At a point in a steel member, major and minor principal stress in 1000 kg/cm2, and minor
principal stress is compressive. If uniaxial tensile yield stress is 1500kg/cm2,then magnitude of
minor principal stress at which yielding will commence, according to maximum shearing stress
theory is-
-
A.
200
-
B.
500
-
C.
600
-
D.
1000
Correct Answer:
B. 500
Explanation:
According to the Maximum Shear Stress Theory (also known as Tresca's Criterion), yielding starts when the maximum shear stress in a material reaches the maximum shear stress observed at the yield point in a simple tension test.
For a 2D stress state with principal stresses σ1 and σ2, the maximum shear stress is calculated as:
τmax = (σ1 - σ2) / 2
In a uniaxial tension test at the point of yielding, the maximum shear stress is:
τyield = σy / 2
Where σy is the uniaxial tensile yield stress.
Equating these two:
(σ1 - σ2) / 2 = σy / 2
σ1 - σ2 = σy
Given:
Major principal stress (σ1) = 1000 kg/cm2
Uniaxial tensile yield stress (σy) = 1500 kg/cm2
Minor principal stress (σ2) is compressive, meaning its value will be negative in the equation.
Plugging in the values:
1000 - (-σ2) = 1500
1000 + σ2 = 1500
σ2 = 1500 - 1000
σ2 = 500 kg/cm2
Thus, the magnitude of the minor principal stress at which yielding will commence is 500 kg/cm2.
Click below to open Discussion & Feedback
0 Issues
Please
login to comment or Report Issues.