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