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Problem 1 (50 points). Consider a column that is loaded and unloaded. Its cross-sectional area and a stress-strain curve of a column material are illustrated in Figure 1. o, ksi (* 1 ksi = 10³ psi = 1000 lb/in2) P Elastic Plastic P Force is applied to this point 75 60 unit: inch -0.0075 -0.002 o 5 + 20 ft 0.002 0.007 € 20 ft 1 -60 8 t 1.25 -80 1 Ground support Plastic Elastic Ground support Perspective view Section view Stress-strain curve Figure 1 Answer the following questions. (*Ignore self-weight of the steel column) The column is loaded with a force of 1000 kips (see the direction of force in Figure 1) and a stress-strain point moves from the origin o to point x on the curve shown in Figure 1. 1) Compute a normal stress (ksi) in the column 2) Compute a normal strain (£) in the column 3) Compute a length (ft) of the column subjected to 1000 kips 4) Compute Young's Modulus (E) of the material Unloading occurs from point X on the diagram. When the load has been entirely removed (o=0 ksi) 5) Compute a length (ft) of the column Reloading then begins at stress = zero and continues to a compressive stress of 70 ksi (let's call it point A). 6) Compute a force applied to the column resulting in a compressive stress of 70 ksi 7) Compute a length (ft) of the column 1 Unloading then begins at point A on the diagram. When the load has been entirely removed (0=0 ksi) 8) Compute an elastic recovery 9) Compute a residual strain 10) Compute a length (ft) of the column Problem 2 (40 points). A column having two different cross-sectional areas is shown in Figure 2. The column is subjected to two concentrated forces. A stress and strain curve of a material used for the column is illustrated in Figure 2. o, ks 1 ksi - 10 psi - 1000 lb/in²) 1400 kips unit: inch Elastic Plastic 1400 kips Force is applied 5 + to each point if 75 60 8 1.25 A A 5 ft I 5 ft 00 kips 3280 Kips Section A -0.0075 -0.002 O 7.5 + 0.002 0.007 E 2 B B 5 ft 60 5 ft 10 -3 -80 Ground support 2 Ground support Section B Plastic Elastic Perspective view Simplified loading conditions Section view Stress-strain curve Figure 2 Answer the following questions. (* Ignore self-weight of the steel column) 1) Compute a length (ft) of the column 2) When the two loads are completely removed, then what is the permanent length (ft) of the column?

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