Stresses and Strains

Question 1

What is the mechanics of materials the study of?

Answer 1

The elastic behavior of materials and the stability of members.

Question 2

When is the mechanics of materials concepts used?

Answer 2

To determine the stress and deformation of axially loaded members, connections, torsional members, thin walled pressure vessels, beams, eccentrically loaded members, and columns.

Question 3

What is stress?

Answer 3

the force per unit area.

Question 4

How many types of stress are there?

Answer 4

Normal stress and shear stress.

Question 5

What is the difference between normal and shear stress?

Answer 5

In normal stress, the force is normal to the surface area and in shear stress, the force is parallel to the surface area.

Question 6

What are the two subcategories of normal stress?

Answer 6

Tensile and compressive stress.

Question 7

What are the sign conventions of tensile and compressive stress?

Answer 7

Tensile stresses make a part elongate in the direction of application and are considered positive. Compressive stresses make a part shrink in the direction of application and are given a negative sign.

Question 8

What is linear strain?

Answer 8

The change in length per unit length.

Question 9

What is shear strain?

Answer 9

Is an angular deformation resulting from shear stress.

Question 10

What is Hooke’s Law?

Answer 10

States that the stress is proportional to the strain.

Question 11

What is Hooke’s Law for normal stress?

Answer 11

The normal stress is equal to the product of the strain and the modulus of elasticity.

Question 12

What is an isotropic material?

Answer 12

The properties of the material are the same in all directions.

Question 13

What is an anisotropic material?

Answer 13

The properties of the material vary with direction.

Question 14

What is Poisson’s ratio?

Answer 14

Is the ratio of the lateral strain to the axial strain for axially loaded members.

Question 15

What is Hooke’s Law for a plane element in pure shear?

Answer 15

The shear stress is equal to the product of the shear strain and the shear modulus.

Question 16

Under what conditions are the Poisson’s ratio, shear and elastic modulus related?

Answer 16

An elastic isotropic material.

Question 17

What is strain energy?

Answer 17

Is the energy per unit volume stored in a deformed material.

Question 18

What is the strain energy equal to?

Answer 18

It is equal to the ratio of the product of the force and the deformation to the product of the length and area.

Question 19

What is the strain energy dependent on for an axially loaded member below the proportionality limit?

Answer 19

It depends on the average force.

Question 20

What is the sign convention for the shear stress in triaxial and biaxial loading?

Answer 20

Clockwise shear stresses are positive and counter clockwise shear stresses are negative.

Question 21

What are principal stresses?

Answer 21

The maximum and minimum normal stresses.

Question 22

Where are principal stresses found?

Answer 22

The normal stresses associated with the plane where the shear stress is zero.

Question 23

What is the Mohr’s circle?

Answer 23

A circle constructed to graphically determine the principal normal and shear stresses.

Question 24

What does the maximum normal stress theory predict?

Answer 24

It uses the normal stresses to predict the failure.

Question 25

Under what conditions is the maximum normal stress theory used?

Answer 25

for brittle materials under static biaxial loading.

Question 26

When is failure expected to occur for tensile and compressive stress?

Answer 26

If the largest principle stress is greater than the ultimate strength.

Question 27

Do brittle materials have larger tensile or compressive strength?

Answer 27

Compressive strength.

Question 28

When are stress concentration factors applicable to brittle materials?

Answer 28

When the brittle materials are under static loading.

Question 29

What are the stress concentration factors?

Answer 29

Factor of safety, allowable stress, and the failure criterion.

Question 30

What does the maximum shear stress theory predict?

Answer 30

Shear stress can be used to predict yielding.

Question 31

Under what conditions is the maximum shear stress theory used?

Answer 31

Ductile materials under static loading.

Question 32

Are can normal stresses be used for the shear stress theory?

Answer 32

Yes

Question 33

According to the maximum shear stress theory. When is yielding expected to occur?

Answer 33

When the maximum shear stress exceeds the yield strength in shear.

Question 34

What is the yield strength equal to in shear for the maximum shear stress theory?

Answer 34

It is equal to half the tensile yield strength.

Question 35

What is the maximum shear stress in three dimensions?

Answer 35

The maximum of the three combined shear stresses.

Question 36

What is the distortion energy theory?

Answer 36

It is used to predict tensile are shear failure.

Question 37

Under what conditions is the distortion energy theory used?

Answer 37

It is used for steel and other ductile parts subjected to static loading.

Question 38

What is the von Mises stress?

Answer 38

It is the stress used in the left hand side of the equation for the distortion energy theory.

Question 39

Can the distortion energy theory be used for biaxial and triaxial loading?

Answer 39

Yes, the left hand of the distortion energy theory has an interchangeable equation for biaxial and triaxial conditions.

Question 40

What is the factor of safety equal to in the distortion energy theory?

Answer 40

It is equal to the tensile yield strength divided by the von Mises stress.

Question 41

If loading is pure torsion at failure then what are the stresses in the von Mises stress equal to?

Answer 41

Normal stress one is equal to normal stress two which is equal to the maximum shear stress and normal stress three is equal to zero.

Question 42

What is the When is the modified Goodman theory used?

Answer 42

A part that is subjected to a combination of static and reversed loadings.

Question 43

What is the alternating stress equal to in the modified Goodman theory?

Answer 43

Half of the range stress or half the difference between the max and minimum normal stress (the range stress).

Question 44

When is the Soderberg theory used?

Answer 44

Under variable loading.