Required information A 920-mm (4) strip of steel (E= 200 GPa) is bent into a full circle by two couples applied as shown. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. M' M mm Determine the maximum thickness t of the strip if the allowable stress of the steel is 420 MPa. The maximum thickness t of the strip is mm.
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- 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 two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?The cross section of a column built up of two steel I-beams (S 150 × 25.7 sections) is shown in the figure. The beams arc connected by spacer bars, or lacing, to ensure that they act together as a single column. (The lacing is represented by dashed lines in the figure.) The column is assumed to have pinned ends and may buckle in any direction. Assuming E = 200 GPa and L = 8.5 m, calculate the critical load PCIfor the column.
- The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?Calculate the critical load PCTfor a W 8 × 35 steel column (see figure) having a length L = 24 ft and E = 30 × 106 psi under the following conditions: The column buckles by bending about its strong axis (axis 1-1). the column buckles by bending about its weak axis (axis 2-2). In both cases, assume that the column has pinned ends.Three pinned-end columns of the same material have the same length and the same cross-sectional area (see figure). The columns are free to buckle in any direction. The columns have cross sections as: (a) a circle, (b) a square, and (e) an equilateral triangle. Determine the ratios Pa: Pb: Pcof the critical loads for these columns.
- A cantilever aluminum column has a square tube cross section with an outer dimension of 150 mm. The column has a length L = 4 m and is designed to support an axial load of 45 kN. Find the minimum required thickness of the section if the factor of safety n = 2.5 with respect to buckling. Assume that the modulus of elasticity is 72 GPa and the proportional limit is 480 MPa.An aluminum tube AB with a circular cross section has a sliding support at the base and is pinned at the top to a horizontal beam supporting a load Q = 200 kN (sec figure). Determine the required thickness t of the tube if its outside diameter d is 200 mm and the desired factor of safety with respect to Eu 1er buckling is n = 3.0. (Assume E = 72 GPa.)A steel column (E = 30 x 103 ksi) with pinned ends is constructed of a W10 x 60 wide-flange shape (sec figure). The column is 24 ft long. The resultant of the axial loads acting on the column is a force P acting with an eccentricity n = 2.0 in. If P = 120 kips, determine the maximum compressive stress ff^ in the column. Determine the allowable load Pallowif the yield stress is ( y =42 ksi and the factor of safety with respect to yielding of the material is n = 2.5.
- A flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?A vertical pole of aluminum is fixed at the base and pulled at the top by a cable having a tensile force T(see figure). The cable is attached at the outer edge of a stiffened cover plate on top of the pole and makes an angle a = 20° at the point of attachment. The pole has length a = 2.5 m and a hollow circular cross section with an outer diameter d2= 280 mm and inner diameter d1= 220 mm. The circular cover plate has diameter 1.5d2 Determine the allowable tensile force Tallow in the cable if the allowable compressive stress in the aluminum pole is 90 MPa.A steel pad supporting heavy machinery rests on Four short, hollow, cast iron piers (see figure). The ultimate strength of the cast iron in compression in 50 ksi. The outer diameter of the piers is d = 4.5 in, and the wall thickness is t = 0.40 in. Using a factor of safety of 3.5 with respect to the ultimate strength, determine the total load P that can be supported by the pad.