CEE370L_LAB2_Vergara, Kailah
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CEE 370 Mechanics of Materials Lab
Stress-Strain Relationships for Concrete – Compression
Kailah Vergara
University of Hawaii at Manoa
CEE 370L Mechanics of Materials
09/19/2023
0
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
EXECUTIVE SUMMARY
In this laboratory experiment, we subjected two distinct concrete cylinder specimens
to a compression test and then analyzed their individual responses using an
extensometer. The analysis encompassed various aspects of their behavior, including
the maximum average stress and average ultimate stress exhibited by both cylinders.
Additionally, we investigated Poisson's effect ratio, the proportional limit, and the
associated strain specifically for Cylinder 2. By utilizing the respective stress-strain
curves and extracting data points at 10% and 40% strain levels from the experimental
data, we were able to ascertain these behaviors. Once these values were computed, we
proceeded to determine key material properties for each specimen, namely Young's
modulus (stiffness) and density. This comprehensive analysis provided us with a deeper
understanding of the characteristics of the specimens.
The study revealed that Concrete Cylinder 1 and Concrete Cylinder 2 exhibited
brittle characteristics under progressively increasing compressive loads. Among the two,
Cylinder 2 displayed the highest density, measuring (
137.84676
lb/ft^3), and was able to
endure the greatest compressive load (Pult = 54428 Ibf). Additionally, it recorded the
highest maximum average stress, reaching 3712.2188 psi. The average ultimate stress
for both specimens was determined to be
4000.2358 psi
. Furthermore, the calculated
average Poisson’s ratio for both Concrete Cylinders was
0.19.
Page
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
TABLE OF CONTENTS
EXECUTIVE SUMMARY………………...
……………………………………………………………...i
1
INTRODUCTION
..................................................................................................................
1
1.1
B
ACKGROUND
....................................................................................................................
1
1.2
R
EASON
FOR
E
XPERIMENT
................................................................................................
1
1.3
T
HEORY
.............................................................................................................................
1
1.4
O
BJECTIVE
.........................................................................................................................
2
2
APPROACH
...........................................................................................................................
3
2.1
T
EST
S
ETUP
AND
I
NSTRUMENTATION
................................................................................
3
2.2
T
EST
S
PECIMENS
...............................................................................................................
3
2.3
T
EST
P
ROCEDURE
..............................................................................................................
5
3
RESULTS
................................................................................................................................
6
3.1
C
ONCRETE
C
YLINDER
1
AND
2
........................................................................................
6
3.2
C
ONCRETE
C
YLENDER
1
..................................................................................................
7
3.3
C
ONCRETE
C
YLENDER
2
..................................................................................................
7
4
ANALYSIS
..............................................................................................................................
9
4.1
C
ONCRETE
C
YLENDER
1
..................................................................................................
9
4.2
C
ONCRETE
C
YLENDER
2
..................................................................................................
9
5
CONCLUSIONS/RECOMMENDATIONS
.......................................................................
10
6
REFERENCES
.....................................................................................................................
11
APPENDIX
TABLE OF FIGURES
Figure 1.3.1: Stress-strain diagram for a typical concrete structure in compression
.......................
2
Figure 2-.1: Compression test specimen 1 with 810 Material test System
......................................
3
Figure 2-1.2:
Humboldt 5080 System.
..........................................................................................
3
Figure 2-2.1:
Compression test specimen 1
....................................................................................
4
Figure 2-2.2:
Compression test specimen 2
...................................................................................
4
Figure 3-1.1:
Stress vs Strain Curve
...............................................................................................
6
Figure 3-1.2:
Magnified view of linear region of stress strain curve with Young’s modulus
..................
7
TABLE OF TABLES
Table 2-2.1: Specimen 1 and 2 Worksheet Data
..............................................................................
4
Table 3-.1:
Specimen 1 and 2 Objectives Data
..............................................................................
6
Table 3-.2:
Specimen 1 and 2 Calculated Data
...............................................................................
6
Table 3-2.1:
Specimen 1: Test 1
......................................................................................................
7
Table 3-3.1:
Specimen 2: Test 1-3
..................................................................................................
7
Table 3-3.2:
Specimen 2: Axial and Transverse Strain
...................................................................
8
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
Page
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
1. Introduction
1.1
Background
This lab builds upon the tension test and focuses on the importance of using specific
concrete specimens to ensure the reliability and durability of structures. By understanding the
specifications for each concrete specimen, engineers can make informed choices to create
enduring and sustainable solutions for the community. The critical properties of these specimens
are established through a compression test. During this experiment, multiple specimens,
including concrete specimens 1 and 2, were subjected to testing. The first cylinder underwent
axial compression testing until failure, while the second cylinder was tested using
circumferential and double-axial extensometers, spanning from a 10% load to a 40% load until
failure. This comprehensive analysis allows for the determination of key parameters such as
density, maximum average stress, average ultimate stress, Young's modulus, Poisson's ratio, and
the proportional limit, thereby enhancing the engineer's design capabilities through an extensive
evaluation process.
