OBJECT: To Determine the Bending Stress and Deflection of Cantilever Beams.

APPARATUS:

• Beam Section (Cantilever)
• Weight, Dial Gauge
• Measuring Tape

THEORY:

BENDING STRESS

1. DEFLECTION
   

Cantilever Beam

METHODOLOGY:

OBSERVATIONS:

• Span of Beam (L) = mm
  
• Width of the Beam(B) = mm
  
• Thickness of the Beam(t)= N
  

RESULTS:

𝒀𝒐𝒖𝒏𝒈^′𝒔 𝑴𝒐𝒅𝒖𝒍𝒖𝒔 N/mm²

or

DEFLECTION TEST ON CANTILEVER BEAM

AIM: Determine the deflection and bending stress of cantilever beam.

APPARATUS:

Beam apparatus, Bending fixture, vernier caliper, meter rod, test piece & dial gauge.

DIAGRAM:

THEORY:

A Cantilever is a Beam one end of which is clamped and other end is free. A beam with a length L and is fixed at one end and the other end is free. Let the moment of inertia of the Beam is ‘I’ about its neutral axis and the Young’s Modulus be ’E’.

Moment of inertia about the neutral axis

𝑰 =𝒃𝒉^𝟑 / 𝟏𝟐

Deflection at the end where point load is acting = 𝛿

The deflection at the end (Max deflection) 𝛿 is related to the load ‘W’, length ‘L’ moment of Inertia ‘I’ and Young’s Modulus ‘E’ through the equation.

𝜹 =𝑾𝑳^𝟑 / 𝟑𝑬𝑰

PROCEDURE:

1. Clamp the Beam horizontally on the clamping support at one end.
   
2. Measure the length of cantilever L (distance from clamp end to loading point)
   
3. Fix the dial gauge under the beam at the loading point to Read down-ward Moment and set o zero.
   
4. Hang the loading Pan at the free end of the cantilever.
   
5. Load the cantilever with different loads (W) and note the dial gauge readings (𝛿)
   
6. Change the length of cantilever for two more different lengths repeat the Experiment.
   
7. Change the position of cantilever and repeat he experiment for the other value of I for rectangular cross-section.
   

TABLE:

CALCULATIONS:

1. I= 𝒃 𝒉𝟑 / 𝟏𝟐
2. 𝜹 = 𝑾𝑳𝟑 / 𝟑𝑬𝑰

PRECAUTIONS:

1. The length of the cantilever should be measured properly.
   
2. The dial gauge spindle knob should always touch the beam at the bottom of loading point.
   
3. Loading hanger should be placed at known distance of cantilever length.
   
4. Al the errors should be eliminated while taking readings.
   
5. Elastic limit of the Beam should not exceed.
   
6. Beam should be positioned horizontally.
   

RESULT: The Bending strength of the given specimen = ^𝑁 / 𝑚𝑚2

VIVA QUESTIONS:

1. Cantilever beam means?
   
2. What is the deflection formula of cantilever beam?
   
3. What is the difference between cantilever and simply supported beam?
   
4. Write types of loads?
   
5. Contra flexure means?
   

APPLICATIONS:

1. In aircraft
   
   
   
2. Cantilever Cranes