ud83dudcda Wood Deck Build Log u2014 19 of 45
u2190 Detail #3: Main Beam Calc Parameters u00b7 Series Index u00b7 Detail #5: Main Beam Redesign (Updated) u2192
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Main Beam (u5927u5f15) Strength Calculation u2014 First Attempt
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Hi, I’m DIY Dad. ^ ^
With all the calculation parameters assembled, it’s time to run the numbers.
Formulas Used
- u03b4: deflection [mm]
- u03c3: allowable bending stress [N/mmu00b2]
- M: bending moment [Nu00b7mm]
- L: clear span [mm]
- W: load [N]
- Z: section modulus [mmu00b3]
- I: second moment of area [mmu2074]
- E: modulus of elasticity (Young’s modulus) u2014 mild steel: 2.05 u00d7 10u2075 N/mmu00b2
Calculation
M = WL / 4 = 240 u00d7 0.5 u00d7 9.8 u00d7 3,700 / 4 = 1,081,800 Nu00b7mm
u03c3 = M / Z = 1,081,800 / 2,990 = 363.8 N/mmu00b2 > 157 N/mmu00b2 u2192 NG
u03b4 = WLu00b3 / (48EI) = 240 u00d7 0.5 u00d7 9.8 u00d7 3,700u00b3 / (48 u00d7 2.05u00d710u2075 u00d7 72,600) = 83.4 mm > 12.3 mm (L/300) u2192 NG
Both stress and deflection fail. The deflection is especially vivid u2014 imagine a 3.7 m span sagging 83 mm.
u2191 Deflection diagram
That would snap. Even if it somehow held, the beam would be so springy it’d feel like a trampoline. That’s obviously not acceptable u2014 I need to revisit the span length.
That’s all for today! (^^)/~~~
ud83dudcda Wood Deck Build Log u2014 19 of 45
u2190 Detail #3: Main Beam Calc Parameters u00b7 Series Index u00b7 Detail #5: Main Beam Redesign (Updated) u2192
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