Biomechanics Quiz 2
in 3D, there are 9 components of stress relative to the prescribed coordinate system. of which, how many components are independent?
6
within a 3d matrix, there are ___ independent components
6
in 3D, how many components of stress relative to the prescribed coordinated system exist?
9
when shear stress is at the maximum, the normal stress at the same point is
average
The figure above shows the state of 2-D stress at a point, p, computed in reference to two different coordinate systems (x-y and x'-y'). As angle ⍺ between the two coordinate systems increases, the value of 𝜎'xx + 𝜎'yy a) Decreases compared to 𝜎xx + 𝜎yy b) Increases compared to 𝜎xx + 𝜎yy c) Is always the same as 𝜎xx + 𝜎yy as long as acting on the same point d) Changes, but it is a function of ⍺
c) Is always the same as 𝜎xx + 𝜎yy as long as acting on the same point
The figure above shows the state of 2-D stress at a point, p, computed in reference to two different coordinate systems (x-y and x'-y'). As angle ⍺ between the two coordinate systems reaches 45 degrees, the value of 𝜎'xx + 𝜎'yy a) Decreases compared to 𝜎xx + 𝜎yy b) Increases compared to 𝜎xx + 𝜎yy c) Is always the same as 𝜎xx + 𝜎yy as long as acting on the same point d) Changes, but it is a function of ⍺
c) Is always the same as 𝜎xx + 𝜎yy as long as acting on the same point
another word for stress
force intensity
define strain
measure of motion (deformation) coinciding with stress
if a force acting on an area is parallel to the outward normal vector (of the area), then the force is called 15
normal force
stress depends on
orientation of an area, orientation of a force, choice of coordinate system
the maximum and minimum normal stresses are also termed as _____ stresses
principal
if a force acting on an area is perpendicular to the outward normal vector (of the area), then the force is called
shear force
____ defines stiffness
slope
the modern concept of stress defined in the 19th century states that stress is a measure of a force acting over an oriented area. thus, it carries information about two directions (of the area and of force), which means that mathematically stress is a _____
tensor
what does the eigenvalue measure
the stretching factor of a linear transformation that points in a direction in which the data/vector/object is stretched
a displacement vector, u (ux, uy), is used to track the motion of a particle and quantifies the difference between two points in space, the current position (denoted by position vector x) and the original position (denoted by position vector X). the relationship between the two positions vectors is then u = ____
u = x - X
When normal stress is at the maximum, the shear stress at the same point is
zero
in 2D, there are 4 components of stress relative to the prescribed coordinate system. of which, how many components are independent?
3
the modern concept of stress was defined in the 19th century by
Cauchy
the earlier concept of stress was defined in the 18th century by
Euler
equation for normal stress
F/A
the earliest concept of stress was recognized in the 17th century by
Hooke
A displacement vector, u (ux, uy), is used to track the motion of a particle and quantified the difference between two points in space, the current position (denoted by position vector X2) and the original position (denoted by position vector X1). The relationship between the two positions vectors is then
X2 = u + X1
when the components of a displacement gradient vector, u (ux,uy) is given by Ux=0.01X and Uy=0 through this displacement, the original point X1 (X,Y) = X1(1,1) will move to a new location X2(X,Y)=
X2(1.01,1)
define stress
a force acting over an oriented area at any point in a body
The figure above shows the state of 2-D stress at a point, p, computed in reference to two different coordinate systems (x-y and x'-y'). As angle ⍺ between the two coordinate systems increases, the value of 𝜎'yy a) does not change compared to 𝜎'yy, it is not a function of ⍺ b) increases compared to 𝜎yy c) decreases compared to 𝜎yy d) is always the same as 𝜎yy because it is the same element
c) decreases compared to 𝜎yy
according to Cauchy's definition, strains are a combination of ______________
displacement gradient
shear strain measures the angle of
displacement gradients
the FBD indicates that the stress is uniform throughout the specimen. as x increases, what happens to the displacement at that x location? and what happens to strain at that x location?
displacement increases, while strain is constant and independent of x