Assignment 2a - hopper design

You can use this excell file as a starting point. I give it to you because it has turned

out that if I don't many student have more problems with proper implementation of

the problem in excell than with the hopper design problem itself. So please use this.

In the sheets 'overview' and 'walltest' you find the basic data.

Most helpfull will be the sheet 'test(1)'. You can use this sheet for the evaluation of

one of the four tests. To use it for the others, make copies. Don't copy parts of this

sheet to new sheets, but copy the sheet as a whole (right click the 'tab' of the sheet,

select 'move or copy', choose 'copy' etc. ) and put the data in the new sheet.

Before makning other changes in sheet 'test(1)' try to change the values in the red cells

(actually you don't have to make other changes in this sheet)

After having made a copy of 'sheet(1)', in the new sheet you can or have to change

the green cells

basic data

tensile normal wall

strength stress shear

test porosity [g/cm2] [g/cm

2] [g/cm

2]

1 0.779 0.5 7.9 3.7

2 0.75 1 16.2 7.5

3 0.728 2 31 14.45

4 0.702 2.45 46.2 21.5

test 1 test 2 test 3 test 4

normal shear normal shear normal shear normal shear

stress stress stress stress stress stress stress stress

[g/cm2] [g/cm

2] [g/cm

2] [g/cm

2] [g/cm

2] [g/cm

2] [g/cm

2] [g/cm

2]

1.75 3.3 1.75 4.8 1.75 8.2 23.45 30.2

3.25 3.65 4.95 7.25 4.95 10.25 31 35

4.95 4.8 7.9 9.2 7.9 13.1 38.75 39.5

6.35 5.85 10.95 11.25 10.95 14.5 42 41.5

7.9 7.5 16.2 15 16.2 18 46.2 43.5

23.45 23

31 29.3

test 1

normal shear

stress stress

[g/cm2] [g/cm

2]

7.9 3.7

16.2 7.5

31 14.45

46.2 21.5

0

5

10

15

20

25

0 10 20 30

sh

ea

r s

tre

ss

normal stress

40 50

test 1 Mohr circle at the terminus

normal shear xendpoint 7.9

stress stress yendpoint 7.5

[g/cm2] [g/cm

2]

-0.5 0 xcenter 15.02025 to be fitted

1.75 3.3 r 10.34157 calculated with the hint

3.25 3.65

4.95 4.8 x y

6.35 5.85 4 #NUM!

7.9 7.5 4.5 #NUM!

5 2.557837

5.5 4.038909

6 5.057968

6.5 5.861168

7 6.528671

7.5 7.098859

8 7.593685

8.5 8.027098

9 8.4086

9.5 8.744988

10 9.041298

10.5 9.301361

11 9.528146

11.5 9.723982

12 9.890706

12.5 10.02977

13 10.14232

13.5 10.22921

14 10.29112

14.5 10.32847

15 10.34155

15.5 10.33043

16 10.29505

16.5 10.23515

17 10.1503

17.5 10.03986

18 9.902985

18.5 9.73855

19 9.545136

19.5 9.320937

20 9.06367

20.5 8.770426

21 8.437454

21.5 8.059831

22 7.630933

22.5 7.141526

23 6.578118

23.5 5.919619

24 5.129537

24.5 4.133086

25 2.711578

25.5 #NUM!

