steel temperature cals

7/31/2019 Steel Temperature Cals

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ShortCourse

ResponseofMaterialsandStructurestoFires

May20

22,

2009

CarletonUniversity,Ottawa,Ontario

Performance of Steel Structures

Exposed to Fire

Noureddine Benichou

National Research Council of Canada

IndustrialResearchChairinFireSafetyEngineeringDepartmentofCivilandEnvironmentalEngineering

Behaviour of Steel Structuresin Fire When steel structures are under fire exposure:

s ee empera ures ncrease

strength and stiffness of the steel are reduced

This leads to deformation and potential failure

Increase in steel temperatures depends on:

fire severity

Short Course Response of Materials and Structures to Fires, May 20 22, 2009

area of steel exposed to fire amount of applied fire protection


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Behaviour of Steel Structures in

Fire Steel has high thermal conductivity values than

Thermal expansion of steel members can cause

damage in other parts of the building

The main factors affecting the behaviour of steel

structures in fire are as follows:


applied loads on the steel members

mechanical properties of steel members

geometry of the steel members

Protection Systems

Protected steel members can have excellent fire resistance

A number of alternative passive fire protection systems are

available to reduce temperature increase in steel structures

exposed to fire

Concrete encasement

Board systems

-


Intumescent paint

Concrete filling


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Design Methods

Design for fire resistance requires:

provided fire resistance > design fire severity

The verification may be in the:

time domain,

temperature domainor


Generic Ratings

The table below is an example taken from NBC

Minimum thickness of solid concrete protection to

steel columns to provide fire resistance (NBC)

Time (hours) 1/2 3/4 1 1.5 2 3 4


Thickness (mm) 25 25 25 25 39 64 89


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Steel Temperatures

Thermal Properties To design steel structures for standard or real,

For calculating these temperatures, knowledgeof materials thermal properties is necessary

The density of steel is 7850 kg/m3 and remainsessentially constant with temperature


Steel Temperatures

Section Factor

The section factor is another characteristic to

determine the rate of temp. rise in steel members

The section factor is a measure of ratio of heated

perimeters to the area of the cross sections as:

F/V (m-1) or Hp / A (m-1)

= 2


V = volume of steel in unit length of member (m3)

Hp = heated perimeter of cross section (m)

A = cross-sectional area of section (m2)


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Section Factor


Temperature Calculation

Methods

Simple calculations can be used to obtain the

empera ures

Simple calculations assume a lumped mass of

steel at a uniform temperature over the cross

section of the steel

The methods are not valid for:


Members with significant temp. gradients over crosssections, e.g. I-beam with a concrete slab on top

members protected with heavy insulating materials


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Best-fit Calculation Method

Unprotected Steel The time t (min) for steel to reach a limiting temp.

lim w en expose o s an ar res:

t = 0.54(Tlim - 50)/(F/V)0.6

F/V is the section factor (m-1)

This expression is valid for:


m n m n

10 F/V 300 m

-1

400C Tlim 600C


Protected Steel

The time t (min) for a steel member protectedw an nsu a on o reac lim w enexposed to standard fires:

t = 40 (Tlim - 140) [(di / ki)/(F/V)]0.77

ki is the thermal conductivity of insulation (W/m-K)

d is the thickness of the insulation m


This equation is valid for:

30 t 240 min

0.1 di/ki 0.3 m2K/W


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Protected Steel For insulation containing moisture, a time delay

tv (min) can be added to the time t using:

tv = m i di2 / (5ki)

i is the insulation density (kg/m3)

m is the insulation moisture content (%)


Step-by-step Calculation Method

Unprotected Steel The calculation method for unprotected steel is:

Ts = (F/V)(1/(s cs)) [hc(Tf-Ts) + (Tf4-Ts

4)] t Ts is the change in steel temperature (C or K)

s is the density of steel (kg/m3)

cs is the specific heat of steel (J/kg K)

hc is the convective heat transfer coefficient (W/m2K)

is the Stefan-Boltzmann constant


is the resultant emissivity (0.50)

