A plate in equilibrium is subjected to uniform stresses along its edges with magnitude o = 30 MPa and ow = 50 MPa as shown in the figure. %3D = 50 MPa %3D y4 O = 30 MPa The Young's modulus of the material is 2 x 1011 N/m2 and the Poisson's ratio is 0.3. If o, is negligibly small and assumed to be zero, then the strain &m is
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- A 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? Answers: (a) v= (b) E= GPaTwo triangular wedges are glued together as shown in the figure. The stress acting normal to the interface, o, is MPa. 100 MPa 100 MPa on 45% 100 MPa -100 MPaQ.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.
- For a given material if the Young's modulus is 200 GN/m² and odulus of rigidity is 80 GN/m?, then the Poisson's ratio will be a. 0.40 b. 0.50 c. 0.25 d. 0.30Time len A material has the stress-strain behavior shown in the Figure below. Calculate the toughness (T) of this material. given that S1=195 Mpa; S2=243.75 Mpa; El=0.19; E2=0.38 E1 Strain E2 Stress - Strain diagram of a metal alloy OA.T= 18.52 Mpa O B.T= 92.62 Mpa O C.T= 37.05 Mpa O D.T= 60.21 Mpa Stress (Mpa) 3Creep exercises You are involved in a design for high temperature alloys and have performed a rupture test of material A and B. After data analysis, you noticed that the master curve (o vs LMP) of both material A and B coincide as shown in the diagram below. Based on the rupture strength o (MPa) AtB LMP = T(C+ Int) Which material will you select if they both have same constant (CA= CB)? Which material will you select if C < C? Motivate your answer by means of a calculation.
- 3. Given the following fatigue data for a brass alloy: Cycles to Failure 2 x 105 1х 106 Stress Amplitude (MPa) 310 223 191 3х 106 168 1 x 107 153 3х 107 143 1х 108 134 3х 108 127 1х 109 a.) Plot the S-N curve for this alloy. b.) Does this material have an endurance limit? Explain. c.) Determine the fatigue strength at 5 x 105 cycles. d.) Determine the fatigue life for 200 MPa. e.) If the loading in part c is uniaxial, what is the minimum diameter of a circular rod required for this application if the maximum load is 500 kN?1.14 The stress-strain relation shown in Figure P1.14 was obtained during the ten- sile test of an aluminum alloy specimen. 60,000 40,000 20,000 0.002 0.004 0.006 0.008 Strain, in./in. FIGURE P1.14 Determine the following: a. Young's modulus within the linear portion b. Tangent modulus at a stress of 45,000 psi c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? Stress, psiExample: the low cycle fatigue of a certain steel is given by life cycle equation-2: (of/E)=0.005 E=0.07 b= -0.08 c= -0,7 a. What is the value of the transition fatigue life, in this case 2 N/when E - Ep b. What is the total strain amplitude at the transition fatigue life?
- The state of stress is showing as a particular point in a stressed body. The diameter of the Mohr's circle for this state of stress is. 50 MPa 50 MPa 100 MPa 50 MPa 100 MPa 50 MPa1.17 Figure P1.17 shows the stress-strain relations of metals A and B during tension tests until fracture. Determine the following for the two metals (show all calcu- lations and units): a. Proportional limit b. Yield stress at an offset strain of 0.002 in./in. 150 - - Metal A 100 • Metal B 50 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Strain, in./in. FIGURE P1.17 c. Ultimate strength d. Modulus of resilience e. Toughness f. Which metal is more ductile? Why? Stress, ksiA brass wire of diameter d = 2.33 mm is stretched tightly between rigid supports so that the tensile force is T = 93 N (see figure). T The coefficient of thermal expansion for the wire is 19.5 x 106/°c, and the modulus of elasticity is E = 110 GPa. (a) What is the maximum permissible temperature drop (in °C) if the allowable shear stress in the wire is 60 MPa? (Enter the magnitude.) °C (b) At what temperature change (in °C) does the wire go slack? °C