02468

101214161820222426

-2 0 2 4

sh

ea

r s

tre

ss

0 1.73E-07

0.5 0.474684

1 0.949367

1.5 1.424051

2 1.898734

2.5 2.373418

3 2.848101

3.5 3.322785

4 3.797468

4.5 4.272152

5 4.746836

5.5 5.221519

6 5.696203

6.5 6.170886

7 6.64557

7.5 7.120253

8 7.594937

8.5 8.06962

9 8.544304

9.5 9.018987

10 9.493671

10.5 9.968354

11 10.44304

11.5 10.91772

12 11.3924

12.5 11.86709

13 12.34177

13.5 12.81646

14 13.29114

14.5 13.76582

15 14.24051

15.5 14.71519

16 15.18987

16.5 15.66456

17 16.13924

17.5 16.61392

18 17.08861

18.5 17.56329

19 18.03797

19.5 18.51266

20 18.98734

20.5 19.46203

21 19.93671

21.5 20.41139

22 20.88608

22.5 21.36076

23 21.83544

23.5 22.31013

24 22.78481

24.5 23.25949

25 23.73418

25.5 24.20886

slope at endpoint

0.949367

Mohr circle through the origin effective yield locus

xendpoint 0

yendpoint 0

effective angle of internal friction

xcenter 2.5 to be fitted feff 43.51213 to be fitted

r 2.5 equal to xcenter

x y x y

0 0 0 0

0.2 0.979796 7.9 7.5

0.4 1.356466

0.6 1.624808

0.8 1.83303

1 2

1.2 2.135416

1.4 2.244994

1.6 2.332381

1.8 2.4

2 2.44949

2.2 2.481935

2.4 2.497999

2.6 2.497999

2.8 2.481935

3 2.44949

3.2 2.4

3.4 2.332381

3.6 2.244994

3.8 2.135416

4 2

4.2 1.83303

4.4 1.624808

4.6 1.356466

4.8 0.979796

5 #NUM!

4 6 8 10 12 14 16 18 20 22 24 26

normal stress

test 1 Mohr circle at the terminus

normal shear xendpoint 16.2

stress stress yendpoint 15

[g/cm2] [g/cm

2]

-1 0 xcenter 30 to be fitted

1.75 4.8 r 20.38235 calculated with the hint

4.95 7.25

7.9 9.2 x y

10.95 11.25 9 #NUM!

16.2 15 9.5 #NUM!

