ENGR 348

Strengths of Materials Lab

Experiment 2: Bending Testing

Andrew Pepel; Frank Porter; Kevin Brosnan11/18/2010

12

Abstract

Bending and Compression tests are important to engineering design. Knowledge of a material’s and ultimate bending and compression strength makes the difference between a successful, safe design and a dangerous product or structure. In this experiment we examined a typical concrete paver. The specimen was analyzed thoroughly before the procedures. First the specimen was subjected to 3 point bending, and then one of the resulting halves was compressed until failure. The resulting data from the test allowed for measurements of ultimate bending and compression strength, as well as the corresponding strains.

Table of Contents

Nomenclature..............................................................................................................................................3

Introduction.................................................................................................................................................3

Procedure....................................................................................................................................................3

Data.............................................................................................................................................................4

Analysis........................................................................................................................................................4

Results.........................................................................................................................................................6

Discussion....................................................................................................................................................7

Conclusions..................................................................................................................................................7

References...................................................................................................................................................7

Appendices..................................................................................................................................................8

12Nomenclature

Bending Stress (σ) – the result of a load applied perpendicular to the surfaceUnits: PSI

σ=MyI

Engineering Stress (σ) – the average uniaxial tensile force (F) on the bar divided by the original cross-sectional area (A0) of the barUnits: PSI

σ= FA0

Engineering Strain (ϵ) – the ratio of the change in length of the sample in of the sample in the direction of the force divided by the original length of the sampleUnits: in./in.

ϵ=l−l0l0

Introduction

This report will present the findings of Group 2B (East) in a bending and compression experiment. Included was one specimen of a concrete paver that was used once more after breaking in the bending portion of the experiment.

Procedure

The issued specimens included 1 concrete paver. Before beginning the procedure the sample was inspected for any obvious defects, such as cracks, dents, or cavities. One half inch was marked on each end of the paver as well as the center for the placement of during the bending test. Once marked, measurements were taken off the specimen and the following values were calculated

o Average Length (in.)o Average Width (in.)o Average Thickness (in.)o Average Volume (in.3)

At this point the first part of the experiment was ready to proceed. The machine was then finely adjusted until the brick was tight to the testing apparatus and there was a miniscule force read on the machine.

12The data was entered into the computer program and the test was started. Slowly the bending force on the specimen was increased, while we took a measurement of the deflection about once a minute. This process lasted nearly 13 minutes until the specimen broke apart. The computer program then stopped the procedure. Once complete the following data for the test were downloaded from the machine’s supplied computer program:

o Time (min.)o Position (in.)o Load (lbf.)

The specimen was removed from the machine and chiseled into a 6in2 cross sectional area for the compression test.

For the compression test the paver was placed between two flat surfaces on the machine that would exert the force on paver. From this point the procedure was much the same as it was for the bending test. The force on the brick gradually increased and we took measurements of the deflection about every minute. The brick failed after about 12 minutes.

Data

See Appendices C&D

Analysis

From the raw data supplied by the testing machine and post-procedure measurements, the first calculations to be made are the bending stress (σ), bending strain (ε), and compressive stress(σ). Bending stress is the bending moment about the neutral axis of the specimen multiplied by the perpendicular distance from the neutral axis, divided by the second moment of area of the specimen. The following is the bending stress from the sample just before breaking:

M=Moment about neutral axis y=perpendicular distance¿ the neutralaxis

I=Secondmoment of areaI=bh3

12=¿¿

M=Fd=(1235 lbf )¿

σ=MyI

=¿¿

Compressive stress is simply the force applied on the specimen divided by the cross-sectional area of the specimen. For example, the compressive stress just before failure:

12F=forceon s pecimen (¿ lbf . )A0=Cross−sectional area of specimen (¿ .2 )

σ= FA0

= 11960 lbf

6∈¿2=1993.333 psi¿Once the stress and strain calculations are made, a stress-strain

curve can be plotted. Strain is represented on the x-axis, while stress is represented on the y-axis.

