Strain Rosette Data REVISED

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New Jersey Institute Of Technology *

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343

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Mechanical Engineering

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Apr 3, 2024

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docx

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INTRODUCTION One of the most important fundamentals in the engineering world is understanding how applied forces, both internally and externally, can affect a system. Failing to properly evaluate the load (with the resultant stress/strain) a material can handle can have a potentially colossal amount of damage. Entire structures like bridges and buildings could collapse under a heavier than usual load. Trucks or cars might bend or break under an extreme load or while towing a heavy object. The purpose of this experiment was to better understand how an applied load can place stresses on a beam along different planes. This experiment also shows how different gages and their positioning can yield different results, a critical factor in an engineer’s decision making. After taking the readings, proper computations and calculations must be performed and analyzed accordingly. For this experiment strain is analyzed with the use of Rosette strain gage. 6 gages were placed along a beam and recorded data of a 10,000-lb. load at 45 and 60 degrees on the beam. Using the following equations, the physical properties of the beam can be computed along with the stress and strain: 𝜎 x = [E/(1-v^2)](ɛ x + vɛ y ) 𝜎 y = [E/(1-v^2)](ɛ y + vɛ x ) These equations relate the Modulus of Elasticity, E, and Poisson’s Ratio, v, to compute the stress of in any direction, either in the x or y planes. This data taken for the normal and shear stresses are then compiled into data tables below and used to generate Mohr’s circle. Mohr’s circle from this data is then compared with a plot computed from theoretically calculated data. Looking at Mohr’s circle, several

data points can be taken where the combined stresses from the applied load can be seen and used for further analysis. The accuracy and validity of the experimental values are then assessed by comparing them with theoretically computed values which can be taken from the information we have. The following equations are used in the theoretical computations: M = PL/2 I = (1/2)bh^3 σ x = -My/I Τ xy = (3V/2A)[1-y^2/c^2] σ MAX = ( σ x + σ y )/2 + [(( σ x + σ y )/2 )^2+( Τ xy )^2]^(1/2) σ MIN = ( σ x + σ y )/2 - [(( σ x + σ y )/2 )^2+( Τ xy )^2]^(1/2) The theoretically computed values are then compared with the experimentally calculated values to prove the precision and validity of the data. If the results fall within a reasonable percent difference, it is safe to assume that the data is indeed correct and the Rosette strain gages are a useful tool in stress and strain measurements. DATA Table 1 Stress x 10 ^ 6 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi)

1 σ x -1875 ε x -187 σ x -1911.01 σ y 0 ε y 65.67 σ y 0 τ xy 468.75 γ xy 132.79 τ xy 544.44 σ max 110.66 σ max 144.224 σ min -1985.66 σ min -2055.23 Table 2 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi) 2 σ x 0 ε x 4 σ x 0 σ y 0 ε y -15 σ y 0 τ xy 625 γ xy 167 τ xy 684.70 σ max 625 σ max 684.70 σ min -625 σ min -684.70 Table 3 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi) 3 σ x 1875 ε x 195 σ x 1972.96 σ y 0 ε y -73.67 σ y 0 τ xy 468.75 γ xy -123.55 τ xy -506.57 σ max 1985.66 σ max 2094.76 σ min -110.66 σ min -122.5 Table 4 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi) 4 σ x -3750 ε x -449 σ x -3976.90 σ y 1667 ε y 318 σ y 1963.02 τ xy 468.75 γ xy 125 τ xy 512.50 σ max 100.625 σ max σ min -2183.63 σ min

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Table 5 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi) 5 σ x 0 ε x -35 σ x -77.79 σ y 833 ε y 85.67 σ y 856.70 τ xy 625 γ xy 167.43 τ xy 686.47 σ max 1167.65 σ max 1178.68 σ min -334.56 σ min -399.77 Table 6 Gage No. Theoretical Experimental stress ( experiment ) stress ( theoretical ) Stress (psi) Strain Stress (psi) 6 σ x 3750 ε x 352 σ x 3778.79 σ y 555.6 ε y -76 σ y 464.20 τ xy -468.75 γ xy -136 τ xy -557.60 σ max 4356.04 σ max 4315.04 σ min -50.44 σ min -72.054