situtations with high roof loading. © Leslie D. Scott, P.E. 2021 Rev.0 0.226806 psi CALCULATED DEFLECTION δ = 5w·L⁴ / (384·E·I) δ = 9.229731 © Leslie D. Scott, P.E. 2021 Rev.0
