मुफ्त बीम विक्षेपण कैलकुलेटर
बीम के विक्षेपण (डिफ्लेक्शन) की गणना करें। भार, लंबाई और सामग्री गुण दर्ज करें।
Maximum Deflection
5.049 mm
Maximum Deflection vs Distributed Load (w)
सूत्र
How Beam Deflection Works
For a simply supported beam carrying a uniformly distributed load, the peak deflection occurs at midspan.
Governing Equation
delta_max = (5 w L^4) / (384 E I)
where w is the load intensity in N/m, L is the clear span, E is the material stiffness (elastic modulus), and I is the second moment of area of the cross-section. Engineers often check that the span-to-deflection ratio exceeds code limits (commonly L/360 for floor beams).
हल किया गया उदाहरण
A W200x46 steel beam spanning 6 m carries 5 kN/m uniformly.
- 01Convert E: 200 GPa = 200 x 10^9 Pa
- 02Convert I: 8356 cm^4 = 8356 x 10^-8 m^4 = 8.356 x 10^-5 m^4
- 03Numerator: 5 x 5000 x 6^4 = 25000 x 1296 = 3.24 x 10^7
- 04Denominator: 384 x 2 x 10^11 x 8.356 x 10^-5 = 6.417 x 10^9
- 05delta = 3.24 x 10^7 / 6.417 x 10^9 = 0.00505 m = 5.05 mm
- 06Span/deflection = 6000 / 5.05 = 1188 (well above L/360 = 16.7 mm limit)
अक्सर पूछे जाने वाले प्रश्न
What is an acceptable beam deflection?
Most building codes limit live-load deflection to L/360 for floors and L/240 for roofs, where L is the span length. More sensitive applications may require L/480 or stricter.
Does beam weight affect deflection?
Yes. The self-weight of the beam adds to the distributed load. For precise analysis, add the beam weight per unit length to the applied load w.
What if the load is a single point load at midspan?
For a central point load P, the midspan deflection is P L^3 / (48 E I), a different coefficient from the uniform-load formula used here.
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