-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.00350

50010001500200025003000350040004500

Bending Stress vs. Strain

Strain

Bend

ing

Stre

ss

The stress-strain curve is a very important piece of data in both the bending and compression strength experiments. Besides being a graphical representation of relationship between stress and strain during the experiments, it also gives an idea of the size of a material’s elastic region, and its ultimate strength.

0 0.005 0.01 0.015 0.02 0.025 0.030

500

1000

1500

2000

2500

Compression Stress vs. Strain

Strain

Stre

ss

Once the stress-strain curve is plotted, it can now be analyzed. There are two major parts of the curve: the elastic region, and the plastic region. If the specimen is only deformed

12within its elastic region, it will return to its original shape undamaged. One it passes through the elastic region and into the plastic region however, it is permanently deformed.

The ultimate stress and fracture stress can be calculated either from the stress-strain curve, or from the raw data itself. The ultimate stress (or tensile stress) is simply the highest stress value reached during the experiment. The fracture stress is the stress experience at the time of the specimen’s break.

The ultimate strength for the bending experiment was 3969.639 psi. The fracture stress was 2986.068 psi. For the compression test, the ultimate stress was 2088.333 psi, and the fracture stress was 1711 psi.

Results

ConcreteBending Compression

Yield Strength 3969.639psi 1993.333 psiUltimate Strength 3969.639psi 2088.333psiFracture Strength 2986.068psi 1711psiUltimate Load 1235 lbf 12530 lbf

Discussion

The bending portion of the experiment took a total of about 13 minutes and resulted in the paver being broken roughly in half. The break occurred in the center as expected, and with an ultimate load of 1235 lbf. The stress – strain graph clearly shows that there is virtually no plastic deformation for the bending test. Therefore we can conclude from the data gathered that the concrete is very brittle under bending conditions such as were applied.

For the compression segment of the experiment, one half of the broken paver was formed into a chunk with roughly a 6in2 surface area that the compression force was applied to. The stress – strain graph shows very little plastic deformation before the failure of the paver. This shows that the paver can be plastically deformed, but only by a small amount before it

12fails. The ultimate load for compression was much higher than that of bending, but that is because of the larger surface area the force was applied to.

Conclusions

Concrete is an especially brittle material, with the only plastic deformation occurring during compression.

References

Ferdinand P. Beer, E. R. (2006). Mechanics of Materials (5th ed.). New York: McGraw Hill.

William F. Smith, J. H. (2006). Foundations of Material Science and Engineering (5 ed.). New York: McGraw Hill.

12Appendices

Appendix A – Bending Test

-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.00350

500

1000

1500

2000

2500

3000

3500

4000

4500

Bending Stress vs. Strain

Strain

Bend

ing

Stre

ss

Appendix B – Compression test

0 0.005 0.01 0.015 0.02 0.025 0.030

500

1000

1500

2000

2500

Compression Stress vs. Strain

Strain

Stre

ss

Appendix C - Bending Test Data (reduced)

12Partner Data Point FileBending Test

Start of Test Wed 13 Oct 2010 11:23:52Time ( min ) Position ( in ) Load ( lbf ) Stress(psi) Strain(in/in)

0 0 0 0 00.16833 0.0023 14 44.99995501 0.0003012840.33667 0.0028 30 96.42847502 0.00036678

0.505 0.0032 47 151.0712775 0.0004191770.67333 0.0035 64 205.71408 0.0004584750.84167 0.0038 81 260.3568826 0.000497773

1.01 0.004 98 314.9996851 0.0005239721.17833 0.0043 115 369.6424876 0.000563271.34667 0.0043 131 421.0710076 0.00056327

1.515 0.0045 148 475.7138101 0.0005894681.68333 0.0048 165 530.3566126 0.0006287661.85167 0.0048 182 584.9994151 0.000628766

