s&m3- laboratory 2010-11
TRANSCRIPT
![Page 1: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/1.jpg)
Concrete Laboratory Preparation 2010-11
Calculation of design and predictedcracking and ultimate loads
Dr Iman Hajirasouliha
Structures & Materials 3
H23SM3
![Page 2: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/2.jpg)
Outline:
Introduction to the laboratory exercise
Bending behaviour
Measurement of strains and deflections
Calculation of predicted loads
Jobs for you to do BEFORE the laboratory
![Page 3: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/3.jpg)
Laboratory 2 - 4 pm on Tuesdays :
Group A 8 February 2011
Group B 15 February 2011
Group C 22 February 2011
Group D 1 March 2011
Others join group A
Report hand-in 2 weeks later.
Feedback Tuesday 3 May 2011
![Page 4: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/4.jpg)
Location : ground floor L2
![Page 5: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/5.jpg)
La a
P
Four-point Bending Test
Load spreader beam
![Page 6: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/6.jpg)
La a
P
Nominal beam dimension 8” deep x 4” wide(203 x 102 mm)
Effective span approx. L = 1.370 m
![Page 7: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/7.jpg)
La a
P
2 no. H16or H10 bars
25 mmcover tomain bars(not thelinks!)
Nominal beam dimension 8” deep x 4” wide(203 x 102 mm)
Effective span approx. L = 1.370 m
![Page 8: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/8.jpg)
1. Mid-span deflection d
Structural response using 2 methods :
![Page 9: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/9.jpg)
1. Mid-span deflection d
Structural response using 2 methods :
Plot P vs d
Dial Deflection Gauge
![Page 10: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/10.jpg)
2. Curvature
M E s
I R y= =
Divide through by E …
R
(Radius of Curvature )
![Page 11: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/11.jpg)
M 1 eE I R y
= =
1/R = M / EI = strain gradient
Curvature = strain gradient
![Page 12: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/12.jpg)
Measurement of strains through the beam
using DEMEC gauge
DEMEC pips (5 pairs willbe glued to your beams)
Centre-line of beam
![Page 13: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/13.jpg)
Measurement of strains through the beam
using DEMEC gauge
DEMEC pips (5 pairs willbe glued to your beams)
Centre-line of beam
Will be demonstrated in the laboratory
![Page 14: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/14.jpg)
DEMEC gauge
Centre-line of beam
200 mm
0.0034
DEMEC factor: 0.001 = 4 x 10-6 strain
![Page 15: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/15.jpg)
Measure the change in the DEMECreading, converting this to strain
DEMEC pips moveapart = tension
DEMEC pips movecloser = compression
![Page 16: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/16.jpg)
Measure the change in the DEMECreading, converting this to strain
DEMEC pips moveapart = tension
DEMEC pips movecloser = compression
![Page 17: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/17.jpg)
Measure the change in the DEMECreading, converting this to strain
using the instrument’s factor
DEMEC pips moveapart = tension
DEMEC pips movecloser = compression
![Page 18: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/18.jpg)
Plot strains e along y-axis of beam for all5 pairs of DEMEC
X
X
e
y
XX
X
![Page 19: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/19.jpg)
X
X
e
y
XX
X
Draw best straight line through 5 values
![Page 20: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/20.jpg)
X
X
e
y
XX
X
Draw best straight line through 5 values
Slope = e /y = M / EI = Pa / 2EI
Plot P v e /y
![Page 21: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/21.jpg)
P
d or e/y
So now you have graphs of load vsdeflection and strain gradient …
![Page 22: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/22.jpg)
Theoretical Predictions
1.“Design” using EC2 with nominalvalues and safety factors
2.“Fundamental” using actual test data
![Page 23: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/23.jpg)
Applied load P orbending moment
Basic load vs deformation behaviour for RC beam
Actual behaviour in a test
Deflection or e/y
![Page 24: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/24.jpg)
Applied load P orbending moment
Basic load vs deformation behaviour for RC beam
Actual behaviour in a test
Theoreticalprediction
Deflection or e/y
![Page 25: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/25.jpg)
Basic load vs deformation behaviour for RC beam
Why different ?
Deflection or e/y
![Page 26: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/26.jpg)
No cracking
Stiffness based onuncracked cross section Iu
Centroidaxis
Centroid isnot the
same asneutral axis
at ULS !
Mo
me
nt
Deflection or e/y
![Page 27: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/27.jpg)
During crackingCentroid
axis
Mo
me
nt
Deflection or e/y
![Page 28: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/28.jpg)
Mo
me
nt
After cracking
Stiffness based on crackedcross section Ic
Centroidaxis
Deflection or e/y
![Page 29: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/29.jpg)
After cracking
Centroidaxis
MRd
Mc
Cracking moment of resistanceMc = fctm Zbottom fctm = 2.90 N/mm2
Deflection or e/y
![Page 30: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/30.jpg)
Now do the flexural stiffness andstrength calculations …
![Page 31: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/31.jpg)
Young’s modulus of steel / concrete = m
Today only m = 200 / 33.3 = 6.0
As mAs
xx
modular ratio
![Page 32: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/32.jpg)
Direct deflection calculation
Say 100
Say 170
Uncracked 2nd MoA
Say200
xu
xu =
Today only b = 100 mm
h = 200 mm
![Page 33: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/33.jpg)
Direct deflection calculation
Say 100
Say 170
Uncracked 2nd MoA
Say200
xu
(m-1)As = 5.0 x 157= 785 mm2
xu =
Why ?
