The objective of the experiment was to measure the strains on a cantilever beam. Then calculate the principal strains and stresses and compare the result to the calculated stress. In the experiment, strains were measured along three different axes oriented at a fixed angle and in a different direction about a point of interest on a cantilever beam using a strain gauge rosette (rectangular type). Rosettes are designed to perform a very practical and important function in experimental stress analysis. The gauges must be zeroed out before taking any readings. Ball bearings, inch diameter each, and numbering 515 were used to obtain the approximate load in this experiment using the beam load equation, . The approximated stress was given as 15, 000 psi or 100 MPa. Principal strains were calculated from the three strains by using the equations: A = and B =. The maximum and the minimum principal strains can be calculated by adding the outcomes of A and B and by subtracting the outcomes of A and B respectively. Poisson\'s ratio can be found by substituting the principal strains obtained from equations A and B into this equation. Principal stresses were calculated by substituting the same principal strains obtained from equations A and B again into the biaxial Hooke\'s Law equations, , and where E, Young\'s Modulus of elasticity, is assumed to be 10.4 Times 10^6psi. Finally, the maximum principal stress can be calculated by using Flexure Formula which is, . The computations of the load, the three strains, the principal and maximum and minimum principal strains and stresses, and Poisson\'s ratio were recorded and presented in Table 1. Also, the measured maximum principal stress was compared to the theoretical maximum principal stress and is included in Table 1. The load obtained was 3.937 Ibf, and it was rounded to 4.00 Ibf. The maximum and minimum principal strains were found to be 1491 mu epsilon, and -460 mu epsilon respectively. The maximum and minimum principal stresses were found to be 15506 psi, and -0.30458 psi respectively. Finally, the measured maximum principal stress was found to be 15, 237 psi compared to the theoretical maximum principal stress 15, 000 psi, and the difference between both values was 1.58%.
Objective:
The objective of the experiment was to measure the strains produces on a cantilever beam. Then calculate the principal stresses and strains developed and compare those result to the calculated stress.
Theory
In this experiment , strains were measuredalong three different axes that are oriented at a same angle and in a different direction about a point interesect on a cantilever beam by using strain gauge rosette that is rectangular type.strain gaugaes are basically thress types those are rectagular ,delta and star.rosettes are used to calculate the strain values in stress analysis. these gauges are zeroed out before taking readings .in this experiemnt load is calculated by ball bearing,inch diameter each and numbering 515 and beam load equation,. theoritically stresses obtained and those are 15,000 psi means 100 Mpa.
Rectagular rosettes are kept in three directions to calculate the strain value in three directions by using given equations ,the maximum value we can obtain directly obtain by simplly adding strains in given directions that A and B . and minumum value is the difference of those two values . poissons ration also be calculated by uisng principal strains eqations . and than principal strains are caculated from principle strans and possons ratio.thoses equations and given below in this E is youngs modules or moduls of Elasticity and it is assumed to be 10.4 * 10^6 psi. and finally by using flexure formula princuple stress can be calculated.
Results
The rosette strain values ,posison\'s ratio, maximum and minumum principle stresses are noted in table 1. and comapre the theoritical value to experimental value obtained . The load we are obtained nearly equal to 4 lbf.
Conclusion
In calculation the maximu and minmum principal stress are obtained 15506 psi and -0.30458 psi.and pricipal straines are 1491 and -460 respectively .At lost 15237 psi calculated as the maximu principle stress and compare it with 15000 psi. and the error percentage is 1.58 .
Homework Sourse
