The factor of safety on the basis of maximum shear stress theory
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- Two 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 wiresAt a critical point in a component, the state of stress is given as Oxx = 100 MPa, Oyy = 220 MPa, Oxy = Oyx = 80 MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is (round off to one decimalThe fluctuating stresses listed in the table are found at a critical location of a component made of steel with Se = 40 ksi, Sy = 80 ksi, Sut = 110 ksi and f= 0.87. These stresses are applied on the part within 10 s. What is the accumulative damage of this part? What is the life of the part in hours if this stress pattern continues to repeat for the remained of the part's life? Use Goodman criterion and Miner's rule in your solution. Loading order |Omin o max |Number of cycles -20 30 -10 50 1 3. -30 30 1
- Quèstion 3 4 p From the following figure shows the tensile stress- strain curve for a plain-carbon steel. What is its modulus of elasticity? 600 MPa 600r 10 psi 50 60 400 400 40 20 100 0.05 0.10 0.15 Stain O A. 320 GPa O B. 500 GPa OC.400 GPa O D.215 GPa Sem (MPThe graphical representation of fatigue strength on the Y axis to the number of stress cycles on the X axis is called as Gerber Line O S-N Curve O Soderberg Line O Goodman LineIn the state of loading as made of brittle material tensile and compression fracture values of the exposed arm, respectively. σUT=200 MPa and σUC=800 MPa and factor of safety n=4 as it is; a) First reduce the applied forces to point B, b) By determining the critical point of the critical section and stresses Calculate it and show it on the stress element. c) Calculate the diameter of the AB part according to the Coulomb criterion. Note: Neglect the effect of cutting forces.
- 1. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For a ductile material that yields according to a von Mises criterion with a yield stress σy, sketch the von Mises surface in σ₁ - 02 space and sketch the stress surface that corresponds to a factor of safety FoS = 2. For a brittle material that yields according to a max normal (Rankine) criterion with a tensile strength Gyt and a compressive strength σvc = 20yt, sketch the yield surface and the surface that corresponds to a factor of safety FoS = 2.Q1. If the yield stress (oy) of a material is 375MPa, determine whether yield is predicted for the stresses acting on both the elements shown below using: P₁=-215 RF 330 (a) Tresca Criterion (b) Von Mises Criterion Q = 200 Element A Note: your values for P (vertical load on Element A) should be negative (i.e. corresponding to a compressive vertical load). Element B S=90DRAW THE STRESS-STRAIN DIAGRAM AND LABEL IT PROPERLY.
- In a stress strain curve of mild steel, the elastic limit will be before the limit of proportionality . Select one: True FalseThe state of plane stress shown occurs at a critical point of a metal machine component. As a result of several tensile tests, it has been found that the tensile yield strength is Fy for the grade of metal used. Determine the ratio of OT/ OH shown in the figure, using the maximum-shearing-stress criterion (Tresca Hexagon). (Using Mohr circle method to calculate principle and average stresses) OX TXy Mpa Mpa Mpa MPa ob σy тху 90 -60 45 310 dy OX x Sx=Sx Sy=sy txy=txy Fy=Yield Strength AnswerExample: Convert the change in length data in Table 3-2 to engineering stress and strain and plot a stress-strain curve Homework- help Table 3-2 The results of a tensile test of a 0.505 in. diameter aluminum alloy test bar, initial length (1o) = 2 in. Calculated LTO Load (Ib) Change in Length (in.) Stress (psi) Strain (in./in.) 0.000 1000 0.001 0.0005 4,993 14,978 24,963 34,948 37,445 39,442 39,941 39,691 37,944 3000 0.003 0.0015 5000 0.005 0.0025 7000 0.007 0.0035 7500 0.030 0.0150 7900 0.080 0.0400 8000 (maximum load) 0.120 0.0600 7950 0.160 0.0800 7600 (fracture) 0.205 0.1025