1.2
Reason for Experiment
The compression test offers insights into a material's mechanical characteristics, assessing
its strength when subjected to controlled compression until it fails. This examination aids in the
selection of suitable materials for a given purpose, guarantees compliance with standards and
specifications, and furnishes valuable observations on how the material behaves under varying
compression conditions.
1.3
Theory
The stress-strain curve in tension for concrete exhibits three distinct regions clearly
discernible on its graphical representation. Starting from the origin and extending to point A,
Page
1
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
stress and strain values follow a linear trend. The slope of this line corresponds to Young's
Modulus, denoted as E0, which characterizes a material's stiffness or its propensity to undergo
deformation. As the applied load surpasses the elastic limit, the concrete's behavior transitions
into a nonlinear plastic phase. Beyond the elastic limit, the curve levels off, reaching its
maximum compressive strength. Subsequent compression of the concrete leads to a reduction in
load and, ultimately, results in structural failure.
Figure 1.3.1: Stress-strain diagram for a typical concrete structure in
compression
1.4
Objective
The objective of this lab was to determine the density of each concrete, maximum average
stress supported by each cylinder, average ultimate stress, E and ν for cylinder 2 based on the
10% to 40% readings, and the proportional limit for cylinder 2.
Page
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
2
Approach
2.1
Test Setup and Instrumentation
Test Specimen: Concrete Cylinder (Diameter: 4.0 - 4.15)
Machinery Used: 810 Material test System and Humboldt 5080
Figure 2-1.1:
Compression test specimen 1 with 810 Material test System.
Figure 2-1.2:
Humboldt 5080 System.
2.2
Test Specimens
Table 2-2.1: Specimen 1 and 2 Worksheet Data
Specimen 1
Specimen 2
Page
3
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
Diameter 1 (in)
4.14
4.05
Diameter 2
4.06
4.01
Diameter 3 (in)
4.15
4
Length (in) (DUAL)
4
4
Length (in)
8
8
Weight (lb)
8.2
8.1
Ultimate Load (Ibf)
49410
54428
Figure 2-2.1:
Compression test specimen 1
Figure 2-2.2:
Compression test specimen 2
Page
4
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
2.3
Test Procedure
Concrete Cylinder 1, the initial specimen, was positioned within the testing framework of
the 810 Material Test System Compression System. After activating the system, it underwent
compressive force application, and the associated load, along with the specimen's contraction,
was meticulously recorded until it ultimately failed. Subsequently, Concrete Cylinder 1 was
extracted from the test frame. Following this, Concrete Cylinder 2 was situated within the 810
Material Test System test frame. Initially, compressive force was applied until it reached 10% of
the ultimate load value, during which axial and diametric deformations were meticulously
logged. The compressive force was then elevated to 40% of the ultimate load value, with
corresponding axial and diametric deformations also recorded. This transition from 10% to 40%
compressive force was replicated a total of three times, with all relevant measurements
meticulously documented. Once this phase was completed, Concrete Cylinder 2 was removed
from the 810 Material Test System and positioned within the Humboldt 5080 System test frame.
Again, the system was activated, and compressive force was applied, with both the load and the
specimen's contraction being recorded until the point of specimen failure was reached.
Page
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Fall 2020
Laboratory (No.)
3
Results
3.1
Concrete Cylinder 1 and 2
Table 3-1.1:
Specimen 1 and 2 Objectives Data
Specimen 1
Specimen 2
Density (lb/ft^2)
133.07182
137.84676
Max AVG stress (psi)
3712.2188
4288.2529
AVG Ult. Stress (psi)
4000.2358
Youngs Modulus (ksi)
3479.4
AVG Poisson’s Ratio
0.19
Table 3-2.2:
Specimen 1 and 2 Calculated Data
Specimen 1
Specimen 2
Radius (in)
2.07
2.025
Avg Diam (in)
4.12
4.02
Area (in^2)
13.46
12.88
Volume(in^3)
107.6912829
103.059947
Figure 3-1.1:
Stress vs Strain Curve
Page
6
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
Figure 3-1.2:
Magnified view of linear region of stress strain curve with Young’s
modulus
3.2
Concrete Cylinder 1
Table 3-2.1:
Specimen 1: Test 1
Specimen 1
Load (Plut)
10%
4941
40%
19764
3.3
