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Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 1
Practical Design to Eurocode 2
The webinar will start at 12.30
Lecture Date Speaker Title
1 21 Sep Jenny Burridge Introduction, Background and Codes
2 28 Sep Charles Goodchild EC2 Background, Materials, Cover and effective spans
3 5 Oct Paul Gregory Bending and Shear in Beams
4 12 Oct Charles Goodchild Analysis
5 19 Oct Paul Gregory Slabs and Flat Slabs
6 26 Oct Charles Goodchild Deflection and Crack Control
7 2 Nov Paul Gregory Columns
8 9 Nov Jenny Burridge Fire
9 16 Nov Paul Gregory Detailing
10 23 Nov Jenny Burridge Foundations
Course Outline
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 2
Fire Design
Lecture 8
9th November 2017
Practical Design to Eurocode 2
Model answers for Lecture 7
Columns
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 3
Column Exercise
Assume the following:
• Axial load: 7146kN
• Top Moment: 95.7kN
• Bottom Moment: -95.7kN
• Nominal cover: 35mm
• Bay width is 6.0 m
• Elastic modulus is the same
for column and slab
Design the column C2
between 1st and 2nd floors
for bending about axis
parallel to line 2.
Take ‘beam’ width
as, say, half the
bay width
Solution - effective length & slenderness (M2)
41.0
9600
1230030002
8600
1230030002
4200
12500
2 33
4
====××××××××
++++××××××××
========
∑∑∑∑b
b
c
c
L
EI
L
EI
k
From Table (Table 4 of How to…Columns)
F = say 0.74
∴∴∴∴ lo = 0.74 x 4.2 = 3.108 m
Check slenderness:
λ = 3.46 lo/h
= 3.46 x 3.108 /0.5 = 21.5
Using PD 6687 method
Clear span is 4500 – 300 = 4200 mm and k1 = k2
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 4
Solution- column moments
MEd = max[M02; M0Ed + M2; M01 + 0.5M2 ; e0NEd]
M02 = M + eiNEd
ei = l0/400 =3108/400 = 7.8 mm
NEd = 7146 kN
= 95.7 + 0.0078 x 7146 = 95.7 + 55.7 = 151.4 kNm
M0Ed = (0.6M02 + 0.4M01) ≥ 0.4M02
= 0.6 × 151.4 + 0.4 × (− 40.0) ≥ 0.4 × 95.7 = 74.8 kNm
M01 = - 95.7 + 0.0078 x 7146 = -95.7 + 55.7 = - 40.0 kNm
e0NEd = 0.02 x 7146 = 142.9 kNm
e0 = Max[h/30,20mm]
= Max[500/30,20mm] = 20 mm
M2 = ?
Limiting slenderness:
A = 0.7 (use default value)
B = 1.1 (use default value)
C = 1.7 – rm = 1.7 – M01/M02 = 1.7 – (-40.0/151.4) = 1.96
n = NEd/Acfcd = 7146 x 1000/(5002 x 0.85 x 50/1.5) = 1.01
λlim = 20 ABC/√n
= 20 x 0.7 x 1.1 x 1.96/√1.01
= 30.0
Slenderness:
30.0 > 21.5 ...section is not slender . . . . M2 = 0
Solution – slenderness limit (M2)
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 5
Solution- column moments
MEd = max[M02; M0Ed + M2; M01 + 0.5M2 ; e0NEd]
M02 = M + eiNEd
ei = l0/400 =3108/400 = 7.8 mm
NEd = 7146 kN
= 95.7 + 0.0078 x 7146 = 95.7 + 55.7 = 151.4 kNm
M0Ed = (0.6M02 + 0.4M01) ≥ 0.4M02
= 0.6 × 151.4 + 0.4 × (− 40.0) ≥ 0.4 × 95.7 = 74.8 kNm
M01 = - 95.7 + 0.0078 x 7146 = -95.7 + 55.7 = - 40.0 kNm
e0NEd = 0.02 x 7146 = 142.9 kNm
e0 = Max[h/30,20mm]
= Max[500/30,20mm] = 20 mm
M2 = 0
By inspection,
max[M02; M0Ed + M2; M01 + 0.5M2 ; e0NEd] = MEd = 151.4 kNm
d2 = cnom + link + ϕ/2 = 35 + 8 + 16 = 59 mm
d2/h = 59/500 = 0.118
MEd/(bh2fck) = 151.4 x 106/(5003 x 50) = 0.024
NEd/(bhfck) = 7146 x 1000/(5002 x 50) = 0.57
Solution – determine As
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 6
Interaction Chart
0.09
0.024
0.57
Solution – determine As
Asfyk/bhfck = 0.09
As = 0.09 x 5002 x 50 / 500 = 2250 mm2 Try 8 H20 (2513 mm2)
But > 4 no bars so check d2/h
Average d2 = (3 x 59 + 1 x 250 [say] ) / 4 = 107 mm : d2/h = 0.214
Interpolating between charts for d2/h = 0.20 and d2/h = 0.25
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 7
Interaction Chart
Asfyk/bhfck
0.100.57
0.024
Solution – determine As
Asfyk/bhfck = 0.09
As = 0.09 x 5002 x 50 / 500 = 2250 mm2 Try 8 H20 (2513 mm2)
