TABLE 00.4 FBC Typical Mansard Beam [AAF] Allowable Span of Mansard Screen Enclosure Self-Mating Beams in accordance with requirements of Table 00.4 (and the 005 Aluminum Design Manual) using 6005T5 alloy: Design pressures from Table 00.4 for 130 mph Exposure B with a mean roof height not to exceed 30 ft using a 0/0 screen mesh: Horizontal design pressure (Windward): p w_wall 18psf Horizontal design pressure (Leeward): p l_wall 14psf Deflection limit (L/60) Vertical design pressure: p roof 5psf Vertical Pressure Pressures shown may act in opposite directions, apply various combinations by load case. Windward Horizontal Pressure Rise Eave Height of Enclosure Table 00.4 FBC Leeward Horizontal Pressure Enclosure Projection Notes: 3. Apply horizontal pressures to the area of the enclosure projected on a vertical plane normal to the assumed wind direction, simultaneously inward on the windward side and outward on the leeward side. 4. Apply vertical pressures upward and downward to the area of the enclosure projected on a horizontal plane. 5. Apply horizontal pressures simultaneously with vertical pressures. host structure (S.F.D.) Typical Schematic Section / Mansard Pool Enclosure Post / Beam Determine the allowable beam span based upon the following project frame geometry: Wall height (eave height): h eave 10ft Vertical distance, height overall less eave height: Rise 3.5ft Center to center spacing of mansard frames: Spacing 7.5ft Approxmate allowable span based upon frame geometry and allowable major axis bending moments for various industry beams (preliminary span): Page 1 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] h eave Horizontal force applied inward at screen eave: P eave p w_wall Spacing P eave 675 lbf Induced beam moment (from P): M P P eave Rise M P 8.35kipin Induced beam moment from windward and leeward mansard legs: Rise M Rise Spacing p w_wall p l_wall M Rise 17.64kipin Sum of moments induced into beam from horizontal pressures: M P M Rise 45.99kipin By inspection of induced moment from horizontal force at the eave and the allowable major axis bending moments, determine preliminary span for design check and final allowable span: By inspection, SELECT trial member for span calculation & enter allowable moment: ENTER beam depth of member selected: Major Axis Allowable Bending Moments Section S x (in 3 ) F b (ksi) M a (in kip) X4 SMB 1.000 8.7 8.7 X5 SMB 1.510 9. 13.9 X6 SMB 1.944 9.0 17.4 X7 SMB.45 9..3 X8 SMB 4.441 15.0 66.7 X9 SMB 6.13 17.5 107.0 X10 SMB 8.46 17.4 147.5 M a d 107kip Net moment from allowable less moment induced at shoulder: M preliminary M a M P M Rise 9in in M preliminary 61.01kipin Preliminary allowable span: L preliminary 8M preliminary Spacingp roof L preliminary 395.03 in Page of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Depth ID t w t f Area I x I y Profile 0 1 3 4 5 6 0 1 3 4 5 6 4 "X4 SMB" 0.046 0.1 0.78 0.47 5 "X5 SMB" 0.05 0.116 0.917 3.644 0.59 6 "X6 SMB" 0.05 0.1 1.0 5.66 0.685 7 "X7 SMB" 0.055 0.1 1.9 8.47 0.849 8 "X8 SMB" 0.07 0.4 1.847 16.577 1.15 9 "X9 SMB" 0.08 0.306.357 7.16 1.54 10 "X10 SMB" 0.09 0.374 3.013 4.8 1.96 Self-Mating Beam trial member selected (values from standard sections listed above): Row d in 4 Extrustion profile nomenclature: ID Profile Row1 ID "X9 SMB" Width: b.00in Flange Thickness: t f Profile Row3 in 0.306 in Web Thickness: t w Profile Row in 0.08 in X-axis support: L d L preliminary is the strong-axis support distance. Weak-axis Support: L b 84in is the weak-axis support distance (purlins spacing) Flange Support: Spacing stitching 4in Self-Mating Beams of alloys 6061T6 OR 6005T5 Aluminum; Development of Properties and Allowable Stresses for the specified profile (i.e. properties by formula and table above from Autocad) in accordance with the 005 Aluminum Design Manual Specifications: Open-channel Properties (one side of SMB) Channel Flange Width used for Buckling: b f b c t w b f 1.478 in Web Height used for Buckling: h w d t f h w 8.388 in Member Flange Width: b m b t w b m 1.836 in Total Area: Area ( bd) h w b t w Channel Flange Width: b c 1.560in Safety Factor: n μ 1.95 Modulus of Elasticity: E 10.10010 3 ksi Web Area: Area web t w h w Flange Area: Area flange t f b Page 3 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Check the area equations: Area = Area web Area flange i.e., Area web Area flange Area Area.6 in Torsional Constant: J t f t w b t w d t f bt w dt f t w t f Moments Of Inertia Section Modulus Radius of Gyration I x Profile Row5 in 4 I x I x S x r d x Area I y Profile Row5 in 4 I y I y S y r b y Area Open Channel properties - In weak axis Channel-width in buckling: b cf b c t w Channel Height: d c d t f b c d c t f Center of Gravity to Outer Fiber Distance: