SPECIFICATION FOR THE DESIGN OF - Transcon Steel

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52 Commentary on the Prescriptive Method for One and Two Family Dwellings - 2004 Φ b = 0.95 Φ b M n = 6,016 ft-lb 2 wL M = 8 L = L = 5.87 ft = 5’-10-1/2” E2.5 Deflection Limit ∆ = L/240 (total loads) Resistance factor for bending strength (per Specification) (for two sections, punched) 8M w = 8(6,016) 1,394 The deflection equation for a simply supported span with distributed load is: 4 5wL 3. 84 ∆ = = L/240 L = 384EI 3 3.84(29,500,000)(9.21) = 3 wEI 1, 208 where I = 9.21 in 4 for two webs and w = 1,208 plf ∆ = L/360 (live loads) = 7’-11” 4 5wL 2.56(29,500,000)(9.21) ∆ = = L/360 L = 384EI 3 360 = 10’-5” E2.6 Shear Capacity where I = 9.21 in 4 for two webs and w = 360 plf Based on the Header Design standard (AISI, 2001c), shear does not control the design of headers. Thus, span will not be limited by shear capacity. E2.7 Combined Bending and Web Crippling Capacity Calculate the web crippling capacity of the header: P n = t 2 kC 1 C 2 C 9 C θ [538 – 0.74(h/t)][1 + 0.007(N/t)] k = 894F y /E = 1.0 C 1 = 1.22 – 0.22k = 1.0 C 2 = 1.06 – 0.06R/t = 0.935 C 9 = 1.0 C θ = 0.7 + 0.3(θ/90) 2 = 1.0 (Eq. C3.4.1-4) (Eq. C3.4.1-20) (Eq. C3.4.1-10) (Eq. C3.4.1-11) (Eq. C3.4.1-19) P n = (0.045) 2 (1.0)(1.0)(0.935)(1.0)(1.0)[538 – 0.74(7.722/0.045)][1 + 0.007(1.625/0.045)] P n = 980 lbs. (for one web) Total P n = 2 x 980 = 1,960 lb (for 2 webs) P n should be adjusted for presence of web holes in each of the C-section members in accordance with the Specification (AISI, 1999). Check applicability of Specification Section C3.4.2:
Commentary on the Prescriptive Method for One and Two Family Dwellings - 2004 53 d 0 /h = 1.5/7.722 = 0.19 < 0.7 h/t = 171.6 < 200 Holes centered at mid-depth of the web Clear distance between holes ≥ 18” Circular hole diameter ≤ 6” Non-circular holes, hole depth (d 0 ) = 1.5” ≤ 2.5” and b = 4” ≤ 4.5” d 0 > 9/16” R c = 0.90 – 0.047d o /h + 0.053x/h ≤ 1.0 R c = 0.90 – 0.047(1.5)/7.722 + 0.053(10)/7.722 = 0.96 (Eq. C3.4.2-2) P n = 1,960 x 0.96 = 1,882 lb (for 2 webs with punchouts) ⎛ Pu ⎞ ⎛ M u ⎞ 1.07 ⎜ ⎟ + ⎜ ⎟ ≤ 1.42 ⎝ Φ wPn ⎠ ⎝ Φ bM nxo ⎠ (Eq. B2.5-2) The following load model is used in checking the combined bending and web crippling equation. The concentrated load is located at mid-span of the beam. The distributed load is located one foot away from the concentrated load on each side (assuming a 2-foot spacing). P L Maximum moment, M = PL ⎛ L − 2 ⎞⎛ L ⎞ ⎛ L − 2 ⎞⎡⎛ L ⎞ ⎛ L − 2 ⎞⎤ + w⎜ ⎟⎜ ⎟ − w⎜ ⎟⎢⎜ ⎟ − ⎜ ⎟ 4 ⎥ ⎝ 2 ⎠⎝ 2 ⎠ ⎝ 2 ⎠⎣⎝ 2 ⎠ ⎝ 2 ⎠ ⎦ Substitute for all the variables in Eq. B2.5-2 and solve for L. where M nxo = 6,333 ft-lb (Unfactored moment) Φ w = 0.75 for box-beam headers Φ b = 0.95 P = 2(w) = 2,788 lbs w = 1,394 plf ⎛ 2788 ⎞ ⎛ M u ⎞ 1.07⎜ ⎟ + ⎜ ⎟ ≤ 1.42 ⎝ 0.75x1882 ⎠ ⎝ 0.95x6333 ⎠ PL ⎛ L − 2 ⎞⎛ L ⎞ ⎛ L − 2 ⎞⎡⎛ L ⎞ ⎛ L − 2 ⎞⎤ Set M u = M = + w⎜ ⎟⎜ ⎟ − w⎜ ⎟⎢⎜ ⎟ − ⎜ ⎟ 4 ⎥ ⎝ 2 ⎠⎝ 2 ⎠ ⎝ 2 ⎠⎣⎝ 2 ⎠ ⎝ 2 ⎠ ⎦ Solve the above equations for L.
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SPECIFICATION FOR THE DESIGN OF - Transcon Steel

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