Tf is the temperature in the fire environment (K)

Ts is the temperature of the steel (K)

t is the time step (30 s is usually used)


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Step-by-step Calculation Method

Spreadsheet calculation for temperatures of steel

Time Steel temperatureTs

Fire temperatureTf

Difference intemperature

Change in steel

temperature Ts

t1 = t Initial steeltemperature Tso

Fire temperaturehalfway through time

step (at t/2)

Tf- Tso Calculate from

equation ofTswith values of Tfand Tso from this

row

t2 = t1 + t Ts from previous time

ste + T from

Fire temperature halfwa throu h time ste

Tf- Ts Calculate from

E uation ofT


previous row (at t1 + t/2) with values of Tf

and Ts from thisrow

WORKED EXAMPLE

Use the step-by-step method to calculate the steel

empera ure o an unpro ec e an pro ec e

beam exposed to the ISO 834 standard fire.

F/V=200 m-1, hc=25 W/m2K, =0.6, =7850 kg/m3,

cs=600 J/kg-K, di=50 mm, ki=0.2 W/m-K,


ci= g , i= g m , = . m n


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WORKED EXAMPLE

The first two minutes of the solution are shownTime Time at half Steel ISO fire Difference in Change in

Ts

half step Tf temperature

0.0 0.25 20.0 184.6 164.6 6.8

0.5 0.75 26.8 311.6 284.7 13.8

1.0 1.25 40.6 379.3 338.7 18.2

1.5 1.75 58.8 425.8 366.9 21.5

2.0 2.25 80.3 461.2 380.9 24.0

2.5

3.0

Time Time at half Steel ISO fire Difference in Change in


m nu es s ep empera ureTs

empera ure ahalf step Tf

empera ure s eetemperature

0.0 0.25 20.0 184.6 164.6 0.62

0.5 0.75 20.6 311.6 290.9 1.101.0 1.25 21.7 379.3 357.6 1.35

1.5 1.75 23.1 425.8 402.7 1.52

2.0 2.25 24.6 461.2 436.6 1.65

2.5

3.0

Typical Steel Temperatures

Typical steel temp. for unprotected/protected steel

eams expose o s an ar res



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Structural Design of Steel

Members The structural design steel structures exposed to

temperatures in the steel and

mechanical properties at elevated temperatures

Structural design requires prevention of:

collapse (strength limit) most important in design


Design methods are grouped in two categories :

simplified methods for individual/single elements

general methods for buildings (frames or structures)

Mechanical properties of steel

Stress-related Strain


Hot rolled steelstress-strain curves

Yield strength and

proof strength


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Mechanical properties of steel

Design values


Yield strength and modulus of elasticity of steel

Design Methods

Verification in the strength domain requires:

U*fire Rfire U*fire is design force resulting from applied loads

at the time of the fire

Rfire is load-bearing capacity in fire situation

(equations in codes/standards can be adapted)


is strength reduction factor (usually equal to 1at high temperatures)


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Design of Individual Members

Tension members The design equation:fire f

Nf= A ky,T fy (uniform temp.)

Nf= i=1,nAi ky,Ti fy (temp. gradient)

A and A area/elemental area of cross section (mm2)


ky,T and ky,Ti - reduction factor for yield strength of steel

fy - yield strength of the steel at ambient (MPa)

T and Ti temperatures


Simply supported beams The design equation is:

*fire f

Mf= S ky,T fy (uniform temp. - plastic)

Mf= Z ky,T fy (uniform temp. - elastic)

Mf= i=1,nAi zi ky,Ti fy (temp. gradient)

i=1,nAi ky,Ti fy = 0 (neutral axis location at time t)


S and Z plastic/elastic section modulus (mm3) zi - distance from the plastic neutral axis to the centroid of

the elemental area Susceptibility of beams to local buckling should be

considered


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Design of Individual Members -

Simply supported beams


The equation for elastic design should be used for Class 3sections (elastic moment without local buckling)

For light cold-rolled sections susceptible to local buckling(Class 4), equations are not applicable

Worked ExampleA simply supported steel beam with a span of8 m,

known load, ield stren th, and section ro erties.Calculate the flexural strength after 15 minutesexposure to the standard fire. The beam has noapplied fire protection and is exposed on 3 sides.

