Evaluate stresses and strains in the cross section of the dam shown in figure for the loads indicated. Take E= 30 GPa and Possion's ratio of 0.25. Choose CST element and apply appropriate constitutive relation. 10KN 4m 1m 20kN 3m 77
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- The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.A steel column ( E = 30 X 103 ksi) that is fixed at the base and free at the top is constructed of a W8 x 35 wide-flange member (sec figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in. If P = 40 kips, what is the maximum compressive stress in the column? If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1, what is the allowable load Pallow?A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?
- A circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shorteningThe state of stress on an element of material is shown in the figure. Calculate the unit volume change of the element if the stresses x and y. are -20 ksi and 10 ksi, respectively. Assume E = 10,600 ksi and v = 0.33.Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.AW310 × 74 wide-flange steel column with length L = 3.8 m is fixed at the base and free at the top (see figure). The load P acting on the column is intended to be centrally applied, but because of unavoidable discrepancies in construction, an eccentricity ratio of 0.25 is specified. Also, the following data are supplied: E = 200 GPa, y = 290 MPa, and P = 310 kN. What is the maximum compressive stress max in the column? What is the factor of safety n with respect to yielding of the steel?A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.
- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?An element of aluminum is subjected to tri- axial stresses. Calculate the strains in the element in and directions if the stresses are -20 MPa, 28 MPa, and -18 MPa. respectively. Assume E = 70 GPa and v = 0.33. Also, find the strain energy density of the element.A short column constructed of a W 12 × 35 wide-flange shape is subjected to a resultant compressive load P = 25 k having its line of action at the midpoint of one flange (see figure). Determine the maximum tensile and compressive stresses d1and d2., respectively, in the column. Locate the neutral axis under this loading condition. Recompute maximum tensile and compressive stresses if a C 10 × 15.3 is attached to one flange, as shown.