A steel rod of length L and uniform cross sectional area A is secured between two walls, as shown. Use L=1.7 m, E = 200 GRa, a = 11.9 x 10- /°C and AT = 70 °C. Calculate the stress for a temperature increase of AT for: a) The walls are fixed. b) The walls move apart a distance 0.4 mm. %3D
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- A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?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?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.
- Truss members supporting a roof are connected to a 26-mm-thick gusset plate by a 22-mm diameter pin, as shown in the figure and photo. The two end plates on the truss members are each 14 mm thick. (a) If the load P = 80 kN, what is the largest bearing stress acting on the pin? (b) If the ultimate shear stress for the pin is 190 MPa, what force Pult is required to cause the pin to fail in shear? Disregard friction between the plates.A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and B (see figure). Each wire has an axial rigidity EA = 120 kips and coefficient of thermal expansion a = 12.5 X 10-6/°F. (a) If a vertical load P = 500 lb acts at point D, what are the tensile forces TAand TBin the wires at A and B, respectively? (b) If both wires have their temperatures raised by 180°F while the load P is acting, what are the forces TAand TB (c) What further increase in temperature will cause the wire at B to become slack?A prismatic bar with a length L = 1 m and cross-sectional area A = 1200 mm2 is supported at the ends. The bar is then subjected to a temperature increase ?T = 25°C. Calculate the complete stale of stress acting on an inclined section .rs that is cut through the bar at an angle ?? = 45*. Use E = 200 GPa and the coefficient of thermal expansion a = 12×10-6/?.
- An aluminum tube is required to transmit an axial tensile force P = 33 k (sec figure part a). The thickness of the wall of the tube is 0.25 in. (a) What is the minimum required outer diameter d minif the allowable tensile stress is 12.000 psi? (b) Repeat part (a) if the tube has a hole of a diameter J/10 at mid-length (see figure parts b and C).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?A brass wire of diameter d = 2.42 mm is stretched tightly between rigid supports so that the tensile force is T = 98 N (see figure). The coefficient of thermal expansion for the wire is 19.5 × 10-6/°C. and the modulus of elasticity is E = 110 GPa. (a) What is the maximum permissible temperature drop AT if the allowable shear stress in the wire is 60 MPa? (b) At what temperature change does the wire go slack?
- (a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressureA 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 copper bar of rectangular cross section (b = 18 mm and k = 40 mm) is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses on the inclined plane pq at mid-span, for which ?? = 55°. are specified as 60 MPa in compression and 30 MPa in shear. (a) What is the maximum permissible temperature rise AT if the allowable stresses on plane pq are not to be exceeded? (Assume a = 17 × 10-6/oC and E = 120 GPa.) (b) If the temperature increases by the maximum permissible amount, what are the stresses on plane pq? (c) If the temperature rises AT = 2SoC how far to the right of end A (distance BL, which is expressed as a fraction of length L) can load P = 15 kN be applied without exceeding allowable stress values in the bar? Assume that a =75 MPa and t = 35 MPa.