2.02 0.005 199 639.6422176 0.0006549652.18833 0.005 216 694.2850202 0.0006549652.35667 0.005 232 745.7135402 0.000654965

2.525 0.0052 249 800.3563427 0.0006811632.69333 0.0052 266 854.9991452 0.0006811632.86167 0.0055 283 909.6419477 0.000720461

3.03 0.0055 300 964.2847502 0.0007204613.19833 0.0055 317 1018.927553 0.0007204613.36667 0.0057 334 1073.570355 0.00074666

3.535 0.0057 350 1124.998875 0.000746663.70333 0.0057 367 1179.641678 0.000746663.87167 0.006 384 1234.28448 0.000785958

4.04 0.006 401 1288.927283 0.0007859584.20833 0.0062 418 1343.570085 0.0008121564.37667 0.0062 434 1394.998605 0.000812156

4.545 0.0062 451 1449.641408 0.0008121564.71333 0.0065 468 1504.28421 0.0008514544.88167 0.0065 485 1558.927013 0.000851454

5.05 0.0065 502 1613.569815 0.0008514545.21833 0.0068 519 1668.212618 0.0008907525.38667 0.0068 536 1722.85542 0.000890752

5.555 0.0068 552 1774.28394 0.0008907525.72333 0.007 569 1828.926743 0.000916955.89167 0.007 586 1883.569545 0.00091695

6.06 0.007 603 1938.212348 0.000916956.22833 0.007 620 1992.85515 0.000916956.39667 0.0073 637 2047.497953 0.000956248

126.565 0.0073 653 2098.926473 0.0009562486.73333 0.0073 670 2153.569275 0.0009562486.90167 0.0075 687 2208.212078 0.000982447

7.07 0.0075 704 2262.854881 0.0009824477.23833 0.0075 721 2317.497683 0.0009824477.40667 0.0077 737 2368.926203 0.001008646

7.575 0.0077 754 2423.569006 0.0010086467.74333 0.0077 771 2478.211808 0.0010086467.91167 0.008 788 2532.854611 0.001047943

8.08 0.008 805 2587.497413 0.0010479438.24833 0.008 822 2642.140216 0.0010479438.41667 0.0082 839 2696.783018 0.001074142

8.585 0.0082 855 2748.211538 0.0010741428.75333 0.0082 872 2802.854341 0.0010741428.92167 0.0082 889 2857.497143 0.001074142

9.09 0.0085 906 2912.139946 0.001113449.25833 0.0085 923 2966.782748 0.001113449.42667 0.0085 939 3018.211268 0.00111344

9.595 0.0087 956 3072.854071 0.0011396389.76333 0.0087 973 3127.496873 0.0011396389.93167 0.0087 990 3182.139676 0.001139638

10.1 0.0087 1007 3236.782478 0.00113963810.26833 0.009 1024 3291.425281 0.00117893610.43667 0.009 1040 3342.853801 0.001178936

10.605 0.009 1057 3397.496603 0.00117893610.77333 0.0092 1074 3452.139406 0.00120513510.94167 0.0092 1091 3506.782208 0.001205135

11.11 0.0092 1108 3561.425011 0.00120513511.27833 0.0092 1125 3616.067813 0.00120513511.44667 0.0095 1142 3670.710616 0.001244433

11.615 0.0095 1158 3722.139136 0.00124443311.78333 0.0095 1175 3776.781938 0.00124443311.95167 0.0095 1192 3831.424741 0.001244433

12.12 0.0098 1209 3886.067543 0.00128373112.28833 0.0098 1226 3940.710346 0.001283731

Appendix D – Compression Test Data (reduced)

12Partner Data Point FileCompression Test

Start of Test Wed 13 Oct 2010 11:50:34

Time ( min ) Position ( in ) Load ( lbf )Stress(psi)

Strain(in/in)