Check d2/h
Average d2 = (3 x 59 + 1 x 250 [say] ) / 4 = 107 mm : d2/h = 0.214
Using chart for d2/h = 0.20
Asfyk/bhfck = 0.10
As = 0.10 x 5002 x 50 / 500 = 2500 mm2
Use 8 H20 (2513 mm2)
Links
Diameter = max (6, 20/4) = 6 say 8mm diam
scl,tmax = min {12 φmin; 0.6b ; 240mm} = 240 mm
Bar centres = 500/2 -59 = 191 mm therefore each bar to be
restrained
With H8 links in 3 legs each way @ 225 cc
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 8
Fire Design
Fire
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 9
a Axis
Distance
Reinforcement cover
Axis distance, a, to centre of bar
a = c + φφφφm/2 + φφφφl
Scope
Part 1-2 Structural fire design gives several methods for fire engineering
Tabulated data for various elements is given in section 5
Structural Fire DesignPart 1-2, Fig 5.2 Figure 4.2
• High strength concrete
• Basis of fire design
• Material properties
• Tabulated data
• Design procedures
– Simplified and advanced calculation methods
– Shear and torsion
– Spalling
– Joints
– Protective layers
• Annexes A, B, C, D and E
• General
Eurocode 2: Part 1.2 Structural Fire Design
100 Pages
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 10
• Requirements:
– Criteria considered are:
“R” Mechanical resistance (load bearing)
“E” Integrity (compartment separation)
“I” Insulation (where required)
“M” Impact resistance (where required)
• Actions - from BS EN 1991-1-2
– Nominal and Parametric Fire Curves
Chapter 2: Basis of Fire Design
• Verification methods Ed,fi ≤ Rd,fi(t)
• Member Analysis Ed,fi = ηfi Ed
Ed is the design value for normal temperature design
ηfi is the reduction factor for the fire situation
ηfi = (Gk + ψfi Qk.1)/(γGGk + γQ.1Qk.1) ψfi is taken as ψψψψ1 or ψψψψ2 (= ψψψψ1 - NA)
Chapter 2: Basis of Fire Design
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 11
• Tabulated data (Chapter 5)
• Simplified calculation methods
• Advanced calculation method
Design Procedures
Which method?
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 12
Provides design solutions for the standard fire exposure up to 4 hours
• The tables have been developed on an empirical basis confirmed by experience and theoretical evaluation of tests
• Values are given for normal weight concrete made with siliceous aggregates
• For calcareous or lightweight aggregates minimum dimension may be reduced by 10%
• No further checks are required for shear, torsion or anchorage
• No further checks are required for spalling up to an axis distance of 70 mm
• For HSC (> C50/60) the minimum cross section dimension should be increased
Section 5. Tabulated DataCl. 5.1 -
Elements
• Approach for Beams and Slabs very similar
– Separate tables for continuous members
– One way, two way spanning and flat slabs
treated separately
• Walls depend on exposure conditions
• Columns depend on load and slenderness
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 13
Continuous BeamsTable 5.6 Table 4.6
Flat Slabs
Table 4.81992-1-2 Table 5.9
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 14
Columns Tabular Approach
Columns more Tricky!
• Two approaches
• Only for braced structures
• Unbraced structures – columns
can be considered braced if
there are columns outside the
fire zone
μfi = NEd,fi/ NRd = Gk + ψ1,1 Qk,1/(1.35Gk + 1.5 Qk) NEd/ NRd Conservatively 0.7
where NEd,fi is the design axial load in the fire condition
NRd is the design axial resistance at normal temperature
The minimum
dimensions are
larger than
BS 8110
Columns: Method ATable 5.2a Table 4.4A
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 15
Limitations to Table 5.2a
Limitations to Table 5.2a for Method A:
• Effective length of the column under fire conditions
l0,fi <= 3m.
