The three-dimensional stress-strain relationship for an isotropic material is given as
{
𝜎xx
𝜎yy
𝜎zz
𝜏yz
𝜏xz
𝜏xy}
=
[
P Q Q
Q P Q
Q Q P
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
R 0 0
0 R 0
0 0 R]
{
𝜀xx
𝜀yy
𝜀zz
𝛾yz
𝛾xz
𝛾xy}
where, P, Q and R are the three elastic constants, 𝜎 and 𝜏 represent normal and shear
stresses and 𝜀 and 𝛾 represent normal and engineering shear strains. Which one of
the following options is correct?
Options:
(A) R = P - Q
2
(B) R = Q - P
2
(C) Q = P - R
2
(D) Q = R - P
2
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.13)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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