Chart C4 Flexural Strength
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Claire AvesChart C4 Flexural Strength
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Claire Aves𝐿𝑏 = 𝑢𝑛𝑏𝑟𝑎𝑐𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ 𝐿𝑝 = 1,76𝑟𝑦 (𝐸/𝐹𝑦) FLEXURAL STRENGTH
𝐸 𝐽𝑐 𝐽𝑐
2
0.7𝐹𝑦
2 Check compactness
𝐿𝑟 = 1.95𝑟𝑡𝑠 + + 6.76 𝜆 < 𝜆𝑟 𝑜𝑟 𝜆 ≤ 𝜆𝑝 : COMPACT
0.7𝐹𝑦 𝑆𝑥 ℎ𝑜 𝑆𝑥 ℎ𝑜 𝐸
𝜆𝑝 < 𝜆 ≤ 𝜆𝑟 𝑜𝑟 𝜆 > 𝜆𝑟 : NONCOMPACT or SLENDER
COMPACT: LTB NON-COMPACT: LTB & FLB; if noncompact due to flange: Mn is smaller of LTB & FLB
𝐿𝑏 ≤ 𝐿𝑝 𝑁𝑂 𝐿𝑇𝐵 : 𝑀𝑛 = 𝑀𝑝 = 𝐹𝑦 𝑍 LTB: same as in COMPACT (Lb ≤ Lp, Lp < Lb ≤ Lr, Lb > Lr)
𝐿 𝑏 − 𝐿𝑝 FLB (FLANGE LOCAL BUCKLING):
𝐿𝑝 < 𝐿𝑏 ≤ 𝐿𝑟 𝑖𝑛𝑒𝑙𝑎𝑠𝑡𝑖𝑐 𝐿𝑇𝐵 : 𝑀𝑛 = 𝐶𝑏 𝑀𝑝 − 𝑀𝑝 − 0.7𝐹𝑦 𝑆𝑥 ≤ 𝑀𝑝
𝐿𝑟 − 𝐿𝑝 𝜆 ≤ 𝜆𝑝𝑓 : NO FLB 𝜆 > 𝜆𝑟 (𝑆𝐿𝐸𝑁𝐷𝐸𝑅 𝐹𝐿𝐴𝑁𝐺𝐸𝑆): 𝑀𝑛 = 0.9𝐸𝑘𝑐 𝑆𝑥 /𝜆2
𝐿𝑏 > 𝐿𝑟 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 𝐿𝑇𝐵 : 𝑀𝑛 = 𝐹𝑐𝑟 𝑆𝑥 ≤ 𝑀𝑝 𝜆 − 𝜆𝑝𝑓
𝜆𝑝𝑓 < 𝜆 ≤ 𝜆𝑟𝑓 FLANGE IS NON − COMPACT : 𝑀𝑛 = 𝑀𝑝 − 𝑀𝑝 − 0.7𝐹𝑦 𝑆𝑥
𝜆𝑟 − 𝜆𝑝𝑓
LRFD ASD
𝑀𝑢 = 𝜙𝑏 𝑀𝑛 ; 𝜙𝑏 = 0.90 𝑀𝑎 = 𝑀𝑛 /Ω𝑏 ; Ω𝑏 = 1.67
Torsional Constant, J c Cb: Smply Supported Cb: Smply Supported
For double-symetric I-shapes: c =1 Concentrated Distirbuted
2𝑏𝑓 𝑡𝑓3 +𝑑′ 𝑡𝑤3 For a channel: c = (ho/2)√(Iy/Cw) - None (loads at Midspan): Cb = 1.32 - None: Cb = 1.14
wide flange: 𝐽 = ; 𝑑 ′ = 𝑑 − 𝑡𝑓 Load Point: Cb = 1.67 - Midpoint: Cb = 1.30
3 For double-symetric w/ rectangluar flange: rts2 = Iyho/2Sx
2𝑏′ 𝑡𝑓 3+𝑑′ 𝑡𝑤3 - None (loads at Third pts): Cb = 1.14 - Third pts: Cb = 1.01
channel: 𝐽 = ; 𝑑 ′ = 𝑑 − 𝑡𝑓 ; 𝑏′ = 𝑏 − 𝑡𝑤 /2 𝑏𝑓 𝐼𝑦 ℎ𝑜 2
3 𝑟𝑡𝑠 = ; 𝐶𝑤 = Load pts: Cb = 1.00 - Quarter pts: Cb = 1.06
𝑏𝑓 𝑡𝑓 3+𝑑′ 𝑡𝑤3 4 - None (Load at Quarter pts): Cb = 1.14
tee: 𝐽 = ; 𝑑 ′ = 𝑑 − 𝑡𝑓 /2 1 ℎ𝑡𝑤 - Fifth pts: Cb = 1.00
3 12 1 + Load pts: Cb = 1.11
6 𝑏𝑓 𝑡𝑓
(𝑏′ +𝑑′ )𝑡 3
angle section: 𝐽 = ; 𝑏 ′ = 𝑑 − 0.5𝑡; 𝑑 ′ = 𝑑 − 0.5𝑡
3
12.5 𝑀𝑚𝑎𝑥
𝐶𝑏 = 𝑅 ≤ 3.0
2.5 𝑀𝑚𝑎𝑥 + 3𝑀𝐴 + 4𝑀𝐵 + 3𝑀𝐶 𝑚