C 1 C t f b c d c t f t 1 0.341 in w t f t w C b c C 1 C 1.19 in C 1 t w 3 d c C 1 d c t f Channel Moment of Inertia: I 3 3 t f C yc I 3 yc 0.5 in 4 I yc Radius of Gyration: r yc d c t w t f b c t w r yc 0.463 in d c t f b c t w Area channel d c b c Area channel 1.178 in Page 4 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Allowable Axial Tension Specification 3.4. Tension: F btf 19ksi (Flat elements in uniform tension) Specification 3.4.4 (Tension): F btw 8ksi (Flat elements bending in their own plane) Allowable Axial Compression Specification 3.4.7 Member Buckling Assume most severe case: k 1 L d Slenderness7 x k r x Slenderness7 y kl b r y Slenderness7 max Slenderness7 x Slenderness7 y Slenderness7 1.68 F cm ( 0. 0.16Slenderness7) ksi if Slenderness7 66 51100 Slenderness7 ksi if Slenderness7 66 F cm 3.418ksi Member Buckling between stitch screws (beam half) [ADM 3.4.7] k channel 0.5 Slenderness channel k channel Spacing stitching r yc F ch 0..16Slenderness channel ksi if Slenderness channel 66 51100ksi Slenderness channel F ch 16.93ksi Page 5 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Specification 3.4.9 Local Web Buckling: Slenderness9 w h w t w F cw 1ksi if Slenderness9 w 7.6 491 ksi if Slenderness9 Slenderness9 w 33 w 3.1 0.47Slenderness9 w ksi F cw 4.800ksi Specification 3.4.8.1 Local Buckling, Flange: Slenderness8 b f t f F cf 1ksi if Slenderness8.4 Slenderness8 9.66 1970 Slenderness8 ksi if Slenderness8 1 ( 3.1 0.787Slenderness8) ksi F cf 15.50ksi Member Elastic Buckling (ADM Eq. 4.7.4-3): π F ec E F Slenderness7 ec 6.668ksi Specification 4.7.1 Local Elastic Buckling of the Web: F crw π E 1.6Slenderness9 w π E Local Elastic Buckling, Flange: F crf ( 5.1Slenderness8) F crf 41.1ksi F cw Area web F cf Area flange Weighted Average: Web / Flange Local Buckling: F ca Area Page 6 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Specification 4.7.4: Local and Member Buckling Interaction: F cr min F crf F crw Structural factor of safety: n μ 1.95 1 3 3 F ec Fcr F cr F rc if F n μ n ec F rc.318ksi μ F cm Maximum allowable Axial compressive stress and Corresponding Axial Load: F c min F rc F ca F ch F crf F ec F cm F c.318 ksi F a F c Area F a 6.06kip Specification 3.4. Allowable Major Axis Bending: L b S x Member Buckling (3.4.14): Slenderness 14 Slenderness 14 87.49 I y J F bcx 1ksi if Slenderness 14 13 3600 ksi if Slenderness Slenderness 14 1680 14 3.9 0.38 Slenderness 14 ksi F bcx 1.00ksi Member Buckling between stitch screws (3.4.11): Slenderness ch Spacing stitching r yc F bcxh 1ksi if Slenderness ch 1 87000 ksi if Slenderness ch 79 Slenderness ch 3.9 0.14Slenderness ch ksi F bcxh 17.47ksi Page 7 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] h w Local Buckling, Web (3.4.18): Slenderness 18 t w F bcxw 8ksi if Slenderness 18 48 F bcxw 14.859ksi 150 ksi if Slenderness Slenderness 18 75 18 40.5 0.70Slenderness 18 ksi b f Local Buckling, Flange (3.4.15): Slenderness 15 Slenderness t 15 9.66 f F bcxf 1ksi if Slenderness 15 6.5 18 ksi if Slenderness Slenderness 15 10 15 7.3 0.930Slenderness 15 ksi F bcxf 18.316ksi Allowable Bending Moment per Section 4.7.3 (Weighted Average Bending Strength): d Dimensions: C cf t w C cf 4.418 in d C cw t w C cw 4.336 in d C if C if 4.5 in C tw C cw C tw 4.336 in 3 bt f d t f Flange Group Moment of Intertia: I f bt 1 f I f 3.139 in 4 Web Group Moment of Intertia: 3 t w d t f I w I 1 w 8.066 in 4 Page 8 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] F bcxf I f F M bcxw I w ac M C cf C ac 13.569kipin cw F btf I f F M btw I w at M C if C cw at 149.781kipin Major Axis Allowable Bending Stress per Section 4.7.3: min M ac M at F bma F S bma 0.473ksi x Weighted Average for Web/Flange Local Buckling (Section 3.4): Area web F bcxf Area flange F bcxw 6 F bcxa F Area bcxa 17.771ksi web Area flange 6 Maximum Allowable Bending Stress for sections 3.4 & 4.7.3: F bx min F bcx F bcxh max F bma F bcxw F bcxf F bx 17.469 ksi Major Axis Allowable Bending Moment: M x F bx S x 105.437kipin Beam net stress capacity based upon axial stress utilization: Axial compression in beam due to horizontal windward pressure at screen eave and windward mansard rise: f a p w_wall Spacing h eave Rise f a 0.30 F a f a Net allowable bending moment: M n M x 1 F a M P M Rise M n 7.557kipin Page 9 of 10
TABLE 00.4 FBC Typical Mansard Beam [AAF] Note: If M n is negative, trial section N.G., select a deeper beam. w Spacingp roof 8M n Allowable span per M n : L M w L M 65.605 in Check span limit based upon allowable deflection: Since deflection limit = L/60, then let: Limit Δ 60 3 L Δ 384E I x Limit Δ 5 w L Δ 48.544 in Allowable beam span based upon frame conditions specified: AllowableSpan min L M L Δ AllowableSpan.134ft Page 10 of 10