In the figure below, a pulley can pull a 1-ton load from rest to 3 m/s upwards at 2 seconds. AB and CD is fixed on both of their ends. If the allowable compressive stress is 140MPA, yield stress 350MPA, modulus of elasticity is 200GPA. Determine the minimum thickness t in millimeters that must be used to prevent both failure by compression and buckling. w=64mm 150mm 800mm 1ton
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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°MPaTwo steel wines support a moveable overhead camera weighing W = 28 lb (see figure part a) used For close-up to viewing of field action at sporting, events. At some instant, wire I is at an angle a = 22° to the horizontal and wire 2 is at angle fi = 40°. Wires I and 2 have diameters of 30and 35 mils, respectively. (Wire diameters are often expressed in mils; one mil equals 0.001 in.) (a) Determine the tensile stresses s and s2 in the two wires. (b) If the stresses in wires 1 and 2 must be the same, what is the required diameter of wire 1 ? (c) To stabilize the camera for windy outdoor conditions, a third wire is added (see figure part b). Assume the three wires meet at a common point coordinates (0, 0. 0) above the camera at the instant shown in figure part b. Wire I is attached to a support at coordinates (75 ft, 48 ft, 70 Ft). Wire 2 is supported at (-70 ft. 55 ft, 80 Ft). Wire 3 is supported at (-10 ft. -85 Ft, 75 ft). Assume that all three wires have a diameter of 30 mils. Find the tensile stresses in all three wires
- A 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., Solve the preceding problem using the numerical data: /) = 90mm, h = 280 mm, d = 210 mm, q = 14 kN/m, and L = L2 m.What is the maximum possible value of the clamping Force C in the jaws of the pliers shown in the figure if the ultimate shear stress in the 5-mm diameter pin is 340 MPa? What is the maximum permissible value of the applied load P to maintain a factor of safety of 3.0 with respect to failure of the pin?
- A shock mount constructed as shown iu the figure is used to support a delicate instrument. The mount consists of an outer steel tube with inside diameter b. a central steel bar of diameter d that supports the load P, and a hollow rubber cylinder (height /r) bonded to the tube and bar (a) Obtain a formula Tor the shear stress t in the rubber at a radial distance r from the center of the shock mount. (b) Obtain a formula Tor the downward displacement S of the central bar due to the load P. assuming that G is the shear modulus of elasticity of the rubber and that the steel tube and bar are rigid.Solve the preceding problem if the mass of the tailgate is MT— 11 kg and that of the crate is hic— 6S kg. Use dimensions H = 305 mm, L = 406 mm, dc= 460 mm, and dT= 350 mm. The cable cross-sectional area is At= 11.0 mm'. (a) Find the tensile Force T and normal stress T in each cable. (b) IF each cable elongatesAn elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (dBC= 3/16 in.) and the washer (dB= 1.0 in.) were designed using a rod tension force of TBC=415 lb. The rod was sized using a factor of safely of 3 against reaching the ultimate stress tru— 60 ksi. An allowable bearing stress sba= 565 psi was used to size the washer at B. A small platform HF is suspended below a section of the elevated track to support some mechanical and electrical equipment. The equipment load is uniform load q = 50 lb/ft and concentrated load WE= 175 lb at mid-span of beam HF. The plan is to drill a hole through beam ABaX £land install the same rod (dBC) and washer) dB) at both D and F to support beam HF. (a) Use s and to check the proposed design for rod DF and washer d,: are they acceptable? (b) Re-check the normal tensile stress in rod BC and bearing stress at 8 if either is inadequate under the additional load from platform HF. Re-design them to meet the original design criteria.
- The 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 Force in the brake cable of the V-brake system shown in the figure is T — 45 lb. The pivot pin at A has a diameter d. = 0.25 in. and length L„ = 5/S in. Use the dimensions shown in the figure. Neglect the weight of the brake system. (a) Find the average shear stress rjm in the pivot pin where it is anchored to the bicycle frame at B. (b) Find the average bearing stress raverin the pivot pin over segment AB. (a) Find support reactions at A and B. (b) Find the resultant force in the shoe boll at A. (c) Find maximum average shear T and bearing AB stresses in the shoe bolt at A.A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1= 24 mm and the bottom shaft has a diameter d2= 16 mm. The punch is used to insert a hole in a 4 mm plate, as shown in the figure. If a force P - 70 kN is required to create the hole, what is the average shear stress in the plate and the average compressive stress in the upper and lower shaft of the punch?