Concrete Cylinder 2
Table 3-3.1:
Specimen 2: Test 1-3
Specimen 2
Load (Plut)
Axial
Transverse
10%
-0.0037
0.0306
40%
-0.0053
0.037
10%
-0.0041
0.03078
40%
-0.0053
0.0311
10%
-0.0041
0.0308
40%
-0.0053
0.0371
Page
7
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
Table 3-3.2:
Specimen 2: Axial and Transverse Strain
Specimen 2
Load
(Plut)
Axial
Delta
Offset
Axial -
Offset
Axial
Strain
Transverse
Delta
Offset
Transverse -
Offset
Transverse
Strain
10%
-3.70E-
03
-3.57E-03
-1.29E-
04
-3.23E-
05
3.06E-02
3.04E-
02
2.03E-04
1.61E-05
40%
-5.30E-
03
-3.57E-03
-1.73E-
03
-4.32E-
04
3.70E-02
3.04E-
02
6.60E-03
5.23E-04
10%
-4.10E-
03
-3.57E-03
-5.29E-
04
-1.32E-
04
3.08E-02
3.04E-
02
3.83E-04
3.03E-05
40%
-5.30E-
03
-3.57E-03
-1.73E-
03
-4.32E-
04
3.11E-02
3.04E-
02
7.03E-04
5.57E-05
10%
-4.10E-
03
-3.57E-03
-5.29E-
04
-1.32E-
04
3.08E-02
3.04E-
02
4.03E-04
3.19E-05
40%
-5.30E-
03
-3.57E-03
-1.73E-
03
-4.32E-
04
3.71E-02
3.04E-
02
6.70E-03
5.31E-04
Specimen
2
AXAIL
STRAIN
TRANSVERSE
STRAIN
10% AVG
-9.89E-
05
2.61E-05
40% AVG
-4.32E-
04
3.70E-04
Page
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
4
Analysis
4.1
Concrete Cylinder 1
Concrete Cylinder 1 endured a peak compressive force of
49410
Ibf before
succumbing to brittle failure. Under increasing compressive load, the specimen
experienced a sudden fracture rather than deformation or strain. To ascertain the
specimen's maximum average stress, we divided the ultimate compressive load by its
cross-sectional area, yielding a value of 3712.2188 Psi. The density of the specimen
was determined using weight and volume measurements, resulting in a density
133.07182
lb/in^3.
4.2
Concrete Cylinder 2
Concrete Cylinder 2 endured a peak compressive force of
54428
Ibf before
succumbing to brittle failure. Under increasing compressive load, the specimen
experienced a sudden fracture rather than deformation or strain. To ascertain the
specimen's maximum average stress, we divided the ultimate compressive load by its
cross-sectional area, yielding a value of
4288.2529
Psi. The density of the specimen
was determined using weight and volume measurements, resulting in a density
137.84676
lb/in^3.
Page
9
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
5
Conclusions
In this laboratory experiment, we conducted compression tests on two distinct
concrete cylinder samples. These tests yielded valuable data concerning the
specimens' deformation, which was induced by the applied force. We conducted these
tests using the 810-material test and Humboldt 5080 Compression systems.
Although there is a dearth of stress and strain data indicating the specific
point at which the specimens failed, both Concrete Cylinder 1 and Concrete
Cylinder 2 displayed a brittle response. As they were subjected to an
escalating compressive load, the specimens exhibited failure by abruptly
fracturing, rather than undergoing deformation or straining.
Concrete Cylinder 2 exhibited the greatest density among the specimens,
measuring (
137.84676
lb/ft^3), while Concrete Cylinder 1 followed closely
behind with (
133.07182 lb
/in3).
Concrete Cylinder 2 demonstrated the highest resistance to compressive
load, withstanding a force of
54428
Ibf. Following closely behind, Concrete
Cylinder 1 exhibited a compressive strength of
49410
Ibf.
Concrete Cylinder 2 exhibited the highest maximum average stress,
measuring 3712.2188 psi, while Concrete Cylinder 1 followed closely with a
stress of
3712.2188
psi.
The Poisson's ratio for Concrete Cylinder 2 was determined to be 0.19.
This
value reflects the specimen's remarkable ability to withstand deformation
Page
10
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
when subjected to compressive loads, showcasing its high resistance to such
forces.
6
References
CEE370L - Mechanics of Solids Laboratory Stress-Strain Relationships for Various
Materials Tension Test. (2023). Dept. of Civil & Environmental Engineering.
Gere, James M. & Goodno, Barry J. (2018). Mechanics of Materials 9th Edition. CL
Engineering.
Page
11
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
Appendix
A-1 Equations and Sample Calculations
Stress
: P/A (P = applied force, A = cross sectional area)
Strain
: δ/L (δ = deformation, L = 4” (starting length))
Density
: w/v (w = weight, v = volume)
Young’s Modulus (Modulus of elasticity)
: The linear region of stress-strain curve
was plotted and a linear fit applied. The slope of the equation outputted by excel
was the modulus of elasticity.
