# PTU SOM II 5 marks Question Answers

**PTU SOM II 5 marks Question Answers**

**Compare the strains produced in a body subjected to same amount of load when applied gradually and suddenly.**

ANS: Let ‘P’ be the gradually applied load and ‘a’ is the area of cross section of the body.

Then stress = P/A

When same load is applied suddenly, its equivalent gradually applied load is twice .

Stress 2P/A

Now stress is two times therefore strain will also be two times when the same load is applied suddenly.

PROOF why equivalent gradually applied load is two times the gradually applied load.

W.D. in suddenly applied lod = P_{sudden } δl

W.D. when the load is applied gradually= 0.5 P_{GAL} δl where GAL is gradually applied load

In order to find the equivalent gradually applied load the W.D. as well as extension should be same. Therefore equate the W.D. in the two cases

P_{sudden } δl = 0.5 P_{GAL} δl

P_{GAL} = 2P_{sudden} and hence is proved

**For a thin cylindrical shell, the length diameter ratio is 3 and its volume is 20 m**^{3}. The safe tensile stress for the shell material is 100 MPa.**Determine the cylinder diameter and wall thickness if it has to contain water at an absolute pressure of 2 MPa.**

ANS: Given L/D =3 and volume V =D^{2}L= D^{2} 3D= 20

D^{3 }= 20

D = 2.04 m

Now hoop stress is the highest stress which taken equal to the safe stress.

σ_{h}=p_{i}D/2t = 100

t = 2x 2.04 x 1000/2×100 = 20 mm

- Distinguish between energy of dilation and energy of distortion.ANS: Every object in universe is under a number of forces. Thus it is under complex loading. From the complex loading, one can determine the three principal stresses σ
_{1}, σ_{2}and σ_{3}respectively. ASSUME- these all principal stresses as tensile and
- σ
_{1}> σ_{2}> σ_{3}

Energy of dilation deals with stresses that cause a change in size (length, width, thickness, depth, area, volume). Definitely these are tensile and compressive stresses. Principal stresses are also tensile and compressive stresses. Then the energy of dilation is given below

u

_{ed}=(1/2E)[ σ_{1}^{2}+ σ_{2}^{2}+ σ_{3}^{2}-2μ σ_{1}σ_{2}-2μ σ_{2}σ_{3}-2μ σ_{3}σ_{1}]where μ is the Poisson’s ratio

Then energy of distortion OR shear strain energy is there under a shear stress when there is no change of size but there is twist or distortion in the body. It is given by the relation given below.

u

_{sse}=(1/12G)[ (σ_{1}–σ_{2})^{2}+ (σ_{2}—σ_{3})^{2}+ (σ_{3}—σ_{1})^{2}]NOTE: if any of the three principal stresses σ

_{1}, σ_{2}and σ_{3}is not tensile, then respective sign must be used in the above relation.- State maximum principal stress theory.

ANS: Every object in universe is under a number of forces. Thus it is under complex loading. From the complex loading, one can determine the three principal stresses σ

_{1}, σ_{2}and σ_{3}respectively. ASSUME- these all principal stresses as tensile and
- σ
_{1}> σ_{2}> σ_{3}

Now Maximum principal stress theory states that a material will fail if largest principal stress in the material exceeds the allowable stress.

Therefore when σ

_{1}= σ_{allowable}=σ_{elastic}/Factor of safety**Q. Distinguish between energy of dilation and energy of distortion.**

ANS: Every object in universe is under a number of forces. Thus it is under complex loading. From the complex loading, one can determine the three principal stresses σ_{1}, σ_{2} and σ_{3} respectively. ASSUME

- these all principal stresses as tensile and
- σ
_{1}> σ_{2}> σ_{3}

Energy of dilation deals with stresses that cause a change in size (length, width, thickness, depth, area, volume). Definitely these are tensile and compressive stresses. Principal stresses are also tensile and compressive stresses. Then the energy of dilation is given below

u_{ed}=(1/2E)[ σ_{1}^{2} + σ_{2}^{2} + σ_{3}^{2} -2μ σ_{1}σ_{2}-2μ σ_{2}σ_{3}-2μ σ_{3}σ_{1}]

Then energy of distortion OR shear strain energy is there under a shear stress when there is no change of size but there is twist or distortion in the body. It is given by the relation given below.

u_{sse}=(1/12G)[ (σ_{1}–σ_{2})^{2} + (σ_{2}—σ_{3})^{2} + (σ_{3}—σ_{1})^{2}]

NOTE: if any of the three principal stresses σ_{1}, σ_{2} and σ_{3} is not tensile, then respective sign must be used in the above relation.