• First order eccentricity under fire conditions:
e = M0Ed,fi / N0Ed,fi <= emax = 0.15 h
• Amount of reinforcement:
As < 0.04 Ac
Method A
� � 120����� ���������
�����.� (Exp 5.7)
where:
���� � 83 1.0 � μ��1 � ω
0.85 α""⁄ � ω
(as αcc = 0.85 in the UK, Rηfi = 83(1.0-μfi))
Ra = 1.6(a-30)
where a is the axis distance
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 16
Method A
� � 120����� ���������
�����.� (Exp 5.7)
Rl = 9.6 (5 - l0,fi)
where l0,fi is the effective length in fire.
For an insitu column in a braced structure this can be
taken is 0.5 l for lower storeys and 0.7 l for the top
storey. (2 m ≤ l0,fi ≤ 6m)
Method A
� � 120����� ���������
�����.� (Exp 5.7)
Rb = 0.09b’
b’ is the width or the diameter of a square or circular
column.
For a rectangular column:
b’ = 2Ac/(b+h)
200mm ≤ b’ ≤ 450mm
h ≤ 1.5 b’
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 17
Method A
� � 120����� ���������
�����.� (Exp 5.7)
Rn = 0 where n=4 (corner bars only)
Rn = 12 where n>4
(n is the number of longitudinal bars)
Method A
� � 120����� � �$ � �% � �& � �'
120��.�
What is the fire resistance period of a 3.5m long, 300 x 600 column,
NEd = 2950kN, NRd = 3600kN, with 25mm bars, 10mm links, cover
25mm?
μfi = 0.7 x 2950/3600 = 0.57 Rηfi = 83(1-0.57) = 35.4
a = 25+10+25/2 = 47mm Ra = 1.6(47-30) = 27.2
l0,fi = 0.5 x 3.5 = 1.75, so l0,fi = 2m Rl = 9.6(5-2) = 28.8
b’ = 2 x b x 1.5b/(b + 1.5b) = 360mm Rb = 0.09 x 360 = 32.4
n>4 Rn = 12
R = 120((35.4 + 27.2 + 28.8 + 32.4 + 12)/120)1.8 = 150 minutes
(from table
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 18
Method A
� � 120����� � �$ � �% � �& � �'
120��.�
What is the fire resistance period of a 3.5m long, 300 x 600 column,
NEd = 2950kN, NRd = 3600kN, with 25mm bars, 10mm links, cover
25mm?
μfi = 0.7 x 2950/3600 = 0.57 Rηfi = 83(1-0.57) = 35.4
a = 25+10+25/2 = 47mm Ra = 1.6(47-30) = 27.2
l0,fi = 0.5 x 3.5 = 1.75, so l0,fi = 2m Rl = 9.6(5-2) = 28.8
b’ = 2 x b x 1.5b/(b + 1.5b) = 360mm Rb = 0.09 x 360 = 32.4
n>4 Rn = 12
R = 120((35.4 + 27.2 + 28.8 + 32.4 + 12)/120)1.8 = 150 minutes
(from table: 90 minutes)
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 19
Columns: Method B
ω = 0.1 � 0.4% steel
ω = 0.5 � 2.0% steel
ω = 1.0 � 4.0% steel
(fck = 30MPa, fyk = 500MPa)
Limitations to Table 5.2b
• l/h (or l/b) ≤ 17.3 for rectangular column (λfi ≤ 30)
• First order eccentricity under fire conditions:
e/b = M0Ed,fi /b N0Ed,fi ≤ 0.25 with emax= 100 mm
• Amount of reinforcement, ω = As fyd / Ac fcd ≤ 1
For other values of these parameters see Annex C (e/b ≤ 0.5, emax ≤ 200 mm)
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 20
• EC2 distinguishes between explosive spalling that can occur
in concrete under compressive conditions, such as in
columns, and the concrete falling off the soffit in the
tension zones of beams and slabs.
• Explosive spalling occurs early on in the fire exposure and is
mainly caused by the expansion of the water/steam particles
trapped in the matrix of the concrete. The denser the
concrete, the greater the explosive force.
