(a) Figure Q4(a). The structural members each has a cross sectional area A, elastic modulus E, shear modulus G, moment of inertia / and polar moment of inertia J. B L. 45 3d Figure Q4(a)
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- 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.Rigid bar ACB is supported by an elastic circular strut DC having an outer diameter of 15 in. and inner diameter of 14.4 in. The strut is made of steel with a modulus elasticity of E = 29,000 ksi. Point load P = 5 kips is applied at B. Calculate the change in length of the circular strut DC. What is the vertical displacement of the rigid bar at point B?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 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?An aluminum bar subjected to tensile Forces P has a length L = 150 in. and cross-sectional area A = 2.0 in2 The stress-strain behavior of the aluminum may be represented approximately by the bilinear stress-strain diagram shown in the figure. Calculate the elongation S of the bar for each of the following axial loads: p = 8 kips, 16 kips. 24 kips, 32 kips, and 40 kips. From these results, plot a diagram of load P versus elongation S (load-displacement diagram).A joint between two glass plates A and B is filled with a flexible epoxy that bonds securely to the glass. The height of the joint is/p = 0.5 in, its length is L = 30 in, and its thickness is/ = 0.5 in. Shear force of I' = 25 kips is applied to the joint. Calculate the displacement of the joint if the shear modulus of elasticity G of the epoxy is 100 ksi. Calculate the average shear strain in the epoxy.
- An elastomeric bearing pad consisting of two steel plates bonded to a chloroprene elastomer (an artificial rubber) is subjected to a shear force V during a static loading test (see figure). The pad has dimensions a = 125 mm and b = 240 mm, and the elastomer has a thickness t = 50 mm. When the Force V equals 12 kN, the top plate is found to have displaced laterally S.O mm with respect to the bottom plate. What is the shear modulus of elasticity G of the chloroprene?A prismatic bar in tension has a length L = 2.0 m and cross-sectional area A =249 mn2. The material of the bar has the stress-strain curve shown in the figure. Determi ne t he elongation 5 of the bar for each of the following axial loads: P = 10 kN, 20 kN, 30 kN, 40 kN. and 45 kN. From these results, plot a diagram of load P versus elongation 5 (load-displacement diagram).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.
- A mountain bike rider going uphill applies a force P = 65 N to each end of the handlebars AB CD, made of aluminum alloy 7075-T6, by pulling on the handlebar extenders (DF on right handlebar segment). Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A), Segments AB and CD are prismatic with lengths Lvand L3 and with outer diameters and thicknesses J01, /01 and d03, /03, respectively, as shown. Segment BC of length L2, however, is tapered, and outer diameter and thickness vary linearly between dimensions at B and C Consider shear, torsion, and bending effects only for segment AD; assume DFis rigid. Find the maximum tensile, compressive, and shear stresses adjacent to support A. Show where each maximum stress value occursA composite bar BCD has a uniform external radius R. = 10 cm. Segment BC is solid steel, while segment CD is composed of a copper core of radius R= 1cm bonded inside a steel sleeve. The lengths of the two segments are Lec= 2 m and Lco= 1 m. The material moduli are Esteel= 200 GPa and Ecopper= 100 GPa. The bar is fixed at B and %3D tensile loads are applied at section D (Fo= 1000 kN) and at section C (Fc= 400 kN). Compute the following: %3D Determine Axial stress of steel in segment CD in MPa. 2m B 1m 400 KN 1000 ΚΝA circular rod of hot-rolled 4340 steel (4340-HR steel – 4mm diameter, 1.35m long) is subjected to a tensile load (applied normal to the circular cross-section). The modulus of elasticity of steel is 207 GPa. What is the maximum load that can be applied without causing permanent deformation? Ultimate Yield Strength, S. Strength, S, ksi MPa ksi MPa Material 6. 41 110 124 16 3003-A 6061-A 6061-T6 Aluminum 18 8. 55 alloys 45 310 40 276 Naval brass-A 54 376 17 117 Copper alloys Cartridge brass-CR 76 524 63 434 66 455 42 290 1020-HR 1045-HR 4340-HR Steel alloys 92 638 60 414 151 1041 132 910 87 600 35 241 Stainless steels 303-A 316-A 440C-A 84 579 42 290 110 759 70 483 Titanium Commercial 80 551 70 482 Table 5.3 alloy *The numerical values given are representative, and values for specific materials could vary with composition and processing. A = annealed, HR = hot-rolled, CR = cold-rolled, and T = tempered. Ultimate and Yield %3D Strengths of Selected Metals*