Stresses and Strains Flashcards
What is the mechanics of materials the study of?
The elastic behavior of materials and the stability of members.
When is the mechanics of materials concepts used?
To determine the stress and deformation of axially loaded members, connections, torsional members, thin walled pressure vessels, beams, eccentrically loaded members, and columns.
What is stress?
the force per unit area.
How many types of stress are there?
Normal stress and shear stress.
What is the difference between normal and shear stress?
In normal stress, the force is normal to the surface area and in shear stress, the force is parallel to the surface area.
What are the two subcategories of normal stress?
Tensile and compressive stress.
What are the sign conventions of tensile and compressive stress?
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.
What is linear strain?
The change in length per unit length.
What is shear strain?
Is an angular deformation resulting from shear stress.
What is Hooke’s Law?
States that the stress is proportional to the strain.
What is Hooke’s Law for normal stress?
The normal stress is equal to the product of the strain and the modulus of elasticity.
What is an isotropic material?
The properties of the material are the same in all directions.
What is an anisotropic material?
The properties of the material vary with direction.
What is Poisson’s ratio?
Is the ratio of the lateral strain to the axial strain for axially loaded members.
What is Hooke’s Law for a plane element in pure shear?
The shear stress is equal to the product of the shear strain and the shear modulus.
Under what conditions are the Poisson’s ratio, shear and elastic modulus related?
An elastic isotropic material.
What is strain energy?
Is the energy per unit volume stored in a deformed material.
What is the strain energy equal to?
It is equal to the ratio of the product of the force and the deformation to the product of the length and area.
What is the strain energy dependent on for an axially loaded member below the proportionality limit?
It depends on the average force.
What is the sign convention for the shear stress in triaxial and biaxial loading?
Clockwise shear stresses are positive and counter clockwise shear stresses are negative.
What are principal stresses?
The maximum and minimum normal stresses.
Where are principal stresses found?
The normal stresses associated with the plane where the shear stress is zero.
What is the Mohr’s circle?
A circle constructed to graphically determine the principal normal and shear stresses.
What does the maximum normal stress theory predict?
It uses the normal stresses to predict the failure.
Under what conditions is the maximum normal stress theory used?
for brittle materials under static biaxial loading.
When is failure expected to occur for tensile and compressive stress?
If the largest principle stress is greater than the ultimate strength.
Do brittle materials have larger tensile or compressive strength?
Compressive strength.
When are stress concentration factors applicable to brittle materials?
When the brittle materials are under static loading.
What are the stress concentration factors?
Factor of safety, allowable stress, and the failure criterion.
What does the maximum shear stress theory predict?
Shear stress can be used to predict yielding.
Under what conditions is the maximum shear stress theory used?
Ductile materials under static loading.
Are can normal stresses be used for the shear stress theory?
Yes
According to the maximum shear stress theory. When is yielding expected to occur?
When the maximum shear stress exceeds the yield strength in shear.
What is the yield strength equal to in shear for the maximum shear stress theory?
It is equal to half the tensile yield strength.
What is the maximum shear stress in three dimensions?
The maximum of the three combined shear stresses.
What is the distortion energy theory?
It is used to predict tensile are shear failure.
Under what conditions is the distortion energy theory used?
It is used for steel and other ductile parts subjected to static loading.
What is the von Mises stress?
It is the stress used in the left hand side of the equation for the distortion energy theory.
Can the distortion energy theory be used for biaxial and triaxial loading?
Yes, the left hand of the distortion energy theory has an interchangeable equation for biaxial and triaxial conditions.
What is the factor of safety equal to in the distortion energy theory?
It is equal to the tensile yield strength divided by the von Mises stress.
If loading is pure torsion at failure then what are the stresses in the von Mises stress equal to?
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.
What is the When is the modified Goodman theory used?
A part that is subjected to a combination of static and reversed loadings.
What is the alternating stress equal to in the modified Goodman theory?
Half of the range stress or half the difference between the max and minimum normal stress (the range stress).
When is the Soderberg theory used?
Under variable loading.