![Page 34: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/34.jpg)
Direct deflection calculation
Say 100
Say 170
Uncracked 2nd MoA
Say200
xu
(m-1)As = 5.0 x 157= 785 mm2
xu =
(m-1) because the steel replacesthe area of concrete it occupies
![Page 35: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/35.jpg)
Direct deflection calculation
Say 100
Say 170
Uncracked 2nd MoA
Say200
xu
xu =100 x 2002/2 + 785 x 170
From thetop
100 x 200 + 785
xu = 102.6 mm
(m-1)As = 5.0 x 157= 785 mm2
![Page 36: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/36.jpg)
Direct deflection calculation
Uncracked 2nd MoA
102.6
xu = 102.6 mm
Iu = 100 x 2003/12
+ 100 x 200 x (102.6 – 200/2)2
+ 785 x (170 – 102.6)2
= 70.4 x 106 mm4
Say 170
Say 100
Say200
(m-1)As = 5.0 x 157= 785 mm2
![Page 37: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/37.jpg)
Direct deflection calculation
Uncracked 2nd MoA
102.6
xu = 102.6 mm
Iu = 100 x 2003/12
+ 100 x 200 x (102.6 – 200/2)2
+ 785 x (170 – 102.6)2
= 70.4 x 106 mm4
and ZB = 70.4 / 97.4 = 0.722 x 106 mm3
97.4
ZB section modulus at the bottom of the beam
![Page 38: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/38.jpg)
Then, just before cracking occurs
Mc ≤ fctm ZB
Mc ≤ 0.722 x 106 x 2.90 x 10-6 = 2.09 kNm
From EC2: fctm= 0.3 fck2/3
fctm is flexural tensile cracking strength
![Page 39: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/39.jpg)
La a
Find Pc
![Page 40: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/40.jpg)
La a
Find PcLoad rig = 38 kg
Concrete = 25 kN/m3
![Page 41: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/41.jpg)
La a
Pc
Self weight w = 0.2 x 0.1 x 25 = 0.5 kN/m
P/2 P/2
F = 0.38 kN
2.09 kNm here
Load rig = 38 kg
Concrete = 25 kN/m3
![Page 42: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/42.jpg)
La a
Pc
Self weight w = 0.2 x 0.1 x 25 = 0.5 kN/m
P/2 P/2
Mc = Pc a/2 + etc etc
F = 0.38 kN
![Page 43: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/43.jpg)
1.37 m0.432
Pc
Self weight w = 0.2 x 0.1 x 25 = 0.5 kN/m
P/2 P/2
Prove yourself that
Pc = 8.75 kN
F = 0.38 kN
0.432
![Page 44: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/44.jpg)
First crackCentroid
axis
P
Pc = 8.75 kN
Deflection or e/y
![Page 45: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/45.jpg)
Anticipated cracking load
? kN
![Page 46: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/46.jpg)
Direct deflection calculation
170
Cracked 2nd MoAxc
xc =100 xc
2/2 + 942 x 170
From thetop
100 xc + 942
mAs = 6.0 x 157 =942 mm2
Say 100
![Page 47: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/47.jpg)
Direct deflection calculation
170
Cracked 2nd MoAxc
xc =100 xc
2/2 + 942 x 170
From thetop
100 xc + 942
mAs = 6.0 x 157 =942 mm2
Say 100
Solving the quadratic
xc = 48 mm
![Page 48: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/48.jpg)
Direct deflection calculation
170
Cracked 2nd MoAxc
xc =100 xc
2/2 + 942 x 550
From thetop
100 xc + 942
mAs = 6.0 x 157 =942 mm2
Say 100
Solving the quadratic
xc = 48 mm
Ic = 100 x 483/3
+ 942 x (170 – 48)2
= 17.7 x 106 mm4
![Page 49: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/49.jpg)
8.75
?
P
Deflection or e/y
![Page 50: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/50.jpg)
z
Fs
Fc
Ultimate moment of resistance :
Fs = 0.87 x 500 x 157 = 68295 N
Fc = 0.567 fck x 100 x 0.8X
fck = 30 N/mm2
![Page 51: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/51.jpg)
z
Fs
Fc
Ultimate moment of resistance :
Fs = 0.87 x 500 x 157 = 68295 N
Fc = 0.567 fck x 100 x 0.8X
X = 50.2 mm < 0.6d
(Note how close this is to xc = 48 mm)
z = 170 – 0.4 x 50.2 = 150 mm
MRd = 68295 x 150 x 10-6 = 10.24 kNm
x
![Page 52: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/52.jpg)
Ultimate moment of resistance :
Fs = 0.87 x 500 x 157 = 68295 N
Fc = 0.567 fck x 100 x 0.8X
X = 50.2 mm < 0.6d
(Note how close this is to xc = 48 mm)
z = 170 – 0.4 x 50.2 = 150 mm
MRd = 68295 x 150 x 10-6 = 10.24 kNm
PRd = 46.5 kN
![Page 53: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/53.jpg)
8.75
46.5
P
Deflection or e/y
![Page 54: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/54.jpg)
If mean partial safety factor fordead and live load is about 1.4
Anticipated failure load
?
![Page 55: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/55.jpg)
Mark crack patterns and loads like this -
![Page 56: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/56.jpg)
Before your lab class :
Repeat these exercises for thedimensions given in the handout, for H10
and H16 bars
including the design gradients of the
load v deflection and e/y graphs
![Page 57: S&M3- Laboratory 2010-11](https://reader033.vdocuments.site/reader033/viewer/2022051819/551984fe4a795939038b46db/html5/thumbnails/57.jpg)
Bring your hard hats
Steel toe cap boots (we have extra pairs)
Wear grubby clothes
Bring calculations and graphs showinganticipated design beam loads, etc.
Camera
Hand-in also includes your Mix Design Sheet
End