ACI Code Expression
: (
w
= concrete density, f
c
’ = maximum average stress)
Poisson’s Ratio
:
'/
Ɛ Ɛ
(
’ = lateral strain,
= axial strain)
Ɛ
Ɛ
Sample Calculations:
Stress= P/A= (49410/1000)/((pi/4)*(4.12)^2) = 3.706 Ksi
Strain=
δ/
L= (-0.0055448506)/(4)=
-0.002386213
Page
12
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
A-2 Raw Data
Load
Dual Extensometer (raw)
Transverse Extensometer (raw)
Unit
s
kip
in
in
-0.091265872
-0.0055552507
0.096069641
-0.10524563
-0.0055497452
0.096073523
-0.11764872
-0.0055568758
0.096071094
-0.12837948
-0.0055516404
0.09607657
-0.1407053
-0.0055474825
0.096069098
-0.15314841
-0.0055614333
0.096074209
-0.1704096
-0.0055448506
0.096076004
-0.18453349
-0.00555587
0.096069127
-0.19911574
-0.0055595795
0.096062191
-0.21092603
-0.0055662943
0.096071549
-0.22417
-0.0055684294
0.096071139
-0.22559276
-0.0055645923
0.096065648
-0.22323458
-0.0055498038
0.096074969
-0.2204572
-0.0055620247
0.09606719
-0.22588226
-0.005569783
0.096069932
-0.23133287
-0.0055567878
0.096076295
-0.2448433
-0.0055603059
0.09607368
-0.26087645
-0.0055585825
0.096074998
-0.28004256
-0.0055600158
0.096062794
-0.29409939
-0.0055600791
0.096077837
-0.31175217
-0.0055650705
0.096068956
-0.32564116
-0.0055603846
0.096069477
-0.34627032
-0.0055685905
0.096067548
-0.36342704
-0.0055666203
0.096075781
-0.3861607
-0.0055750031
0.096073329
-0.40029198
-0.0055777556
0.096075073
-0.42222163
-0.0055844993
0.09606646
-0.4426634
-0.0055753831
0.096068405
-0.4639729
-0.0055789594
0.096077345
-0.48787639
-0.0055835885
0.096077256
-0.51176953
-0.0055780336
0.096077114
-0.53451991
-0.0055803424
0.096077785
-0.55718577
-0.0055968775
0.096073359
-0.58798611
-0.0055913315
0.096079141
Page
13
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-0.61345476
-0.0055944575
0.096073434
-0.64286476
-0.0055890409
0.096077688
-0.67389584
-0.005593271
0.096080124
-0.70439374
-0.005592234
0.096085943
-0.73527437
-0.0056067985
0.096081488
-0.76986492
-0.0056054406
0.096081845
-0.80636656
-0.0056124725
0.096073225
-0.84425211
-0.0056122467
0.096079752
-0.88147682
-0.005608296
0.096088372
-0.9205451
-0.0056131636
0.09607587
-0.96314216
-0.0056253737
0.096073583
-1.0052361
-0.0056238701
0.0960797
-1.0532029
-0.0056278757
0.096077763
-1.0982302
-0.0056270934
0.096078612
-1.1459846
-0.005640313
0.096079357
-1.1989751
-0.0056418162
0.096086852
-1.251012
-0.0056389016
0.096087955
-1.302704
-0.0056449398
0.096089609
-1.3597889
-0.0056583569
0.09608423
-1.417196
-0.0056606424
0.096086577
-1.4735069
-0.0056700883
0.096093878
-1.5384797
-0.0056667426
0.096088804
-1.6029301
-0.0056742537
0.096094392
-1.6714324
-0.0056795469
0.096098296
-1.7311648
-0.0056838132
0.096096382
-1.8094001
-0.0056950026
0.096097954
-1.8832262
-0.0057077101
0.096096314
-1.961265
-0.0056978422
0.096100718
-2.0329266
-0.0057061273
0.096106336
-2.1077774
-0.005708511
0.096094549
-2.1955612
-0.0057213255
0.096103899
-2.2792988
-0.0057330835
0.096108235
-2.3621135
-0.0057336781
0.096104078
-2.4452705
-0.0057514887
0.096104316
-2.5457721
-0.005755248
0.096102834
-2.632046
-0.0057684151
0.096108466
-2.7267237
-0.0057664448
0.096113965
-2.8285296
-0.005774294
0.096111923
-2.926506
-0.0057957545
0.096119493
-3.031666
-0.0057987263
0.096117549
-3.1399813
-0.0058083599
0.096127115
-3.2463932
-0.0058237487
0.096124277
Page
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-3.3490825
-0.0058096014
0.096124306
-3.4579749
-0.0058352402
0.096133329
-3.5902896
-0.0058395229
0.096124746
-3.7038577
-0.0058514625
0.096122317
-3.8188951
-0.0058553121
0.096122161
-3.9475327
-0.0058740098
0.096130185
-4.0644631
-0.0058825407
0.096131466
-4.1879764
-0.0058984784
0.096143633
-4.3208389
-0.0059051677
0.096150756
-4.4505415
-0.0059290207
0.096144274
-4.5861096
-0.0059292014
0.096149541
-4.7265096
-0.0059352661
0.096158355
-4.8609095
-0.005959841
0.096155867
-4.993917
-0.0059682876
0.096166544
-4.8813472
-0.0059680748