10 3.929377

10.5 5.932116

11 7.378347

11.5 8.555115

12 9.562426

12.5 10.4494

13 11.24455

13.5 11.9662

14 12.62696

14.5 13.23594

15 13.8

15.5 14.32445

16 14.81351

16.5 15.27056

17 15.69841

17.5 16.09938

18 16.47544

18.5 16.82825

19 17.15925

19.5 17.46969

20 17.76063

20.5 18.03303

21 18.2877

21.5 18.52539

22 18.74673

22.5 18.95231

23 19.14262

23.5 19.31813

24 19.47922

24.5 19.62626

25 19.75955

25.5 19.87939

26 19.986

26.5 20.07959

27 20.16036

27.5 20.22845

28 20.28398

28.5 20.32708

29 20.3578

29.5 20.37621

30 20.38235

30.5 20.37621

31 20.3578

31.5 20.32708

32 20.28398

32.5 20.22845

33 20.16036

33.5 20.07959

34 19.986

34.5 19.87939

35 19.75955

35.5 19.62626

36 19.47922

36.5 19.31813

37 19.14262

37.5 18.95231

38 18.74673

38.5 18.52539

39 18.2877

39.5 18.03303

40 17.76063

40.5 17.46969

41 17.15925

41.5 16.82825

42 16.47544

42.5 16.09938

43 15.69841

43.5 15.27056

slope at endpoint

0.92

Mohr circle through the origin effective yield locus

xendpoint 0

yendpoint 0

effective angle of internal friction

xcenter 7.3 to be fitted feff 42.61406

r 7.3 equal to xcenter

x y x y x y

0 0.096 0 0 0 0

0.5 0.556 0.2 1.697056 7.9 7.268

1 1.016 0.4 2.383275

1.5 1.476 0.6 2.898275

2 1.936 0.8 3.32265

2.5 2.396 1 3.687818

3 2.856 1.2 4.009988

3.5 3.316 1.4 4.298837

9 8.376 1.6 4.560702

9.5 8.836 1.8 4.8

10 9.296 2 5.01996

10.5 9.756 2.2 5.223026

11 10.216 2.4 5.4111

11.5 10.676 2.6 5.585696

12 11.136 2.8 5.748043

12.5 11.596 3 5.899152

13 12.056 3.2 6.039868

13.5 12.516 3.4 6.170899

14 12.976 3.6 6.292853

14.5 13.436 3.8 6.406247

15 13.896 4 6.511528

15.5 14.356 4.2 6.609085

16 14.816 4.4 6.699254

16.5 15.276 4.6 6.78233

17 15.736 4.8 6.858571

17.5 16.196 5 6.928203

18 16.656 5.2 6.991423

18.5 17.116 5.4 7.048404

19 17.576 5.6 7.099296

19.5 18.036 5.8 7.144228

20 18.496 6 7.183314

20.5 18.956 6.2 7.216647

21 19.416 6.4 7.244308

21.5 19.876 6.6 7.266361

22 20.336 6.8 7.282857

22.5 20.796 7 7.293833

23 21.256 7.2 7.299315

23.5 21.716 7.4 7.299315

24 22.176 7.6 7.293833

24.5 22.636 7.8 7.282857

25 23.096 8 7.266361

25.5 23.556 8.2 7.244308

26 24.016 8.4 7.216647

26.5 24.476 8.6 7.183314

27 24.936 8.8 7.144228

27.5 25.396 9 7.099296

0

2

4

6

8

10

12

14

16

18

20

22

-4 -2 0 2 4 6 8 10121416182022242628303234363840424446

sh

ea

r s

tres

s

normal stress

28 25.856 9.2 7.048404

28.5 26.316 9.4 6.991423

29 26.776 9.6 6.928203

29.5 27.236 9.8 6.858571

30 27.696 10 6.78233

30.5 28.156 10.2 6.699254

31 28.616 10.4 6.609085

31.5 29.076 10.6 6.511528

32 29.536 10.8 6.406247

32.5 29.996 11 6.292853

33 30.456 11.2 6.170899

33.5 30.916 11.4 6.039868

34 31.376 11.6 5.899152

34.5 31.836 11.8 5.748043

35 32.296 12 5.585696

35.5 32.756 12.2 5.4111

36 33.216 12.4 5.223026

36.5 33.676 12.6 5.01996

37 34.136 12.8 4.8

37.5 34.596 13 4.560702

38 35.056 13.2 4.298837

38.5 35.516 13.4 4.009988

13.6 3.687818

13.8 3.32265

14 2.898275

14.2 2.383275

14.4 1.697056

14.6 5.33E-07

14.8 #NUM!

15 #NUM!

slope at endpoint

0.92

effective angle of internal friction

to be fitted

test 1 Mohr circle at the terminus

normal shear xendpoint 31

stress stress yendpoint 29.3

[g/cm2] [g/cm

2]

