Sample Calculation

Sample Calculations

I-Beam (S8x18.4) Dimensions:

D= 8 in; h= 7.148 in; bf= 4.001 in; tw= 0.271in; tf= 0.426in; L (length of the beam) =18.4 in
I= (bf*D3 – h3 (bf – tw))/12= 57.6 in4; E (Referenced value of Young’s modulus) = 29X106 psi
Theoretical Strain: ε= σ/E= (M*y)/(E*I)
P = load a = distance from support to the applied load (48 in) y = distance from neutral axis to the extreme element in y-direction
The sing in the theoretical strain (±) determines if the strain is in compression or tension. * For P = 2000lbs: ε = (2000*48*±4)/( 29X106 *57.6) = ± 230 x 10-6. * For P = 4000lbs: ε = (4000*48*±4)/( 29X106*57.6) = ± 460 x 10-6. * For P = 6000lbs: ε = (6000*48*±4)/( 29X106*57.6) = ± 690 x 10-6

Data Analysis

Positions of the electrical Strains Gages: Gauge Number | Distance from bottom(in) | Distance from NA (in) | 1 | 8 | 4 | 2 | 6.69 | 2.69 | 3 | 5.93 | 1.93 | 4 | 5.12 | 1.12 | 5 | 4.5 | 0.5 | 6 | 3.77 | -0.23 | 7 | 3 | -1 | 8 | 2.18 | -1.82 | 9 | 1.4 | -2.6 | 10 | 0.4 | -3.6 |

Raw Data (Electrical Strain)

Zeroed Data (Electrical Strain)

| | σ, (psi) at | bottom | σ,(psi) at | top | Loads, P | (lbs) | Theoretical | electrical | Theoretical | electrical | | | | strain | | strain | | | | gage | | gage | | 2000 | -230 | -222 | 230 | 176 | Loading | 4000 | -460 | -445 | 460 | 388 | | 6000 | -690 | -643 | 690 | 625 | Unloading | 4000 | -460 | -418 | 460 | 434 | | 2000 | -230 | -213 | 230 | 222 |

δ = (M)(3L2-4a2)/24EI (Deflection Equation)

| Loads, P (lbs) | Theoretical (in) | Experimental (in) | δ(exp)/δ(theo) | | 2000 | 0.12 | 0.13 | 1.083333333 | Loading | 4000 | 0.24 | 0.26 | 1.083333333 | | 6000 | 0.353 | 0.393 | 1.113314448 | | 4000 | 0.236 | 0.268 | 1.13559322 | Unloading | 2000 | 0.118 | 0.138 | 1.169491525 |

Discussion
During the experiment, the theoretical and experimental data were very close to each other. The factors that may have caused