A beam 8 m. long is fixed at its ends. It carries a uniformly distributed load of 4500 N/m over the whole span. Find the maximum bending moment and maximum deflection. Take E-200KN.mm^2 and I=5x10^7 mm^4.
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Step-by-step explanation:
To find the maximum bending moment (M) and maximum deflection (δ) of the beam, we can use the following formulas:
Maximum Bending Moment (M):
M max = wL^2 /8Mmax = (4500 N/m *8 m^2) /8Mmax =4500 N *8 m Mmax =36000 Nm Maximum Deflection (δ):
δ max = (5 * w * L^4) / (384 * E * I)
δ max = (5 *4500 N/m * (8 m)^4) / (384 *200 KN/mm^2 *5 *10^7 mm^4)
δmax = (5 *4500 *4096) / (384 *200 *5 *10^7)
δmax =92160000 /1920000000δmax =0.048 mmTherefore, the maximum bending moment is36000 Nm and the maximum deflection is0.048 mm.
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