A compound bar consisting of bronze, aluminum, and steel segments is loaded axially as shown in the figure. Determine the maximum allowable value of P if the change in length of the bar is limited to 2 mm and the working stresses prescribed in the table are not to be exceeded. A (mm?) E (GPa) o, (MPa) Bronze 450 83 120 Aluminum 600 70 80 Steel 300 200 140 Bronze Aluminum Steel 3P 2P 4P 0.6 m- 1,0m 08 m ANSWER KN
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- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPaA capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.
- A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?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 occursThe strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as Rs/w= in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress Uas the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
- The wood column is pinned at its base and top. Take E= 10 GPa and or = 15 MPa. (Figure 1) Figure 150 mm" 25 mm 25 mm 75 mm 75 mm 1 of 1 Part A If the eccentric force P = 11.8 kN is applied to the column, determine the maximum normal stress. Express your answer to three significant figures and include the appropriate units. TIGB = Submit Part B Value Request Answer Submit Units If the eccentric force P = 11.8 kN is applied to the column, investigate whether the column is adequate to support this loading without buckling or yielding. ? O The column is adequate to support this loading without buckling or yielding. O The column is inadequate to support this loading without buckling or yielding. Request Answergure 1 shows a compound bar with three different diameters, d1-9mm, d2-22mm, and d3-14mm machined from solid aluminium alloy stock, subjected to a tensile load of 30kN. If Young's odulus for the alloy is 69GPA determine the stress in section 2. Answer to be provided in MPa, correct to three decimal places - do not include a unit with your answer. L1 L2 L3 d2 d3 P Figure 1An aluminum [E-9600 ksi] control rod with a circular cross section must not stretch more than 0.34 in. when the tension in the rod is 2070 lb. If the maximum allowable normal stress in the rod is 12.9 ksi, determine: (a) the smallest diameter d that can be used for the rod. (b) the corresponding maximum length L of the rod. Answers: (a) d- i in. (b) L- in.
- (CLO 1, 2)Determine the stress in the Aluminum rod (Psi) after the load 68 (kips) is applied. The light rigid bar ABCD is pinned at B and connected to two vertical rods. Assuming that the bar was initially horizontal and the rods stress-free. Steel L= 3 ft A = 0.5 in? E = 29 x 10° psi 4 ft B C D Aluminum L= 4 ft A = 0.75 in? E = 10 x 10° psi 2 ft 2 ft → O a =48335 O b. =41535 Oc =55135 O d. =67375 O e =56155 O f. =57855 Og =53775 Oh =619353. The vertical force F applied at A is 50 kN. Compute the minimumdiameter of the steel wire, if the allowed elongation on steel wire4mm and its stress is limited to 250 MPa. Use Est = 200 GPa. Answer: d = ___________________The bar is made from steel and has an allowable stress of allow = 19.7 ksi (Figure 1) Figure P 1.875 in. 0.75 in. -0.125 in. 1.25 in. r 0.25 in. 1 of 1 Part A Determine the maximum axial force P that can be applied to the bar. Express your answer to three significant figures and include the appropriate units. P = Submit μA Value Request Answer < Return to Assignment Units Provide Feedback ?