-2 0 xcenter 15.02025 to be fitted

1.75 8.2 r 33.37428 calculated with the hint

4.95 10.25

7.9 13.1 x y

10.95 14.5 4 31.50232

16.2 18 4.5 31.67281

23.45 23 5 31.83452

31 29.3 5.5 31.98761

6 32.13219

6.5 32.26837

7 32.39626

7.5 32.51597

8 32.62757

8.5 32.73116

9 32.8268

9.5 32.91457

10 32.99454

10.5 33.06675

11 33.13125

11.5 33.1881

12 33.23733

12.5 33.27898

13 33.31307

13.5 33.33963

14 33.35868

14.5 33.37022

15 33.37427

15.5 33.37083

16 33.35989

16.5 33.34146

17 33.31551

17.5 33.28202

18 33.24099

18.5 33.19237

19 33.13614

19.5 33.07226

20 33.00067

20.5 32.92134

21 32.8342

21.5 32.7392

22 32.63626

22.5 32.52531

23 32.40626

23.5 32.27904

24 32.14353

24.5 31.99964

25 31.84724

25.5 31.68623

02468

101214161820222426283032343638404244464850

-4 -2 0 2 4

sh

ea

r s

tre

ss

0 46.2069

0.5 45.93421

1 45.66152

1.5 45.38882

2 45.11613

2.5 44.84344

3 44.57075

3.5 44.29806

4 44.02536

4.5 43.75267

5 43.47998

5.5 43.20729

6 42.9346

6.5 42.6619

7 42.38921

7.5 42.11652

8 41.84383

8.5 41.57114

9 41.29844

9.5 41.02575

10 40.75306

10.5 40.48037

11 40.20768

11.5 39.93499

12 39.66229

12.5 39.3896

13 39.11691

13.5 38.84422

14 38.57153

14.5 38.29883

15 38.02614

15.5 37.75345

16 37.48076

16.5 37.20807

17 36.93537

17.5 36.66268

18 36.38999

18.5 36.1173

19 35.84461

19.5 35.57191

20 35.29922

20.5 35.02653

21 34.75384

21.5 34.48115

22 34.20845

22.5 33.93576

23 33.66307

23.5 33.39038

24 33.11769

24.5 32.845

25 32.5723

25.5 32.29961

slope at endpoint

-0.54538

Mohr circle through the origin effective yield locus

xendpoint 0

yendpoint 0

effective angle of internal friction

xcenter 2.5 to be fitted feff -28.6073 to be fitted

r 2.5 equal to xcenter

x y x y

0 0 0 0

0.2 0.979796 7.9 -4.30853

0.4 1.356466

0.6 1.624808

0.8 1.83303

1 2

1.2 2.135416

1.4 2.244994

1.6 2.332381

1.8 2.4

2 2.44949

2.2 2.481935

2.4 2.497999

2.6 2.497999

2.8 2.481935

3 2.44949

3.2 2.4

3.4 2.332381

3.6 2.244994

3.8 2.135416

4 2

4.2 1.83303

4.4 1.624808

4.6 1.356466

4.8 0.979796

5 #NUM!

4 6 8 10121416182022242628303234

normal stress

test 1 Mohr circle at the terminus

normal shear xendpoint 46.2

stress stress yendpoint 43.5

[g/cm2] [g/cm

2]

-2.45 0 xcenter 15.02025 to be fitted

23.45 30.2 r 53.52034 calculated with the hint

31 35

38.75 39.5 x y

42 41.5 4 52.37347

46.2 43.5 4.5 52.47619

5 52.57396

5.5 52.6668

6 52.75473

6.5 52.83779

7 52.91599

7.5 52.98936

8 53.05792

8.5 53.12168

9 53.18067

9.5 53.23489

10 53.28437

10.5 53.32911

11 53.36913

11.5 53.40444

12 53.43505

12.5 53.46097

13 53.4822

13.5 53.49874

14 53.51061

14.5 53.51781

15 53.52033

15.5 53.51819

16 53.51137

16.5 53.49988

17 53.48371

17.5 53.46286

18 53.43733

18.5 53.4071

19 53.37217

19.5 53.33253

20 53.28817

20.5 53.23907

21 53.18524

21.5 53.12664

22 53.06326

22.5 52.99509

23 52.92212

23.5 52.8443

24 52.76164

24.5 52.6741

25 52.58166

25.5 52.4843

0246810121416182022242628303234363840424446485052545658606264666870727476788082

-6-4-20 2 4 6 8

sh

ea

r s

tre

ss

0 76.61504

0.5 76.25665

1 75.89827

1.5 75.53988

2 75.18149

2.5 74.8231

3 74.46471

3.5 74.10633

4 73.74794

4.5 73.38955

5 73.03116

5.5 72.67277

6 72.31439

6.5 71.956

7 71.59761

7.5 71.23922

8 70.88084

8.5 70.52245

9 70.16406

9.5 69.80567

10 69.44728

10.5 69.0889

11 68.73051

11.5 68.37212

12 68.01373

12.5 67.65534

13 67.29696

13.5 66.93857

14 66.58018

14.5 66.22179

15 65.8634

15.5 65.50502

16 65.14663

16.5 64.78824

17 64.42985

17.5 64.07147

18 63.71308

18.5 63.35469

19 62.9963

19.5 62.63791

20 62.27953

20.5 61.92114

21 61.56275

21.5 61.20436

22 60.84597

22.5 60.48759

23 60.1292

23.5 59.77081

24 59.41242

24.5 59.05403

25 58.69565

25.5 58.33726

slope at endpoint

-0.71678

Mohr circle through the origin effective yield locus

xendpoint 0

yendpoint 0

effective angle of internal friction

xcenter 2.5 to be fitted feff -35.632 to be fitted

r 2.5 equal to xcenter

x y x y

0 0 0 0

0.2 0.979796 7.9 -5.66253

0.4 1.356466

0.6 1.624808

0.8 1.83303

1 2

1.2 2.135416

1.4 2.244994

1.6 2.332381

1.8 2.4

2 2.44949

2.2 2.481935

2.4 2.497999

2.6 2.497999

2.8 2.481935

3 2.44949

3.2 2.4

3.4 2.332381

3.6 2.244994

3.8 2.135416

4 2

4.2 1.83303

4.4 1.624808

4.6 1.356466

4.8 0.979796

5 #NUM!

6 8101214161820222426283032343638404244464850

normal stress