Principal Stresses and Plane
Trending Questions
Q. The major and minor principal stresses at a point are 3 MPa and -3 MPa respectively. The maximum shear stress at the point is
- Zero
- 3 MPa
- 6 MPa
- 9 MPa
Q. In a plane stress problem, there are normal tensile stresses σxandσywithσx>σy, accompanied by shear stressτxy at a point in the x-plane. If it is observed that the minimum principal stress on a certain section is zero, then
τxy=√σx⋅σy
τxy=√σxσy
τxy=√σx−σy
- τxy=√σx+σy
Q. The state of stresses on an element is shown in the given figure. The value of stresses are σx(=32 MPa);σy(=−10 MPa) and major principal stress σ1(=40 MPa). The minor principal stress σ2 is
- -22 MPa
- -18 MPa
- 22 MPa
- indeterminable due to insufficient data
Q. Consider the following statements :
I. On a principal plane, only normal stress acts.
II. On a principal plane, both normal and shear stresses act.
III. On a principal plane, only shear stress acts.
IV. Isotropic state of stress is independent of frame of reference.
The TRUE statements are
I. On a principal plane, only normal stress acts.
II. On a principal plane, both normal and shear stresses act.
III. On a principal plane, only shear stress acts.
IV. Isotropic state of stress is independent of frame of reference.
The TRUE statements are
- I and IV
- II
- II and IV
- II and III
Q. In a stressed body, an elementary cube of material is taken at a point with its faces perpendicular to X and Y reference axes. Tensile stresses equal to 15kN/cm2 and 9 kN/cm2 are observed on these respective faces. They are also accompanied by shear equal to 4 kN/cm2. The magnitude of the principal stresses at the point are
- 12 kN/cm2 tensile and 3 kN/cm2 tensile
- 17 kN/cm2 tensile and 7 kN/cm2 tensile
- 9.5 kN/cm2 compressive and 6.5kN/cm2 tensile compressive
- 12 kN/cm2 tensile and 3 kN/cm2 tensile
Q. The rectangular block shown in the given figure is subjected to pure shear of intensity 'q'. If BE represents the principal plane and the principal stresses are σ1, σ2; then the value of θ, σ1 and σ2 will be respectively.
- 0°, 90°;+q and -q
- 30°, 120°;+q and -q
- 45°, 135°; +q2 and −q2
- 45°, 135°; + q and - q
Q. At a certain point in a strained material, there are two mutually perpendicular stresses σx=100N/mm2 (tensile) and σy=500 N/mm2 (compressive).
[Notation : tension (+); compression (-)]
What are the values of the principal stresses in N/mm2 at the point?
[Notation : tension (+); compression (-)]
What are the values of the principal stresses in N/mm2 at the point?
- 100, -50
- -100, 50
- 75, -25
- -75, 25
Q. If the maximum principal stress for an element under bi-axial stress situation is 100 MPa (tensile) and the maximum shear stress is also 100 MPa, then what is the other principal stress?
- 200 MPa (tensile)
- 200 MPa (compressive)
- 100 MPa (compressive)
- zero
Q. For a case of plane stress, σx=40MN/m2, σy=0, τxy=80MN/m2. What are the principal stresses(inMN/m2) and their orientation with x and y axes?
- σ1=80, σ2=40, θ1=30∘
- σ1=100, σ2=−60, θ1=32∘
- σ1=102.5, σ2=−62.5, θ1=36∘
- σ1=105, σ2=62, θ1=36∘
Q. Figure below shows a state of plane stress.
If the minimum principal stress is −7 MN/m2 then what is the value of σx?
If the minimum principal stress is −7 MN/m2 then what is the value of σx?
- 30 MN/m2
- 68 MN/m2
- 98 MN/m2
- 105 MN/m2
Q. For the state of stress shown in the figure, the maximum and minimum principal stresses (taking tensile stress + and compressive stress as -) will be
- 95 MPa and (-35) MPa
- 60 MPa and 30 MPa
- 95 MPa and (-30) MPa
- 60 MPa and 35 MPa
Q. At a point in the web of a girder, the bending and the shearing stresses are 90 N/mm2 (tensile) and 45 N/mm2 respectively. The principal stresses are
- 108.64 N/mm2 (tensile) and 18.64 N/mm2 (compressive)
- 107.60 N/mm2 (compressive) and 18.64 N/mm2 (tensile)
- 108.64 N/mm2 (compressive) and 18.64 N/mm2 (tensile)
- 0.64 N/mm2 (tensile) and 0.78 N/mm2 (compressive)
Q. In a plane stress problem there are normal tensile stresses σx and σy accompained by shear stress τxy at a point along orthogonal Cartesian co-ordinates x and y respectively. If it is observed that the minimum principal stress on certain plane is zero then
τxy=√σx+σy
τxy=√σx−σy
τxy=√σxσy
- τxy=√σxσy
Q. The principal stresses at a point in a stressed material are
σ1=200 N/mm2, σ2=150 N/mm2, and σ3=200 N/mm2. E = 210 kN/mm2 and μ = 0.3. The volumetric strain will be
σ1=200 N/mm2, σ2=150 N/mm2, and σ3=200 N/mm2. E = 210 kN/mm2 and μ = 0.3. The volumetric strain will be
- 8.945×10−4
- 8.945×10−2
- 6.54×10−3
- 6.54×10−4
Q. The state of two-dimensional stresses acting on a concrete lamina consists of a direct tensile stress σx=1.5 N/mm2 and shear stress τ=1.20 N/mm2, when cracking of concrete is just impending. The permissible tensile strength of the concrete is
- 1.50 N/mm2
- 2.17 N/mm2
- 2.08 N/mm2
- 2.29 N/mm2
Q. In a strained material, the principal stresses in the X and Y directions respectively are 100 N/mm2 (Tensile) and 60 N/mm2 (Compressive). On an inclined plane, the normal to which makes an angle of 30° to the X-axis, the major prinipal stress, in N/mm2, would be
- 60
- 80
- 20
- 40