Question

A colleague in a foreign country reports that the Young's modulus of a certain layer has been back-calculated from the deformations of a stress increase due to a surcharge, from \(20 \mathrm{kPa}\) to \(40 \mathrm{kPa}\). This modulus is given as \(E=2000 \mathrm{kPa}\). A new surcharge is being planned, from \(40 \mathrm{kPa}\) to \(60 \mathrm{kPa}\), and your colleague wants your advice on the value of \(E\) to be used then. What is your suggestion?

Short answer

Answer: The value of Young's modulus (E) for the next surcharge change from 40 kPa to 60 kPa is the same as the given value for the initial surcharge change, which is E = 2000 kPa.

Step-by-step solution

Identify given information

In the problem, we are given the following information: - Initial surcharge change: 20 kPa to 40 kPa - Current Young's modulus: E = 2000 kPa We need to determine the Young's modulus for the next surcharge change, from 40 kPa to 60 kPa.

Assume linear elasticity

As the problem doesn't provide any information about the non-linear behavior of the material, we can assume that the material behaves in a linear elastic manner. This means that the relationship between stress and strain is proportional, and the Young's modulus remains constant throughout the different stress levels.

Determine the Young's modulus for the next surcharge

Since the material behaves linearly elastic, the Young's modulus for the next surcharge change (from 40 kPa to 60 kPa) will be the same as the given Young's modulus for the initial surcharge change (from 20 kPa to 40 kPa). That is, the Young's modulus remains as: E = 2000 kPa

Suggest the value of E for the next surcharge

Based on the assumption of linear elasticity and the given information, the value of Young's modulus E for the next surcharge change from 40 kPa to 60 kPa should be the same as the given value for the initial surcharge change: E = 2000 kPa Hence, we suggest using the same Young's modulus value (E=2000 kPa) for the new surcharge change from 40 kPa to 60 kPa.