Engineering Science 1021A/B Lecture Notes - Lecture 5: Shear Stress, Stress (Mechanics), Modulus Guitars
17 May 2018
School
Department
Professor
Stress
Stress: force acting per unit area over which the force is applied
•
Tensile and compressive stresses are normal stress
•
Normal stress: act in a direction perpendicular to the cross-section that
supports them
•
Tension causes elongation in the direction of the applied
𝐹
, whereas
compression causes shortening
•
Shear stress: occurs when the applied
𝐹"
acts in a direction parallel to the area
of interest
•
Strain
Strain: change in dimension per unit length
•
Elastic Strain: fully recoverable strain resulting from an applied stress
Develops instantaneously (as soon as
𝐹
is applied)
○
Remains as long as stress is applied
○
Recovers when
𝐹
is withdrawn
○
Elastomers have large elastic deformations
○
•
Plastic Strain: material does not go to original shape when stress is removed
Causes plastic deformation
○
•
Stress-Strain Curve
𝐴 = yield point
After this point, the specimen will be permanently deformed and will not
go to its original form
○
•
After the yield point, the strain is both elastic and plastic•
Young's Modulus (Modulus of elasticity)
Slope of a tensile stress strain curve in the linear regime•
•
Total Strain
Total strain is the sum of the elastic strain and plastic strain•
•
Unit of elastic energy stored:
Pa ×[no units]
○
=𝑁
𝑚(=𝑁 ) 𝑚
𝑚*=𝐽
𝑚*
○
•
Stress, Strain and Young's Modulus
Stress
Stress: force acting per unit area over which the force is applied•
Tensile and compressive stresses are normal stress•
Normal stress: act in a direction perpendicular to the cross-section that
supports them
•
Tension causes elongation in the direction of the applied 𝐹, whereas
compression causes shortening
•
Shear stress: occurs when the applied 𝐹"acts in a direction parallel to the area
of interest
•
Strain
Strain: change in dimension per unit length•
Elastic Strain: fully recoverable strain resulting from an applied stress
Develops instantaneously (as soon as 𝐹is applied)
○
Remains as long as stress is applied
○
Recovers when 𝐹is withdrawn
○
Elastomers have large elastic deformations
○
•
Plastic Strain: material does not go to original shape when stress is removed
Causes plastic deformation
○
•
Stress-Strain Curve
𝐴 = yield point
After this point, the specimen will be permanently deformed and will not
go to its original form
○
•
After the yield point, the strain is both elastic and plastic•
Young's Modulus (Modulus of elasticity)
Slope of a tensile stress strain curve in the linear regime•
•
Total Strain
Total strain is the sum of the elastic strain and plastic strain•
•
Unit of elastic energy stored:
Pa ×[no units]
○
=𝑁
𝑚(=𝑁 ) 𝑚
𝑚*=𝐽
𝑚*
○
•
Stress, Strain and Young's Modulus
Stress
Stress: force acting per unit area over which the force is applied•
Tensile and compressive stresses are normal stress•
Normal stress: act in a direction perpendicular to the cross-section that
supports them
•
Tension causes elongation in the direction of the applied 𝐹, whereas
compression causes shortening
•
Shear stress: occurs when the applied 𝐹"acts in a direction parallel to the area
of interest
•
Strain
Strain: change in dimension per unit length•
Elastic Strain: fully recoverable strain resulting from an applied stress
Develops instantaneously (as soon as 𝐹is applied)
○
Remains as long as stress is applied
○
Recovers when 𝐹is withdrawn
○
Elastomers have large elastic deformations
○
•
Plastic Strain: material does not go to original shape when stress is removed
Causes plastic deformation
○
•
Stress-Strain Curve
𝐴 =
yield point
After this point, the specimen will be permanently deformed and will not
go to its original form
○
•
After the yield point, the strain is both elastic and plastic
•
Young's Modulus (Modulus of elasticity)
Slope of a tensile stress strain curve in the linear regime
•
•
Total Strain
Total strain is the sum of the elastic strain and plastic strain•
•
Unit of elastic energy stored:
Pa ×[no units]
○
=𝑁
𝑚(=𝑁 ) 𝑚
𝑚*=𝐽
𝑚*
○
•
Stress, Strain and Young's Modulus
