Strength of Materials (EMCH 213): Intro and Stress and Strain

surface, body

A body is subjected to only two types of external loads: blank and blank forces

scalar

A physical quantity that has magnitude only.

vector

A quantity that has magnitude and direction

force ΔF,direction, ΔFx,ΔFy, ΔFz

A typical finite yet very small blank, acting on ΔA will have a unique blank, but compared to other forces, we'll replace it by its component's blank, blank and blank

separated ,draw a free body diagram

After cutting the section through the region where the internal loading are determined, the two parts are blank and you can then blank of each part

distribution of internal force

After drawing a free body diagram of each part that was separated by the section, you can see that there is a blank acting on the exposed area of the section

each , single concentrated force

Although body forces affect blank of the particles composing the body, these forces are normally represented by a blank acting on the body

force of the ground on bicycle wheels

An example of a concentrated force

two small punch marks

Before testing( tension and compression), blank are placed along the specimen's uniform length.

σ = P/A_o

Equation for the nominal or engineering stress in conventional stress diagram

balance of forces, balance of moments

Equilibrium of a body requires both a blank, to prevent the body from translating or having accelerated motion along a straight or curved path, and a blank, to prevent the body from rotating.

F_fail/F_allow

Factor of safety equation

greater than 1

Factor of safety must be blank to avoid potential failure

coplanar

For two-dimensional problems, i.e., bodies subjected to blank force systems

Stress-strain diagram

From the tension and compression test, we get blank

normal force, shear force, bending moment

If a body is subjected to coplanar system of forces, the only forces that will exist in the section are

single concentrated force, point

If the area of contact is small compared to the total surface of the body, then the surface force can be idealized as a blank, which is applied to a blank on the body

Σ Fx = 0 , Σ Fy = 0 , ΣMo = 0

If the forces lie only in the x-y plane, then the conditions for equilibrium can be specified with only three scalar equilibrium equations

tensile stress, compressive stress

If the normal force or stress pulls on ΔA , then it is a blank, whereas if it pushes on ΔA it is a blank

linear distributed load

If the surface loading is applied along a narrow strip area, the loading can be idealized as blank

limit ΔA-0 ΔF_x/ΔA

If we have a shear force in the x direction and a normal force in the x direction, then τ_zx equals

limit ΔA-0 ΔF_y/ΔA

If we have a shear force in the y direction and a normal force in the x direction, then τ_zy equals

shape, yielding

If you stretch past the elastic limit, you'll affect the blank leading to a breakdown in material -This behavior is known as blank

lim ΔA-0 ΔF_z/ΔA

If ΔFz is normal to the area, then σ_z =

positive

If θ' is larger than π/2, then the shear strain is blank

moments about point O in z-direction, normal force, shear force

In a coplanar system of forces, the bending moment (M_O) can be determined by summing blank in order to determine the moments caused by unknown blank and blank

area of contact

In all cases, the surface forces are distributed over the blank between the bodies

imaginary section,through the region

In order to obtain the internal loadings acting on a specific region within the body, it is necessary to pass an blank or "cut" blank where the internal loadings are to be determined.

F_R and M_RO, normal and perpendicular

In order to relate the resultant loadings, F_R and M_RO, to the distribution of the force on the sectioned area, we must consider the components blank acting both blank to the sectioned area

weight

In the case of gravitation, this force is called the blank of the body and acts through the body's center of gravity

normal stress

Intensity of force acting normal to the area (ΔA)

decrease, necking

Just after, at the ultimate stress, the cross-sectional area will begin to blank in a localized region of the specimen. As a result, a constriction or blank tends to form in this region as the specimen elongates further

ε = L - L_o/ L_o

Nominal or engineering strain equation

stretching, perfectly plastic

Once yield point is reached, specimen experiences a constant blank and referred to as blank

tension, compression

P, internal resultant force, is always positive if it causes blank, but negative if it causes blank

couple moment

Since the member can freely rotate about the roller, a blank cannot be developed on the member.

in/in, m/m

Strain is usually expressed in units blank or blank

yield point, σy

Stress that causes yielding is known as blank and is represented as blank -Deforms plastically

internal force

The blank on the exposed area of the section represent the effects of the material of the top part of the body acting on the adjacent material of the bottom part.

shear stress

The intensity of the force acting tangent to ΔA

length of a beam

The loading along the blank is a typical example of where this idealization that the resultant acts through the centroid is often applied.

force/length, a series of arrows

The loading of the surface that is applied to a narrow surface of land is measured as having an intensity of blank along the strip and is represented graphically by blank along the lines

reactions

The surface forces that develop at the supports or points of contact between bodies are called

conventional and true

The two types of stress-strain diagrams

cross section, gauge length

This calculation for the nominal or engineering stress assumes that the stress is constant over the blank and throughout the blank

torque, T

This effect is developed when the external loads tend to twist one segment of the body with respect to the other about an axis perpendicular to the area.

normal force, N

This force acts perpendicular to the area

shear stress, V

This force lies in the plane of the area and it is developed when the external loads tend to cause the two segments of the body to slide over one another.

