Sample Calculation

Topics: Beam, Theory, Experiment Pages: 3 (628 words) Published: April 24, 2013
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 the...
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