A solid circular rod with a diameter d= 16 mm is shown in Figure Q-3. The rod is made Q-3 of an aluminum alloy that has an elastic modulus E = 72 GPa and a Poisson's ratio v= 0.33. When subjected to the axial load P, the diameter of the rod decreases by 0.024 mm. a) Determine the magnitude of load P. b) If we have a 10 mm diameter hole theough the rod, making it a hollow member (a pipe), other things remaining the same as in part (a), determine the magnitude of load P P Figure Q-3

A solid circular rod with a diameter d= 16 mm is shown in Figure Q-3. The rod is made Q-3 of an aluminum alloy that has an elastic modulus E = 72 GPa and a Poisson's ratio v= 0.33. When subjected to the axial load P, the diameter of the rod decreases by 0.024 mm. a) Determine the magnitude of load P. b) If we have a 10 mm diameter hole theough the rod, making it a hollow member (a pipe), other things remaining the same as in part (a), determine the magnitude of load P P Figure Q-3

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.7.2P: A round bar of 10 mm diameter is made of aluminum alloy 7075-T6 (see figure). When the bar is...

See similar textbooks

Similar questions

Around brass bar of a diameter d1= 20mm has upset ends each with a diameter d2= 26 mm (see figure). The lengths of the segments of the bar are L1= 0.3 m and L2= 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress ??maxin the bar?
The horizon Lai rigid beam A BCD is supported by vertical bars BE and CF and is loaded by vertical Forces P, = 400 KN arid P2= 360 kN acting at points A and D, respectively (see figure). Bars BE and CF are made of steel (£ = 200 GPa} and have cross-sectional areas Ag=11,100 mm" and ABE= 9280 mm-. The distances between various points on the bars are shown in the figure. Determine the vertical displacements SAand SDof points A and D, respectively.
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
A steel riser pipe hangs from a drill rig. Individual segments of equal length L = 50 ft are joined to get her using bolted flange plates (see figure part b). There are six bolts at each pipe segment connection. The outer and inner pipe diameters are t2= 14 in. and d1= 13 in.; flange plate thickness tf= 1.5 in.; and boll and washer diameters are db= 1.125 in. and dn. = 1.875 in. Find the number n of permissible segments of pipe based on following allowable stresses. (a) The allowable tensile stress in the pipe is 50 ksi. (b) The allowable tensile stress in a bolt is 120 ksi. Find number of segments n for two cases: pipe hanging in air and pipe hanging in seawater.
A circular steel rod AB? (diameter d, = 1.0 in., length L1= 3.0 Ft) has a bronze sleeve (outer diameter d2= 1-25 in., length L2= 1.0 ft) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation 6 of the steel bar ¦due to a temperature rise AT = 500°F. (Material properties are as follows: For steel, Es= 30 ×106 psi and as= 6.5 × lO6/?; for bronze, Eb= 15 × 106psi and ab= 11 × l0-6/?.)
Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.
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?
Repeat Problem 2.4-8, but assume that the bar is made of aluminum alloy and that BC is prismatic. Assume that P = 20 kim. L = 3 ft.t = 314 in., b1 2m.b 2.Sin.andElO.400ksi.
Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
Repeat Problem 2.3-18, but assume that the bar is made of aluminum alloy. If P2= 200 kN, what is P1so that displacement
A uniformly tapered lube AB of circular cross section and length L is shown in the figure. The average diameters at the ends are dAand d£= 2d t. Assume E is constant. Find the elongation S of the tube when it is subjected to loads P acting at the ends. Use the following numerical data:^ = 35 mm, L = WO mm, E = 2.1 GPa. and P = 25 tN. Consider the following cases. (a) A hole of constant diameter dAis drilled from B toward A to form a hollow section of length x - U2. (b) A hole of variable diameter a\.x) is drilled, from B toward A to form a hollow section of length x = L/2 and constant thickness t = dA/20.
A crank arm consists of a solid segment of length bxand diameter rf, a segment of length bltand a segment of length byas shown in the figure. Two loads P act as shown: one parallel to — vand another parallel to —y. Each load P equals 1.2 kN. The crankshaft dimensions are A] = 75 mm, fr> = 125 mm, and b3= 35 mm. The diameter of the upper shaft isd = 22 mm, (a) Determine the maximum tensile, compressive, and shear stresses at point A, which is located on the surface of the shaft at the z axis. (b) Determine the maximum tensile, compressive, and shear stresses at point B, which is located on the surface of the shaft at the y axis