Lab Manual 9 Cantilever PDF

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Lab Manual for cantilever beam experiment...

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National University of Sciences & Technology Course: ME 206-Mechanics of Materials Lab Manual Instructor: LE Muhammad Umar Masood

Muhammad Awais Name: ______________________ 40 Degree/Syndicate: ____A __ 05/21/2020 Date: _________________

Experiment 09: Deflection in Cantilever Beam and Stiffness Safety Precautions: • •

Safety Precautions are very important to be known while working in Lab Must read the “Safety in Lab” document before starting work

Introduction: The objective of this experiment is 1. To find the deflection of cantilever beam at end point / loading point 2. To find the bending stiffness of fixed-free beam 3. Plot the graph between deflection and load on the free end 4. Plot the graph between bending stiffness and load on the free end 5. Confirm the results theoretically

Theory: The deflection in a cantilever beam with point load at one end is given by Delta = (Pl^3)/EI where P is the applied load l is the length of the bar from fixed point to load point E is the elastic modulus I is the moment of Inertia The moment of inertia of beam is given by I = b*t ^ 3/12 b is width t is thickness Bending Stiffness is given by k = 3EI/l^3

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National University of Sciences & Technology Course: ME 204-Mechanics of Materials Lab Manual Instructor: LE Muhammad Umar Masood

Equipment: • • •

Rectangular Cross section rod with one clamping supports (configuration for Cantilever) Weight (s) with hanger Deflection gauge

Procedure: 1. 2. 3. 4. 5. 6.

Clamp the thicker steel strip in the position shown in diagram so that it forms a cantilever. Fix the hanger clamp ahead from the roller support and setup a dial gauge over it. Apply a load of 1 N and take the reading of maximum deflection. (where would it be? Think) Repeat step 4 with increasing load Tabulate the maximum deflection against load. Plot stiffness and deflection versus load o Theoretical o Experimental

Observations and Discussion: 50 Measured at ____ cm from the fixed end of the beam

Sr 1 2 3 4 5 6

Theoretical % Error in Bending Bending Stiffness Stiffness

% Error in Deflection

Force (N)

Deflection

Theoretical deflection

Bending Stiffness

0.0098

1

0.606

1000

1635

38.8

39

0.0196

2.14

1.219

934.5

1635

42.8

42.9

0.0294

3.36

1.827

892.8

1635

45.3

45.5

0.0392

4.47

2.442

894.8

1635

45.2

45.4

0.049

5.51

3.054

907.4

1635

44.4

44.6

0.0588

6.46

3.658

928.7

1635

43.1

43.2

30 Measured at ____ cm from the fixed end of the beam

Sr 1 2 3 4 5 6

Theoretical deflection

Bending Stiffness

Theoretical % Error in Bending Bending Stiffness Stiffness

% Error in Deflection

Force (N)

Deflection

0.0098

0.47

0.264

2127

3785

43

44.6

0.0196

1.11

0.523

1801

3785

52.1

53

0.0294

1.65

0.791

1818

3785

51

52

0.0392

2.16

1.049

1851

3785

51

51.3

0.049

2.65

1.324

1886

3785

50

50

0.0588

3.16

1.576

1898

3785

50

50

Department of Mechatronics Engineering College of EME NUST Page 2 of 3

National University of Sciences & Technology Course: ME 204-Mechanics of Materials Lab Manual Instructor: LE Muhammad Umar Masood

Bending stiffness is defined as the force required to bend a bar by a unit length at a certain point on the bar this suggests that for same bar bending stiffness will be different at different distances from the support. It also depends on temperature, atmospheric conditions and composition of the material. This is one of the cause of error in values.

Conclusion: Their is a considerable difference in theoretical and experimental values which owes to temperature difference , composition of the material and homogeneousness.

References:

I/we certify that the work presented in this document is not plagiarized by any definition. I am the sole creator of this work else the readings which were given to me by the instructor. I understand that commit of plagiarism is an academic offence which leads to strict disciplinary action which may affect my educational career. Digitally signed

Muhammad Muhamm by Awais ad Awais Date: 2020.05.30 12:21:37 +05'00'

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