ε << 1

This is considered the small strain analysis

made, standard shape and size

To perform a tension or compression test a specimen of the material is blank into a blank

continuous, cohesive

Two assumptions about the body when discussing stress are that the body is blank and blank

x-direction, y-direction

Using x, y, and z coordinate axes then normal force will be obtained by applying net forces in the blank direction and the shear force by applying net forces in the blank direction

1 Pascal

What unit equals 1 N/m^2 and represents the unit for stress

ΔF, components, finite limit

When a typical finite force acts on on area and the ΔA approaches zero, so do blank and its blank, however, the quotient of the force and area will approach a blank

elastic behavior

When drawing a curve for a stress- strain diagram, the strain within the specimen are within a certain region of diagram -stress is proportional to the strain

z-axis

When forces lie in the x-y direction, the moments summed at point O will be directed along the blank

increase, rising, ultimate stress

When the yielding ends, an blank in load can be supported by the specimen leading to a blank curve until it reaches blank

strain

a measure of the deformation of the body

cohesive

all portions of it are connected together, without having breaks, cracks, or separations

torsonial moment

another word for torque

surface forces

are caused by the direct contact of one body with the surface of another

stress

associated with the strength of the material from which the body is made

ε = Δs' -Δs / Δs

average normal strain equation

σ = P/A

average normal stress equation

τ_avg = V/A, same

average shear stress equation, is assumed to be blank at each point located on the section

deformation

changes in the size and shape -depending on the force and another factor, can be noticeable or unnoticeable

continuous

consists of continuum or uniform distribution of matter having no voids

shear strain

deformations can cause strains to change direction

stress

describes the intensity of the internal force acting on a specific plane (area) passing through a point

body forces

developed when one body exerts a force on another body without direct physical contact between the bodies

δ = L- L_o

equation used to measure the elongation of the tick marks

effects caused by the earth's gravitation or its electromagnetic field

examples of body forces

σ_fail/ σ_allow, τ_fail/τ_allow

factor of safety equation in terms of normal stress and factor of safety equation in terms of shear stress

by experiments

how is strain measured

perpendicular

if a member is long and slender, as in the case of a rod or beam, the section to be considered for the section of the sectioned area is generally taken blank to the longitudinal axis of the member.

couple moment

if rotation is prevented, a blank must be exerted on the member.

same direction

if the support prevents translation in a given direction, then a force must be developed on the member in blank

mechanics of materials

includes the study of the body's stability when a body such as a column is subjected to compressive loading

Bending moment, M

is caused by the external loads that tend to bend the body about an axis lying within the plane of the area.

coplanar

on the same plane

yield strength

point where stress is beginning

factor of safety, F.S.

ratio of the failure load F_load to the allowable load F_allow and can be denoted as blank

Σ F

represents the sum of all the forces acting on the body

Σ M

represents the sum of the moments of all the forces about any point O either on or off the body.

resultant force

the blank of the linear distributed load is equivalent to the area under the distributed loading curve, and this acts through the centroid C

normal strain

the change in length of a line per unit length

centroid, C

the geometric center of the area

strain hardening

the name of the rising curve after the yielding ends

σ, sigma

the normal stress is represented by what symbol

perpendicular or normal, normal

the roller support only prevents translation blank to the surface which is why the roller exerts a blank force on the member at its point of contact.

cross section

the section taken perpendicular to the longitudinal axis of the member

τ, tau

the shear force is represented by the symbol

uniaxial stress

two normal stress components on the element must be equal in magnitude but opposite in direction

tension and compression test

used to measure the relationship between the average normal stress and average normal strain

M_RO

variable for moment

F_R

variable for resultant force

w(s)

variable that represents the linear distributive load

Equations of Equilibrium

we can use blank to relate the external forces on the bottom part of the body to the distribution's resultant force and moment at any specific point O on the sectioned are

P

what represents the internal resultant force acting through the centroid of the cross-sectional area in the average normal stress equation

V

what symbol represents the internal shear force on the section that can also be determined from the equations of equilibrium