Measurements 17GN1001 Measurement of FORCE and STRAIN Session:07 Measurement of FORCE and STRAIN By D.Kalyan Asst.Professor DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Measurements 17GN1001 STUDENT OUTCOME Able to understand the parameters Able to define and represent with units Understand the conventional methods to measure. Learn a specific instrument to measure. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 FORCE A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Measurements 17GN1001 Force is a quantity that is measured using the standard metric unit known as the Newton. A Newton is abbreviated by an "N." To say "10.0 N" means 10.0 Newton of force. One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. Thus, the following unit equivalency can be stated: 1 Newton = 1 kg • m/s2 DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Measurement of force can be done by any two methods: Direct Method: This involves a direct comparison with a known gravitational force on a standard mass. Example: Physical Balance. Indirect Method: This involves the measurement of effect of force on a body. E.g. Force is calculated from acceleration due to gravity and the mass of the component. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

Force measurement using Spring A spring balance is an example where a force may be converted to a displacement based on the spring constant. For a spring element (it need not actually be a spring in the form of a coil of wire) the relationship between force F and displacement x is linear and given by F = K x DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 a spring balance The spring is fixed at one end and at the other end hangs a pan. The object to be weighed is placed in the pan and the position of the needle along the graduated scale gives the weight of the object. For a coiled spring like the one shown in the illustration, the spring constant is given by DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 In this equation Es is the shear modulus of the material of the spring, Dw is the diameter of the wire from which the spring is wound, Dm is the mean diameter of the coil and N is the number of coils in the spring. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Stress & Strain The restoring force per unit area, set up inside a body is called stress. It is measured by the magnitude of the deforming force acting on unit area of the body.   Stress  =  Restoring force / area =    , where F is the deforming force acting on an area A of the body. Its unit :  N m-2  in SI system and dyne cm-2  in CGS system Dimensional formula is  =   ML-1 T-2 DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Different types of stress : Stress is of two different types mainly  (i) Normal Stress  (ii) Shearing  or Tangential Stress Normal Stress : If the stress is normal to the surface, it is called normal stress. Stress is always normal in the case of a change in length or a wire or in the case of change in volume of a body. Longitudinal Stress : When a normal stress change the length of a body then it is called longitudinal stress. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Shearing Stress : When the Stress is tangential to the surface due to the application of forces parallel to the surface, then the stress is called tangential or shearing stress. It changes the shape of the body.          Shearing Stress = Force / Surface Area  =  F  /  A DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

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DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Strain The ratio of change produced in the dimensions of a body by  a system of forces or couples, in equilibrium, to its original dimensions is called strain. Strain is of three types depending upon the change produced in a body and the stress applied. The three types of strain are (i)Longitudinal strain (ii) Volume strain and (iii) Shearing strain DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Longitudinal Strain : It is the ratio of the change in length of a body to the original length of the body Longitudinal Strain = Change in length / Original length = dL / L DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 It is the ratio of the change in volume of a body to its original volume Volume Strain  =  Change in volume  / Original volume  =   DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Shearing Strain : If is the angle through which a face originally perpendicular to the fixed face is turned. (or)  It is the ratio of the displacement of a layer to its distance from the fixed layer. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Hooke’s Law : states that “ strain is proportional to the stress producing it”. A material is said to be elastic if all the deformations are proportional to the load. Relation between stress and strain: The ratio of the direct stress to the strain produced is called young’s modules or the modules of Elasticity, i.e E = / DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

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Various Types of Stress-Strain Measurements 1) Mechanical method 2) Grid method 3) Electrical stain gauges DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

Electrical strain guage It is a very fine metal grid which is cemented in paper base material on the surface of the any structural component to measure the surface normal strains in any desired direction. Lord Kevin (1856) first gives the principle of working of strain gauges. He proved that the resistance of conductor changes with the change in length. The idea was used to measure the strain first in 1936 by US Defense department. Strain can be positive (tensile) or negative (compressive). DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Construction of strain gauge Length of filament varies from 2 to 25mm. Normally 10- 25mm is used for tension members and 2-4mm for compression members. Safe current is 25mA – 50 mA. Range of voltage is 35 – 50 V Metal used are Copper (55%) + Nickel (45%) Alloy or can be >Nickel + Chromium Alloy DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

Axial Sensitivity of Strain Gauge The change in the resistance of a wire is directly proportional to axial sensitivity of the strain gauge. It is also called gauge factor (G.F). DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Advantages of Electric Resistance Gauge Normal strains can be measured in any desired direction on surface of the structural component. Shear strains can be measured by using some special arrangements. Remote reading is possible. Once the strain gauge is cemented it will be long period of time until the bond between strain gauge and component breaks. Static as well as dynamic strains can be measured. Strain can be measured in any desired position e.g Top fibers, bottom fibers and at neutral axis DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 To measure such small changes in resistance, strain gages are almost always used in a bridge configuration with a voltage excitation source. Consists of four resistive arms with an excitation voltage, VEX, that is applied across the bridge. The output voltage of the bridge, Vo When R1/R2 = R4/R3, the voltage output VO is zero DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

Quarter bridge configuration: DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Half bridge DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Full Bridge DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

Temperature compensation: A strain gage configuration where one gage is active (RG + DR) and a second gage is placed transverse to the applied strain. Therefore, the strain has little effect on the second gage, called the dummy gage. However, any changes in temperature affect both gages in the same way. Because the temperature changes are identical in the two gages, the ratio of their resistance does not change, the voltage VO does not change, and the effects of the temperature change are minimized. DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Strain gauge rosette: A strain gauge rosette is, by definition, an arrangement of two or more closely positioned gage grids, separately oriented to measure the normal strains along different directions in the underlying surface of the test part. Rosettes are designed to perform a very practical and important function in experimental stress analysis DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

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DEPARTMENT OF BASIC ENGINEERING SCIENCES-1 Positioning strain gages to monitor bending, axial, shear, and torsion loads DEPARTMENT OF BASIC ENGINEERING SCIENCES-1

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Velocity and Acceleration Measurements DEPARTMENT OF BASIC ENGINEERING SCIENCES-1