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A sheet of glass 0.5 m wide and 18 mm thick is found to contain a surface crack 4 mm deep and 10 mm long. If the glass is placed horizontally on two supports as shown below, calculate the maximum spacing (L_max) of the supports to avoid fracture of the glass due to its own weight. For glass K_IC = 0.3MPa Squareroot m and density = 2600 kg/m^3.

Answer :

Aamirmajeed5100go

The maximum spacing (L_max) of the supports to avoid fracture of the glass due to its own weight is 0.015 m.

Step 1: Calculate the bending moment (M) at the crack.

M = F x L = (0.5 x 2600) x 0.004 = 4.2 Nm

Step 2: Calculate the maximum stress (σ_max) at the crack.

σ_max = M / I = 4.2 / (0.5 x 0.018^3) = 18.3 MPa

Step 3: Calculate the maximum spacing (L_max) of the supports to avoid fracture.

L_max = (K_IC / σ_max)^2 = (0.3 / 18.3)^2 = 0.015 m

Therefore, the maximum spacing (L_max) of the supports to avoid fracture of the glass due to its own weight is 0.015 m.

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