Given Dead load Gk = 8.0 kN/m (including self weight)


k . Beam size 410 mm deep and 54 kg/m (section class 1)

Plastic section modulus S = 1060 x 103 mm3

Section factor F/V = 190 m-1

Yield strength fy = 300 MPa


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Worked Example

Cold Calculations

reng re uc on ac or = .

Design load (cold) wc = 1.2Gk+ 1.6Qk = 33.6 kN/m

Bending moment M*cold = wcL2/8 = 269 kN-m

Bending strength Mn = Sfy = 318 kN-m (assume adequate

lateral restraint)

Desi n flexural stren th M = 286 kN-m


Design is OK (M*cold < Mn)

Worked Example

Fire Calculations Strength reduction factor = 1.0 (hence not used in the

calculations)

Design load (fire) wf= Gk+0.4Qk = 14.0 kN/m

Bending moment M*fire = wfL2/8 = 112 kN-m

Temperature after time t:

= 0.6+


.

Temperature after 15 minutes:

T = 1.85 x 15 x 1900.6 + 50 = 696C

Yield strength reduction ky,T = (905-T)/690 = 0.30


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Worked Example

Flexural capacity:

f y,T y

Mf= 1060 x 103 x 0.30 x 300/106 = 95 kN-m

Design fails (M*fire > Mf)

(Note: For more accurate temperature calculations, the

step-by-step method could be used. The flexural

calculation method would be the same.)



Columns The design equation is:

*re

Nf= (fi/1.2) A ky,Tm fy (Eurocode approximation)

The whole cross section is assumed at the maximumtemperature Tm

fi is the ambient buckling factor, calculated using theeffective bucklin len th for fire desi n cases


1.2 is an empirical correction factor

A is the area of the cross section, ky,Tm is the reductionfactor for the yield strength of steel at Tm, and fy is theyield strength of the steel at ambient


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Design of Steel Buildings

Exposed to Fire

Steel buildings design cannot be cost-effective

by the simple methods described previously

It is necessary to use computer programs for

analysis of the fire-exposed structure

Programs will impose deformations on the

structure and calculate the total strain in a


member resulting from the deformations

Calculated fire resistance of a structural steelmember is enhanced when part of a frame

Layout of the car park structure

Fire in a Car Park Structure -

Example

- vera mens ons

- Type of steel sections used

Composite slabThickness = 0.12 m

HEA500

3.33 m


3.2 m

10.0 m

15.0 m

4.2 m

IPE550

HEB240

IPE500

IPE550

3.33 m

HEB240


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Example


Ignition of one of the cars Fully developed fire


Example

BEAM:columns

used for modelling

the structure

SHELL : concrete slab


BEAM : steel sections, profiled

steel sheets and concrete ribsPIPE : connection between

steel sections and

composite slab


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Example

the floor after 32

minutes of fire



Example

Stress distribution

on the exposed side

of the concrete slab

after 32 minutes of

fire



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Example


Strains of steel mesh within the

concrete slab after 32 minutesMaximum temperatures

within structural elements

References ZHAO B. & KRUPPA J. (March 2002). Numerical modelling of structural

behaviour of open car parks under natural fires. SIF 02 Structures inFire 2ndInternational Workshop Christchurch (NZ)

Buchanan A., Structural Design for Fire Safety, Wiley, 2001



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steel temperature cals

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