0.096158318
-4.8325548
-0.0059527773
0.09615583
-4.9993134
-0.0059687868
0.096158512
-4.8126197
-0.0059595276
0.096150659
-5.1072459
-0.0059817107
0.096163288
-5.3215313
-0.00600689
0.096167795
-5.5229454
-0.0060294522
0.096173003
-5.7137847
-0.0060303817
0.096177608
-5.901825
-0.006065073
0.096178956
-6.090487
-0.006072246
0.096177407
-6.2649717
-0.0060923649
0.09618976
-6.4478531
-0.0061046123
0.096193872
-6.6399012
-0.006123465
0.096203454
-6.8334036
-0.0061357445
0.09620066
-7.0280175
-0.0061656428
0.096218579
-7.2268925
-0.0061713927
0.096211255
-7.427783
-0.0061936593
0.096215591
-7.6225905
-0.0062134205
0.09622515
-7.8214011
-0.0062226802
0.096230276
-8.0245247
-0.0062372559
0.096238561
-8.244751
-0.0062589869
0.096252039
-8.4634104
-0.0062849782
0.096251413
-8.6623268
-0.0063092103
0.096258886
-8.8901939
-0.0063199406
0.096259199
-9.1263857
-0.006337984
0.096274659
-9.345685
-0.0063636736
0.09627746
-9.5581875
-0.0063873697
0.096295454
-9.8164759
-0.0064053726
0.096289247
Page
15
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-10.069158
-0.0064341379
0.096307226
-10.316349
-0.0064478819
0.096309863
-10.582748
-0.006475518
0.096324824
-10.838801
-0.0064976471
0.09633401
-11.104809
-0.0065291673
0.096343547
-11.363857
-0.0065615014
0.096356332
-11.620617
-0.0065961573
0.096366256
-11.913419
-0.0066144853
0.096371934
-12.196465
-0.0066477582
0.096383013
-12.488147
-0.0066652945
0.096397005
-12.792008
-0.0067015323
0.096408062
-13.108022
-0.0067292419
0.096416943
-13.418591
-0.0067521003
0.096425973
-13.713594
-0.0067815138
0.096435912
-14.041944
-0.0068031391
0.096454628
-14.37635
-0.0068461779
0.096464552
-14.692205
-0.0068701599
0.096476883
-15.01671
-0.0069211745
0.096495904
-15.368409
-0.0069439346
0.096512452
-15.708858
-0.0069774515
0.096527986
-16.08534
-0.0070119514
0.096539974
-16.421167
-0.0070531955
0.096565135
-16.780638
-0.0070834435
0.096590988
-17.175013
-0.0071315598
0.096607432
-17.583399
-0.0071710367
0.096616536
-17.998402
-0.007203666
0.096642397
-18.383839
-0.0072368099
0.096670203
-18.78154
-0.0072824783
0.096688807
-19.177069
-0.0073255869
0.096696913
-19.591255
-0.0073549789
0.096730359
-20.023649
-0.0073890504
0.096756652
-19.75362
-0.0074061705
0.096766271
-19.806
-0.0074324878
0.096780308
-19.514574
-0.0074179699
0.09679085
-18.686989
-0.007350849
0.096771017
-18.040762
-0.0073091807
0.096760988
-17.388727
-0.0072597526
0.096739605
-16.75701
-0.0072093131
0.096728578
-16.12837
-0.0071631493
0.096712753
-15.546237
-0.0071124462
0.096701846
-14.950274
-0.0070764478
0.096684501
-14.384302
-0.0070338305
0.096666731
Page
16
CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-13.838973
-0.0069774869
0.09666083
-13.311502
-0.0069394959
0.096641265
-12.806674
-0.0068963771
0.096627943
-12.353043
-0.0068516354
0.096616559
-11.89872
-0.0068258932
0.096593872
-11.445903
-0.0067843138
0.096586198
-11.020988
-0.0067488644
0.09655942
-10.599079
-0.0067059551
0.096558772
-10.200525
-0.0066774287
0.096553169
-9.8336897
-0.0066365935
0.096538752
-9.4614925
-0.0066108345
0.096516274
-9.1203804
-0.0065602041
0.096506581
-8.8029222
-0.0065451162
0.096501611
-8.4657555
-0.0065094912
0.09648902
-8.1502733
-0.006472108
0.096478656
-7.8602705
-0.006446552
0.096465163
-7.571753
-0.0064172498
0.096449383
-7.2966738
-0.0063993535
0.096458204
-7.0370078
-0.0063738483
0.096438937
-6.80339
-0.0063485042
0.096428923
-6.5599337
-0.0063260966
0.096426561
-6.3164778
-0.0062994319
0.096422456
-6.0951362
-0.0062819952
0.096403189
-5.8677177
-0.0062554153
0.096398622
-5.6593413
-0.0062411707
0.09640041
-5.4897032
-0.0062235701
0.096391685
-5.6269107
-0.0062383786
0.096387632
-5.2730727
-0.0062034489
0.096382625
-5.0943041
-0.0061814999
0.096371785
-4.9377184
-0.0061689918
0.09636575
-4.9672666
-0.0061791474
0.096365131
-5.1424437
-0.0061908411
0.096372508
-4.7809258
-0.0061509525
0.096362002
-5.3870149
-0.0061869291
0.096370958