0 0 0 0 00.16833 0.0007 164 27.33333 0.0003110.33667 0.0013 333 55.5 0.000578

0.505 0.0017 501 83.5 0.0007560.67333 0.0022 669 111.5 0.0009780.84167 0.0025 838 139.6667 0.001111

1.01 0.003 1006 167.6667 0.0013331.17833 0.0033 1174 195.6667 0.0014671.34667 0.0035 1343 223.8333 0.001556

1.515 0.0035 1511 251.8333 0.0015561.68333 0.0038 1679 279.8333 0.0016891.85167 0.004 1848 308 0.001778

2.02 0.0043 2016 336 0.0019112.18833 0.0045 2185 364.1667 0.0022.35667 0.0048 2353 392.1667 0.002133

2.525 0.0048 2521 420.1667 0.0021332.69333 0.005 2690 448.3333 0.0022222.86167 0.0053 2858 476.3333 0.002356

3.03 0.0053 3026 504.3333 0.0023563.19833 0.0055 3195 532.5 0.0024443.36667 0.0058 3362 560.3333 0.002578

3.535 0.0058 3531 588.5 0.0025783.70333 0.006 3699 616.5 0.0026673.87167 0.006 3868 644.6667 0.002667

4.04 0.0063 4036 672.6667 0.00284.20833 0.0065 4205 700.8333 0.0028894.37667 0.0065 4373 728.8333 0.002889

4.545 0.0067 4541 756.8333 0.0029784.71333 0.0067 4709 784.8333 0.0029784.88167 0.007 4878 813 0.003111

5.05 0.007 5046 841 0.0031115.21833 0.0072 5215 869.1667 0.00325.38667 0.0072 5383 897.1667 0.0032

5.555 0.0075 5551 925.1667 0.0033335.72333 0.0075 5720 953.3333 0.0033335.89167 0.0078 5888 981.3333 0.003467

6.06 0.008 6056 1009.333 0.0035566.22833 0.008 6225 1037.5 0.003556

126.39667 0.0082 6393 1065.5 0.0036446.565 0.0082 6561 1093.5 0.003644

6.73333 0.0085 6730 1121.667 0.0037786.90167 0.0087 6898 1149.667 0.003867

7.07 0.009 7066 1177.667 0.0047.23833 0.009 7235 1205.833 0.0047.40667 0.0092 7403 1233.833 0.004089

7.575 0.0095 7571 1261.833 0.0042227.74333 0.0098 7740 1290 0.0043567.91167 0.01 7908 1318 0.004444

8.08 0.0102 8076 1346 0.0045338.24833 0.0105 8244 1374 0.0046678.41667 0.0108 8413 1402.167 0.0048

8.585 0.0108 8581 1430.167 0.00488.75333 0.011 8749 1458.167 0.0048898.92167 0.0112 8918 1486.333 0.004978

9.09 0.0115 9086 1514.333 0.0051119.25833 0.0117 9255 1542.5 0.00529.42667 0.012 9423 1570.5 0.005333

9.595 0.0123 9591 1598.5 0.0054679.76333 0.0125 9759 1626.5 0.0055569.93167 0.0127 9928 1654.667 0.005644

10.1 0.013 10096 1682.667 0.00577810.26833 0.0132 10264 1710.667 0.00586710.43667 0.0135 10433 1738.833 0.006

10.605 0.0135 10601 1766.833 0.00610.77333 0.014 10769 1794.833 0.00622210.94167 0.0142 10938 1823 0.006311

11.11 0.0145 11106 1851 0.00644411.27833 0.0147 11275 1879.167 0.00653311.44667 0.015 11443 1907.167 0.006667

11.615 0.0152 11611 1935.167 0.00675611.78333 0.0157 11779 1963.167 0.00697811.95167 0.016 11948 1991.333 0.007111

12.12 0.0165 12116 2019.333 0.00733312.28833 0.0172 12284 2047.333 0.00764412.45667 0.0185 12453 2075.5 0.008222