Thin-walled T-section Tapered Cantilever Beam

The Problem

A thin-walled T-section cantilevered beam is fixed at one end and is subjected to a vertically downward point load of 368N at the free end.

The section is of uniform thickness of 2mm.

The Young's modulus value is 200kN/mm2and Poisson’s ratio is 0.25

368N

2mm

100mm

100mm

2mm

t=2mm

N.B. the dimensions represent only the free end and gets bigger towards the fixed end. The web in middle of the beam 500mm from the free end is 150mm instead of 100mm

Finite Element Model

1 Work in units of N (force) and mm (length) and MPa (=N/mm2modulus/stress).

2 Use Plate/Shell QUAD8 element.

3 Take the global axes origin to be at the bottom left corner the fixed end- (X,Y, Z).

4 Generate the nodes and element manually for three elements model. UseTools Subdivide for generation of more elements.

Use QUAD8 elements as required

4@25

A

4@ 250mm

200mm

Q S

R

X

Z

B

P

4@ 25mm

Finite Element Output

1 Vertical deflection (DY) along the line AB.

2 Bending stress (SZZ), in Global axes, along the line AB.

3 Bending stress (SZZ), in Global axes, along the line PQ.

4 Vertical shear stress (SYZ), in Global axes, along the line PQ.

Theory

1 Use the double integration method to find the vertical deflection along the top surface (line AB).

2 Use the bending theory to find the bending stress along the top surface (line AB).

3 Use the bending theory to find the bending stress along the web (line PQ).

4 Use the bending theory to find the vertical shear stress distribution along the web (line PQ).

Results–DY-Vertical deflection (mm) along AB

Distance from fixed end (mm) Theory FE

0

150

300

450

600

750

900

1050

1200

Results–SZZ (Global axes)-Bending stress (N/mm2) along AB

Distance from fixed end (mm) Theory FE

0

150

300

450

600

750

900

1050

1200

Results–SZZ (Global axes) –Bending stress (N/mm2) along PQ

Distance from bottom(mm) Theory FE

0(P)

12.5

25

37.5

50

62.5

75

87.5

100(Q)

Results–SYZ (Global axes)-Shear stress(N/mm2) along PQ

Distance from bottom(mm) Theory FE

0(P)

12.5

25

37.5

50

62.5

75

87.5

100(Q)

Plot Graph

1 Plot on the same graph the span wise finite element vertical deflectionvalues (along AB) superimposed on the theoretical values.

2 Plot on the same graph the span wise the finite element bending stress values (along AB) superimposed on the theoretical values.

3 Plot on the same graph the finite element bending stress values (along PQ) superimposed on the theoretical values.

4 Plot on the same graph the finite element vertical shear stress values (along PQ) superimposed on the theoretical values.

The experimental values I are shown below but does not have to be same as theory and

strand7.

Load (N) Deflection (mm) Stress@ Flange 1 Stress@Flange 2 Stress @Web

0 0 0 0 0

18 0.14 0.9 0.4 0.2

28 0.22 1 0.6 0.2

38 0.3 1.4 0.6 0.1

48 0.38 1.5 1 -0.2

58 0.47 1.7 1.2 -0.3

68 0.55 1.8 1.3 -0.5

88 0.73 2.2 1.7 -0.8

108 0.89 2.5 1.9 -0.8

128 1.06 2.8 2.2 -1.1

148 1.24 3 2.7 -1.3

168 1.42 3.4 3 -1.6

188 1.64 3.7 3.2 -1.8

208 1.84 3.9 3.6 -2

228 2.07 4.3 4 -2.2

248 2.32 4.6 4.4 -2.6

268 2.65 4.9 4.7 -2.8

288 3.05 5.2 5.2 -3

308 3.39 5.3 5.5 -3.2

328 3.8 5.6 5.9 -3.4

348 4.19 6 6.3 -3.6

368 4.58 6.4 6.7 -4

The Problem

A thin-walled T-section cantilevered beam is fixed at one end and is subjected to a vertically downward point load of 368N at the free end.

The section is of uniform thickness of 2mm.

