Aluminum beam AB (E=10x106 psi) is simply supported as shown. Magnesium rod CD (a = 14.5 x 106 in/in/°F and E=6.5x106 psi) with cross-sectional area A=1.0 in² and length l=12"is connected to AB via a pin joint as shown. It is unloaded at room temperature. If the temperature in CD is reduced by 100 degrees: Determine the deflection of beam AB at point C Determine the magnitude of the maximum bending stress in beam AB and its location (x coordinate) along its length Determine the magnitude of the maximum horizontal shear stress in beam AB and identify its location on the beam cross-section. 8 ft 2" 6 ft 4" A B Beam cross-section D

Aluminum beam AB (E=10x106 psi) is simply supported as shown. Magnesium rod CD (a = 14.5 x 106 in/in/°F and E=6.5x106 psi) with cross-sectional area A=1.0 in² and length l=12"is connected to AB via a pin joint as shown. It is unloaded at room temperature. If the temperature in CD is reduced by 100 degrees: Determine the deflection of beam AB at point C Determine the magnitude of the maximum bending stress in beam AB and its location (x coordinate) along its length Determine the magnitude of the maximum horizontal shear stress in beam AB and identify its location on the beam cross-section. 8 ft 2" 6 ft 4" A B Beam cross-section D

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.12.11P: A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through...

See similar textbooks

Similar questions

A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)
A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.
A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ Pr
Rectangular bars of copper and aluminum are held by pins at their ends, as shown in the figure. Thin spacers provide a separation between the bars. The copper bars have cross-sectional dimensions 0.5 in. × 2.0 in., and the aluminum bar has dimensions 1.0 in. × 2.0 in. Determine the shear stress in the 7/16-in. diameter pins if the temperature is raised by 100°F. (For copper, Et= 18,000 ksi and ac = 9.5 × 10-6/?; for aluminum, Ea= 10,000 ksi and aa= 13 × 10-6/?.) Suggestion: Use the results of Example 2-10
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?
Solve the preceding problem for an aluminum plate with sx= 12,000 psi (tension). sy= -3000 psi (compression), dimensions 20 × 30 × 0.5 in.. E = 10.5 × 106 psi, and v = 0.33.
A pipe carrying steam at 3.5 MPa has an outside diameter of 450 mm and a wall thickness of 10 mm. A gasket is inserted between the flange at one end of the pipe and a flat plate used to cap the end. How many 47-mm-diameter bolts must be used to hold the cap on if the allowable stress in the bolts is 80 MPa, of which 55 MPa is the initial stress?
A closed-ended compound cylinder is formed by shrinking a steel [E = 200 GPa; v = 0.3] tube that has an external diameter of 320 mm and an internal diameter of 250 mm onto a brass [E =100 GPa; v = 0.35] tube that has an internal diameter of 200 mm. The radial interference is 0.050 mm. Determine the largest circumferential stress in the finished assembly after an internalpressure of pi = 50 MPa is applied.
A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 70 lb/ft^2 against the full area of the sign. The dimensions of the poles and sign are h1 = 16 ft, h2 = 7 ft, and b = 13 ft. To prevent buckling of the walls of the poles, the thickness t is specified as one tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7100 psi in the aluminum. Round your answer to two decimal places. d = ___ in. (b) Determine the minimum required diameter based upon an allowable shear stress of 2100 psi. Round your answer to two decimal places. d = ___ in.
5. In the CN Railwayproject,steel railroad rails of 9.5meters long are to be installed.If the modulus of elasticity of steel is207GPa, and if the lowest temperature considered is 18°C and a maximum temperature of 36°C is designed for, determine the clearance between the rails such that adjoining will just touch at maximum design temperature. Assume α for steel is 11.6 x 10-6/°C
An engineering machine component operating in a high temperature environment consists of a copper pipe having a cross-sectional area of 2 000 mm2 and 0.3 m long, which is placed between two rigid caps. Four M22 steel bolts are symmetrically arranged around the tube and parallel to the axis of the tube and are lightly tightened. 3.1 Find the stress in the pipe and the bolts if the temperature of the assembly is increased from 25 0C to 95 0C. 3.2 What load will each bolt carry at the raised temperature? 3.3 Make a neat sketch of the assembly. (ESt = 200 GPa, ECu = 100 GPa, αSt = 12 × 10-6/ oC, αCu = 16 × 10-6/ oC)
A thin copper tube, 14 mm internal diameter and 0,5 mm wall thickness has closed ends and rotates at 1200 r/min while it is subjected to an internal gauge pressure of 222 Pa. Calculate the total hoop stress in the wall of the tube if the density of copper is 8900 kg/m3.