Stress-Strain-CE

A 2D thin plate with modulus of elasticity, 𝐸 = 1.0 N/m 2 , and Poisson’s ratio, 𝜇 = 0.5, is in plane stress condition. The displacement field in the plate is given by 𝑢 = 𝐶𝑥 2 𝑦 and 𝑣 = 0, where 𝑢 and 𝑣 are dis...

For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio (v), and shear modulus (G) is

An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion a, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress $...

The Poisson's ratio is defined as

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ weight $$W$$ is dropped vertically from a height $$h\left( { < L} \right)$$ on to the flange. The axial...

A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield stress for mild steel are $$2 \times {10^5}\,\,MPa$$ and $$250$$ $$MPa$$ respectively. The maximum amount of strain energy per unit volume...

A thin walled cylindrical pressure vessel having a radius of $$0.5$$ $$m$$ and wall thickness of $$25$$ $$mm$$ is subjected to an internal pressure of $$700$$ $$kPa$$. The hoop stress developed is

A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by $$10^o$$C. If the coefficient of thermal expansion is 12 x$$10^{-6}$$ per $$^o$$C and the Young’s modulus is 2 x $$10...

For an isotropic material, the relationship between the young’s modulus (E), shear modulus (G) and Poisson’s ratio (μ) is given by

The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions.

The symmetry of stress tensor at a point in the body under equilibrium is obtained from

$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the same bar due to combined action of $${P_1...

For linear elastic systems, the type of displacement function for the strain energy is

A thin cylindrical vessel of mean diameter $$D$$ and of length $$'L'$$ closed at both the ends is subjected to a water pressure $$'P'$$. The value of hoop stress and longitudinal stress in the shell shall be respectively...

The maximum value of Poisson's ratio for an elastic material is

A cantilever beam of tubular section consists of 2 materials copper as outer cylinder and steel as inner cylinder. It is subjected to a temperature rise of $$20^\circ C$$ and $$\alpha_{copper}\;>\;\alpha_{steel}$$ the st...

The principle of superposition is made use of in structural computations when:

A cylindrical tank of radius $$'r'$$ and wall thickness $$'t'$$ has flat end closures. The tank is subjected to an internal pressure $$P.$$ The longitudinal $$\left( {{\sigma _x}} \right)$$ and the circumferential $$\lef...