Maximum Principal Stress Theory

Q. A cylindrical pressure vessel is 1200 mm in diameter. It is made of rolled mild steel plate. The vessel is subjected to an internal pressure of 2 $N/m{m}^2$. If the material yields at 200 $N/m{m}^2$, what should be the minimum safe thickness of the plate, based on Maximum Principal Stress Theory?

1. 18 mm
2. 15 mm
3. 12 mm
4. 9 mm

Q. As per the maximum principal stress theory, when a shaft is subjected to a bending moment M and torque T. And $\sigma$ is the allowable stress in axial tension, then the diameter d of the shaft is given by

1. $d^3=\frac{16}{\pi \sigma }[M+\sqrt{M^2+T^2}]$
2. $d^3=\frac{4}{\pi \sigma }[M+\sqrt{M^2+T^2}]$
3. $d^3=\frac{32}{\pi \sigma }[M+\sqrt{M^2+T^2}]$
4. $d^3=\frac{8}{\pi \sigma }[M+\sqrt{M^2+T^2}]$

Q. The limit of proportionality of a certain steel sample is 300 MPa in simple tension. It is subjected to principal stresses of 150 MPa (tensile), 60 MPa (tensile) and 30 MPa (tensile). According to the maximum principal stress theory, the factor of safety in this case would be

1. 10
2. 5
3. 4
4. 2

Q. For the design of a cast iron member, the most appropriate theory of failure is

1. Mohr's theory
2. Rankine's theory
3. Maximum stress theory
4. Maximum shear energy theory

Q. A structural element is subjected to pure shear of 80 $N/m{m}^2$, as shown in the figure. The yield stresses both in tension and in compression are 240 $N/m{m}^2$. According to the maximum normal stress theory, the factors of safety in tension and compression are, respectively,

1. 2 and 2
2. 2.5 and 2.5
3. 3 and 3
4. 4 and 4