-5.7638063
-0.0062305164
0.096379183
-6.0966539
-0.0062611899
0.096382722
-6.3932829
-0.0062823119
0.096383572
-6.6721358
-0.0063056303
0.096387856
-6.9881978
-0.0063344459
0.096405491
-7.2990861
-0.0063691377
0.096409172
-7.5945415
-0.0063830167
0.096414089
-7.9078798
-0.0064197369
0.096415818
Page
17
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-8.2146339
-0.0064399131
0.096424423
-8.5225744
-0.0064697233
0.096428461
-8.8414116
-0.0065027406
0.096435234
-9.1285067
-0.0065225763
0.096449621
-9.4508677
-0.0065620192
0.096447311
-9.7804184
-0.0065929359
0.096463695
-10.115463
-0.0066168783
0.096476935
-10.453632
-0.0066578658
0.096481964
-10.805099
-0.0066839852
0.096489474
-11.165272
-0.0067152041
0.096495375
-11.508778
-0.006744219
0.096503772
-11.863832
-0.0067678364
0.096524596
-12.248354
-0.0068086721
0.096527711
-12.618418
-0.0068341712
0.09654519
-13.008482
-0.0068672434
0.096558176
-13.41218
-0.0068951054
0.096565917
-13.812988
-0.0069354312
0.096585631
-14.233513
-0.0069702696
0.096598566
-14.625216
-0.0070084287
0.096600026
-15.038273
-0.0070364978
0.096619211
-15.476296
-0.0070717866
0.09663824
-15.930491
-0.0071139415
0.096646115
-16.380688
-0.0071422649
0.096658319
-16.849144
-0.0071835495
0.096683867
-17.318302
-0.0072327117
0.096698016
-17.785496
-0.0072592865
0.096710451
-18.268486
-0.007298877
0.096722513
-18.754498
-0.0073417169
0.096744016
-19.269644
-0.0073796916
0.096768253
-19.785187
-0.00742405
0.096785448
-20.312941
-0.0074704615
0.0968161
-18.752462
-0.0073742275
0.096799232
-18.086168
-0.0073215179
0.096781135
-17.453794
-0.0072771064
0.096762545
-16.803793
-0.0072299065
0.096746221
-16.176035
-0.0071833399
0.096735805
-15.575554
-0.0071290247
0.096718051
-14.999756
-0.0070767575
0.096702293
-14.423226
-0.0070396112
0.096688591
-13.870681
-0.0069936481
0.096672148
-13.342734
-0.0069449418
0.096653871
-12.822156
-0.0069147735
0.096641451
Page
18
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-12.326622
-0.0068707988
0.096627012
-11.8641
-0.0068343543
0.096612841
-11.442558
-0.0067953854
0.096598387
-10.996543
-0.0067511727
0.096582711
-10.568041
-0.0067243055
0.096576609
-10.174111
-0.0066815517
0.096560247
-9.7817297
-0.0066504674
0.096545517
-9.4179573
-0.006628369
0.096535996
-9.0532398
-0.0065824641
0.096521802
-8.7038908
-0.0065313871
0.096507132
-8.3991709
-0.0065066726
0.096506253
-8.073844
-0.0064798971
0.09648326
-7.758224
-0.006443528
0.096479714
-7.4651957
-0.0064238175
0.096467577
-7.1881542
-0.0063943337
0.096466765
-6.9137688
-0.0063744751
0.096463405
-6.6551676
-0.0063387803
0.096437365
-6.4199896
-0.0063215038
0.09643928
-6.1866555
-0.0063037621
0.096433535
-5.9510541
-0.00627993
0.09641955
-5.7262149
-0.0062552528
0.096408226
-5.5039873
-0.0062306579
0.096411295
-5.2941184
-0.0062150178
0.096397035
-5.0967155
-0.0061981748
0.096383855
-4.9006529
-0.0061766393
0.096379124
-4.9364061
-0.0061806543
0.096383281
-5.1118841
-0.0061857896
0.096378855
-5.2322006
-0.0061958637
0.096375935
-5.6782174
-0.0062358109
0.096377
-5.9841866
-0.0062684235
0.096382372
-6.302712
-0.006283557
0.096397318
-6.6210709
-0.0063145682
0.096401677
-6.9348588
-0.0063399067
0.096407816
-7.2578068
-0.0063711819
0.096408196
-7.5708671
-0.0063955234
0.09642759
-7.8876128
-0.0064298315
0.096431285
-8.2039175
-0.006458025
0.096430741
-8.5003166
-0.0064937007
0.096437529
-8.8391943
-0.006510817
0.096447863
-9.1689959
-0.0065402603
0.096455246
-9.5092964
-0.0065954872
0.096464723
-9.8483238
-0.0066122683
0.096474171
Page
19
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-10.205125
-0.0066453754
0.096476644
-10.564853
-0.0066660414
0.096490756
-10.904894
-0.0067075654
0.096503355
-11.272828
-0.0067401482
0.096516319
-11.666002
-0.0067734825
0.096528962
-12.029578
-0.0068008159
0.096532799
-12.432233
-0.0068228943
0.0965451
-12.841772
-0.0068734381
0.096559316
-13.240222
-0.0069000805
0.096576281
-13.655843
