Consider the pictured bar with axial loads of PB = 50 kip and Pc = 68.5 kip, and the indicated material properties. A = 5 in² E = 12 × 103 ksi Oy = = 35 ksi for this material B C PB PC PB РС 18 in 24 in 36 in 0.01 in a)For the chosen values of PB and Pc, determine the reaction at D b)Given PB = 50 kip, what value of Pc will produce yielding of the bar? kip kip
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- 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?,5-9 A flat aluminum alloy bar is fixed at both ends. Segment AB has a slight taper. If the temperature of the bar is raised uniformly by an amount AT = 20PF, find reactions al A and C. What is the displacement at B? Assume that L = 3 ft, t = 1/4 in., b1= 2 in., b2= 2.5 in., E = 10,400 ksi, and the coefficient of thermal expansion a = 13 X l0-6/'F.A prismatic bar of length L = 1.8 m and cross-sectional area A = 480 mm" is loaded by forces P{= 30 kN and A = 60 kN (see figure) The bar is constructed of magnesium alloy having a stress-strain curve described by the Ram berg-Osgood equation: 45.000 618 UW id which u has units of mega pascals (MPa). (a) Calculate the displacement 8t- of the end of the bar when the load P:acts alone. (b) Calculate the displacement when the load P, acts alone. (c) Calculate the displacement when both loads act simultaneously.
- A high-strength steel bar used in a large crane has a diameter d = 2.00 in. (sec figure). The steel has a modulus of elasticity E = 29 × 10 psi and Poisson’s ratio is v = 0.29. Because of clearance requirements, the diameter of the bar is limited to 2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmaxthat is permitted?A slightly tapered bar AB of solid circular crass section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dAand dB. respectively. Determine the length of the bar if the elongation of the bar due to the load P = 45 kips is 0.02 in. Assume that E = 10,400 ksi.An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
- Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300A W 8 × 28 beam of a length 10 ft is held between immoveable supports. The beam has a modulus of elasticity E = 29,000 ksi and coefficient of thermal expansion a = 6.5 ×10-6 /?. If the temperature of the beam is raised uniformly by an amount AT = 20°F, calculate the thermal stress aTin the beam.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?
- Consider the pictured bar with axial loads of PB = 46 kip and Pc = 32 kip, and the indicated material properties. A PB BC AB PB 18 in B PC. PC 24 in A = 5 in² E = 12 x 10³ ksi dy = 35 ksi for this material C D 36 in a)For the chosen values of P_B and P_C, determine the reaction at D 48.0 b)Given PB = 46 kip, what value of Pc will produce yielding of the bar? and in which section will it occur? O CD 0.01 in o kip kip3. A 5-m rod having a uniform cross-sectional area of 1000 sq.mm. is secured between two walls5 meters apart. The load on the rod is zero at 27 °C. E = 200 GPa, α = 11.25x10-6 m/m-°C. Whenthe temperature rises to 57°C:a) What is the stress in the rod assuming that the walls are rigid.b) What is the stress in the rod if the walls spring together a total distance of 0.5 mm.H.W 1. Consider a two degree of freedom bar elements as shown in figure. Using finite element method to formulate the equilibrium equation of it. If the cross sectional area is 12 mm and E=200 GN/m². 20KN +30KN 15KN 300 * 600- + 350 All Dimension in mm 2. Consider a two degree of freedom bar element as shown in figure. Using finite element method to formulate the equilibrium equation of it, and then estimate the stress distributions. If Esteel-200 GN/m, Ecopper 110GN/m and EAL= 120 GN/m?. d=3 Steel AL Соpper 20KN - 30KN →15KN 300 * 200 - 400 * 350 All Dimension in mm