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- 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?The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?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°MPaThe 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.For the stresses given with the cube below: 1. Compute the center, radius (R), principal normal stresses (0₁ and 03), and max shear stress (Tmax) 2. Draw the Mohr's circle. 3. The yield point stress (0yp) is 6 kPa. Determine if the material will fail under stresses shown using Tresca's Hexagon. ay = 5 Element न Txy = 3 σx =
- For the stresses given with the cube below: 1. Compute the center, radius (R), principal normal stresses (0₁ and 03), max shear stress (Tmax) and draw the Mohr's Circle. 2. Compute the normal and shear stresses when the cube is rotated 20° clockwise from the horizontal plane and draw them on the cube. 3. The yield point stress (σyp) is 6 kPa. Determine if the material will fail under stresses shown using Tresca's Hexagon. вкра акра 6 экра 8 кра экра 4краConsider the frame in (Figure 1). The crate weighs 400 lb. Follow the sign convention. Figure 4 ft A B 1.5 ft 1.5 ft 1.5 ft 1.5 ft F C E D 0.4 ft 1 of 1 Part A Determine the normal force at point F Express your answer in pounds to three significant figures. N₂ = Submit Part B Vp = Determine the shear force at point F. Express your answer in pounds to three significant figures. Submit Part C VAΣ Ivec ΑΣΦ Request Answer Mp= [V=| ΑΣΦ Request Answer vec 4 Determine the moment at point F. Express your answer in pound-feet to three significant figures. 197| ΑΣΦ ↓↑ vec ? wwwww. ? B ? lb lb lb-ftDraw and stress tensonr with the following characteristics The stress cube visualization at point A would depict the normal stress (σ_x) acting on two opposite faces and the shear stress (τ_xy) acting tangentially on the four sides associated with torsion.
- Determine the state of stress acting at point D. Take P₁ = 120 kN and P₂ = 45 kN. (Figure 1) Figure L -1.5m- +1.5m-1.5 m- 0.5 m 40 mm 100 mm 60 mm 80 mm 1 of 1 > Find op- Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of compression and positive value in the case of tension. od= - 154.88 Submit Part B Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining MPa Find TD- Express your answer to three significant figures and include the appropriate units. JA TD= Value Units ?Part A The lever is attached to the shaft A using a key that has a width d and length of 26 mm .If the shaft is fixed and a vertical force of 200 N is applied perpendicular to the handle, determine the dimension d if the allowable shear stress for the key is T = 37 MPa (Figure 1) Express your answer with the appropriate units. HA d = Value mm Submit Request Answer Provide Feedback Next > Figure d -20 mm 500 mm 200 NThe bolt in the following figure when tightened, we measure a &=13µm decrease in the bolt diameter d. Bolt material properties are given as G=77 GPa and v=0.3. i. Determine the internal force at the bolt due to bolt tightening. ww 09 = p