1 answer

1. Consider a bar under tension. The bar has length L, rectangular cross-section of sides b...

Question:

1. Consider a bar under tension. The bar has length L, rectangular cross-section of sides b and h, Youngs modulus E, density

1. Consider a bar under tension. The bar has length L, rectangular cross-section of sides b and h, Young's modulus E, density p, and applied tensile force P. a) If all parameters are fixed except for h, find the value of h that minimizes the mass of the bar under stress, elongation, and stiffness constraints. Assume safety factors oo, Os, and Ok and failure values o*, 8*, and k* b) Also find the minimum mass of the bar m under these constraints 2. Using your results from Problem 1, plot the minimum value of m considering stress failure criterion for a range of tensile forces 100 NSP < 10000 N. The bar has a stress safety factor 0o = 1.5 and dimensions L = 1 m and b = 1 mm. Consider the following cases: a) The bar is comprised of titanium alloy (E = 120 GPa, p= 4500 kg/m3. o* = 1000 MPa) b) The bar is comprised of aluminum alloy (E = 70 GPa, p = 2700 kg/m3, o* = 300 MPa) c) The bar is comprised of steel (E = 200 GPa, p = 8000 kg/m3, o* = 500 MPa) Show all the 3 plots from a), b), and c) in the same figure.

Answers

PAGE 1

Sody Griven, Length of the bar = L . width of the cross section = b. Depth of the cross section =h Youngs Modulus z E . Dens

PAGE 2

, minimum mass of the lay under stress constraint is given by . m s Density x Voluwie .</p><p>: x 5 x 1. . . .. =($6L) h Substituti

PAGE 3

The stiffness of the bar duie to tessile ecad.</p><p>P is given by; K: AE = (bdE = be Under Stifriess constraint) KZ 6. k* fuck*

.

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