-0.0069419416
0.096585467
-14.061072
-0.0069748475
0.096603133
-14.4734
-0.0070109437
0.096612059
-14.929976
-0.0070513133
0.096628167
-15.383804
-0.0070874966
0.096639834
-15.847892
-0.0071197203
0.096654683
-16.322466
-0.0071595302
0.096668407
-16.803402
-0.0072022369
0.096697517
-17.268047
-0.0072378581
0.096707128
-17.779438
-0.0072784037
0.096724734
-18.268213
-0.0073176352
0.09673883
-18.791342
-0.0073584146
0.096758649
-19.320688
-0.0073969071
0.096775122
-19.876047
-0.0074538221
0.096801914
-20.426117
-0.007486722
0.096826494
-19.713047
-0.0074571311
0.096829258
-20.251551
-0.0075002578
0.096837051
-20.998236
-0.0075560184
0.096866682
-21.56076
-0.0076029291
0.096872114
-22.117207
-0.0076448461
0.096889526
-22.719591
-0.0077041415
0.096918456
-23.348122
-0.0077607851
0.096953757
-23.940969
-0.0078041414
0.097005583
-24.530392
-0.0078635747
0.097037077
-25.090551
-0.0079181669
0.097072847
-25.673235
-0.0079882871
0.097110055
-26.235958
-0.0080404384
0.097160585
-26.78087
-0.0081059821
0.097205505
-27.372469
-0.0081682708
0.097262524
-27.922007
-0.0082395216
0.097299673
-28.488516
-0.0082986811
0.097354926
-29.034872
-0.008362283
0.097414933
-29.552631
-0.0084181335
0.097468212
Page
20
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-30.111326
-0.008498379
0.097531237
-30.663771
-0.0085621746
0.097596876
-31.175991
-0.0086235274
0.097657301
-31.756609
-0.0086901551
0.097722068
-32.291595
-0.0087644309
0.097795367
-32.801151
-0.0088349786
0.097870134
-33.354504
-0.0089060599
0.097953849
-33.839558
-0.0089654475
0.09804076
-34.318783
-0.009035659
0.098121315
-34.788837
-0.0090997089
0.098203085
-35.268818
-0.0091676461
0.098291606
-35.731953
-0.0092480434
0.098384805
-36.173729
-0.009310781
0.098482937
-36.597488
-0.0093675666
0.098570414
-36.990986
-0.0094282553
0.098675683
-37.43787
-0.0095085986
0.098782875
-37.894325
-0.0095835244
0.098903619
-38.321201
-0.009642832
0.09902171
-38.782246
-0.0097160097
0.099144638
-39.298038
-0.0098013021
0.099301949
-39.809883
-0.0098956265
0.099449903
-40.262787
-0.0099712647
0.099622943
-40.790836
-0.010071798
0.099810854
-41.337086
-0.010171724
0.10002151
-41.831104
-0.010274068
0.10025625
-42.366608
-0.01038644
0.10051819
-42.86721
-0.010496925
0.1007912
-43.362999
-0.010626786
0.10110191
-43.898594
-0.010745101
0.10143808
-44.366138
-0.010867124
0.10180905
-44.859577
-0.011010731
0.10221592
-45.362511
-0.011161263
0.10266904
-45.836475
-0.011310388
0.10318803
-46.264912
-0.011467678
0.10375313
-46.693188
-0.011619351
0.1043779
-47.162605
-0.01181896
0.10510325
-47.542587
-0.012007912
0.10595022
-47.915493
-0.012198268
0.10689681
-48.3218
-0.012425405
0.1079994
-48.65152
-0.012650942
0.10931939
-48.927704
-0.012911566
0.11086652
-49.195694
-0.013187931
0.11271407
Page
21
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CEE 370L Mechanics of Materials
Fall 2020
Laboratory (No.)
-49.405983
-0.013528575
0.11505027
-49.553902
-0.013893946
0.1179196
-49.63588
-0.0143517
0.12176469
-49.570847
-0.014987202
0.12769213
-49.01321
-0.016108109
0.14102232
Page
22
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Related Documents
Related Questions
Problem 1: (50 points)
In Avengers 2, Captain America's improved
shield is made from unobtainium, a new
material that will soon be available in a store
near you. Unobtainium has the normal stress-
strain diagram shown. The proportional limit,
the elastic limit and the yield point are
identical in this material.
o [MPa]
2001
175
150
125
100
Fig.1 Normal stress-strain
75
50
25
0
0. 0.05 0.1 0.15 0.2 0.25
Unobtainium has a Poisson's ratio of 0.3.
a. [6pts] Identify the yield point oy, the ultimate stress ou and the fracture
stress of. Include units.
c. [25pts] A bar of unobtainium has a length of
1.5 m, a width of 100mm and a height of 50
mm, as shown. The cross-sectional area is
50mm 100mm = 5 x 10-³m². The bar is
subjected to an axial force of 375 kN.
