C6Jet Impingement

Slide 1

EPRI PSECivil/Structural, Module 6-Jet Impingement and Pressure

Loading Analysis

EPRI 1010809CIVIL/STRUCTURAL SERIES

MODULE 6JET IMPINGEMENT AND PRESSURE

LOADING ANALYSIS

Slide 2


Loading Analysis

MODULE OBJECTIVES

The objectives of this module are as follows:

» Describe the nature of the pressure/impulsive loads.

» Summarize aspects of structural response.

» Describe the design methods.

» Apply the above principles to solve example jet impingement problems.

» Discuss Computer Methods.

Slide 3


Loading Analysis

DEFINITIONSImpulsive loads» Transient (time varying) loads that are determined by an external

source and are relatively insensitive to structural response.» Independent of the target inertial and stiffness properties.» Generally force, but not energy, limited.» May result from jet impingement, accidental sub-compartment

pressure, etc.

Impactive loads» Caused by one body striking another.» The load is limited by the kinetic energy of the colliding bodies.» Affected by the inertial and stiffness properties of the striking

bodies.

Slide 4


Loading Analysis

PARAMETERS DEFINING PRESSUREDESIGN RANGES

L O A D

TIME

Resistance

Pressure

Resistance

Pressure

TIME

Resistance

Pressure

tmto tmto tm toTIME TIME

L O A DL O A D

Pressure - Design Range HIGH LOW VERY LOW

Design Load Impulse Pressure-Time Pressure

Incident Pressure 100 psi 100 psi 10 psi

Pressure Duration short intermediate long

Response Time long intermediate short

Relationship of tm/to tm/to 3 3 tm/to 0.1 tm/to 0.1

Slide 5


Loading Analysis

TYPICAL HIGH ENERGY LINE BREAKPRESSURE-TIME

Peak Load

Steady StatePressure

Rise

Time

Decay Time

Pres

sure

Time

Slide 6


Loading Analysis

FLUID JET MODELS

Velocity, Pressure & Temperature Profiles

Non-expanding jet

DownstreamPlane

AsymptoticPlane

Break (Exit)Plane

Velocity, Pressure & Temperature Profiles

Break (Exit)Plane

CoreRegion

Jet Boundary

Expanding jet

Slide 7


Loading Analysis

YIELD STRESS of A-7 and REINFORCINGSTEEL (1 ksi = 6.9 Mpa)

50

60

40

10-1 110-2

Yie

ld s

tress

, (ks

i)

Time to yield, (sec)

Intermediate grade

A-7 and structuralgrade-average curve

A-7 and structuralgrade- 90% curve

Slide 8


Loading Analysis

EFFECT OF RATE OF STRAIN ONCOMPRESSIVE STRENGTH OF STEEL

190

170

110

130

150

9010-6 10-5 10-4 10-3 10-2 10-1 1 10 100

Rate of 6.95x10-3 in./in./sec. is used as base Watstein-weak concrete

Watstein-strong concrete Abrams

Bureau of reclamation

Rate of straining, in inches per inch per second

Perce

nt of

static

stren

gth ob

taine

d

Slide 9


Loading Analysis

DISPLACEMENT-RESPONSE SPECTRAFOR THREE TYPES OF IMPULSE

Impulse length ratio, Tt1

Half sine waveRectangular

Triangular

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

2.4

2.0

1.6

1.2

0.8

0.4Dynamic

Magnif

ication F

actor

Slide 10


Loading Analysis

EFFECT OF DAMPING ON THE RESPONSETO IMPULSE LOADING

Undamped

= 5%

0 0.05 0.10 0.15 0.20 0.25

20

40

60

-60

-80

80

0

-20

-40

100

-100

Time (sec.)

Elas

tic R

espo

nse

Forc

e (k

ips)

Blast load

Slide 11


Loading Analysis

SINGLE-DEGREE OF FREEDOM SYSTEM

Linearly Elastic Resistance Function

X(t)

f(t)

K-Stiffness

Displacement X

Force f(t)

Time t

R

Xe

Res

ista

nce

R

Stiffness K Mass M

Xm

F1

td

RM

System Schematic

Triangular Impulse Load Time History

Elasto-Plastic Resistance Function

Slide 12


Loading Analysis

XM / XE CURVES FOR ELASTIC-PLASTICSYSTEM, RECTANGULAR IMPULS LOAD

V a lu e o f Tt

C dT

0 . 1 1 .0 1 0 4 0

R m X m

t m

D i s p l a c e m e n tfu n c t i o nR e s i s t a n c e fu n c t i o n1F

RC m

R

E l a s t i c1 . 0

1 0

0 . 1

1 0 0

1 . 00 .9

1 . 6

1 . 0 2

1 . 0 5

1 . 80

1 . 2

0 . 4

1 . 3

0 . 6

1 . 4

1 . 1

0 . 2

C R = 2 .0

R e c ta n g u la r l o a d

t d t

F 1

F ( t ) R

XX e

t

X

Xm/X

e

Slide 13


Loading Analysis

ASSUMED STATIC DEFORMED SHAPES FORDETERMINATION OF TRANSFORMATION FACTORS

Elastic hinges

Plastic hinges

Plastic hinges

Slide 14


Loading Analysis

STRUCTURES WITH DISTRIBUTED MASSAND STIFFNESS

Equivalent Mass – The equivalent mass of the single-degree-of-freedom system is derived to maintain equality of kinetic energy with the real system.

Equivalent Load Time History – The equivalent load is derived by equating work done by the actual load in deflecting the real structure to the assumed deflected shape, to the work done by the equivalent load on the equivalent system.

Equivalent Resistance-Displacement Function – The equivalent resistance-displacement function is obtained by first determining the resistance-displacement function for the real structure, then converting to the equivalent system using the transformation factor KR.

Slide 15


Loading Analysis

COEFFICIENT FOR MOMENT OFCRACKED SECTIONS

1.0

10-1

Ratio n1.0

10-1

10-2

10-2

Coeff

ecien

t, FIer= Fbd3

0.75

1.0

0.500.25

0

Value of

'

Slide 16


Loading Analysis

JET EXPANSION MODEL

Asymptotic PlaneBreak Plane

Djet(exit)

Djet(asym)

X = 5Djet(exit)

= 10

Slide 17


Loading Analysis

DETERMINATION OF SHAPE FACTORSFOR JET IMPINGEMENT

K = c o s

D 0

K = 0 . 5 7 6D j = 2 r j

r s i n

0

424.1

D

DK j

P l a n e S u r f a c e I m p i n g e m e n t l e s s t h a n p i p e d i a m e t e r

I m p i n g e m e n t g r e a t e r t h a n p i p e / c o n d u i t d i a m e t e r

A 1T D 0r j

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C6Jet Impingement