− Unlikely if moisture content is less than 3% (NDP) by
weight. The assumption is that in exposure class X0 or
XC1 the moisture class is less than 3%
− Tabular data OK for axis distance up to 70 mm
• Falling off of concrete occurs in the latter stage of fire
exposure
Spalling
Minimum cross section should be increased:
• For walls and slabs exposed on one side only by:
For Class 1: 0.1a for C55/67 to C60/75
For Class 2: 0.3a for C70/85 to C80/95
• For all other structural members by:
For Class 1: 0.2a for C55/67 to C60/75
For Class 2: 0.6a for C70/85 to C80/95
Axis distance, a, increased by factor:
For Class 1: 1.1 for C55/67 to C60/75
For Class 2: 1.3 for C70/85 to C80/95
High Strength Concrete -Tabulated Data
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 21
• For C 55/67 to C 80/95 the rules for normal strength concrete apply.
provided that the maximum content of silica fume is less than 6% by
weight.
• For C 80/95 to C 90/105 there is a risk of spalling and at least
one of the following should be provided (NA):
Method A: A reinforcement mesh
Method B: A type of concrete which resists spalling
Method C: Protective layers which prevent spalling
Method D: Monofilament polypropylene fibres.
High Strength Concrete -Spalling
Other Methods
• Simplified calculation method for beams, slabs
and columns
• Full Non-linear temperature dependent ……..
• But all of these must have the caveat that they
are unproven for shear and torsion.
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 22
Rd1,fi
MRd,fi,Span
MRd2,fi
M
M = w l / 8Ed,fi Ed,fi eff
1
1 - Free moment diagram for UDL under fire conditions
Annex E: Simplified Calculation Method for Beams and Slabs
Free bending moment in fire condition MEd,fi:
MEd,fi = wEd,fileff2/8
where
wEd,fi = gk + ψ1qk
Moments of resistance in fire condition:
MRd,fi,Span = (γs /γs,fi ) ks(θ) MEd (As,prov /As,req)
MRd,fi,Support = (γs /γs,fi ) MEd (As,prov /As,req) (d-a)/d
Where a is the required bottom axis distance given in Section 5
As,prov /As,req should not be taken greater than 1.3
Annex E: Simplified Calculation Method for Beams and Slabs
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 23
500°C Isotherm Method
Ignore concrete > 500°C
Strength of rebar
dependent on steel
temperature
500°C Isotherm Method
Charts in BS EN 1992-1-2
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 24
Decrease in strength of reinforcement (Figure 4.2)
Zone Method
Divide concrete into zones and work out average
temperature of each zone, to calculate strength
Zones
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 25
Zone Method
Factors for
concrete
strength
Zone Method
Balance forces with Fst,fi to calculate MRd,fi
Calculate compression forces in zones
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 26
Worked Example
• NEd= 1824kN
• Myy,Ed= 78.5kNm
• Mzz,Ed= 76.8kNm
• 2 hour fire resistance
required
• External, but no de-icing
salts
• fck = 30MPa
Worked Example
Cover:
cmin,b = diameter of bar (assume 25mm bars with 8mm links)
cmin,dur = (XC3/XC4) 25mm
say Δcdev = 10mm
cnom (to main bars) = max{(25+10),(25+8+10)} = 43mm
Use cnom = 35mm to 8 mm links
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 27
Worked Example
Check fire resistance of R120 to Method A
eccentricity e < 0.15b
e = MEd/NEd = 78.5x103/1824 = 43mm
0.15 x 350 = 52.5mm ∴ OK
Assume 8 bars ∴ OK
l0,fi = 0.7l = 2.8m < 3m ∴ OK
From Table 5.2a: min dimensions = 350/57
Column is 350mm, axis distance required = 57mm
Check cover – 35mm + 8 (link) + φ/2 = 55.5mm
∴ Increase links to 10 mm diam
or increase nominal cover to 40mm.
Design exercise for next week
Using Equation 5.7, work out the fire resistance of a 250
x 750 column with an axial capacity of 3750kN and an
axial load in cold conditions of 3500kN. The column is on
the ground floor of a three storey building and the length
is 4.5m. The cover is 30mm, main bars are 20mm and
the links are 10mm diameter.
Practical Design to Eurocode 2 Autumn 2017
Week 8: Fire 28
Design Exercise
� � 120����� � �$ � �% � �& � �'
120��.�
μfi = Rηfi =
a = Ra =
l0,fi = Rl =
b’ = Rb =
n = Rn =
R = 120((Rηfi + Ra + Rl + Rb + Rn)/120)1.8 =
End of Lecture 8