Test: Analysis of Stress & Strain Level - 3 - Mechanical Engineering MCQ

Two wooden joists 50mm and 100mm are glued together along the joist AB as shown. Determine the normal and tangential stress in the glue if P = 200 kN

In a strained material the normal stress on one plane is 10t/cm² tensile and the shear stress is 5t/cm². On a plane perpendicular to this plane there is only shear stress. The center for Mohr’s circle

In a material under a state of plane strain, a square centered at a point gets deformed as shown in figure.

Find the shear strain γ_xy

Assuming E = 160 GPa and G = 100 GPa for a material, a strain tensor is given as

The shear stress, τ_xy is

n a strained material, normal stresses on two mutually perpendicular planes are σx and σy (both alike) accompanied by a shear stress τ_xy, one of the principal stresses will be zero, only if,

For which one of the following stress conditions the diameter of Mohr’s stress circle is zero?

Where σ₁ =major principal stress,

σ₂ = Minor principal stress and

q = Shear stress

If Normal stresses of same nature px and py and shear stress q is acting on two perpendicular planes and q = (pxpy)^1/2, then the major and minor principal stresses respectively are

A tensile specimen with 12 mm initial diameter and 50 mm initial length is subjected to a load of 90 kN. After sometime, the diameter is 10mm. Assuming it as in compressible material, calculate true strain along the length. (Give answer upto 3 decimal places)

A square plate of side 4 units undergoes deformation. The angle between the diagonals becomes 60°. Calculate τ_45° (4 decimal places)

A square plate of side 4 units experiences the following strain components.

ϵ_x = 0.001

ϵ_y = 0.002

τ_xy = 0.003

Find the elongation of the diagonal (4 decimal places)

For which of the following cases distortion energy theory is more liberal when compared to shear stress theory.

I. σ₁ , σ₂ are equal and are tensile in nature.

II. σ₁ , σ₂ are equal and are compressive in nature.

III. σ₁ is compressive and σ₂ is tensile and the magnitudes are the same.

IV. σ₁ is tensile and σ₂ is compressive and the magnitudes are same

Following stress Tensor represents tri-axial state of stress at a point. Determine strain energy per unit volume in kJ/m³ .

Consider, Poisson’s ratio = 0.3 and Young’s modulus of elasticity = 200 GPa

τ =

Following stress Tensor represents tri-axial state of stress at a point. Determine the distortion energy per unit volume in terms of kJ/m³ . Take μ = 0.3, E = 200 GPa

[σ] =

Consider the below shown loading conditions, which one will fail first according to principal strain energy theory [μ = 0.3]

I.

II.

Consider the below shown loading conditions. Which one will fail first according to distortion energy theory? [take, σ/τ = 2]

I.

II.

An I-beam with flanges of size 200 mm × 200 mm and a web of 600 mm × 12 mm is subjected to a bending moment of 450 kNm and a shear force of 400 kN at a section. The major principal stress at a point 200 mm above the neutral axis is __________ MPa

(A) 114.0

(B) 116.0

A circle of diameter 500 mm is inscribed on a square plate of copper, before the application of stresses as shown, σ₁ = 160 MPa, σ₂ = 80 MPa, τ = 30 MPa. After the application of stresses, the circle is deformed into an ellipse. Then the major and minor axes of the ellipse will be Given E = 100 GPa, ν = 0.35.