The Young's modulus value is 200kN/mm2and Poisson’s ratio is 0.25

368N

2mm

100mm

100mm

2mm

t=2mm

N.B. the dimensions represent only the free end and gets bigger towards the fixed end. The web in middle of the beam 500mm from the free end is 150mm instead of 100mm

Finite Element Model

1 Work in units of N (force) and mm (length) and MPa (=N/mm2modulus/stress).

2 Use Plate/Shell QUAD8 element.

3 Take the global axes origin to be at the bottom left corner the fixed end- (X,Y, Z).

4 Generate the nodes and element manually for three elements model. UseTools Subdivide for generation of more elements.

Use QUAD8 elements as required

4@25

A

4@ 250mm

200mm

Q S

R

X

Z

B

P

4@ 25mm

Finite Element Output

1 Vertical deflection (DY) along the line AB.

2 Bending stress (SZZ), in Global axes, along the line AB.

3 Bending stress (SZZ), in Global axes, along the line PQ.

4 Vertical shear stress (SYZ), in Global axes, along the line PQ.

Theory

1 Use the double integration method to find the vertical deflection along the top surface (line AB).

2 Use the bending theory to find the bending stress along the top surface (line AB).

3 Use the bending theory to find the bending stress along the web (line PQ).

4 Use the bending theory to find the vertical shear stress distribution along the web (line PQ).

Results–DY-Vertical deflection (mm) along AB

Distance from fixed end (mm) Theory FE

0

150

300

450

600

750

900

1050

1200

Results–SZZ (Global axes)-Bending stress (N/mm2) along AB

Distance from fixed end (mm) Theory FE

0

150

300

450

600

750

900

1050

1200

Results–SZZ (Global axes) –Bending stress (N/mm2) along PQ

Distance from bottom(mm) Theory FE

0(P)

12.5

25

37.5

50

62.5

75

87.5

100(Q)

Results–SYZ (Global axes)-Shear stress(N/mm2) along PQ

Distance from bottom(mm) Theory FE

0(P)

12.5

25

37.5

50

62.5

75

87.5

100(Q)

Plot Graph

1 Plot on the same graph the span wise finite element vertical deflectionvalues (along AB) superimposed on the theoretical values.

2 Plot on the same graph the span wise the finite element bending stress values (along AB) superimposed on the theoretical values.

3 Plot on the same graph the finite element bending stress values (along PQ) superimposed on the theoretical values.

4 Plot on the same graph the finite element vertical shear stress values (along PQ) superimposed on the theoretical values.

The experimental values I are shown below but does not have to be same as theory and

strand7.

Load (N) Deflection (mm) Stress@ Flange 1 Stress@Flange 2 Stress @Web

0 0 0 0 0

18 0.14 0.9 0.4 0.2

28 0.22 1 0.6 0.2

38 0.3 1.4 0.6 0.1

48 0.38 1.5 1 -0.2

58 0.47 1.7 1.2 -0.3

68 0.55 1.8 1.3 -0.5

88 0.73 2.2 1.7 -0.8

108 0.89 2.5 1.9 -0.8

128 1.06 2.8 2.2 -1.1

148 1.24 3 2.7 -1.3

168 1.42 3.4 3 -1.6

188 1.64 3.7 3.2 -1.8

208 1.84 3.9 3.6 -2

228 2.07 4.3 4 -2.2

248 2.32 4.6 4.4 -2.6

268 2.65 4.9 4.7 -2.8

288 3.05 5.2 5.2 -3

308 3.39 5.3 5.5 -3.2

328 3.8 5.6 5.9 -3.4

348 4.19 6 6.3 -3.6

368 4.58 6.4 6.7 -4

Assessment 3ASSESSMENTThis module is assessed through a portfolio submission which comprises 70% of individual coursework and 30% of a group presentation. The group members are expected to work together...powerpointwill need discussion to startENGINEERING DESIGN FOR INNOVATIONASSESSMENT BRIEF | 1CWK100This is an assignment for students on the following postgraduate programmes:• MSc Engineering Smart Systems•...2.2.2 Formative 1Week 7 Find a gap in practice for evidence translation - Formative Assessment 1Introduction to the Formative assessment Upon completing this lesson, you should be able to: • Find a knowledge...Global Business Environment Deadline: 29th October 2021Assessment GuidelinesWord Count: 500 (+-10%)Scenario:You are to select a UK company and conduct a PESTEL analysis on the firms operating environment...Assessment: Individual portfolio up to 4000 words or equivalent This assignment is to develop either a brand brief for a new brand OR a brand audit and recommendations for a failing brand. The portfolio...Assessment: Individual Coursework Assessment methods which enable students to demonstrate the learning outcomes for the module: Weighting: Learning Outcomes demonstrated Individual Coursework (3,000 words...Dissertation (All chapters) - Indicative table of contents provided in the brief.Topic - ESG investing and portfolio perfomancePlease refer to the brief attached for more information.Total word count -...**Show All Questions**