过程装备与控制工程专业英语翻译3

Reading material 3

Theories of strength

1.

Principal stresses

The state of the stress at a point in a structural member under a complex system of loading

is

described

by

the

magnitude

and

direction

of

the

principal

stresses.

The

principal

stresses

are the maximum values of the normal stresses at the point; which act on the planes on which the

shear

stress

is

zero.

In

a

two-dimensional

stress

system,

Fig.1.11,

the

principal

stresses

at

any

poin

t are related to the normal stress in the x and y directions σ

x

and σ

y

and the shear stress τ

xy

at

the point by the following equation:

?

?

1

1

2

(

?

y

?

?

x

)

2

?

4

?

xy

Principal stresses,

?

< br>?

(

?

y

?

?

x

)

?

?

2

?

2

2

The maximum shear stress at the point is equal to half the algebraic difference between the

principal stresses.

stresses:

Maximum shear stress,

?

max

?

1

(

?

1< /p>

?

?

2

)

2

Compressive stresses are conventionally taken as negative; tensile as positive.

2.

Classification of pressure vessels

For

the

purpose

of

design

and

analysis,

pressure

vessels

are

sub-divided

into

two

classes

depending on the ratio of the wall thickness to vessel diameter

:

thin-wall vessels, with a thickness

ratio of less than 1/10, and thick-walled above this ratio.

The principal stresses acting at a point in the wall of a vessel, due to a pressure load, are

shown in Fig.1.12. If the wall is thin, the radial stress

σ

3

will be small and can be neglected in

comparison with the other stresses , and the longitudinal and circumferential stresses

σ

1

and

σ

2

can

be taken as constant over the wall thickness. In a thick wall, the magnitude of the radial stress will

be significant, and the circumferential stress will vary across the wall. The majority of the vessels

used

in

the

chemical

and

allied

industries

are

classified

as

thin-walled

vessels.

Thick-walled

vessels are used for high pressures.

3.

Allowable stress

In the first two sections of this unit equations were developed for finding the normal stress

and average shear stress in a structural member. These equations can also be used to select the size

of

a

member

if

the

member’s

strength

is

known.

The

strength

of

a

material

can

be

defined

in

several

ways,

depending

on

the

material

and

the

environment

in

which

it

is

to

be

used.

One

definition

is

the

ultimate

strength

or

stress.

Ultimate

strength

of

a

material

will

rupture

when

subjected to a purely axial load. This property is determined from a tensile test of the material.

This

is

a

laboratory

test

of

an

accurately

prepared

specimen,

which

usually

is

conducted

on

a

universal testing machine. The load is applied slowly and is continuously monitored. The ultimate

stress or strength is the maximum load divided by the original cross- sectional area. The ultimate

strength for most engineering materials has been accurately determined and is readily available

If

a

member

is

loaded

beyond

its

ultimate

strength

it

will

fail---- rupture.

In

the

most

engineering structures it is desirable that the structure not fail. Thus design is based on some lower

value called

allowable stress

or design stress. If, for example, a certain steel is known to have an

ultimate strength of 110000 psi, a lower allowable stress would be used for design, say 55000 psi.

this allowable stress would allow only half the load the ultimate strength would allow. The ratio of

the ultimate strength to the allowable stress is known as the

factor of safety

:

Factor

of

saf

ety

?

ultimate

strength

Su

or

n

?

allowable

stress

Sa

We use S for strength or allowable and σ for the actual stress in material. In a design:

This

so-called

factor

of

safety

covers

a

multitude

of

sins.

It

includes

such

factors

as

the

uncertainty of the load, the uncertainty of the material properties and the inaccuracy of the stress

analysis. It could more accurately be called a factor of ignorance! In general, the more accurate,

extensive, and expensive the analysis, the lower the factor of safety necessary.

4.

Theories of failure

The failure of a simple structural element under unidirectional stress (tensile or compressive)

is easy to relate to the tensile strength of the material, as determined in a standard tensile test, but

for

components

subjected

to

combined

stresses

(normal

and

shear

stress)

the

position

is

not

so

simple,

and

several

theories

of

failure

have

been

proposed.

The

three

theories

most

commonly

used are described below:

Maximum principal stress theory: which postulates that a member will fail when one of the

principal

stresses

reaches

the

failure

value

in

simple

tension,

σ

’

e

.

The

failure

point

in

a

simple

tension

is

taken

as

the

yield- point

stress,

or

the

tensile

strength

of

the

material

divided

by

a

suitable factor of safety.

Maximum

shear

stress

theory:

which

postulates

that

failure

will

occur

in

a

complex

stress

system when the maximum shear stresses reaches the value of the shear stress at failure in simple

tension.

For a system of combined stresses there are three shear stresses maxima:

In the tensile test,

?

e

?

?

e