Question

A cantilever beam, which is made of an alloy with Young’s modulus of elasticity E=72×(10)9N/m2, is loaded transversely at its free end. If the length of the beam is 750 mm and the beam has an annular cross-section with inner and outer diameters of 110 mm and 120 mm, respectively, then determine the equivalent stiffness (in N/m) of this beam.


1.531×(10)6


3.06×(10)6


2×(10)6


4×(10)6​

Answer 1

The equivalent stiffness of this beam is K = 3.06 x 10^6 N/m

Explanation:

• k = 3 EL / L^3   ----(i)
• The moment of inertia will b determined as;
• I = π / 32 [d^4 (outer) - d^4 (inner)]

I= π/32 [ (120 x 10^-3)^4 - (110 x 10^-3)^4]

I = 5.98 x 10^-6 m^4    ----(ii)

From equation (i)

K = 3 x (72 x 10^9) x (5.98 x 10^-6) / (750 x 10^3)^3

K = 3.06 x 10^6 N/m

Thus when the length is increased from 750 mm to 1500 mm then stiffness decreases from 3.06 x 10^6 N/m to 0.383 x 10^6 N/m.