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Madison Industries <br />Designed by: ML/JFB <br />August 4, 2016 <br />Job No: WCA17860-1 <br />Customer: Mobil Fueling Canopy <br />Structure: 65'-0" x 54'-4" (4) Column Canopy <br />Location: Tracy, CA 95377 <br />Sheet 18 <br />Roof Support Beam B2, cont. <br />Factored Service Load Moments: <br />Bottom flanges cantilever & span in compression: <br />Case 1: Full DL + LL over entire beam --Checks critical negative bending in span & cantilever <br />mull (cant) = Mu"(span) = max{[(Wu2)a2/2 + (P1u2)(a)]AW.2)b2/2 + (P2u2)(b)I} = 49.9 ft -k <br />Top flange span in compression: <br />Case 2: Full DL + LL over span; DL only on cantilever -- Checks crit. pos. bending stress in span <br />Case 2A: Actual loads x'= 13.00 ft <br />Mu'(span) = [R1 Case2(fact)-(0.9P1 pL+0.9WoLa)](x')/2 - [2(0.9P1 DJ+0.9WpLa](a)/2 = 31.5 ft -k <br />Case 26: For roof members <br />Is this a roof member? (y/n) y <br />Mut <br />t(span) = (w.1)(L2)/8 + P'L/4 = 25.5 ft -k <br />Where P'= (1.4)(200 lbs) if tributary area < 200 ft2 or <br />(1.4)(2000 lbs) for larger tributary areas <br />Factored moment for design of span top flange = Mu'(span) = 31.5 ft -k <br />Bottom flange span & top flange cantilever in compression: <br />Case 3: Full DL + WIND UPLIFT over entire length -- Checks crit. neg. bending stress in span <br />& crit. pos. bending stress in cantilever <br />Case 3A: Span <br />Case 313: Cantilever <br />Factored service load design moments: <br />Mull <br />l(span) = (Wu3)(L2)/8 = <br />Mu'(cant) = (Wu3)(a2)/2 + max[P1u3a,P2u3b] = <br />Top flange span in compression: <br />Mu'(span) = <br />Bottom flange span in compression: <br />Mu"(span) = <br />Top flange cantilever in compression: <br />Mu'(cant) = <br />Bottom flange cantilever in compression: <br />Mull (cant) = <br />Unbraced Length Limits: <br />Lp = 300ry/sgrt(Fy) = <br />L, = ryX,/FL(1+sgrt(1+X2FL2))1i2 = <br />3.68 ft <br />9.68 ft <br />Where: X, = (7E/SX)(EGJA/2)" = 1612 <br />X2 = (4C,/ly)(SX/GJ)2 = 0.027 <br />FL = (FY_ 10) = 40 ksi <br />31.5 ft -k <br />49.9 ft -k <br />26.5 ft -k <br />49.9 ft -k <br />20.3 ft -k <br />26.5 ft -k <br />JUN 08 2011 <br />El`V173O%i'r-!' F,= ALTH <br />