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- A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?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 is 400 MPa. The total load P that may be supported by the pad is 900 kN. Using a factor or safely 3.0 with respect to ultimate strength, determine the outer diameter of the pier if the thickness, is of the cross section is 12 mm.- A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.
- A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?A spherical tank of diameter 48 in. and wall thickness 1.75 in. contains compressed air at a pressure of 2200 psi. The tank is constructed of two hemispheres joined by a welded seam (see figure). (a) What is the tensile load/ (lb per in. of length of weld) carried by the weld? (b) What is the maximum shear stress rm2Xin the wall of the tank? (c) What is the maximum normal strain e in the wall? (For steel, assume E = 30 X 10 psi and v = 0.29.)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/?.
- -15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?,10-6 A prismatic bar with a diameter d0= 20 mm is being compared with a stepped bar of the same diameter(d| = 20 mm) that is enlarged in the middle region lo a diameter d2= 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm. (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load for the prismatic bar and the maximum permissible load F, for the enlarged bar, assuming that the allowable stress for the material is 80 MPa. (b) What should be the diameter d0of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar?
- With a thick walled cyclinder the inner radius is 0.05m and out radius is 0.2m. The internal pressure is 200 MPa - What is the hoop and radial stress at the inner surface? - What would be a suitaable material for the cyclinder under von mises criterion?The cross sectional area of the bar is 5cm^2. Use E = 70GPa for aluminum, and E = 200 GPa for steel a. What is the elongation in segment AB (Aluminum)? b. What is the elongation in segment BC (Steel)? c. What is the elongation in segment CD (Aluminum)? d. What is the total elongation of the bar? -Draw and label the diagram correctly, No diagram in the solution will be marked wrong. -Shortcut solution will be marked wrong.- Direction of the assumption of the equilibrium equation must be shown, no direction will be marked wrong.A solid cylindrical rod 12 mm in diameter and 50 mm in length is attached to a rigid support at one end and twisted at its free end by 14°. If the Poisson’s ratio for this isotropic material is 0.34 and Young’s modulus is 70 GPa, what is the maximum shear stress induced?