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A cantilever beam 2m long carrie a load of 10kn/m over 1m portion from fixed end and a point load of 20kn at free end. Calculate the maximum deflection of the cantilever beam. Take EI=2 x 10^9 KNmm^2

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Answer:

The maximum deflection of a cantilever beam can be found using the equation for a cantilever beam under a point load and a distributed load:

δ = (PL^3)/(3 * EI) + (wl^2)/8 * (2L - wl)

where δ is the maximum deflection, P is the point load (20 kN), L is the length of the beam (2 m), w is the distributed load (10 kN/m), E is the Young's modulus of the material, I is the moment of inertia, and l is the length of the distributed load (1 m).

First, let's convert the loads to N and the length to mm:

P = 20 kN * 1000 N/kN = 20000 N

L = 2 m * 1000 mm/m = 2000 mm

w = 10 kN/m * 1000 N/kN * 1000 mm/m = 10000 N/mm

l = 1 m * 1000 mm/m = 1000 mm

EI = 2 x 10^9 KNmm^2

Next, let's plug the values into the equation for maximum deflection:

δ = (P * L^3)/(3 * EI) + (w * l^2)/8 * (2L - l)

δ = (20000 N * 2000^3 mm^3)/(3 * 2 x 10^9 KNmm^2) + (10000 N/mm * 1000^2 mm^2)/8 * (2 * 2000 mm - 1000 mm)

δ = (20000 * 8 x 10^9 mm^3)/(3 * 2 x 10^9 KNmm^2) + (10000 * 10^6 mm^2)/8 * (4000 mm - 1000 mm)

δ = 1.6 x 10^3 mm + 6.25 x 10^4 mm

δ = 6.41 x 10^4 mm = 64.1 mm

So the maximum deflection of the cantilever beam is 64.1 mm.

Step-by-step explanation:

User Barunsthakur
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