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GATE ME stress — practice questions

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Traction T at a point on a surface is defined as:Stress is INTERNAL force per unit area, while traction is EXTERNAL force per unit area. Why is traction descriHow many INDEPENDENT components does the 3D stress tensor have at a point in equilibrium?Why is the stress tensor SYMMETRIC (σ_xy = σ_yx, etc.)?The relationship between TENSORIAL shear strain ε_xy and ENGINEERING shear strain γ_xy is:In the figure, F acts on surface S to produce a traction T. As $\Delta S \to 0$, T approaches: ![](https://qaThe 3D equation of equilibrium in a body (without body forces) is:Cauchy's STRESS THEOREM states that the traction vector T(n) on any surface with outward normal n can be compuHow many INDEPENDENT elastic constants describe an ISOTROPIC linear-elastic material?How many INDEPENDENT elastic constants describe an ORTHOTROPIC material (three mutually perpendicular planes oHow many INDEPENDENT elastic constants describe a TRANSVERSELY ISOTROPIC material (one preferred axis, isotropHow many INDEPENDENT elastic constants does a GENERAL ANISOTROPIC linear-elastic material have?In stress/strain analysis, COMPATIBILITY CONDITIONS ensure that:Refer to the stress-cube figure. The 9 components σ_ij at a point split into normal and shear. After accountinHooke's law in STIFFNESS form is σ = C·ε. In COMPLIANCE form: ε = S·σ. The relationship between C and S is:For an isotropic material, the shear modulus G is related to E and ν by:An incompressible isotropic material has Poisson's ratio:In Voigt (engineering) NOTATION, the contracted 6×1 stress vector is typically ordered as: