SIMPLE STRESSES-STRAIN SHORT QUESTION ANSWERSCLASS NOTES

SIMPLE STRESSES-STRAINS

SHORT QUESTION ANSWERS

CLASS NOTES  

Simple stresses & strains include

tensile and compressive. There is

simple shear stress & strain. All

failure take place to simple stresses.

Question answers on stresses increase

depth of knowledge. It helps to have

clear idea about deformation. Further

it is helpful in the design of components.

2. What is a stress?

It is the internal resistance of a material against external force. It is non- visible. Mathematically it is force per unit area. Therefore its units are N/mm2.

3. What are the various types of stresses?

Various types of stresses are

(i)  Tensile stress

(ii) Compression stress

(iii) Shear stress

(iv) Thermal stress

(v)  Bending stress

(vi) Torsional shear stress

(vii) Buckling stress

(viii) Complex stress

(ix) Principal Stress

4. What is a tensile stress?

When external load is perpendicular to the area on which it is acting. This force is directed outwards on the area. It increases the dimension in which the force is applied. Its symbol is σ (sigma). Its units are N/mm2. It is uniform at every point of the area.

Fig. Body under Tensile Load

σt (sigma) = Ft /(A perpendicular to Ft)

Where Ft is the tensile force in N

and A is the area of cross-section in mmand is perpendicular to Ft 

  5. Explain a compression stress, its symbol and units.

When external load is perpendicular to the area on which it is acting. This force is directed inwards on the area. It decreases the dimension in which the force is applied. Its symbol is σ (sigma). Its units are N/mm2. It is uniform at every point of the area.

Fig. Body Under Compressive Load

σc (sigma) = Fc /(A perpendicular to Fc)

Where Fc is the compression force in N

and A is the area of cross-section in mm

6. Describe a shear stress, its symbol and its units.

When external load is parallel to the area on which it is acting. It causes angular strain. It causes distortion. . Its symbol is τ (tau). Its units are N/mm2. It is uniform at every point of the area.

τ (tau) = Fs/( A // Fs)

Where Fs is the shear force in N

and A is the area of cross-section in mm2

7.  What is thermal stress, its symbol and units? 

Thermal stress is due prevention of expansion because of  rise of temperature. If expansion is prevented, there will be a compression stress. If contraction is prevented there will be a tensile stress. The symbol of thermal stress is σ (sigma). Its symbol is σth. Its units are N/mm2.

8.  What do you understand by 0.2 % proof stress?

 Draw a tangent to the stress strain diagram from the origin. Then draw a line parallel to this tangent from a point on x-axis for a strain value of 0.2 %. This tangent meets the stress strain diagram at some point. The value of stress at this point is 0.2 % proof stress.

Fig. Finding Yield Point by Offset Method

Draw a tangent to curve from the origin.

Draw a line parallel to the tangent from 0.2 % strain point . It meets the stress strain curve at point ‘B’. Point B is the proof stress or yield stress.

Q9.  Write the relationship between true strain and conventional strain.  Also give the relationship between true stress and conventional stress.

TRUE STRAIN

True strain is given by the relation given below:

εt = ln(Li/Lo)

Conventional strain is  ε = (Li — Lo)/Lo = Li/Lo—1

Therefore   Li/Lo = ε + 1

Taking log on both sides

ln(Li/Lo) = ln(ε + 1)

εt  = ln(ε + 1)

It is the relationship between true strain and conventional strain.

Relationship between true stress σt and conventional stress σ

TRUE STRESS

Real or True stress = instantaneous load/instantaneous area of cross section

σt = Fi /Ai

Conventional (unit stress or engineering stress) stress, load divided by original area                                σ = Fi/Ao

ASSUMPTION: Volume of the test piece remains constant under all conditions of loadings.

AoLo = AiLi

Ai = AoLo/Li

Therefore σ­t = Fi / Ai = Fi /( AoLo/Li)

                        = (Fi / Ao) (Li/L0)

σ­t =σ(ε+1)

Thus, it is the relationship between true stress and conventional stress.

Q10. Define shear modulus or modulus of rigidity. What is its symbol? What are its units?

A. It is a ratio of shear stress to shear strain. Its symbol is G.  G = τ / γ  Its units are GN/m2. Its value for steel is 80 GN/m2. But when used in solving problems it is used as 80 x 1000 N/mm2

 Q11. Give the definition of bulk modulus? What is its symbol? What are its units?

Bulk modulus is the ratio of volumetric stress to volumetric strain. Its symbol is ‘K’. Its units are GN/m2. It is due to pressure exerted by a fluid on a solid causing change in volume of a solid. For example, change in volume of a cylinder is caused by the pressure of the fluid. Thus there is volumetric strain in the solid. Its symbol is ‘K’. Its units are GN/m2. It is given as

K =  p / δV/V

  1. What is a strain? Give the symbol of strain. Also mention the units of strain.

A strain is the ratio of change in length to original length. This change is caused by a tensile force or a compressive force. The change in length will be positive due to tensile force. It is negative due to a compressive force. Hence will be the corresponding strains. Tensile and compression causes deformation. There is a change of size.

Symbol of tensile and compressive strain is ε (epsilon). Strain has no units since it is a ratio.

2. Discuss in brief linear strain.

Linear strain is in the direction of the force, thus, it will be maximum. It is caused either by a pure (simple) tensile stress or by a pure (simple) compressive stress or by a principal stress.

3. Explain lateral strain? Write its symbol. Explain its units.

Lateral strain is in the perpendicular direction of the force. It is less than the linear strain. Nature of lateral strain is opposite nature to the linear strain. For example, if the linear strain is compressive, then lateral strain will be tensile and vice versa. Symbol of lateral strain is, also, ε (epsilon). It has no units.

4. What is the relation between lateral and linear strain?

This ratio of lateral strain to linear strain is called Poisson’s ratio. Its symbol is μ (pronounced as mu). Since lateral strain is less than linear strain. This ratio is less than one. Since it is ratio of two strains, it has no units.

Poisson’s Ratio μ = lateral strain/linear strain

Lateral and linear strains are of opposite nature. Therefore, there is always a negative sign attached to the Poisson’s ratio.

5. Define a shear strain? What is its symbol? What are its units?

This strain is an angular strain. This strain is due to a shear stress. Its symbol is γ . Its unit is radian. Shear strain causes distortion. There is no change of size in shear strain. Shear strain has ± sign. It is because of induced and applied shear strains co-exist. These are clockwise and anticlockwise respectively. If the applied shear strain is clockwise, then, induced shear strain is anticlockwise and also vice versa.

https://www.mesubjects.net/wp-admin/post.php?post=7658&action=edit                MCQ Simple stresses

https://www.mesubjects.net/wp-admin/post.php?post=3454&action=edit                Bending stresses