Structures · MCQ practice Principal Stress and Principal Planes MCQs – Part 2
15 questions. Tap an option to check it instantly, then read the solution.
Part 2 of 2 Question 16 Medium
The locus of the end point of the resultant of the normal and tangential components of stress on an inclined plane is:
A a circle B a parabola C an ellipse D a straight line
Answer: C. an ellipse
The resultant stress vector on planes of every orientation traces the ellipse of stress, with semi-axes σ₁ and σ₂.
Question 17 Medium
Mohr's strength theory is based on which of the following facts?
A The material fails essentially by shear B The ultimate strength of the material is determined by the stress on the plane of slip C The failure criterion is independent of the intermediate principal stress D All options are correct
Answer: D. All options are correct
Mohr's theory assumes shear failure on a slip plane, governed by σ and τ on that plane, using the largest Mohr circle (σ₁, σ₃) — so σ₂ has no effect. All three are its bases.
Question 18 Medium
In a Mohr's circle drawn on the σ–τ plane (σ = normal stress, τ = shear stress), the vertical diameter represents:
A maximum shear stress B maximum normal stress C principal stress D minimum normal stress
Answer: A. maximum shear stress
The ends of the vertical diameter are the points of maximum shear (±τmax = ±R); its half-length is τmax.
Question 19 Easy
The angle between a principal plane and the plane of maximum shear is:
A 45° B 90° C 135° D 60°
Answer: A. 45°
τ = (σ/2) sin 2θ is maximum at 2θ = 90°, i.e. θ = 45°.
Question 20 Easy
A square element carries a tensile stress σ in the horizontal direction and a compressive stress σ in the vertical direction (normal stresses only). The radius of its Mohr's circle is:
A σ B σ/2 C 2σ D 0.6σ
Answer: A. σ
R = (σ₁ − σ₂)/2 = (σ − (−σ))/2 = σ.
Question 21 Easy
The total strain energy theory for the failure of a material at the elastic limit is known as:
A Guest's or Tresca's theory B St. Venant's theory C Rankine's theory D Haigh's theory
Answer: D. Haigh's theory
Total strain energy theory = Haigh's (Beltrami–Haigh) theory.
Question 22 Easy
The maximum shear stress theory for the failure of a material at the elastic limit is known as:
A Guest's or Tresca's theory B St. Venant's theory C Rankine's theory D Haigh's theory
Answer: A. Guest's or Tresca's theory
Maximum shear stress theory = Guest's or Tresca's theory: failure when τmax = σy/2.
Question 23 Medium
According to the maximum strain energy theory, the yield locus is:
A a rectangle B a circle C a hexagon D an ellipse
Answer: D. an ellipse
σ₁² + σ₂² − 2μσ₁σ₂ = σy² is an ellipse in the σ₁–σ₂ plane.
Question 24 Easy
In the case of biaxial stress, the maximum value of shear stress is given by:
A the difference of the normal stresses B the sum of the normal stresses C half the sum of the normal stresses D none of these
Answer: D. none of these
τmax = (σ₁ − σ₂)/2 — half the difference, which is not listed.
Question 25 Easy
The maximum strain theory for the failure of a material at the elastic limit is known as:
A Guest's or Tresca's theory B St. Venant's theory C Rankine's theory D Haigh's theory
Answer: B. St. Venant's theory
Maximum principal strain theory = St. Venant's theory.
Question 26 Medium
A block of brittle material of cross-section 4 m² carries an axial tensile load of 20 tonnes. The maximum shear stress in the block is:
A 1250 kg/cm² B 1000 kg/cm² C 500 kg/cm² D none of these
Answer: D. none of these
A = 40 000 cm², W = 20 000 kg ⇒ σ = 0.5 kg/cm² ⇒ τmax = σ/2 = 0.25 kg/cm². Not listed.
Question 27 Easy
The maximum principal stress theory for the failure of a material at the elastic limit is known as:
A Guest's or Tresca's theory B St. Venant's theory C Rankine's theory D Haigh's theory
Answer: C. Rankine's theory
Maximum principal stress theory = Rankine's theory: failure when σ₁ reaches σy.
Question 28 Easy
The shear strain energy theory for the failure of a material at the elastic limit is due to:
A Rankine B Guest or Tresca C St. Venant D von Mises
Answer: D. von Mises
Shear strain energy (distortion energy) theory = von Mises (von Mises–Hencky) theory.
Question 29 Easy
Modulus of rigidity is expressed as:
A compressive stress / compressive strain B tensile stress / tensile strain C shear stress / shear strain D stress / volumetric strain
Answer: C. shear stress / shear strain
G = shear stress / shear strain.
Question 30 Easy
In a tensile test, when the material is stressed beyond the elastic limit, the tensile strain ______ compared with the stress.
A decreases slowly B increases slowly C decreases more quickly D increases more quickly
Answer: D. increases more quickly
Beyond the elastic limit, Hooke's law no longer holds: strain grows much faster than stress (plastic deformation).
Part 2 of 2