OBJECT

INTRODUCTION

EXPERIMENT 1

Concept
Procedure

EXPERIMENT 2

Concept
Procedure

ASSIGNMENT

REFERENCES

To become familiar with strain gages and use such gages to determine the unknown quantities at prescribed conditions of a cantilever beam and a thin walled pressure vessel.

There are various types of methods to analyse strains and stresses at a point. Strain gage methods use either electrical or mechanical means to measure strains. In these types of strain gages, electrical resistance strain gages are the most accurate ones. In these experiments gages will be used to determine the flexural rigidity of a cantilever beam, inside pressure of a pressure vessel, the principle stresses at a given point on the pressure vessel and the Poisson’s ratio of the vessel material.

NAME: Force Measurement and Determination of Flexural Rigidity EI

CONCEPT:

Force Measurement can be done by a cantilever beam which is known as a force transducer.In this experiment three axial strain gages are used in two gage locations as shown in the figure.At gage location 1, the gage B on the lower surface is located precisely under the gage A which is located on the top surface.Gages A and B measure the bending strains that are of equal magnitudes but of opposite signs.Any resistance change in the active gage resulting from strains of like sign produced by axial loads will be canceled because the active gages are in adjacent arms of the Wheatstone Bridge.The gage C on the upper surface is located 300 mm from the free end of the beam.This gage also measures the bending strains.

PROCEDURE:

1. Set the strain gage indicator to half bridge for the gage location 1.(for gages A and B)

2. Adjust the gage factor setting for the given gage factor value and balance the indicator.

3. Set the second indicator to quarter bridge (for gage C) and adjust the gage factor controller and balance the indicator.

4. Set the dial gage at the free end of the beam and adjust to zero.

5. Apply the supplied known F to the free end of the beam.

6. Measure the strains at locations 1 and 2 and measure the deflection d _D at the free end of the beam.

7. Remove the load and dial gage from the beam.

8. Apply the supplied unknown load P at point E.

9. Measure the strains at gage locations 1 and 2.

GIVEN:

REQUIRED:
 

1. Find the flexural rigidity (EI) of the beam.

2. Calculate the height (h) of the beam

3. Determine the distance L.(Distance between the free end of the beam and the gage location 1)

4. Determine the distance X.(Distance between the applied load and free end of the beam.)

5. Calculate the applied unknown load P.

NAME : Measurement of Principle Strains on a Thin Walled Pressure Vessel

CONCEPT:

Cylindrical pressure vessels, hydraulic cylinders, gun barrels, and pipes carrying fluid at high pressure develop both radial and tangential stresses with values which are dependent upon the radius of the element under consideration. When the wall thickness of the cylindrical pressure vessel is about one-twentieth, or less, of its radius, the radial stress which results from pressurizing the vessel is quite small compared to the tangential stress. Under these conditions the tangential stress can be assumed to be uniformly distributed across the wall thickness. When this assumption is made, the vessel is called Thin Walled Pressure Vessel.

Consider a cylindrical vessel of inside radius r and wall thickness t containing a fluid under pressure. Because of the axismmetry of the vessel and its contents, it is clear that no shearing stresses are exerted on the element.

The normal stresses s₁ and s₂ shown in the figure are therefore principal stresses. The stress s₁ is known as the hoop (circumferential) stress and the stress s₂ is called the longitudinal stress. Principal stresses then can be calculated as

where p is the internal pressure,

r is the inner radius of the cylinder

t is the wall thickness of the cylinder.
 

In this experiment a three element rectangular rosette forming an angle a with the horizontal plane is used to determine the gage pressure in the cylindrical steel tank.

Hint : Take gageA direction as x’x’, and gageC direction as y’y’ axes.

 

PROCEDURE :
 

1 - Connect the strain gages to the strain indicator (use quarter bridge configuration)

2 - Set the gage factor setting to 2.10

3 - Balance the indicator

4 - Load the pressure vessel

5 - Read the strain values from the indicator.

GIVEN :

Gage factor : Sg = 2.10

Outer diameter do= 112.5 mm

Modulus of Elasticity E = 200 Gpa

Inner diameter di = 107.9 mm

REQUIRED :

1 - Determine the Poisson`s ratio of the cylindrical material

2 - Calculate the principal strains and their directions

3 - Calculate the principal stresses

4 - Determine the inner pressure.

Make a detailed research about the .............................. method.(The method will be assigned in the experiment.)

1. Daily, J. W. and W. F. Riley., "Experimental Stress Analysis", McGraw-Hill, 1965

2. Timoshenko, S.P.Goodier, J. N., "Theory of Elasticity",McGraw-Hill,1982.

3. Peterson, R.E. "Stress Concentration Design Factors", John Wiley and Sons, 1953.