Find the normal stress in a cross-section of the bar.
b. [5pts] How do you find Young's modulus from this graph? Find its value with units.
whesta fins dus al hoss
P = 375 KN
1.5 m
0.3
50 mm
100 mm
& [mm/mm]
Is the material within its…
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Hi can you please help me with the attached question?
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Can someone please help me to correctly solve all the following parts of this question. Thank you!
arrow_forward
Test Specimen
4140 CF steel
6061 T6 Al
Gray Cast iron 40
FC Brass 360
Impact Energy (J or ft-lb)
48.5 ft-lb
25 ft-lb
12 ft-lb
27 ft-lb
Impact Strength (J/m
or ft-lb/in)
123.096 ft-lb/in
63.452 ft-lb/in
What is the final analysis/ overall observation from the data?
30.457 ft-lb/in
68.528 ft-lb/in
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UzNDU3NTYyMjk0/a/MjYOMzAwMjMOOTM5/details
Further questions
4.The graphs show how the extension changes with stretching force for four different materials.
a. Which two graphs show materials that follow Hooke's law?
A
B
b. Which two graphs show materials that become less stiff as
they are stretched?
force
force
D
C. Which graph shows a material that maintains the same
stiffness throughout?
force
force
1. A force of 20N stretches a spring by 0.5m. The spring obeys Hooke's law.
a. Calculate the spring constant including a suitable unit.
b. How much force must a man use to stretch it by 1.5m?
5. A car has a weight of 240OON which is distributed equally over all four wheels. Each wheel has a spring of
spring constant 400N/cm.
a.
Determine the force through the spring on each wheel.
b. Calculate the compression of each spring when the car rests on the ground.
6.In a spring experiment the results were as follows:
Force (N)
Length (mpm
1
2
4
6.
7
50
58
70
74
82
9n
102
125
LELL
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PHYS X PHYS X
印 PHYS X
PHYS X
POTPHYS X
PHYS X
E PHYS X E PHYS
top/semester2/physics%20for%20engineers/PHYS220_CH15_Lecture%20Notes_Problems%2015 19,15.29 S
(D Page view
A Read aloud
V Draw
Problem-15-19: page-475
A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion
with an amplitude of 10.0 cm. Calculate the maximum value of its
(a) speed, and acceleration.
(b) the speed and the acceleration when the object is 6.00 em from the equilibrium position, and
(c) the time interval required for the object to move from.r50 to r5 8.O0 cm.
Solution:
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A structural member 10 cm long must be able to support a load of 50,000 N without experiencing any plastic deformation. Given the following data for brass, steel, aluminum, and
titanium, rank them from least to greatest weight in accordance with these criteria.
Yield strength
Ultimate tensile
Alloy
Density (g/cm3)
(MPa)
strength (MPa)
Brass
415
600
8.5
Steel
860
800
7.9
Aluminum
310
435
2.7
* 700
Titanium
550
4.5
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dear tutor please provide neat and clean and detailed answer.
dont copy from google
adress both questions well
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Question 2
You are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture
fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates
implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial
weight bearing activities.
Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to
verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into
solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending
test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the
yield stress for the…
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Figure 1 shows the tensile testing results for different materials. All specimens have an initial
diameter of 12 mm and an initial gauge length of 50 mm.
300
250
Low carbon steel
Network polymer
200
Crystalline polymer
150
Amorphous polymer
100
50
5
10
15
20
25
30
Strain (%)
Figure 1: Stress-strain curve
b. Determine the following parameters for each material:
• the tensile strength
the 0.2% offset yield strength
the modulus of elasticity
• the ductility
Stress (MPa)
LO
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please solve part b, this is past paper and just iam studying, mechanical engineering
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You have been given the following test sample data following mechanical testing of 15
test pieces of Silicon Nitride.
What is the Weibull modulus of this material?
Would you advise the use of a similar material with a Weibull Modulus of 16.3 and a
mean failure stress of 485 MPa, if you anticipate that the peak stress on the material
could be 430 MPa?
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Select one or more:
O a. No
O b. 18.6
O C.
13.4
O d. Yes
O e. 15.7
f. 17.1
Failure Stress (MPa)
423
459
496
432
447
467
473
499
485
479
505
530
526
490
510
<
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You have been given the following test sample data following mechanical testing of 15
test pieces of a modified Alumina.
What is the Weibull modulus of this material?
Would you advise the use of this material over one with a Weibull Modulus of 19.6 and a
mean failure stress of 270 MPa, if you anticipate that the peak stress on the material
could be 255 MPa?
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Select one or more:
a. 185
b. No
Yes
□d. 49
□e. 28.6
3.7
Failure Stress (MPa)
297
293
270
300
g. 22.8
260
296
265
295
280
288
263
290
298
275
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